Sample records for solving linear inequalities

  1. Analysis of junior high school students' attempt to solve a linear inequality problem

    NASA Astrophysics Data System (ADS)

    Taqiyuddin, Muhammad; Sumiaty, Encum; Jupri, Al

    2017-08-01

    Linear inequality is one of fundamental subjects within junior high school mathematics curricula. Several studies have been conducted to asses students' perform on linear inequality. However, it can hardly be found that linear inequality problems are in the form of "ax + b < dx + e" with "a, d ≠ 0", and "a ≠ d" as it can be seen on the textbook used by Indonesian students and several studies. This condition leads to the research questions concerning students' attempt on solving a simple linear inequality problem in this form. In order to do so, the written test was administered to 58 students from two schools in Bandung followed by interviews. The other sources of the data are from teachers' interview and mathematics books used by students. After that, the constant comparative method was used to analyse the data. The result shows that the majority approached the question by doing algebraic operations. Interestingly, most of them did it incorrectly. In contrast, algebraic operations were correctly used by some of them. Moreover, the others performed expected-numbers solution, rewriting the question, translating the inequality into words, and blank answer. Furthermore, we found that there is no one who was conscious of the existence of all-numbers solution. It was found that this condition is reasonably due to how little the learning components concern about why a procedure of solving a linear inequality works and possibilities of linear inequality solution.

  2. Robust stability of bidirectional associative memory neural networks with time delays

    NASA Astrophysics Data System (ADS)

    Park, Ju H.

    2006-01-01

    Based on the Lyapunov Krasovskii functionals combined with linear matrix inequality approach, a novel stability criterion is proposed for asymptotic stability of bidirectional associative memory neural networks with time delays. A novel delay-dependent stability criterion is given in terms of linear matrix inequalities, which can be solved easily by various optimization algorithms.

  3. Errors Analysis of Solving Linear Inequalities among the Preparatory Year Students at King Saud University

    ERIC Educational Resources Information Center

    El-khateeb, Mahmoud M. A.

    2016-01-01

    The purpose of this study aims to investigate the errors classes occurred by the Preparatory year students at King Saud University, through analysis student responses to the items of the study test, and to identify the varieties of the common errors and ratios of common errors that occurred in solving inequalities. In the collection of the data,…

  4. A dual method for optimal control problems with initial and final boundary constraints.

    NASA Technical Reports Server (NTRS)

    Pironneau, O.; Polak, E.

    1973-01-01

    This paper presents two new algorithms belonging to the family of dual methods of centers. The first can be used for solving fixed time optimal control problems with inequality constraints on the initial and terminal states. The second one can be used for solving fixed time optimal control problems with inequality constraints on the initial and terminal states and with affine instantaneous inequality constraints on the control. Convergence is established for both algorithms. Qualitative reasoning indicates that the rate of convergence is linear.

  5. An Application of Sylvester's Rank Inequality

    ERIC Educational Resources Information Center

    Kung, Sidney H.

    2011-01-01

    Using two well known criteria for the diagonalizability of a square matrix plus an extended form of Sylvester's Rank Inequality, the author presents a new condition for the diagonalization of a real matrix from which one can obtain the eigenvectors by simply multiplying some associated matrices without solving a linear system of simultaneous…

  6. Global asymptotic stabilisation of rational dynamical systems based on solving BMI

    NASA Astrophysics Data System (ADS)

    Esmaili, Farhad; Kamyad, A. V.; Jahed-Motlagh, Mohammad Reza; Pariz, Naser

    2017-08-01

    In this paper, the global asymptotic stabiliser design of rational systems is studied in detail. To develop the idea, the state equations of the system are transformed to a new coordinate via polynomial transformation and the state feedback control law. This in turn is followed by the satisfaction of the linear growth condition (i.e. Lipschitz at zero). Based on a linear matrix inequality solution, the system in the new coordinate is globally asymptotically stabilised and then, leading to the global asymptotic stabilisation of the primary system. The polynomial transformation coefficients are derived by solving the bilinear matrix inequality problem. To confirm the capability of this method, three examples are highlighted.

  7. Review of LFTs, LMIs, and mu. [Linear Fractional Transformations, Linear Matrix Inequalities

    NASA Technical Reports Server (NTRS)

    Doyle, John; Packard, Andy; Zhou, Kemin

    1991-01-01

    The authors present a tutorial overview of linear fractional transformations (LFTs) and the role of the structured singular value, mu, and linear matrix inequalities (LMIs) in solving LFT problems. The authors first introduce the notation for LFTs and briefly discuss some of their properties. They then describe mu and its connections with LFTs. They focus on two standard notions of robust stability and performance, mu stability and performance and Q stability and performance, and their relationship is discussed. Comparisons with the L1 theory of robust performance with structured uncertainty are considered.

  8. A novel neural network for variational inequalities with linear and nonlinear constraints.

    PubMed

    Gao, Xing-Bao; Liao, Li-Zhi; Qi, Liqun

    2005-11-01

    Variational inequality is a uniform approach for many important optimization and equilibrium problems. Based on the sufficient and necessary conditions of the solution, this paper presents a novel neural network model for solving variational inequalities with linear and nonlinear constraints. Three sufficient conditions are provided to ensure that the proposed network with an asymmetric mapping is stable in the sense of Lyapunov and converges to an exact solution of the original problem. Meanwhile, the proposed network with a gradient mapping is also proved to be stable in the sense of Lyapunov and to have a finite-time convergence under some mild condition by using a new energy function. Compared with the existing neural networks, the new model can be applied to solve some nonmonotone problems, has no adjustable parameter, and has lower complexity. Thus, the structure of the proposed network is very simple. Since the proposed network can be used to solve a broad class of optimization problems, it has great application potential. The validity and transient behavior of the proposed neural network are demonstrated by several numerical examples.

  9. Finite-time H∞ filtering for non-linear stochastic systems

    NASA Astrophysics Data System (ADS)

    Hou, Mingzhe; Deng, Zongquan; Duan, Guangren

    2016-09-01

    This paper describes the robust H∞ filtering analysis and the synthesis of general non-linear stochastic systems with finite settling time. We assume that the system dynamic is modelled by Itô-type stochastic differential equations of which the state and the measurement are corrupted by state-dependent noises and exogenous disturbances. A sufficient condition for non-linear stochastic systems to have the finite-time H∞ performance with gain less than or equal to a prescribed positive number is established in terms of a certain Hamilton-Jacobi inequality. Based on this result, the existence of a finite-time H∞ filter is given for the general non-linear stochastic system by a second-order non-linear partial differential inequality, and the filter can be obtained by solving this inequality. The effectiveness of the obtained result is illustrated by a numerical example.

  10. Observers for Systems with Nonlinearities Satisfying an Incremental Quadratic Inequality

    NASA Technical Reports Server (NTRS)

    Acikmese, Ahmet Behcet; Corless, Martin

    2004-01-01

    We consider the problem of state estimation for nonlinear time-varying systems whose nonlinearities satisfy an incremental quadratic inequality. These observer results unifies earlier results in the literature; and extend it to some additional classes of nonlinearities. Observers are presented which guarantee that the state estimation error exponentially converges to zero. Observer design involves solving linear matrix inequalities for the observer gain matrices. Results are illustrated by application to a simple model of an underwater.

  11. Bohnenblust-Hille inequalities: analytical and computational aspects.

    PubMed

    Cavalcante, Wasthenny V; Pellegrino, Daniel M

    2018-02-01

    The Bohnenblust-Hille polynomial and multilinear inequalities were proved in 1931 and the determination of exact values of their constants is still an open and challenging problem, pursued by various authors. The present paper briefly surveys recent attempts to attack/solve this problem; it also presents new results, like connections with classical results of the linear theory of absolutely summing operators, and new perspectives.

  12. Parameterized LMI Based Diagonal Dominance Compensator Study for Polynomial Linear Parameter Varying System

    NASA Astrophysics Data System (ADS)

    Han, Xiaobao; Li, Huacong; Jia, Qiusheng

    2017-12-01

    For dynamic decoupling of polynomial linear parameter varying(PLPV) system, a robust dominance pre-compensator design method is given. The parameterized precompensator design problem is converted into an optimal problem constrained with parameterized linear matrix inequalities(PLMI) by using the conception of parameterized Lyapunov function(PLF). To solve the PLMI constrained optimal problem, the precompensator design problem is reduced into a normal convex optimization problem with normal linear matrix inequalities (LMI) constraints on a new constructed convex polyhedron. Moreover, a parameter scheduling pre-compensator is achieved, which satisfies robust performance and decoupling performances. Finally, the feasibility and validity of the robust diagonal dominance pre-compensator design method are verified by the numerical simulation on a turbofan engine PLPV model.

  13. A sequential linear optimization approach for controller design

    NASA Technical Reports Server (NTRS)

    Horta, L. G.; Juang, J.-N.; Junkins, J. L.

    1985-01-01

    A linear optimization approach with a simple real arithmetic algorithm is presented for reliable controller design and vibration suppression of flexible structures. Using first order sensitivity of the system eigenvalues with respect to the design parameters in conjunction with a continuation procedure, the method converts a nonlinear optimization problem into a maximization problem with linear inequality constraints. The method of linear programming is then applied to solve the converted linear optimization problem. The general efficiency of the linear programming approach allows the method to handle structural optimization problems with a large number of inequality constraints on the design vector. The method is demonstrated using a truss beam finite element model for the optimal sizing and placement of active/passive-structural members for damping augmentation. Results using both the sequential linear optimization approach and nonlinear optimization are presented and compared. The insensitivity to initial conditions of the linear optimization approach is also demonstrated.

  14. Finite-time H∞ control for linear continuous system with norm-bounded disturbance

    NASA Astrophysics Data System (ADS)

    Meng, Qingyi; Shen, Yanjun

    2009-04-01

    In this paper, the definition of finite-time H∞ control is presented. The system under consideration is subject to time-varying norm-bounded exogenous disturbance. The main aim of this paper is focused on the design a state feedback controller which ensures that the closed-loop system is finite-time bounded (FTB) and reduces the effect of the disturbance input on the controlled output to a prescribed level. A sufficient condition is presented for the solvability of this problem, which can be reduced to a feasibility problem involving linear matrix inequalities (LMIs). A detailed solving method is proposed for the restricted linear matrix inequalities. Finally, examples are given to show the validity of the methodology.

  15. An Algebraic Approach for Solving Quadratic Inequalities

    ERIC Educational Resources Information Center

    Mahmood, Munir; Al-Mirbati, Rudaina

    2017-01-01

    In recent years most text books utilise either the sign chart or graphing functions in order to solve a quadratic inequality of the form ax[superscript 2] + bx + c < 0 This article demonstrates an algebraic approach to solve the above inequality. To solve a quadratic inequality in the form of ax[superscript 2] + bx + c < 0 or in the…

  16. Fast Combinatorial Algorithm for the Solution of Linearly Constrained Least Squares Problems

    DOEpatents

    Van Benthem, Mark H.; Keenan, Michael R.

    2008-11-11

    A fast combinatorial algorithm can significantly reduce the computational burden when solving general equality and inequality constrained least squares problems with large numbers of observation vectors. The combinatorial algorithm provides a mathematically rigorous solution and operates at great speed by reorganizing the calculations to take advantage of the combinatorial nature of the problems to be solved. The combinatorial algorithm exploits the structure that exists in large-scale problems in order to minimize the number of arithmetic operations required to obtain a solution.

  17. Robust distributed model predictive control of linear systems with structured time-varying uncertainties

    NASA Astrophysics Data System (ADS)

    Zhang, Langwen; Xie, Wei; Wang, Jingcheng

    2017-11-01

    In this work, synthesis of robust distributed model predictive control (MPC) is presented for a class of linear systems subject to structured time-varying uncertainties. By decomposing a global system into smaller dimensional subsystems, a set of distributed MPC controllers, instead of a centralised controller, are designed. To ensure the robust stability of the closed-loop system with respect to model uncertainties, distributed state feedback laws are obtained by solving a min-max optimisation problem. The design of robust distributed MPC is then transformed into solving a minimisation optimisation problem with linear matrix inequality constraints. An iterative online algorithm with adjustable maximum iteration is proposed to coordinate the distributed controllers to achieve a global performance. The simulation results show the effectiveness of the proposed robust distributed MPC algorithm.

  18. Cutting planes for the multistage stochastic unit commitment problem

    DOE PAGES

    Jiang, Ruiwei; Guan, Yongpei; Watson, Jean -Paul

    2016-04-20

    As renewable energy penetration rates continue to increase in power systems worldwide, new challenges arise for system operators in both regulated and deregulated electricity markets to solve the security-constrained coal-fired unit commitment problem with intermittent generation (due to renewables) and uncertain load, in order to ensure system reliability and maintain cost effectiveness. In this paper, we study a security-constrained coal-fired stochastic unit commitment model, which we use to enhance the reliability unit commitment process for day-ahead power system operations. In our approach, we first develop a deterministic equivalent formulation for the problem, which leads to a large-scale mixed-integer linear program.more » Then, we verify that the turn on/off inequalities provide a convex hull representation of the minimum-up/down time polytope under the stochastic setting. Next, we develop several families of strong valid inequalities mainly through lifting schemes. In particular, by exploring sequence independent lifting and subadditive approximation lifting properties for the lifting schemes, we obtain strong valid inequalities for the ramping and general load balance polytopes. Lastly, branch-and-cut algorithms are developed to employ these valid inequalities as cutting planes to solve the problem. Our computational results verify the effectiveness of the proposed approach.« less

  19. Cutting planes for the multistage stochastic unit commitment problem

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Jiang, Ruiwei; Guan, Yongpei; Watson, Jean -Paul

    As renewable energy penetration rates continue to increase in power systems worldwide, new challenges arise for system operators in both regulated and deregulated electricity markets to solve the security-constrained coal-fired unit commitment problem with intermittent generation (due to renewables) and uncertain load, in order to ensure system reliability and maintain cost effectiveness. In this paper, we study a security-constrained coal-fired stochastic unit commitment model, which we use to enhance the reliability unit commitment process for day-ahead power system operations. In our approach, we first develop a deterministic equivalent formulation for the problem, which leads to a large-scale mixed-integer linear program.more » Then, we verify that the turn on/off inequalities provide a convex hull representation of the minimum-up/down time polytope under the stochastic setting. Next, we develop several families of strong valid inequalities mainly through lifting schemes. In particular, by exploring sequence independent lifting and subadditive approximation lifting properties for the lifting schemes, we obtain strong valid inequalities for the ramping and general load balance polytopes. Lastly, branch-and-cut algorithms are developed to employ these valid inequalities as cutting planes to solve the problem. Our computational results verify the effectiveness of the proposed approach.« less

  20. Robust shrinking ellipsoid model predictive control for linear parameter varying system

    PubMed Central

    Yan, Yan

    2017-01-01

    In this paper, a new off-line model predictive control strategy is presented for a kind of linear parameter varying system with polytopic uncertainty. A nest of shrinking ellipsoids is constructed by solving linear matrix inequality. By splitting the objective function into two parts, the proposed strategy moves most computations off-line. The on-line computation is only calculating the current control to assure the system shrinking into the smaller ellipsoid. With the proposed formulation, the stability of the closed system is proved, followed with two numerical examples to demonstrate the proposed method’s effectiveness in the end. PMID:28575028

  1. Filtering of Discrete-Time Switched Neural Networks Ensuring Exponential Dissipative and $l_{2}$ - $l_{\\infty }$ Performances.

    PubMed

    Choi, Hyun Duck; Ahn, Choon Ki; Karimi, Hamid Reza; Lim, Myo Taeg

    2017-10-01

    This paper studies delay-dependent exponential dissipative and l 2 - l ∞ filtering problems for discrete-time switched neural networks (DSNNs) including time-delayed states. By introducing a novel discrete-time inequality, which is a discrete-time version of the continuous-time Wirtinger-type inequality, we establish new sets of linear matrix inequality (LMI) criteria such that discrete-time filtering error systems are exponentially stable with guaranteed performances in the exponential dissipative and l 2 - l ∞ senses. The design of the desired exponential dissipative and l 2 - l ∞ filters for DSNNs can be achieved by solving the proposed sets of LMI conditions. Via numerical simulation results, we show the validity of the desired discrete-time filter design approach.

  2. Inequalities, assessment and computer algebra

    NASA Astrophysics Data System (ADS)

    Sangwin, Christopher J.

    2015-01-01

    The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students' own answers to such problems are correct. We review how inequalities arise in contemporary curricula. We consider the formal mathematical processes by which such inequalities are solved, and we consider the notation and syntax through which solutions are expressed. We review the extent to which current CAS can accurately solve these inequalities, and the form given to the solutions by the designers of this software. Finally, we discuss the functionality needed to deal with students' answers, i.e. to establish equivalence (or otherwise) of expressions representing unions of intervals. We find that while contemporary CAS accurately solve inequalities there is a wide variety of notation used.

  3. Multi-Mode Estimation for Small Fixed Wing Unmanned Aerial Vehicle Localization Based on a Linear Matrix Inequality Approach

    PubMed Central

    Elzoghby, Mostafa; Li, Fu; Arafa, Ibrahim. I.; Arif, Usman

    2017-01-01

    Information fusion from multiple sensors ensures the accuracy and robustness of a navigation system, especially in the absence of global positioning system (GPS) data which gets degraded in many cases. A way to deal with multi-mode estimation for a small fixed wing unmanned aerial vehicle (UAV) localization framework is proposed, which depends on utilizing a Luenberger observer-based linear matrix inequality (LMI) approach. The proposed estimation technique relies on the interaction between multiple measurement modes and a continuous observer. The state estimation is performed in a switching environment between multiple active sensors to exploit the available information as much as possible, especially in GPS-denied environments. Luenberger observer-based projection is implemented as a continuous observer to optimize the estimation performance. The observer gain might be chosen by solving a Lyapunov equation by means of a LMI algorithm. Convergence is achieved by utilizing the linear matrix inequality (LMI), based on Lyapunov stability which keeps the dynamic estimation error bounded by selecting the observer gain matrix (L). Simulation results are presented for a small UAV fixed wing localization problem. The results obtained using the proposed approach are compared with a single mode Extended Kalman Filter (EKF). Simulation results are presented to demonstrate the viability of the proposed strategy. PMID:28420214

  4. Interior point techniques for LP and NLP

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Evtushenko, Y.

    By using surjective mapping the initial constrained optimization problem is transformed to a problem in a new space with only equality constraints. For the numerical solution of the latter problem we use the generalized gradient-projection method and Newton`s method. After inverse transformation to the initial space we obtain the family of numerical methods for solving optimization problems with equality and inequality constraints. In the linear programming case after some simplification we obtain Dikin`s algorithm, affine scaling algorithm and generalized primal dual interior point linear programming algorithm.

  5. New Passivity Criteria for Fuzzy Bam Neural Networks with Markovian Jumping Parameters and Time-Varying Delays

    NASA Astrophysics Data System (ADS)

    Vadivel, P.; Sakthivel, R.; Mathiyalagan, K.; Thangaraj, P.

    2013-02-01

    This paper addresses the problem of passivity analysis issue for a class of fuzzy bidirectional associative memory (BAM) neural networks with Markovian jumping parameters and time varying delays. A set of sufficient conditions for the passiveness of the considered fuzzy BAM neural network model is derived in terms of linear matrix inequalities by using the delay fractioning technique together with the Lyapunov function approach. In addition, the uncertainties are inevitable in neural networks because of the existence of modeling errors and external disturbance. Further, this result is extended to study the robust passivity criteria for uncertain fuzzy BAM neural networks with time varying delays and uncertainties. These criteria are expressed in the form of linear matrix inequalities (LMIs), which can be efficiently solved via standard numerical software. Two numerical examples are provided to demonstrate the effectiveness of the obtained results.

  6. Observer-based H∞ resilient control for a class of switched LPV systems and its application

    NASA Astrophysics Data System (ADS)

    Yang, Dong; Zhao, Jun

    2016-11-01

    This paper deals with the issue of observer-based H∞ resilient control for a class of switched linear parameter-varying (LPV) systems by utilising a multiple parameter-dependent Lyapunov functions method. First, attention is focused upon the design of a resilient observer, an observer-based resilient controller and a parameter and estimate state-dependent switching signal, which can stabilise and achieve the disturbance attenuation for the given systems. Then, a solvability condition of the H∞ resilient control problem is given in terms of matrix inequality for the switched LPV systems. This condition allows the H∞ resilient control problem for each individual subsystem to be unsolvable. The observer, controller, and switching signal are explicitly computed by solving linear matrix inequalities (LMIs). Finally, the effectiveness of the proposed control scheme is illustrated by its application to a turbofan engine, which can hardly be handled by the existing approaches.

  7. Improved Stability and Stabilization Results for Stochastic Synchronization of Continuous-Time Semi-Markovian Jump Neural Networks With Time-Varying Delay.

    PubMed

    Wei, Yanling; Park, Ju H; Karimi, Hamid Reza; Tian, Yu-Chu; Jung, Hoyoul; Yanling Wei; Park, Ju H; Karimi, Hamid Reza; Yu-Chu Tian; Hoyoul Jung; Tian, Yu-Chu; Wei, Yanling; Jung, Hoyoul; Karimi, Hamid Reza; Park, Ju H

    2018-06-01

    Continuous-time semi-Markovian jump neural networks (semi-MJNNs) are those MJNNs whose transition rates are not constant but depend on the random sojourn time. Addressing stochastic synchronization of semi-MJNNs with time-varying delay, an improved stochastic stability criterion is derived in this paper to guarantee stochastic synchronization of the response systems with the drive systems. This is achieved through constructing a semi-Markovian Lyapunov-Krasovskii functional together as well as making use of a novel integral inequality and the characteristics of cumulative distribution functions. Then, with a linearization procedure, controller synthesis is carried out for stochastic synchronization of the drive-response systems. The desired state-feedback controller gains can be determined by solving a linear matrix inequality-based optimization problem. Simulation studies are carried out to demonstrate the effectiveness and less conservatism of the presented approach.

  8. Calibration of Lévy Processes with American Options

    NASA Astrophysics Data System (ADS)

    Achdou, Yves

    We study options on financial assets whose discounted prices are exponential of Lévy processes. The price of an American vanilla option as a function of the maturity and the strike satisfies a linear complementarity problem involving a non-local partial integro-differential operator. It leads to a variational inequality in a suitable weighted Sobolev space. Calibrating the Lévy process may be done by solving an inverse least square problem where the state variable satisfies the previously mentioned variational inequality. We first assume that the volatility is positive: after carefully studying the direct problem, we propose necessary optimality conditions for the least square inverse problem. We also consider the direct problem when the volatility is zero.

  9. Fuzzy Model-based Pitch Stabilization and Wing Vibration Suppression of Flexible Wing Aircraft.

    NASA Technical Reports Server (NTRS)

    Ayoubi, Mohammad A.; Swei, Sean Shan-Min; Nguyen, Nhan T.

    2014-01-01

    This paper presents a fuzzy nonlinear controller to regulate the longitudinal dynamics of an aircraft and suppress the bending and torsional vibrations of its flexible wings. The fuzzy controller utilizes full-state feedback with input constraint. First, the Takagi-Sugeno fuzzy linear model is developed which approximates the coupled aeroelastic aircraft model. Then, based on the fuzzy linear model, a fuzzy controller is developed to utilize a full-state feedback and stabilize the system while it satisfies the control input constraint. Linear matrix inequality (LMI) techniques are employed to solve the fuzzy control problem. Finally, the performance of the proposed controller is demonstrated on the NASA Generic Transport Model (GTM).

  10. Optimal Full Information Synthesis for Flexible Structures Implemented on Cray Supercomputers

    NASA Technical Reports Server (NTRS)

    Lind, Rick; Balas, Gary J.

    1995-01-01

    This paper considers an algorithm for synthesis of optimal controllers for full information feedback. The synthesis procedure reduces to a single linear matrix inequality which may be solved via established convex optimization algorithms. The computational cost of the optimization is investigated. It is demonstrated the problem dimension and corresponding matrices can become large for practical engineering problems. This algorithm represents a process that is impractical for standard workstations for large order systems. A flexible structure is presented as a design example. Control synthesis requires several days on a workstation but may be solved in a reasonable amount of time using a Cray supercomputer.

  11. Mixed H∞ and passive control for linear switched systems via hybrid control approach

    NASA Astrophysics Data System (ADS)

    Zheng, Qunxian; Ling, Youzhu; Wei, Lisheng; Zhang, Hongbin

    2018-03-01

    This paper investigates the mixed H∞ and passive control problem for linear switched systems based on a hybrid control strategy. To solve this problem, first, a new performance index is proposed. This performance index can be viewed as the mixed weighted H∞ and passivity performance. Then, the hybrid controllers are used to stabilise the switched systems. The hybrid controllers consist of dynamic output-feedback controllers for every subsystem and state updating controllers at the switching instant. The design of state updating controllers not only depends on the pre-switching subsystem and the post-switching subsystem, but also depends on the measurable output signal. The hybrid controllers proposed in this paper can include some existing ones as special cases. Combine the multiple Lyapunov functions approach with the average dwell time technique, new sufficient conditions are obtained. Under the new conditions, the closed-loop linear switched systems are globally uniformly asymptotically stable with a mixed H∞ and passivity performance index. Moreover, the desired hybrid controllers can be constructed by solving a set of linear matrix inequalities. Finally, a numerical example and a practical example are given.

  12. Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems

    NASA Astrophysics Data System (ADS)

    Szederkényi, Gábor; Hangos, Katalin M.

    2004-04-01

    We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities.

  13. A solid criterion based on strict LMI without invoking equality constraint for stabilization of continuous singular systems.

    PubMed

    Zhang, Xuefeng; Chen, YangQuan

    2017-11-01

    The paper considers the stabilization issue of linear continuous singular systems by dealing with strict linear matrix inequalities (LMIs) without invoking equality constraint and proposes a complete and effective solved LMIs formulation. The criterion is necessary and sufficient condition and can be directly solved the feasible solutions with LMI toolbox and is much more tractable and reliable in numerical simulation than existing results, which involve positive semi-definite LMIs with equality constraints. The most important property of the criterion proposed in the paper is that it can overcome the drawbacks of the invalidity caused by the singularity of Ω=PE T +SQ for stabilization of singular systems. Two counterexamples are presented to avoid the disadvantages of the existing condition of stabilization of continuous singular systems. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

  14. Robust H(infinity) tracking control of boiler-turbine systems.

    PubMed

    Wu, J; Nguang, S K; Shen, J; Liu, G; Li, Y G

    2010-07-01

    In this paper, the problem of designing a fuzzy H(infinity) state feedback tracking control of a boiler-turbine is solved. First, the Takagi and Sugeno fuzzy model is used to model a boiler-turbine system. Next, based on the Takagi and Sugeno fuzzy model, sufficient conditions for the existence of a fuzzy H(infinity) nonlinear state feedback tracking control are derived in terms of linear matrix inequalities. The advantage of the proposed tracking control design is that it does not involve feedback linearization technique and complicated adaptive scheme. An industrial boiler-turbine system is used to illustrate the effectiveness of the proposed design as compared with a linearized approach. 2010 ISA. Published by Elsevier Ltd. All rights reserved.

  15. Synchronization of generalized reaction-diffusion neural networks with time-varying delays based on general integral inequalities and sampled-data control approach.

    PubMed

    Dharani, S; Rakkiyappan, R; Cao, Jinde; Alsaedi, Ahmed

    2017-08-01

    This paper explores the problem of synchronization of a class of generalized reaction-diffusion neural networks with mixed time-varying delays. The mixed time-varying delays under consideration comprise of both discrete and distributed delays. Due to the development and merits of digital controllers, sampled-data control is a natural choice to establish synchronization in continuous-time systems. Using a newly introduced integral inequality, less conservative synchronization criteria that assure the global asymptotic synchronization of the considered generalized reaction-diffusion neural network and mixed delays are established in terms of linear matrix inequalities (LMIs). The obtained easy-to-test LMI-based synchronization criteria depends on the delay bounds in addition to the reaction-diffusion terms, which is more practicable. Upon solving these LMIs by using Matlab LMI control toolbox, a desired sampled-data controller gain can be acuqired without any difficulty. Finally, numerical examples are exploited to express the validity of the derived LMI-based synchronization criteria.

  16. Linear Matrix Inequality Method for a Quadratic Performance Index Minimization Problem with a class of Bilinear Matrix Inequality Conditions

    NASA Astrophysics Data System (ADS)

    Tanemura, M.; Chida, Y.

    2016-09-01

    There are a lot of design problems of control system which are expressed as a performance index minimization under BMI conditions. However, a minimization problem expressed as LMIs can be easily solved because of the convex property of LMIs. Therefore, many researchers have been studying transforming a variety of control design problems into convex minimization problems expressed as LMIs. This paper proposes an LMI method for a quadratic performance index minimization problem with a class of BMI conditions. The minimization problem treated in this paper includes design problems of state-feedback gain for switched system and so on. The effectiveness of the proposed method is verified through a state-feedback gain design for switched systems and a numerical simulation using the designed feedback gains.

  17. An Efficacious Multi-Objective Fuzzy Linear Programming Approach for Optimal Power Flow Considering Distributed Generation.

    PubMed

    Warid, Warid; Hizam, Hashim; Mariun, Norman; Abdul-Wahab, Noor Izzri

    2016-01-01

    This paper proposes a new formulation for the multi-objective optimal power flow (MOOPF) problem for meshed power networks considering distributed generation. An efficacious multi-objective fuzzy linear programming optimization (MFLP) algorithm is proposed to solve the aforementioned problem with and without considering the distributed generation (DG) effect. A variant combination of objectives is considered for simultaneous optimization, including power loss, voltage stability, and shunt capacitors MVAR reserve. Fuzzy membership functions for these objectives are designed with extreme targets, whereas the inequality constraints are treated as hard constraints. The multi-objective fuzzy optimal power flow (OPF) formulation was converted into a crisp OPF in a successive linear programming (SLP) framework and solved using an efficient interior point method (IPM). To test the efficacy of the proposed approach, simulations are performed on the IEEE 30-busand IEEE 118-bus test systems. The MFLP optimization is solved for several optimization cases. The obtained results are compared with those presented in the literature. A unique solution with a high satisfaction for the assigned targets is gained. Results demonstrate the effectiveness of the proposed MFLP technique in terms of solution optimality and rapid convergence. Moreover, the results indicate that using the optimal DG location with the MFLP algorithm provides the solution with the highest quality.

  18. An Efficacious Multi-Objective Fuzzy Linear Programming Approach for Optimal Power Flow Considering Distributed Generation

    PubMed Central

    Warid, Warid; Hizam, Hashim; Mariun, Norman; Abdul-Wahab, Noor Izzri

    2016-01-01

    This paper proposes a new formulation for the multi-objective optimal power flow (MOOPF) problem for meshed power networks considering distributed generation. An efficacious multi-objective fuzzy linear programming optimization (MFLP) algorithm is proposed to solve the aforementioned problem with and without considering the distributed generation (DG) effect. A variant combination of objectives is considered for simultaneous optimization, including power loss, voltage stability, and shunt capacitors MVAR reserve. Fuzzy membership functions for these objectives are designed with extreme targets, whereas the inequality constraints are treated as hard constraints. The multi-objective fuzzy optimal power flow (OPF) formulation was converted into a crisp OPF in a successive linear programming (SLP) framework and solved using an efficient interior point method (IPM). To test the efficacy of the proposed approach, simulations are performed on the IEEE 30-busand IEEE 118-bus test systems. The MFLP optimization is solved for several optimization cases. The obtained results are compared with those presented in the literature. A unique solution with a high satisfaction for the assigned targets is gained. Results demonstrate the effectiveness of the proposed MFLP technique in terms of solution optimality and rapid convergence. Moreover, the results indicate that using the optimal DG location with the MFLP algorithm provides the solution with the highest quality. PMID:26954783

  19. Delay-Dependent Stability Criterion for Bidirectional Associative Memory Neural Networks with Interval Time-Varying Delays

    NASA Astrophysics Data System (ADS)

    Park, Ju H.; Kwon, O. M.

    In the letter, the global asymptotic stability of bidirectional associative memory (BAM) neural networks with delays is investigated. The delay is assumed to be time-varying and belongs to a given interval. A novel stability criterion for the stability is presented based on the Lyapunov method. The criterion is represented in terms of linear matrix inequality (LMI), which can be solved easily by various optimization algorithms. Two numerical examples are illustrated to show the effectiveness of our new result.

  20. H∞ robust fault-tolerant controller design for an autonomous underwater vehicle's navigation control system

    NASA Astrophysics Data System (ADS)

    Cheng, Xiang-Qin; Qu, Jing-Yuan; Yan, Zhe-Ping; Bian, Xin-Qian

    2010-03-01

    In order to improve the security and reliability for autonomous underwater vehicle (AUV) navigation, an H∞ robust fault-tolerant controller was designed after analyzing variations in state-feedback gain. Operating conditions and the design method were then analyzed so that the control problem could be expressed as a mathematical optimization problem. This permitted the use of linear matrix inequalities (LMI) to solve for the H∞ controller for the system. When considering different actuator failures, these conditions were then also mathematically expressed, allowing the H∞ robust controller to solve for these events and thus be fault-tolerant. Finally, simulation results showed that the H∞ robust fault-tolerant controller could provide precise AUV navigation control with strong robustness.

  1. Computer as a Medium for Overcoming Misconceptions in Solving Inequalities

    ERIC Educational Resources Information Center

    Abramovich, Sergei; Ehrlich, Amos

    2007-01-01

    Inequalities are considered among the most useful tools of investigation in pure and applied mathematics; yet their didactical aspects have not received much attention in mathematics education research until recently. An important aspect of teaching problem solving at the secondary level deals with the notion of equivalence of algebraic…

  2. Model predictive control of non-linear systems over networks with data quantization and packet loss.

    PubMed

    Yu, Jimin; Nan, Liangsheng; Tang, Xiaoming; Wang, Ping

    2015-11-01

    This paper studies the approach of model predictive control (MPC) for the non-linear systems under networked environment where both data quantization and packet loss may occur. The non-linear controlled plant in the networked control system (NCS) is represented by a Tagaki-Sugeno (T-S) model. The sensed data and control signal are quantized in both links and described as sector bound uncertainties by applying sector bound approach. Then, the quantized data are transmitted in the communication networks and may suffer from the effect of packet losses, which are modeled as Bernoulli process. A fuzzy predictive controller which guarantees the stability of the closed-loop system is obtained by solving a set of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed method. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

  3. Using MathCAD to Teach One-Dimensional Graphs

    ERIC Educational Resources Information Center

    Yushau, B.

    2004-01-01

    Topics such as linear and nonlinear equations and inequalities, compound inequalities, linear and nonlinear absolute value equations and inequalities, rational equations and inequality are commonly found in college algebra and precalculus textbooks. What is common about these topics is the fact that their solutions and graphs lie in the real line…

  4. Digital Image Restoration Under a Regression Model - The Unconstrained, Linear Equality and Inequality Constrained Approaches

    DTIC Science & Technology

    1974-01-01

    REGRESSION MODEL - THE UNCONSTRAINED, LINEAR EQUALITY AND INEQUALITY CONSTRAINED APPROACHES January 1974 Nelson Delfino d’Avila Mascarenha;? Image...Report 520 DIGITAL IMAGE RESTORATION UNDER A REGRESSION MODEL THE UNCONSTRAINED, LINEAR EQUALITY AND INEQUALITY CONSTRAINED APPROACHES January...a two- dimensional form adequately describes the linear model . A dis- cretization is performed by using quadrature methods. By trans

  5. Almost output regulation of LFT systems via gain-scheduling control

    NASA Astrophysics Data System (ADS)

    Yuan, Chengzhi; Duan, Chang; Wu, Fen

    2018-05-01

    Output regulation of general uncertain systems is a meaningful yet challenging problem. In spite of the rich literature in the field, the problem has not yet been addressed adequately due to the lack of an effective design mechanism. In this paper, we propose a new design framework for almost output regulation of uncertain systems described in the general form of linear fractional transformation (LFT) with time-varying parametric uncertainties and unknown external perturbations. A novel semi-LFT gain-scheduling output regulator structure is proposed, such that the associated control synthesis conditions guaranteeing both output regulation and ? disturbance attenuation performance are formulated as a set of linear matrix inequalities (LMIs) plus parameter-dependent linear matrix equations, which can be solved separately. A numerical example has been used to demonstrate the effectiveness of the proposed approach.

  6. Non-fragile consensus algorithms for a network of diffusion PDEs with boundary local interaction

    NASA Astrophysics Data System (ADS)

    Xiong, Jun; Li, Junmin

    2017-07-01

    In this study, non-fragile consensus algorithm is proposed to solve the average consensus problem of a network of diffusion PDEs, modelled by boundary controlled heat equations. The problem deals with the case where the Neumann-type boundary controllers are corrupted by additive persistent disturbances. To achieve consensus between agents, a linear local interaction rule addressing this requirement is given. The proposed local interaction rules are analysed by applying a Lyapunov-based approach. The multiplicative and additive non-fragile feedback control algorithms are designed and sufficient conditions for the consensus of the multi-agent systems are presented in terms of linear matrix inequalities, respectively. Simulation results are presented to support the effectiveness of the proposed algorithms.

  7. Optimal design of FIR triplet halfband filter bank and application in image coding.

    PubMed

    Kha, H H; Tuan, H D; Nguyen, T Q

    2011-02-01

    This correspondence proposes an efficient semidefinite programming (SDP) method for the design of a class of linear phase finite impulse response triplet halfband filter banks whose filters have optimal frequency selectivity for a prescribed regularity order. The design problem is formulated as the minimization of the least square error subject to peak error constraints and regularity constraints. By using the linear matrix inequality characterization of the trigonometric semi-infinite constraints, it can then be exactly cast as a SDP problem with a small number of variables and, hence, can be solved efficiently. Several design examples of the triplet halfband filter bank are provided for illustration and comparison with previous works. Finally, the image coding performance of the filter bank is presented.

  8. Optimal trace inequality constants for interior penalty discontinuous Galerkin discretisations of elliptic operators using arbitrary elements with non-constant Jacobians

    NASA Astrophysics Data System (ADS)

    Owens, A. R.; Kópházi, J.; Eaton, M. D.

    2017-12-01

    In this paper, a new method to numerically calculate the trace inequality constants, which arise in the calculation of penalty parameters for interior penalty discretisations of elliptic operators, is presented. These constants are provably optimal for the inequality of interest. As their calculation is based on the solution of a generalised eigenvalue problem involving the volumetric and face stiffness matrices, the method is applicable to any element type for which these matrices can be calculated, including standard finite elements and the non-uniform rational B-splines of isogeometric analysis. In particular, the presented method does not require the Jacobian of the element to be constant, and so can be applied to a much wider variety of element shapes than are currently available in the literature. Numerical results are presented for a variety of finite element and isogeometric cases. When the Jacobian is constant, it is demonstrated that the new method produces lower penalty parameters than existing methods in the literature in all cases, which translates directly into savings in the solution time of the resulting linear system. When the Jacobian is not constant, it is shown that the naive application of existing approaches can result in penalty parameters that do not guarantee coercivity of the bilinear form, and by extension, the stability of the solution. The method of manufactured solutions is applied to a model reaction-diffusion equation with a range of parameters, and it is found that using penalty parameters based on the new trace inequality constants result in better conditioned linear systems, which can be solved approximately 11% faster than those produced by the methods from the literature.

  9. H∞ control for uncertain linear system over networks with Bernoulli data dropout and actuator saturation.

    PubMed

    Yu, Jimin; Yang, Chenchen; Tang, Xiaoming; Wang, Ping

    2018-03-01

    This paper investigates the H ∞ control problems for uncertain linear system over networks with random communication data dropout and actuator saturation. The random data dropout process is modeled by a Bernoulli distributed white sequence with a known conditional probability distribution and the actuator saturation is confined in a convex hull by introducing a group of auxiliary matrices. By constructing a quadratic Lyapunov function, effective conditions for the state feedback-based H ∞ controller and the observer-based H ∞ controller are proposed in the form of non-convex matrix inequalities to take the random data dropout and actuator saturation into consideration simultaneously, and the problem of non-convex feasibility is solved by applying cone complementarity linearization (CCL) procedure. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed new design techniques. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

  10. Some Geometric Inequalities Relating to an Interior Point in Triangle

    ERIC Educational Resources Information Center

    Wu, Yu-Dong; Zhang, Zhi-Hua; Liang, Chun-Lei

    2010-01-01

    In this short note, by using one of Li and Liu's theorems [K.-H. Li, "The solution of CIQ. 39," "Commun. Stud. Inequal." 11(1) (2004), p. 162 (in Chinese)], "s-R-r" method, Cauchy's inequality and the theory of convex function, we solve some geometric inequalities conjectures relating to an interior point in triangle. (Contains 1 figure.)

  11. Variationally consistent discretization schemes and numerical algorithms for contact problems

    NASA Astrophysics Data System (ADS)

    Wohlmuth, Barbara

    We consider variationally consistent discretization schemes for mechanical contact problems. Most of the results can also be applied to other variational inequalities, such as those for phase transition problems in porous media, for plasticity or for option pricing applications from finance. The starting point is to weakly incorporate the constraint into the setting and to reformulate the inequality in the displacement in terms of a saddle-point problem. Here, the Lagrange multiplier represents the surface forces, and the constraints are restricted to the boundary of the simulation domain. Having a uniform inf-sup bound, one can then establish optimal low-order a priori convergence rates for the discretization error in the primal and dual variables. In addition to the abstract framework of linear saddle-point theory, complementarity terms have to be taken into account. The resulting inequality system is solved by rewriting it equivalently by means of the non-linear complementarity function as a system of equations. Although it is not differentiable in the classical sense, semi-smooth Newton methods, yielding super-linear convergence rates, can be applied and easily implemented in terms of a primal-dual active set strategy. Quite often the solution of contact problems has a low regularity, and the efficiency of the approach can be improved by using adaptive refinement techniques. Different standard types, such as residual- and equilibrated-based a posteriori error estimators, can be designed based on the interpretation of the dual variable as Neumann boundary condition. For the fully dynamic setting it is of interest to apply energy-preserving time-integration schemes. However, the differential algebraic character of the system can result in high oscillations if standard methods are applied. A possible remedy is to modify the fully discretized system by a local redistribution of the mass. Numerical results in two and three dimensions illustrate the wide range of possible applications and show the performance of the space discretization scheme, non-linear solver, adaptive refinement process and time integration.

  12. Algebraic Thinking in Solving Linier Program at High School Level: Female Student’s Field Independent Cognitive Style

    NASA Astrophysics Data System (ADS)

    Hardiani, N.; Budayasa, I. K.; Juniati, D.

    2018-01-01

    The aim of this study was to describe algebraic thinking of high school female student’s field independent cognitive style in solving linier program problem by revealing deeply the female students’ responses. Subjects in this study were 7 female students having field independent cognitive style in class 11. The type of this research was descriptive qualitative. The method of data collection used was observation, documentation, and interview. Data analysis technique was by reduction, presentation, and conclusion. The results of this study showed that the female students with field independent cognitive style in solving the linier program problem had the ability to represent algebraic ideas from the narrative question that had been read by manipulating symbols and variables presented in tabular form, creating and building mathematical models in two variables linear inequality system which represented algebraic ideas, and interpreting the solutions as variables obtained from the point of intersection in the solution area to obtain maximum benefit.

  13. Switching State-Feedback LPV Control with Uncertain Scheduling Parameters

    NASA Technical Reports Server (NTRS)

    He, Tianyi; Al-Jiboory, Ali Khudhair; Swei, Sean Shan-Min; Zhu, Guoming G.

    2017-01-01

    This paper presents a new method to design Robust Switching State-Feedback Gain-Scheduling (RSSFGS) controllers for Linear Parameter Varying (LPV) systems with uncertain scheduling parameters. The domain of scheduling parameters are divided into several overlapped subregions to undergo hysteresis switching among a family of simultaneously designed LPV controllers over the corresponding subregion with the guaranteed H-infinity performance. The synthesis conditions are given in terms of Parameterized Linear Matrix Inequalities that guarantee both stability and performance at each subregion and associated switching surfaces. The switching stability is ensured by descent parameter-dependent Lyapunov function on switching surfaces. By solving the optimization problem, RSSFGS controller can be obtained for each subregion. A numerical example is given to illustrate the effectiveness of the proposed approach over the non-switching controllers.

  14. Inequalities, Assessment and Computer Algebra

    ERIC Educational Resources Information Center

    Sangwin, Christopher J.

    2015-01-01

    The goal of this paper is to examine single variable real inequalities that arise as tutorial problems and to examine the extent to which current computer algebra systems (CAS) can (1) automatically solve such problems and (2) determine whether students' own answers to such problems are correct. We review how inequalities arise in contemporary…

  15. Control of discrete time systems based on recurrent Super-Twisting-like algorithm.

    PubMed

    Salgado, I; Kamal, S; Bandyopadhyay, B; Chairez, I; Fridman, L

    2016-09-01

    Most of the research in sliding mode theory has been carried out to in continuous time to solve the estimation and control problems. However, in discrete time, the results in high order sliding modes have been less developed. In this paper, a discrete time super-twisting-like algorithm (DSTA) was proposed to solve the problems of control and state estimation. The stability proof was developed in terms of the discrete time Lyapunov approach and the linear matrix inequalities theory. The system trajectories were ultimately bounded inside a small region dependent on the sampling period. Simulation results tested the DSTA. The DSTA was applied as a controller for a Furuta pendulum and for a DC motor supplied by a DSTA signal differentiator. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

  16. Parameter identification using a creeping-random-search algorithm

    NASA Technical Reports Server (NTRS)

    Parrish, R. V.

    1971-01-01

    A creeping-random-search algorithm is applied to different types of problems in the field of parameter identification. The studies are intended to demonstrate that a random-search algorithm can be applied successfully to these various problems, which often cannot be handled by conventional deterministic methods, and, also, to introduce methods that speed convergence to an extremal of the problem under investigation. Six two-parameter identification problems with analytic solutions are solved, and two application problems are discussed in some detail. Results of the study show that a modified version of the basic creeping-random-search algorithm chosen does speed convergence in comparison with the unmodified version. The results also show that the algorithm can successfully solve problems that contain limits on state or control variables, inequality constraints (both independent and dependent, and linear and nonlinear), or stochastic models.

  17. Research on Centralized Voltage and Effective Inequality Identification Based on Circuit Analysis Method

    NASA Astrophysics Data System (ADS)

    Su, Yi; Wang, Feifeng; Lu, Yufeng; Huang, Huimin; Xia, Xiaofei

    2017-09-01

    This paper is based on affine function equation of the grid and OPF problem, discusses the equivalent of some inequality constraints variables optimizing. Further, we propose the model of injection current and set up the constraint sensitivity index of affine characteristics. The index can be used to identify the central point voltage and effective inequality of the system automatically. And then we can know how to compensate reactive power of the corresponding generator node and control the voltage to ensure the quality of the system voltage. When checking the effective inequalities we introduce cross-solving method of power flow. This provide a different idea for solving the power flow. The paper uses the results of the IEEE5 node examples to illustrate the validity and practicality of the proposed method.

  18. A fast linearized conservative finite element method for the strongly coupled nonlinear fractional Schrödinger equations

    NASA Astrophysics Data System (ADS)

    Li, Meng; Gu, Xian-Ming; Huang, Chengming; Fei, Mingfa; Zhang, Guoyu

    2018-04-01

    In this paper, a fast linearized conservative finite element method is studied for solving the strongly coupled nonlinear fractional Schrödinger equations. We prove that the scheme preserves both the mass and energy, which are defined by virtue of some recursion relationships. Using the Sobolev inequalities and then employing the mathematical induction, the discrete scheme is proved to be unconditionally convergent in the sense of L2-norm and H α / 2-norm, which means that there are no any constraints on the grid ratios. Then, the prior bound of the discrete solution in L2-norm and L∞-norm are also obtained. Moreover, we propose an iterative algorithm, by which the coefficient matrix is independent of the time level, and thus it leads to Toeplitz-like linear systems that can be efficiently solved by Krylov subspace solvers with circulant preconditioners. This method can reduce the memory requirement of the proposed linearized finite element scheme from O (M2) to O (M) and the computational complexity from O (M3) to O (Mlog ⁡ M) in each iterative step, where M is the number of grid nodes. Finally, numerical results are carried out to verify the correction of the theoretical analysis, simulate the collision of two solitary waves, and show the utility of the fast numerical solution techniques.

  19. An algorithm for the solution of dynamic linear programs

    NASA Technical Reports Server (NTRS)

    Psiaki, Mark L.

    1989-01-01

    The algorithm's objective is to efficiently solve Dynamic Linear Programs (DLP) by taking advantage of their special staircase structure. This algorithm constitutes a stepping stone to an improved algorithm for solving Dynamic Quadratic Programs, which, in turn, would make the nonlinear programming method of Successive Quadratic Programs more practical for solving trajectory optimization problems. The ultimate goal is to being trajectory optimization solution speeds into the realm of real-time control. The algorithm exploits the staircase nature of the large constraint matrix of the equality-constrained DLPs encountered when solving inequality-constrained DLPs by an active set approach. A numerically-stable, staircase QL factorization of the staircase constraint matrix is carried out starting from its last rows and columns. The resulting recursion is like the time-varying Riccati equation from multi-stage LQR theory. The resulting factorization increases the efficiency of all of the typical LP solution operations over that of a dense matrix LP code. At the same time numerical stability is ensured. The algorithm also takes advantage of dynamic programming ideas about the cost-to-go by relaxing active pseudo constraints in a backwards sweeping process. This further decreases the cost per update of the LP rank-1 updating procedure, although it may result in more changes of the active set that if pseudo constraints were relaxed in a non-stagewise fashion. The usual stability of closed-loop Linear/Quadratic optimally-controlled systems, if it carries over to strictly linear cost functions, implies that the saving due to reduced factor update effort may outweigh the cost of an increased number of updates. An aerospace example is presented in which a ground-to-ground rocket's distance is maximized. This example demonstrates the applicability of this class of algorithms to aerospace guidance. It also sheds light on the efficacy of the proposed pseudo constraint relaxation scheme.

  20. A Refined Cauchy-Schwarz Inequality

    ERIC Educational Resources Information Center

    Mercer, Peter R.

    2007-01-01

    The author presents a refinement of the Cauchy-Schwarz inequality. He shows his computations in which refinements of the triangle inequality and its reverse inequality are obtained for nonzero x and y in a normed linear space.

  1. A transformation method for constrained-function minimization

    NASA Technical Reports Server (NTRS)

    Park, S. K.

    1975-01-01

    A direct method for constrained-function minimization is discussed. The method involves the construction of an appropriate function mapping all of one finite dimensional space onto the region defined by the constraints. Functions which produce such a transformation are constructed for a variety of constraint regions including, for example, those arising from linear and quadratic inequalities and equalities. In addition, the computational performance of this method is studied in the situation where the Davidon-Fletcher-Powell algorithm is used to solve the resulting unconstrained problem. Good performance is demonstrated for 19 test problems by achieving rapid convergence to a solution from several widely separated starting points.

  2. Spacecraft inertia estimation via constrained least squares

    NASA Technical Reports Server (NTRS)

    Keim, Jason A.; Acikmese, Behcet A.; Shields, Joel F.

    2006-01-01

    This paper presents a new formulation for spacecraft inertia estimation from test data. Specifically, the inertia estimation problem is formulated as a constrained least squares minimization problem with explicit bounds on the inertia matrix incorporated as LMIs [linear matrix inequalities). The resulting minimization problem is a semidefinite optimization that can be solved efficiently with guaranteed convergence to the global optimum by readily available algorithms. This method is applied to data collected from a robotic testbed consisting of a freely rotating body. The results show that the constrained least squares approach produces more accurate estimates of the inertia matrix than standard unconstrained least squares estimation methods.

  3. Non-fragile multivariable PID controller design via system augmentation

    NASA Astrophysics Data System (ADS)

    Liu, Jinrong; Lam, James; Shen, Mouquan; Shu, Zhan

    2017-07-01

    In this paper, the issue of designing non-fragile H∞ multivariable proportional-integral-derivative (PID) controllers with derivative filters is investigated. In order to obtain the controller gains, the original system is associated with an extended system such that the PID controller design can be formulated as a static output-feedback control problem. By taking the system augmentation approach, the conditions with slack matrices for solving the non-fragile H∞ multivariable PID controller gains are established. Based on the results, linear matrix inequality -based iterative algorithms are provided to compute the controller gains. Simulations are conducted to verify the effectiveness of the proposed approaches.

  4. Power allocation for SWIPT in K-user interference channels using game theory

    NASA Astrophysics Data System (ADS)

    Wen, Zhigang; Liu, Ying; Liu, Xiaoqing; Li, Shan; Chen, Xianya

    2018-12-01

    A simultaneous wireless information and power transfer system in interference channels of multi-users is considered. In this system, each transmitter sends one data stream to its targeted receiver, which causes interference to other receivers. Since all transmitter-receiver links want to maximize their own average transmission rate, a power allocation problem under the transmit power constraints and the energy-harvesting constraints is developed. To solve this problem, we propose a game theory framework. Then, we convert the game into a variational inequalities problem by establishing the connection between game theory and variational inequalities and solve the variational inequalities problem. Through theoretical analysis, the existence and uniqueness of Nash equilibrium are both guaranteed by the theory of variational inequalities. A distributed iterative alternating optimization water-filling algorithm is derived, which is proved to converge. Numerical results show that the proposed algorithm reaches fast convergence and achieves a higher sum rate than the unaided scheme.

  5. Performance optimization for rotors in hover and axial flight

    NASA Technical Reports Server (NTRS)

    Quackenbush, T. R.; Wachspress, D. A.; Kaufman, A. E.; Bliss, D. B.

    1989-01-01

    Performance optimization for rotors in hover and axial flight is a topic of continuing importance to rotorcraft designers. The aim of this Phase 1 effort has been to demonstrate that a linear optimization algorithm could be coupled to an existing influence coefficient hover performance code. This code, dubbed EHPIC (Evaluation of Hover Performance using Influence Coefficients), uses a quasi-linear wake relaxation to solve for the rotor performance. The coupling was accomplished by expanding of the matrix of linearized influence coefficients in EHPIC to accommodate design variables and deriving new coefficients for linearized equations governing perturbations in power and thrust. These coefficients formed the input to a linear optimization analysis, which used the flow tangency conditions on the blade and in the wake to impose equality constraints on the expanded system of equations; user-specified inequality contraints were also employed to bound the changes in the design. It was found that this locally linearized analysis could be invoked to predict a design change that would produce a reduction in the power required by the rotor at constant thrust. Thus, an efficient search for improved versions of the baseline design can be carried out while retaining the accuracy inherent in a free wake/lifting surface performance analysis.

  6. Algorithm Optimally Allocates Actuation of a Spacecraft

    NASA Technical Reports Server (NTRS)

    Motaghedi, Shi

    2007-01-01

    A report presents an algorithm that solves the following problem: Allocate the force and/or torque to be exerted by each thruster and reaction-wheel assembly on a spacecraft for best performance, defined as minimizing the error between (1) the total force and torque commanded by the spacecraft control system and (2) the total of forces and torques actually exerted by all the thrusters and reaction wheels. The algorithm incorporates the matrix vector relationship between (1) the total applied force and torque and (2) the individual actuator force and torque values. It takes account of such constraints as lower and upper limits on the force or torque that can be applied by a given actuator. The algorithm divides the aforementioned problem into two optimization problems that it solves sequentially. These problems are of a type, known in the art as semi-definite programming problems, that involve linear matrix inequalities. The algorithm incorporates, as sub-algorithms, prior algorithms that solve such optimization problems very efficiently. The algorithm affords the additional advantage that the solution requires the minimum rate of consumption of fuel for the given best performance.

  7. Approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays: a robust stability problem.

    PubMed

    Pandiselvi, S; Raja, R; Cao, Jinde; Rajchakit, G; Ahmad, Bashir

    2018-01-01

    This work predominantly labels the problem of approximation of state variables for discrete-time stochastic genetic regulatory networks with leakage, distributed, and probabilistic measurement delays. Here we design a linear estimator in such a way that the absorption of mRNA and protein can be approximated via known measurement outputs. By utilizing a Lyapunov-Krasovskii functional and some stochastic analysis execution, we obtain the stability formula of the estimation error systems in the structure of linear matrix inequalities under which the estimation error dynamics is robustly exponentially stable. Further, the obtained conditions (in the form of LMIs) can be effortlessly solved by some available software packages. Moreover, the specific expression of the desired estimator is also shown in the main section. Finally, two mathematical illustrative examples are accorded to show the advantage of the proposed conceptual results.

  8. A Hierarchical Linear Model for Estimating Gender-Based Earnings Differentials.

    ERIC Educational Resources Information Center

    Haberfield, Yitchak; Semyonov, Moshe; Addi, Audrey

    1998-01-01

    Estimates of gender earnings inequality in data from 116,431 Jewish workers were compared using a hierarchical linear model (HLM) and ordinary least squares model. The HLM allows estimation of the extent to which earnings inequality depends on occupational characteristics. (SK)

  9. Synchronization error estimation and controller design for delayed Lur'e systems with parameter mismatches.

    PubMed

    He, Wangli; Qian, Feng; Han, Qing-Long; Cao, Jinde

    2012-10-01

    This paper investigates the problem of master-slave synchronization of two delayed Lur'e systems in the presence of parameter mismatches. First, by analyzing the corresponding synchronization error system, synchronization with an error level, which is referred to as quasi-synchronization, is established. Some delay-dependent quasi-synchronization criteria are derived. An estimation of the synchronization error bound is given, and an explicit expression of error levels is obtained. Second, sufficient conditions on the existence of feedback controllers under a predetermined error level are provided. The controller gains are obtained by solving a set of linear matrix inequalities. Finally, a delayed Chua's circuit is chosen to illustrate the effectiveness of the derived results.

  10. Proposal of Evolutionary Simplex Method for Global Optimization Problem

    NASA Astrophysics Data System (ADS)

    Shimizu, Yoshiaki

    To make an agile decision in a rational manner, role of optimization engineering has been notified increasingly under diversified customer demand. With this point of view, in this paper, we have proposed a new evolutionary method serving as an optimization technique in the paradigm of optimization engineering. The developed method has prospects to solve globally various complicated problem appearing in real world applications. It is evolved from the conventional method known as Nelder and Mead’s Simplex method by virtue of idea borrowed from recent meta-heuristic method such as PSO. Mentioning an algorithm to handle linear inequality constraints effectively, we have validated effectiveness of the proposed method through comparison with other methods using several benchmark problems.

  11. Problem Solving through an Optimization Problem in Geometry

    ERIC Educational Resources Information Center

    Poon, Kin Keung; Wong, Hang-Chi

    2011-01-01

    This article adapts the problem-solving model developed by Polya to investigate and give an innovative approach to discuss and solve an optimization problem in geometry: the Regiomontanus Problem and its application to football. Various mathematical tools, such as calculus, inequality and the properties of circles, are used to explore and reflect…

  12. A Conceptual Approach to Absolute Value Equations and Inequalities

    ERIC Educational Resources Information Center

    Ellis, Mark W.; Bryson, Janet L.

    2011-01-01

    The absolute value learning objective in high school mathematics requires students to solve far more complex absolute value equations and inequalities. When absolute value problems become more complex, students often do not have sufficient conceptual understanding to make any sense of what is happening mathematically. The authors suggest that the…

  13. On the pth moment estimates of solutions to stochastic functional differential equations in the G-framework.

    PubMed

    Faizullah, Faiz

    2016-01-01

    The aim of the current paper is to present the path-wise and moment estimates for solutions to stochastic functional differential equations with non-linear growth condition in the framework of G-expectation and G-Brownian motion. Under the nonlinear growth condition, the pth moment estimates for solutions to SFDEs driven by G-Brownian motion are proved. The properties of G-expectations, Hölder's inequality, Bihari's inequality, Gronwall's inequality and Burkholder-Davis-Gundy inequalities are used to develop the above mentioned theory. In addition, the path-wise asymptotic estimates and continuity of pth moment for the solutions to SFDEs in the G-framework, with non-linear growth condition are shown.

  14. Semiantichains and Unichain Coverings in Direct Products of Partial Orders.

    DTIC Science & Technology

    1980-09-01

    34 Discrete Math . 5 (1973), 305-337. 13) G. B. Dantsig and A. J. 11offman, "Dilworth’s theorem on partially ordered sets,* in Linear Inequalities and Related...Sperner theorem,* Discrete Math . 17 (1977), 281-289. 118) A. J. Hoffman, ’The role of unimodularity in applying linear inequalities to combinatorial

  15. Using the Wonder of Inequalities between Averages for Mathematics Problems Solving

    ERIC Educational Resources Information Center

    Shaanan, Rachel Mogilevsky; Gordon, Moshe Stupel

    2016-01-01

    The study presents an introductory idea of using mathematical averages as a tool for enriching mathematical problem solving. Throughout students' activities, a research was conducted on their ability to solve mathematical problems, and how to cope with a variety of mathematical tasks, in a variety of ways, using the skills, tools and experiences…

  16. Nonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous media

    NASA Astrophysics Data System (ADS)

    Yang, Haijian; Sun, Shuyu; Yang, Chao

    2017-03-01

    Most existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.

  17. Missile Guidance Law Based on Robust Model Predictive Control Using Neural-Network Optimization.

    PubMed

    Li, Zhijun; Xia, Yuanqing; Su, Chun-Yi; Deng, Jun; Fu, Jun; He, Wei

    2015-08-01

    In this brief, the utilization of robust model-based predictive control is investigated for the problem of missile interception. Treating the target acceleration as a bounded disturbance, novel guidance law using model predictive control is developed by incorporating missile inside constraints. The combined model predictive approach could be transformed as a constrained quadratic programming (QP) problem, which may be solved using a linear variational inequality-based primal-dual neural network over a finite receding horizon. Online solutions to multiple parametric QP problems are used so that constrained optimal control decisions can be made in real time. Simulation studies are conducted to illustrate the effectiveness and performance of the proposed guidance control law for missile interception.

  18. Explicit asymmetric bounds for robust stability of continuous and discrete-time systems

    NASA Technical Reports Server (NTRS)

    Gao, Zhiqiang; Antsaklis, Panos J.

    1993-01-01

    The problem of robust stability in linear systems with parametric uncertainties is considered. Explicit stability bounds on uncertain parameters are derived and expressed in terms of linear inequalities for continuous systems, and inequalities with quadratic terms for discrete-times systems. Cases where system parameters are nonlinear functions of an uncertainty are also examined.

  19. Shape in Picture: Mathematical Description of Shape in Grey-Level Images

    DTIC Science & Technology

    1992-09-11

    representation is scale-space, derived frrr- the linear isotropic diffusion equation; recently other types of equations have been considered. Multiscale...recognition of dimensions in the general case of an arbitrary denominator is similar to that just explained. 3 Linear Inequalities in the Two-Dimensional...solid region containing all pixels of the space, whose coordinates satisfy a linear inequality. A Um C scspt fr Digital Geometry 41 s a a v--’ -0 7 O

  20. Robust cooperation of connected vehicle systems with eigenvalue-bounded interaction topologies in the presence of uncertain dynamics

    NASA Astrophysics Data System (ADS)

    Li, Keqiang; Gao, Feng; Li, Shengbo Eben; Zheng, Yang; Gao, Hongbo

    2017-12-01

    This study presents a distributed H-infinity control method for uncertain platoons with dimensionally and structurally unknown interaction topologies provided that the associated topological eigenvalues are bounded by a predesigned range.With an inverse model to compensate for nonlinear powertrain dynamics, vehicles in a platoon are modeled by third-order uncertain systems with bounded disturbances. On the basis of the eigenvalue decomposition of topological matrices, we convert the platoon system to a norm-bounded uncertain part and a diagonally structured certain part by applying linear transformation. We then use a common Lyapunov method to design a distributed H-infinity controller. Numerically, two linear matrix inequalities corresponding to the minimum and maximum eigenvalues should be solved. The resulting controller can tolerate interaction topologies with eigenvalues located in a certain range. The proposed method can also ensure robustness performance and disturbance attenuation ability for the closed-loop platoon system. Hardware-in-the-loop tests are performed to validate the effectiveness of our method.

  1. Optimal exponential synchronization of general chaotic delayed neural networks: an LMI approach.

    PubMed

    Liu, Meiqin

    2009-09-01

    This paper investigates the optimal exponential synchronization problem of general chaotic neural networks with or without time delays by virtue of Lyapunov-Krasovskii stability theory and the linear matrix inequality (LMI) technique. This general model, which is the interconnection of a linear delayed dynamic system and a bounded static nonlinear operator, covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks (CNNs), bidirectional associative memory (BAM) networks, and recurrent multilayer perceptrons (RMLPs) with or without delays. Using the drive-response concept, time-delay feedback controllers are designed to synchronize two identical chaotic neural networks as quickly as possible. The control design equations are shown to be a generalized eigenvalue problem (GEVP) which can be easily solved by various convex optimization algorithms to determine the optimal control law and the optimal exponential synchronization rate. Detailed comparisons with existing results are made and numerical simulations are carried out to demonstrate the effectiveness of the established synchronization laws.

  2. Pre-Service Teachers' Linear and Quadratic Inequalities Understandings

    ERIC Educational Resources Information Center

    Bicer, Ali; Capraro, Robert M.; Capraro, Mary M.

    2014-01-01

    The National Council of Teachers of Mathematics [NCTM] noted that middle and high school students are expected to be able to both explain inequalities by using mathematical symbols and understand meanings by interpreting the solutions of inequalities. Unfortunately, research has revealed that not only do middle and high school students hold…

  3. Time trends in absolute and relative socioeconomic inequalities in leisure time physical inactivity in northern Sweden.

    PubMed

    Szilcz, Máté; Mosquera, Paola A; Sebastián, Miguel San; Gustafsson, Per E

    2018-02-01

    The aim was to investigate the time trends in educational, occupational, and income-related inequalities in leisure time physical inactivity in 2006, 2010, and 2014 in northern Swedish women and men. This study was based on data obtained from the repeated cross-sectional Health on Equal Terms survey of 2006, 2010, and 2014. The analytical sample consisted of 20,667 (2006), 31,787 (2010), and 21,613 (2014) individuals, aged 16-84. Logistic regressions were used to model the probability of physical inactivity given a set of explanatory variables. Slope index of inequality (SII) and relative index of inequality (RII) were used as summary measures of the social gradient in physical inactivity. The linear trend in inequalities and difference between gender and years were estimated by interaction analyses. The year 2010 displayed the highest physical inactivity inequalities for all socioeconomic position indicators, but educational and occupational inequalities decreased in 2014. However, significant positive linear trends were found in absolute and relative income inequalities. Moreover, women had significantly higher RII of education in physical inactivity in 2014 and significantly higher SII and RII of income in physical inactivity in 2010, than did men in the same years. The recent reduction in educational and occupational inequalities following the high inequalities around the time of the great recession in 2010 suggests that the current policies might be fairly effective. However, to eventually alleviate inequities in physical inactivity, the focus of the researchers and policymakers should be directed toward the widening trends of income inequalities in physical inactivity.

  4. Reframing inequality? The health inequalities turn as a dangerous frame shift.

    PubMed

    Lynch, Julia

    2017-12-01

    Politicians in many countries have embraced the notion that health inequalities derive from socioeconomic inequalities, but European governments have for the most part failed to enact policies that would reduce underlying social inequalities. Data are drawn from 84 in-depth interviews with policy-makers in four European countries between 2012 and 2015, qualitative content analysis of recent health inequalities policy documents, and secondary literature on the barriers to implementing evidence-based health inequalities policies. Institutional and political barriers are important barriers to effective policy. Both policy-making institutions and the ideas and practices associated with neoliberalism reinforce medical-individualist models of health, strengthen actors with material interests opposed to policies that would increase equity, and undermine policy action to tackle the fundamental causes of social (including health) inequalities. Medicalizing inequality is more appealing to most politicians than tackling income and wage inequality head-on, but it results in framing the problem of social inequality in a way that makes it technically quite difficult to solve. Policy-makers should consider adopting more traditional programs of taxation, redistribution and labor market regulation in order to reduce both health inequalities and the underlying social inequalities. © The Author 2017. Published by Oxford University Press on behalf of Faculty of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com

  5. Income inequality and child maltreatment in the United States.

    PubMed

    Eckenrode, John; Smith, Elliott G; McCarthy, Margaret E; Dineen, Michael

    2014-03-01

    To examine the relation between county-level income inequality and rates of child maltreatment. Data on substantiated reports of child abuse and neglect from 2005 to 2009 were obtained from the National Child Abuse and Neglect Data System. County-level data on income inequality and children in poverty were obtained from the American Community Survey. Data for additional control variables were obtained from the American Community Survey and the Health Resources and Services Administration Area Resource File. The Gini coefficient was used as the measure of income inequality. Generalized additive models were estimated to explore linear and nonlinear relations among income inequality, poverty, and child maltreatment. In all models, state was included as a fixed effect to control for state-level differences in victim rates. Considerable variation in income inequality and child maltreatment rates was found across the 3142 US counties. Income inequality, as well as child poverty rate, was positively and significantly correlated with child maltreatment rates at the county level. Controlling for child poverty, demographic and economic control variables, and state-level variation in maltreatment rates, there was a significant linear effect of inequality on child maltreatment rates (P < .0001). This effect was stronger for counties with moderate to high levels of child poverty. Higher income inequality across US counties was significantly associated with higher county-level rates of child maltreatment. The findings contribute to the growing literature linking greater income inequality to a range of poor health and well-being outcomes in infants and children.

  6. H∞ output tracking control of discrete-time nonlinear systems via standard neural network models.

    PubMed

    Liu, Meiqin; Zhang, Senlin; Chen, Haiyang; Sheng, Weihua

    2014-10-01

    This brief proposes an output tracking control for a class of discrete-time nonlinear systems with disturbances. A standard neural network model is used to represent discrete-time nonlinear systems whose nonlinearity satisfies the sector conditions. H∞ control performance for the closed-loop system including the standard neural network model, the reference model, and state feedback controller is analyzed using Lyapunov-Krasovskii stability theorem and linear matrix inequality (LMI) approach. The H∞ controller, of which the parameters are obtained by solving LMIs, guarantees that the output of the closed-loop system closely tracks the output of a given reference model well, and reduces the influence of disturbances on the tracking error. Three numerical examples are provided to show the effectiveness of the proposed H∞ output tracking design approach.

  7. Further studies on stability analysis of nonlinear Roesser-type two-dimensional systems

    NASA Astrophysics Data System (ADS)

    Dai, Xiao-Lin

    2014-04-01

    This paper is concerned with further relaxations of the stability analysis of nonlinear Roesser-type two-dimensional (2D) systems in the Takagi-Sugeno fuzzy form. To achieve the goal, a novel slack matrix variable technique, which is homogenous polynomially parameter-dependent on the normalized fuzzy weighting functions with arbitrary degree, is developed and the algebraic properties of the normalized fuzzy weighting functions are collected into a set of augmented matrices. Consequently, more information about the normalized fuzzy weighting functions is involved and the relaxation quality of the stability analysis is significantly improved. Moreover, the obtained result is formulated in the form of linear matrix inequalities, which can be easily solved via standard numerical software. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed result.

  8. Exponential synchronization of neural networks with discrete and distributed delays under time-varying sampling.

    PubMed

    Wu, Zheng-Guang; Shi, Peng; Su, Hongye; Chu, Jian

    2012-09-01

    This paper investigates the problem of master-slave synchronization for neural networks with discrete and distributed delays under variable sampling with a known upper bound on the sampling intervals. An improved method is proposed, which captures the characteristic of sampled-data systems. Some delay-dependent criteria are derived to ensure the exponential stability of the error systems, and thus the master systems synchronize with the slave systems. The desired sampled-data controller can be achieved by solving a set of linear matrix inequalitys, which depend upon the maximum sampling interval and the decay rate. The obtained conditions not only have less conservatism but also have less decision variables than existing results. Simulation results are given to show the effectiveness and benefits of the proposed methods.

  9. On the stability, storage capacity, and design of nonlinear continuous neural networks

    NASA Technical Reports Server (NTRS)

    Guez, Allon; Protopopsecu, Vladimir; Barhen, Jacob

    1988-01-01

    The stability, capacity, and design of a nonlinear continuous neural network are analyzed. Sufficient conditions for existence and asymptotic stability of the network's equilibria are reduced to a set of piecewise-linear inequality relations that can be solved by a feedforward binary network, or by methods such as Fourier elimination. The stability and capacity of the network is characterized by the post synaptic firing rate function. An N-neuron network with sigmoidal firing function is shown to have up to 3N equilibrium points. This offers a higher capacity than the (0.1-0.2)N obtained in the binary Hopfield network. Moreover, it is shown that by a proper selection of the postsynaptic firing rate function, one can significantly extend the capacity storage of the network.

  10. Typical Werner states satisfying all linear Bell inequalities with dichotomic measurements

    NASA Astrophysics Data System (ADS)

    Luo, Ming-Xing

    2018-04-01

    Quantum entanglement as a special resource inspires various distinct applications in quantum information processing. Unfortunately, it is NP-hard to detect general quantum entanglement using Bell testing. Our goal is to investigate quantum entanglement with white noises that appear frequently in experiment and quantum simulations. Surprisingly, for almost all multipartite generalized Greenberger-Horne-Zeilinger states there are entangled noisy states that satisfy all linear Bell inequalities consisting of full correlations with dichotomic inputs and outputs of each local observer. This result shows generic undetectability of mixed entangled states in contrast to Gisin's theorem of pure bipartite entangled states in terms of Bell nonlocality. We further provide an accessible method to show a nontrivial set of noisy entanglement with small number of parties satisfying all general linear Bell inequalities. These results imply typical incompleteness of special Bell theory in explaining entanglement.

  11. A new polytopic approach for the unknown input functional observer design

    NASA Astrophysics Data System (ADS)

    Bezzaoucha, Souad; Voos, Holger; Darouach, Mohamed

    2018-03-01

    In this paper, a constructive procedure to design Functional Unknown Input Observers for nonlinear continuous time systems is proposed under the Polytopic Takagi-Sugeno framework. An equivalent representation for the nonlinear model is achieved using the sector nonlinearity transformation. Applying the Lyapunov theory and the ? attenuation, linear matrix inequalities conditions are deduced which are solved for feasibility to obtain the observer design matrices. To cope with the effect of unknown inputs, classical approach of decoupling the unknown input for the linear case is used. Both algebraic and solver-based solutions are proposed (relaxed conditions). Necessary and sufficient conditions for the existence of the functional polytopic observer are given. For both approaches, the general and particular cases (measurable premise variables, full state estimation with full and reduced order cases) are considered and it is shown that the proposed conditions correspond to the one presented for standard linear case. To illustrate the proposed theoretical results, detailed numerical simulations are presented for a Quadrotor Aerial Robots Landing and a Waste Water Treatment Plant. Both systems are highly nonlinear and represented in a T-S polytopic form with unmeasurable premise variables and unknown inputs.

  12. Employing the National Open University of Nigeria English Programme as a Tool for the Displacement of Gender Inequality

    ERIC Educational Resources Information Center

    Omolara, Daniel Iyabode

    2013-01-01

    Gender inequality has been a constant refrain among those that desire social justice. To this end, a global conference on gender equality was organized by the United Nations in 1995 in Beijing, China. However, a recent study questioned the effectiveness of the conference to solve this problem as it found that women themselves are giving hegemonic…

  13. Teaching between Desks

    ERIC Educational Resources Information Center

    Ermeling, Bradley A.; Graff-Ermeling, Genevieve

    2014-01-01

    Watch one of the Japan videos from the Trends in International Mathematics and Science Study (TIMSS)--more specifically, mathematics video 3 on solving inequalities1--and you'll see that after giving his students a word problem to solve, the 8th grade math teacher strolls among the students' desks for almost 15 minutes, leaning over to see what…

  14. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Baker, Kyri; Toomey, Bridget

    Evolving power systems with increasing levels of stochasticity call for a need to solve optimal power flow problems with large quantities of random variables. Weather forecasts, electricity prices, and shifting load patterns introduce higher levels of uncertainty and can yield optimization problems that are difficult to solve in an efficient manner. Solution methods for single chance constraints in optimal power flow problems have been considered in the literature, ensuring single constraints are satisfied with a prescribed probability; however, joint chance constraints, ensuring multiple constraints are simultaneously satisfied, have predominantly been solved via scenario-based approaches or by utilizing Boole's inequality asmore » an upper bound. In this paper, joint chance constraints are used to solve an AC optimal power flow problem while preventing overvoltages in distribution grids under high penetrations of photovoltaic systems. A tighter version of Boole's inequality is derived and used to provide a new upper bound on the joint chance constraint, and simulation results are shown demonstrating the benefit of the proposed upper bound. The new framework allows for a less conservative and more computationally efficient solution to considering joint chance constraints, specifically regarding preventing overvoltages.« less

  15. Solutions to variational inequalities of parabolic type

    NASA Astrophysics Data System (ADS)

    Zhu, Yuanguo

    2006-09-01

    The existence of strong solutions to a kind of variational inequality of parabolic type is investigated by the theory of semigroups of linear operators. As an application, an abstract semi permeable media problem is studied.

  16. Bekenstein inequalities and nonlinear electrodynamics

    NASA Astrophysics Data System (ADS)

    Peñafiel, M. L.; Falciano, F. T.

    2017-12-01

    Bekenstein and Mayo proposed a generalized bound for the entropy, which implies some inequalities between the charge, energy, angular momentum, and size of the macroscopic system. Dain has shown that Maxwell's electrodynamics satisfies all three inequalities. We investigate the validity of these relations in the context of nonlinear electrodynamics and show that Born-Infeld electrodynamics satisfies all of them. However, contrary to the linear theory, there is no rigidity statement in Born-Infeld. We study the physical meaning and the relationship between these inequalities, and in particular, we analyze the connection between the energy-angular momentum inequality and causality.

  17. An Evaluation of an Algorithm for Linear Inequalities and Its Applications

    NASA Technical Reports Server (NTRS)

    Jurgensen, J.

    1973-01-01

    An algorithm is presented for obtaining a solution alpha to a set of inequalities (A alpha) 0 where A is an N x m-matrix and alpha is an m-vector. If the set of inequalities is consistant, then the algorithm is guaranteed to arrive at a solution in a finite number of steps. Also, if in the iteration, a negative vector is obtained, then the initial set of inequalities is inconsistant, and the iteration is terminated.

  18. The Dynamics of Wealth Inequality and the Effect of Income Distribution.

    PubMed

    Berman, Yonatan; Ben-Jacob, Eshel; Shapira, Yoash

    2016-01-01

    The rapid increase of wealth inequality in the past few decades is one of the most disturbing social and economic issues of our time. Studying its origin and underlying mechanisms is essential for policy aiming to control and even reverse this trend. In that context, controlling the distribution of income, using income tax or other macroeconomic policy instruments, is generally perceived as effective for regulating the wealth distribution. We provide a theoretical tool, based on the realistic modeling of wealth inequality dynamics, to describe the effects of personal savings and income distribution on wealth inequality. Our theoretical approach incorporates coupled equations, solved using iterated maps to model the dynamics of wealth and income inequality. Notably, using the appropriate historical parameter values we were able to capture the historical dynamics of wealth inequality in the United States during the course of the 20th century. It is found that the effect of personal savings on wealth inequality is substantial, and its major decrease in the past 30 years can be associated with the current wealth inequality surge. In addition, the effect of increasing income tax, though naturally contributing to lowering income inequality, might contribute to a mild increase in wealth inequality and vice versa. Plausible changes in income tax are found to have an insignificant effect on wealth inequality, in practice. In addition, controlling the income inequality, by progressive taxation, for example, is found to have a very small effect on wealth inequality in the short run. The results imply, therefore, that controlling income inequality is an impractical tool for regulating wealth inequality.

  19. The Dynamics of Wealth Inequality and the Effect of Income Distribution

    PubMed Central

    Berman, Yonatan; Shapira, Yoash

    2016-01-01

    The rapid increase of wealth inequality in the past few decades is one of the most disturbing social and economic issues of our time. Studying its origin and underlying mechanisms is essential for policy aiming to control and even reverse this trend. In that context, controlling the distribution of income, using income tax or other macroeconomic policy instruments, is generally perceived as effective for regulating the wealth distribution. We provide a theoretical tool, based on the realistic modeling of wealth inequality dynamics, to describe the effects of personal savings and income distribution on wealth inequality. Our theoretical approach incorporates coupled equations, solved using iterated maps to model the dynamics of wealth and income inequality. Notably, using the appropriate historical parameter values we were able to capture the historical dynamics of wealth inequality in the United States during the course of the 20th century. It is found that the effect of personal savings on wealth inequality is substantial, and its major decrease in the past 30 years can be associated with the current wealth inequality surge. In addition, the effect of increasing income tax, though naturally contributing to lowering income inequality, might contribute to a mild increase in wealth inequality and vice versa. Plausible changes in income tax are found to have an insignificant effect on wealth inequality, in practice. In addition, controlling the income inequality, by progressive taxation, for example, is found to have a very small effect on wealth inequality in the short run. The results imply, therefore, that controlling income inequality is an impractical tool for regulating wealth inequality. PMID:27105224

  20. Clausius inequality beyond the weak-coupling limit: the quantum Brownian oscillator.

    PubMed

    Kim, Ilki; Mahler, Günter

    2010-01-01

    We consider a quantum linear oscillator coupled at an arbitrary strength to a bath at an arbitrary temperature. We find an exact closed expression for the oscillator density operator. This state is noncanonical but can be shown to be equivalent to that of an uncoupled linear oscillator at an effective temperature T*(eff) with an effective mass and an effective spring constant. We derive an effective Clausius inequality deltaQ*(eff)< or =T*(eff)dS , where deltaQ*(eff) is the heat exchanged between the effective (weakly coupled) oscillator and the bath, and S represents a thermal entropy of the effective oscillator, being identical to the von-Neumann entropy of the coupled oscillator. Using this inequality (for a cyclic process in terms of a variation of the coupling strength) we confirm the validity of the second law. For a fixed coupling strength this inequality can also be tested for a process in terms of a variation of either the oscillator mass or its spring constant. Then it is never violated. The properly defined Clausius inequality is thus more robust than assumed previously.

  1. Northwest Laboratory for Integrated Systems, University of Washington, Semiannual Technical Report Number 1, July 1-November 8, 1991

    DTIC Science & Technology

    1991-11-08

    only simple bounds on delays but also relate the delays in linear inequalities so that tradeoffs are apparent. We model circuits as communicating...set of linear inequalities constraining the variables. These relations provide synthesis tools with information about tradeoffs between circuit delays...available to express the original circuit as a graph of elementary gates and then cover the graph’s fanout-free trees with collections of three-input

  2. Socioeconomic hierarchy and health gradient in Europe: the role of income inequality and of social origins.

    PubMed

    Chauvel, Louis; Leist, Anja K

    2015-11-14

    Health inequalities reflect multidimensional inequality (income, education, and other indicators of socioeconomic position) and vary across countries and welfare regimes. To which extent there is intergenerational transmission of health via parental socioeconomic status has rarely been investigated in comparative perspective. The study sought to explore if different measures of stratification produce the same health gradient and to which extent health gradients of income and of social origins vary with level of living and income inequality. A total of 299,770 observations were available from 18 countries assessed in EU-SILC 2005 and 2011 data, which contain information on social origins. Income inequality (Gini) and level of living were calculated from EU-SILC. Logit rank transformation provided normalized inequalities and distributions of income and social origins up to the extremes of the distribution and was used to investigate net comparable health gradients in detail. Multilevel random-slope models were run to post-estimate best linear unbiased predictors (BLUPs) and related standard deviations of residual intercepts (median health) and slopes (income-health gradients) per country and survey year. Health gradients varied across different measures of stratification, with origins and income producing significant slopes after controls. Income inequality was associated with worse average health, but income inequality and steepness of the health gradient were only marginally associated. Linear health gradients suggest gains in health per rank of income and of origins even at the very extremes of the distribution. Intergenerational transmission of status gains in importance in countries with higher income inequality. Countries differ in the association of income inequality and income-related health gradient, and low income inequality may mask health problems of vulnerable individuals with low status. Not only income inequality, but other country characteristics such as familial orientation play a considerable role in explaining steepness of the health gradient.

  3. Mixed H2/H∞ distributed robust model predictive control for polytopic uncertain systems subject to actuator saturation and missing measurements

    NASA Astrophysics Data System (ADS)

    Song, Yan; Fang, Xiaosheng; Diao, Qingda

    2016-03-01

    In this paper, we discuss the mixed H2/H∞ distributed robust model predictive control problem for polytopic uncertain systems subject to randomly occurring actuator saturation and packet loss. The global system is decomposed into several subsystems, and all the subsystems are connected by a fixed topology network, which is the definition for the packet loss among the subsystems. To better use the successfully transmitted information via Internet, both the phenomena of actuator saturation and packet loss resulting from the limitation of the communication bandwidth are taken into consideration. A novel distributed controller model is established to account for the actuator saturation and packet loss in a unified representation by using two sets of Bernoulli distributed white sequences with known conditional probabilities. With the nonlinear feedback control law represented by the convex hull of a group of linear feedback laws, the distributed controllers for subsystems are obtained by solving an linear matrix inequality (LMI) optimisation problem. Finally, numerical studies demonstrate the effectiveness of the proposed techniques.

  4. Robust sensor fault detection and isolation of gas turbine engines subjected to time-varying parameter uncertainties

    NASA Astrophysics Data System (ADS)

    Pourbabaee, Bahareh; Meskin, Nader; Khorasani, Khashayar

    2016-08-01

    In this paper, a novel robust sensor fault detection and isolation (FDI) strategy using the multiple model-based (MM) approach is proposed that remains robust with respect to both time-varying parameter uncertainties and process and measurement noise in all the channels. The scheme is composed of robust Kalman filters (RKF) that are constructed for multiple piecewise linear (PWL) models that are constructed at various operating points of an uncertain nonlinear system. The parameter uncertainty is modeled by using a time-varying norm bounded admissible structure that affects all the PWL state space matrices. The robust Kalman filter gain matrices are designed by solving two algebraic Riccati equations (AREs) that are expressed as two linear matrix inequality (LMI) feasibility conditions. The proposed multiple RKF-based FDI scheme is simulated for a single spool gas turbine engine to diagnose various sensor faults despite the presence of parameter uncertainties, process and measurement noise. Our comparative studies confirm the superiority of our proposed FDI method when compared to the methods that are available in the literature.

  5. Essentially Entropic Lattice Boltzmann Model

    NASA Astrophysics Data System (ADS)

    Atif, Mohammad; Kolluru, Praveen Kumar; Thantanapally, Chakradhar; Ansumali, Santosh

    2017-12-01

    The entropic lattice Boltzmann model (ELBM), a discrete space-time kinetic theory for hydrodynamics, ensures nonlinear stability via the discrete time version of the second law of thermodynamics (the H theorem). Compliance with the H theorem is numerically enforced in this methodology and involves a search for the maximal discrete path length corresponding to the zero dissipation state by iteratively solving a nonlinear equation. We demonstrate that an exact solution for the path length can be obtained by assuming a natural criterion of negative entropy change, thereby reducing the problem to solving an inequality. This inequality is solved by creating a new framework for construction of Padé approximants via quadrature on appropriate convex function. This exact solution also resolves the issue of indeterminacy in case of nonexistence of the entropic involution step. Since our formulation is devoid of complex mathematical library functions, the computational cost is drastically reduced. To illustrate this, we have simulated a model setup of flow over the NACA-0012 airfoil at a Reynolds number of 2.88 ×106.

  6. Event-triggered distributed filtering over sensor networks with deception attacks and partial measurements

    NASA Astrophysics Data System (ADS)

    Bu, Xianye; Dong, Hongli; Han, Fei; Li, Gongfa

    2018-07-01

    This paper is concerned with the distributed filtering problem for a class of time-varying systems subject to deception attacks and event-triggering protocols. Due to the bandwidth limitation, an event-triggered communication strategy is adopted to alleviate the data transmission pressure in the algorithm implementation process. The partial nodes-based filtering problem is considered, where only a partial of nodes can measure the information of the plant. Meanwhile, the measurement information possibly suffers the deception attacks in the transmission process. Sufficient conditions can be established such that the error dynamics satisfies the prescribed average ? performance constraints. The parameters of designed filters can be calculated by solving a series of recursive linear matrix inequalities. A simulation example is presented to demonstrate the effectiveness of the proposed filtering method in this paper.

  7. Robust output feedback H∞ control for networked control systems based on the occurrence probabilities of time delays

    NASA Astrophysics Data System (ADS)

    Guo, Chenyu; Zhang, Weidong; Bao, Jie

    2012-02-01

    This article is concerned with the problem of robust H ∞ output feedback control for a kind of networked control systems with time-varying network-induced delays. Instead of using boundaries of time delays to represent all time delays, the occurrence probability of each time delay is considered in H∞ stability analysis and stabilisation. The problem addressed is the design of an output feedback controller such that, for all admissible uncertainties, the resulting closed-loop system is stochastically stable for the zero disturbance input and also simultaneously achieves a prescribed H∞ performance level. It is shown that less conservativeness is obtained. A set of linear matrix inequalities is given to solve the corresponding controller design problem. An example is provided to show the effectiveness and applicability of the proposed method.

  8. Exponential Boundary Observers for Pressurized Water Pipe

    NASA Astrophysics Data System (ADS)

    Hermine Som, Idellette Judith; Cocquempot, Vincent; Aitouche, Abdel

    2015-11-01

    This paper deals with state estimation on a pressurized water pipe modeled by nonlinear coupled distributed hyperbolic equations for non-conservative laws with three known boundary measures. Our objective is to estimate the fourth boundary variable, which will be useful for leakage detection. Two approaches are studied. Firstly, the distributed hyperbolic equations are discretized through a finite-difference scheme. By using the Lipschitz property of the nonlinear term and a Lyapunov function, the exponential stability of the estimation error is proven by solving Linear Matrix Inequalities (LMIs). Secondly, the distributed hyperbolic system is preserved for state estimation. After state transformations, a Luenberger-like PDE boundary observer based on backstepping mathematical tools is proposed. An exponential Lyapunov function is used to prove the stability of the resulted estimation error. The performance of the two observers are shown on a water pipe prototype simulated example.

  9. A polyhedral study of production ramping

    DOE PAGES

    Damci-Kurt, Pelin; Kucukyavuz, Simge; Rajan, Deepak; ...

    2015-06-12

    Here, we give strong formulations of ramping constraints—used to model the maximum change in production level for a generator or machine from one time period to the next—and production limits. For the two-period case, we give a complete description of the convex hull of the feasible solutions. The two-period inequalities can be readily used to strengthen ramping formulations without the need for separation. For the general case, we define exponential classes of multi-period variable upper bound and multi-period ramping inequalities, and give conditions under which these inequalities define facets of ramping polyhedra. Finally, we present exact polynomial separation algorithms formore » the inequalities and report computational experiments on using them in a branch-and-cut algorithm to solve unit commitment problems in power generation.« less

  10. Linear matrix inequality approach to exponential synchronization of a class of chaotic neural networks with time-varying delays

    NASA Astrophysics Data System (ADS)

    Wu, Wei; Cui, Bao-Tong

    2007-07-01

    In this paper, a synchronization scheme for a class of chaotic neural networks with time-varying delays is presented. This class of chaotic neural networks covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks, and bidirectional associative memory networks. The obtained criteria are expressed in terms of linear matrix inequalities, thus they can be efficiently verified. A comparison between our results and the previous results shows that our results are less restrictive.

  11. Passivity analysis for uncertain BAM neural networks with time delays and reaction-diffusions

    NASA Astrophysics Data System (ADS)

    Zhou, Jianping; Xu, Shengyuan; Shen, Hao; Zhang, Baoyong

    2013-08-01

    This article deals with the problem of passivity analysis for delayed reaction-diffusion bidirectional associative memory (BAM) neural networks with weight uncertainties. By using a new integral inequality, we first present a passivity condition for the nominal networks, and then extend the result to the case with linear fractional weight uncertainties. The proposed conditions are expressed in terms of linear matrix inequalities, and thus can be checked easily. Examples are provided to demonstrate the effectiveness of the proposed results.

  12. On the development of HSCT tail sizing criteria using linear matrix inequalities

    NASA Technical Reports Server (NTRS)

    Kaminer, Isaac

    1995-01-01

    This report presents the results of a study to extend existing high speed civil transport (HSCT) tail sizing criteria using linear matrix inequalities (LMI). In particular, the effects of feedback specifications, such as MIL STD 1797 Level 1 and 2 flying qualities requirements, and actuator amplitude and rate constraints on the maximum allowable cg travel for a given set of tail sizes are considered. Results comparing previously developed industry criteria and the LMI methodology on an HSCT concept airplane are presented.

  13. Boundary Korn Inequality and Neumann Problems in Homogenization of Systems of Elasticity

    NASA Astrophysics Data System (ADS)

    Geng, Jun; Shen, Zhongwei; Song, Liang

    2017-06-01

    This paper is concerned with a family of elliptic systems of linear elasticity with rapidly oscillating periodic coefficients, arising in the theory of homogenization. We establish uniform optimal regularity estimates for solutions of Neumann problems in a bounded Lipschitz domain with L 2 boundary data. The proof relies on a boundary Korn inequality for solutions of systems of linear elasticity and uses a large-scale Rellich estimate obtained in Shen (Anal PDE, arXiv:1505.00694v2).

  14. A scalable variational inequality approach for flow through porous media models with pressure-dependent viscosity

    NASA Astrophysics Data System (ADS)

    Mapakshi, N. K.; Chang, J.; Nakshatrala, K. B.

    2018-04-01

    Mathematical models for flow through porous media typically enjoy the so-called maximum principles, which place bounds on the pressure field. It is highly desirable to preserve these bounds on the pressure field in predictive numerical simulations, that is, one needs to satisfy discrete maximum principles (DMP). Unfortunately, many of the existing formulations for flow through porous media models do not satisfy DMP. This paper presents a robust, scalable numerical formulation based on variational inequalities (VI), to model non-linear flows through heterogeneous, anisotropic porous media without violating DMP. VI is an optimization technique that places bounds on the numerical solutions of partial differential equations. To crystallize the ideas, a modification to Darcy equations by taking into account pressure-dependent viscosity will be discretized using the lowest-order Raviart-Thomas (RT0) and Variational Multi-scale (VMS) finite element formulations. It will be shown that these formulations violate DMP, and, in fact, these violations increase with an increase in anisotropy. It will be shown that the proposed VI-based formulation provides a viable route to enforce DMP. Moreover, it will be shown that the proposed formulation is scalable, and can work with any numerical discretization and weak form. A series of numerical benchmark problems are solved to demonstrate the effects of heterogeneity, anisotropy and non-linearity on DMP violations under the two chosen formulations (RT0 and VMS), and that of non-linearity on solver convergence for the proposed VI-based formulation. Parallel scalability on modern computational platforms will be illustrated through strong-scaling studies, which will prove the efficiency of the proposed formulation in a parallel setting. Algorithmic scalability as the problem size is scaled up will be demonstrated through novel static-scaling studies. The performed static-scaling studies can serve as a guide for users to be able to select an appropriate discretization for a given problem size.

  15. A Special Application of Absolute Value Techniques in Authentic Problem Solving

    ERIC Educational Resources Information Center

    Stupel, Moshe

    2013-01-01

    There are at least five different equivalent definitions of the absolute value concept. In instances where the task is an equation or inequality with only one or two absolute value expressions, it is a worthy educational experience for learners to solve the task using each one of the definitions. On the other hand, if more than two absolute value…

  16. Gaussian Curvature as an Identifier of Shell Rigidity

    NASA Astrophysics Data System (ADS)

    Harutyunyan, Davit

    2017-11-01

    In the paper we deal with shells with non-zero Gaussian curvature. We derive sharp Korn's first (linear geometric rigidity estimate) and second inequalities on that kind of shell for zero or periodic Dirichlet, Neumann, and Robin type boundary conditions. We prove that if the Gaussian curvature is positive, then the optimal constant in the first Korn inequality scales like h, and if the Gaussian curvature is negative, then the Korn constant scales like h 4/3, where h is the thickness of the shell. These results have a classical flavour in continuum mechanics, in particular shell theory. The Korn first inequalities are the linear version of the famous geometric rigidity estimate by Friesecke et al. for plates in Arch Ration Mech Anal 180(2):183-236, 2006 (where they show that the Korn constant in the nonlinear Korn's first inequality scales like h 2), extended to shells with nonzero curvature. We also recover the uniform Korn-Poincaré inequality proven for "boundary-less" shells by Lewicka and Müller in Annales de l'Institute Henri Poincare (C) Non Linear Anal 28(3):443-469, 2011 in the setting of our problem. The new estimates can also be applied to find the scaling law for the critical buckling load of the shell under in-plane loads as well as to derive energy scaling laws in the pre-buckled regime. The exponents 1 and 4/3 in the present work appear for the first time in any sharp geometric rigidity estimate.

  17. Determination of optimum values for maximizing the profit in bread production: Daily bakery Sdn Bhd

    NASA Astrophysics Data System (ADS)

    Muda, Nora; Sim, Raymond

    2015-02-01

    An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear. An ILP has many applications in industrial production, including job-shop modelling. A possible objective is to maximize the total production, without exceeding the available resources. In some cases, this can be expressed in terms of a linear program, but variables must be constrained to be integer. It concerned with the optimization of a linear function while satisfying a set of linear equality and inequality constraints and restrictions. It has been used to solve optimization problem in many industries area such as banking, nutrition, agriculture, and bakery and so on. The main purpose of this study is to formulate the best combination of all ingredients in producing different type of bread in Daily Bakery in order to gain maximum profit. This study also focuses on the sensitivity analysis due to changing of the profit and the cost of each ingredient. The optimum result obtained from QM software is RM 65,377.29 per day. This study will be benefited for Daily Bakery and also other similar industries. By formulating a combination of all ingredients make up, they can easily know their total profit in producing bread everyday.

  18. On the existence of touch points for first-order state inequality constraints

    NASA Technical Reports Server (NTRS)

    Seywald, Hans; Cliff, Eugene M.

    1993-01-01

    The appearance of touch points in state constrained optimal control problems with general vector-valued control is studied. Under the assumption that the Hamiltonian is regular, touch points for first-order state inequalities are shown to exist only under very special conditions. In many cases of practical importance these conditions can be used to exclude touch points a priori without solving an optimal control problem. The results are demonstrated on a simple example.

  19. Constructing space difference schemes which satisfy a cell entropy inequality

    NASA Technical Reports Server (NTRS)

    Merriam, Marshal L.

    1989-01-01

    A numerical methodology for solving convection problems is presented, using finite difference schemes which satisfy the second law of thermodynamics on a cell-by-cell basis in addition to the usual conservation laws. It is shown that satisfaction of a cell entropy inequality is sufficient, in some cases, to guarantee nonlinear stability. Some details are given for several one-dimensional problems, including the quasi-one-dimensional Euler equations applied to flow in a nozzle.

  20. Numerical evidences for the angular momentum-mass inequality for multiple axially symmetric black holes

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Dain, Sergio; Ortiz, Omar E.; Facultad de Matematica, Astronomia y Fisica, Universidad Nacional de Cordoba, Ciudad Universitaria

    2009-07-15

    We present numerical evidences for the validity of the inequality between the total mass and the total angular momentum for multiple axially symmetric (nonstationary) black holes. We use a parabolic heat flow to solve numerically the stationary axially symmetric Einstein equations. As a by-product of our method, we also give numerical evidences that there are no regular solutions of Einstein equations that describe two extreme, axially symmetric black holes in equilibrium.

  1. Sum-of-squares-based fuzzy controller design using quantum-inspired evolutionary algorithm

    NASA Astrophysics Data System (ADS)

    Yu, Gwo-Ruey; Huang, Yu-Chia; Cheng, Chih-Yung

    2016-07-01

    In the field of fuzzy control, control gains are obtained by solving stabilisation conditions in linear-matrix-inequality-based Takagi-Sugeno fuzzy control method and sum-of-squares-based polynomial fuzzy control method. However, the optimal performance requirements are not considered under those stabilisation conditions. In order to handle specific performance problems, this paper proposes a novel design procedure with regard to polynomial fuzzy controllers using quantum-inspired evolutionary algorithms. The first contribution of this paper is a combination of polynomial fuzzy control and quantum-inspired evolutionary algorithms to undertake an optimal performance controller design. The second contribution is the proposed stability condition derived from the polynomial Lyapunov function. The proposed design approach is dissimilar to the traditional approach, in which control gains are obtained by solving the stabilisation conditions. The first step of the controller design uses the quantum-inspired evolutionary algorithms to determine the control gains with the best performance. Then, the stability of the closed-loop system is analysed under the proposed stability conditions. To illustrate effectiveness and validity, the problem of balancing and the up-swing of an inverted pendulum on a cart is used.

  2. Robust synthetic biology design: stochastic game theory approach.

    PubMed

    Chen, Bor-Sen; Chang, Chia-Hung; Lee, Hsiao-Ching

    2009-07-15

    Synthetic biology is to engineer artificial biological systems to investigate natural biological phenomena and for a variety of applications. However, the development of synthetic gene networks is still difficult and most newly created gene networks are non-functioning due to uncertain initial conditions and disturbances of extra-cellular environments on the host cell. At present, how to design a robust synthetic gene network to work properly under these uncertain factors is the most important topic of synthetic biology. A robust regulation design is proposed for a stochastic synthetic gene network to achieve the prescribed steady states under these uncertain factors from the minimax regulation perspective. This minimax regulation design problem can be transformed to an equivalent stochastic game problem. Since it is not easy to solve the robust regulation design problem of synthetic gene networks by non-linear stochastic game method directly, the Takagi-Sugeno (T-S) fuzzy model is proposed to approximate the non-linear synthetic gene network via the linear matrix inequality (LMI) technique through the Robust Control Toolbox in Matlab. Finally, an in silico example is given to illustrate the design procedure and to confirm the efficiency and efficacy of the proposed robust gene design method. http://www.ee.nthu.edu.tw/bschen/SyntheticBioDesign_supplement.pdf.

  3. Finite-time robust passive control for a class of switched reaction-diffusion stochastic complex dynamical networks with coupling delays and impulsive control

    NASA Astrophysics Data System (ADS)

    Syed Ali, M.; Yogambigai, J.; Kwon, O. M.

    2018-03-01

    Finite-time boundedness and finite-time passivity for a class of switched stochastic complex dynamical networks (CDNs) with coupling delays, parameter uncertainties, reaction-diffusion term and impulsive control are studied. Novel finite-time synchronisation criteria are derived based on passivity theory. This paper proposes a CDN consisting of N linearly and diffusively coupled identical reaction- diffusion neural networks. By constructing of a suitable Lyapunov-Krasovskii's functional and utilisation of Jensen's inequality and Wirtinger's inequality, new finite-time passivity criteria for the networks are established in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Finally, two interesting numerical examples are given to show the effectiveness of the theoretical results.

  4. Measuring and decomposing socioeconomic inequality in healthcare delivery: A microsimulation approach with application to the Palestinian conflict-affected fragile setting.

    PubMed

    Abu-Zaineh, Mohammad; Mataria, Awad; Moatti, Jean-Paul; Ventelou, Bruno

    2011-01-01

    Socioeconomic-related inequalities in healthcare delivery have been extensively studied in developed countries, using standard linear models of decomposition. This paper seeks to assess equity in healthcare delivery in the particular context of the occupied Palestinian territory: the West Bank and the Gaza Strip, using a new method of decomposition based on microsimulations. Besides avoiding the 'unavoidable price' of linearity restriction that is imposed by the standard methods of decomposition, the microsimulation-based decomposition enables to circumvent the potentially contentious role of heterogeneity in behaviours and to better disentangle the various sources driving inequality in healthcare utilisation. Results suggest that the worse-off do have a disproportinately greater need for all levels of care. However with the exception of primary-level, utilisation of all levels of care appears to be significantly higher for the better-off. The microsimulation method has made it possible to identify the contributions of factors driving such pro-rich patterns. While much of the inequality in utilisation appears to be caused by the prevailing socioeconomic inequalities, detailed analysis attributes a non-trivial part (circa 30% of inequalities) to heterogeneity in healthcare-seeking behaviours across socioeconomic groups of the population. Several policy recommendations for improving equity in healthcare delivery in the occupied Palestinian territory are proposed. Copyright © 2010 Elsevier Ltd. All rights reserved.

  5. Robust fuzzy output feedback controller for affine nonlinear systems via T-S fuzzy bilinear model: CSTR benchmark.

    PubMed

    Hamdy, M; Hamdan, I

    2015-07-01

    In this paper, a robust H∞ fuzzy output feedback controller is designed for a class of affine nonlinear systems with disturbance via Takagi-Sugeno (T-S) fuzzy bilinear model. The parallel distributed compensation (PDC) technique is utilized to design a fuzzy controller. The stability conditions of the overall closed loop T-S fuzzy bilinear model are formulated in terms of Lyapunov function via linear matrix inequality (LMI). The control law is robustified by H∞ sense to attenuate external disturbance. Moreover, the desired controller gains can be obtained by solving a set of LMI. A continuous stirred tank reactor (CSTR), which is a benchmark problem in nonlinear process control, is discussed in detail to verify the effectiveness of the proposed approach with a comparative study. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

  6. Fuzzy observer-based control for maximum power-point tracking of a photovoltaic system

    NASA Astrophysics Data System (ADS)

    Allouche, M.; Dahech, K.; Chaabane, M.; Mehdi, D.

    2018-04-01

    This paper presents a novel fuzzy control design method for maximum power-point tracking (MPPT) via a Takagi and Sugeno (TS) fuzzy model-based approach. A knowledge-dynamic model of the PV system is first developed leading to a TS representation by a simple convex polytopic transformation. Then, based on this exact fuzzy representation, a H∞ observer-based fuzzy controller is proposed to achieve MPPT even when we consider varying climatic conditions. A specified TS reference model is designed to generate the optimum trajectory which must be tracked to ensure maximum power operation. The controller and observer gains are obtained in a one-step procedure by solving a set of linear matrix inequalities (LMIs). The proposed method has been compared with some classical MPPT techniques taking into account convergence speed and tracking accuracy. Finally, various simulation and experimental tests have been carried out to illustrate the effectiveness of the proposed TS fuzzy MPPT strategy.

  7. Decentralized Feedback Controllers for Exponential Stabilization of Hybrid Periodic Orbits: Application to Robotic Walking.

    PubMed

    Hamed, Kaveh Akbari; Gregg, Robert D

    2016-07-01

    This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially stabilize periodic orbits for a class of hybrid dynamical systems arising from bipedal walking. The algorithm assumes a class of parameterized and nonlinear decentralized feedback controllers which coordinate lower-dimensional hybrid subsystems based on a common phasing variable. The exponential stabilization problem is translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities, which can be easily solved with available software packages. A set of sufficient conditions for the convergence of the iterative algorithm to a stabilizing decentralized feedback control solution is presented. The power of the algorithm is demonstrated by designing a set of local nonlinear controllers that cooperatively produce stable walking for a 3D autonomous biped with 9 degrees of freedom, 3 degrees of underactuation, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg.

  8. A fast numerical method for the valuation of American lookback put options

    NASA Astrophysics Data System (ADS)

    Song, Haiming; Zhang, Qi; Zhang, Ran

    2015-10-01

    A fast and efficient numerical method is proposed and analyzed for the valuation of American lookback options. American lookback option pricing problem is essentially a two-dimensional unbounded nonlinear parabolic problem. We reformulate it into a two-dimensional parabolic linear complementary problem (LCP) on an unbounded domain. The numeraire transformation and domain truncation technique are employed to convert the two-dimensional unbounded LCP into a one-dimensional bounded one. Furthermore, the variational inequality (VI) form corresponding to the one-dimensional bounded LCP is obtained skillfully by some discussions. The resulting bounded VI is discretized by a finite element method. Meanwhile, the stability of the semi-discrete solution and the symmetric positive definiteness of the full-discrete matrix are established for the bounded VI. The discretized VI related to options is solved by a projection and contraction method. Numerical experiments are conducted to test the performance of the proposed method.

  9. Decentralized Feedback Controllers for Exponential Stabilization of Hybrid Periodic Orbits: Application to Robotic Walking*

    PubMed Central

    Hamed, Kaveh Akbari; Gregg, Robert D.

    2016-01-01

    This paper presents a systematic algorithm to design time-invariant decentralized feedback controllers to exponentially stabilize periodic orbits for a class of hybrid dynamical systems arising from bipedal walking. The algorithm assumes a class of parameterized and nonlinear decentralized feedback controllers which coordinate lower-dimensional hybrid subsystems based on a common phasing variable. The exponential stabilization problem is translated into an iterative sequence of optimization problems involving bilinear and linear matrix inequalities, which can be easily solved with available software packages. A set of sufficient conditions for the convergence of the iterative algorithm to a stabilizing decentralized feedback control solution is presented. The power of the algorithm is demonstrated by designing a set of local nonlinear controllers that cooperatively produce stable walking for a 3D autonomous biped with 9 degrees of freedom, 3 degrees of underactuation, and a decentralization scheme motivated by amputee locomotion with a transpelvic prosthetic leg. PMID:27990059

  10. Intelligent robust control for uncertain nonlinear time-varying systems and its application to robotic systems.

    PubMed

    Chang, Yeong-Chan

    2005-12-01

    This paper addresses the problem of designing adaptive fuzzy-based (or neural network-based) robust controls for a large class of uncertain nonlinear time-varying systems. This class of systems can be perturbed by plant uncertainties, unmodeled perturbations, and external disturbances. Nonlinear H(infinity) control technique incorporated with adaptive control technique and VSC technique is employed to construct the intelligent robust stabilization controller such that an H(infinity) control is achieved. The problem of the robust tracking control design for uncertain robotic systems is employed to demonstrate the effectiveness of the developed robust stabilization control scheme. Therefore, an intelligent robust tracking controller for uncertain robotic systems in the presence of high-degree uncertainties can easily be implemented. Its solution requires only to solve a linear algebraic matrix inequality and a satisfactorily transient and asymptotical tracking performance is guaranteed. A simulation example is made to confirm the performance of the developed control algorithms.

  11. Matching CT and ultrasound data of the liver by landmark constrained image registration

    NASA Astrophysics Data System (ADS)

    Olesch, Janine; Papenberg, Nils; Lange, Thomas; Conrad, Matthias; Fischer, Bernd

    2009-02-01

    In navigated liver surgery the key challenge is the registration of pre-operative planing and intra-operative navigation data. Due to the patients individual anatomy the planning is based on segmented, pre-operative CT scans whereas ultrasound captures the actual intra-operative situation. In this paper we derive a novel method based on variational image registration methods and additional given anatomic landmarks. For the first time we embed the landmark information as inequality hard constraints and thereby allowing for inaccurately placed landmarks. The yielding optimization problem allows to ensure the accuracy of the landmark fit by simultaneous intensity based image registration. Following the discretize-then-optimize approach the overall problem is solved by a generalized Gauss-Newton-method. The upcoming linear system is attacked by the MinRes solver. We demonstrate the applicability of the new approach for clinical data which lead to convincing results.

  12. Dwell time-based stabilisation of switched delay systems using free-weighting matrices

    NASA Astrophysics Data System (ADS)

    Koru, Ahmet Taha; Delibaşı, Akın; Özbay, Hitay

    2018-01-01

    In this paper, we present a quasi-convex optimisation method to minimise an upper bound of the dwell time for stability of switched delay systems. Piecewise Lyapunov-Krasovskii functionals are introduced and the upper bound for the derivative of Lyapunov functionals is estimated by free-weighting matrices method to investigate non-switching stability of each candidate subsystems. Then, a sufficient condition for the dwell time is derived to guarantee the asymptotic stability of the switched delay system. Once these conditions are represented by a set of linear matrix inequalities , dwell time optimisation problem can be formulated as a standard quasi-convex optimisation problem. Numerical examples are given to illustrate the improvements over previously obtained dwell time bounds. Using the results obtained in the stability case, we present a nonlinear minimisation algorithm to synthesise the dwell time minimiser controllers. The algorithm solves the problem with successive linearisation of nonlinear conditions.

  13. A Self-Calibrating Radar Sensor System for Measuring Vital Signs.

    PubMed

    Huang, Ming-Chun; Liu, Jason J; Xu, Wenyao; Gu, Changzhan; Li, Changzhi; Sarrafzadeh, Majid

    2016-04-01

    Vital signs (i.e., heartbeat and respiration) are crucial physiological signals that are useful in numerous medical applications. The process of measuring these signals should be simple, reliable, and comfortable for patients. In this paper, a noncontact self-calibrating vital signs monitoring system based on the Doppler radar is presented. The system hardware and software were designed with a four-tiered layer structure. To enable accurate vital signs measurement, baseband signals in the radar sensor were modeled and a framework for signal demodulation was proposed. Specifically, a signal model identification method was formulated into a quadratically constrained l1 minimization problem and solved using the upper bound and linear matrix inequality (LMI) relaxations. The performance of the proposed system was comprehensively evaluated using three experimental sets, and the results indicated that this system can be used to effectively measure human vital signs.

  14. Dissipative stability analysis and control of two-dimensional Fornasini-Marchesini local state-space model

    NASA Astrophysics Data System (ADS)

    Wang, Lanning; Chen, Weimin; Li, Lizhen

    2017-06-01

    This paper is concerned with the problems of dissipative stability analysis and control of the two-dimensional (2-D) Fornasini-Marchesini local state-space (FM LSS) model. Based on the characteristics of the system model, a novel definition of 2-D FM LSS (Q, S, R)-α-dissipativity is given first, and then a sufficient condition in terms of linear matrix inequality (LMI) is proposed to guarantee the asymptotical stability and 2-D (Q, S, R)-α-dissipativity of the systems. As its special cases, 2-D passivity performance and 2-D H∞ performance are also discussed. Furthermore, by use of this dissipative stability condition and projection lemma technique, 2-D (Q, S, R)-α-dissipative state-feedback control problem is solved as well. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

  15. Tightness of correlation inequalities with no quantum violation

    NASA Astrophysics Data System (ADS)

    Ramanathan, Ravishankar; Quintino, Marco Túlio; Sainz, Ana Belén; Murta, Gláucia; Augusiak, Remigiusz

    2017-01-01

    We study the faces of the set of quantum correlations, i.e., the Bell and noncontextuality inequalities without any quantum violation. First, we investigate the question of whether every proper (facet-defining) Bell inequality for two parties, other than the trivial ones from positivity, normalization, and no-signaling, can be violated by quantum correlations, i.e., whether the classical Bell polytope or the smaller correlation polytope share any facets with their respective quantum sets. To do this, we develop a recently derived bound on the quantum value of linear games based on the norms of game matrices to give a simple sufficient condition to identify linear games with no quantum advantage. Additionally we show how this bound can be extended to the general class of unique games. We then show that the paradigmatic examples of correlation Bell inequalities with no quantum violation, namely the nonlocal computation games, do not constitute facet-defining Bell inequalities, not even for the correlation polytope. We also extend this to an arbitrary prime number of outcomes for a specific class of these games. We then study the faces in the simplest Clauser-Horne-Shimony-Holt Bell scenario of binary dichotomic measurements, and identify edges in the set of quantum correlations in this scenario. Finally, we relate the noncontextual polytope of single-party correlation inequalities with the cut polytope CUT(∇ G ) , where G denotes the compatibility graph of observables in the contextuality scenario and ∇ G denotes the suspension graph of G . We observe that there exist facet-defining noncontextuality inequalities with no quantum violation, and furthermore that this set of inequalities is beyond those implied by the consistent exclusivity principle.

  16. ALPS: A Linear Program Solver

    NASA Technical Reports Server (NTRS)

    Ferencz, Donald C.; Viterna, Larry A.

    1991-01-01

    ALPS is a computer program which can be used to solve general linear program (optimization) problems. ALPS was designed for those who have minimal linear programming (LP) knowledge and features a menu-driven scheme to guide the user through the process of creating and solving LP formulations. Once created, the problems can be edited and stored in standard DOS ASCII files to provide portability to various word processors or even other linear programming packages. Unlike many math-oriented LP solvers, ALPS contains an LP parser that reads through the LP formulation and reports several types of errors to the user. ALPS provides a large amount of solution data which is often useful in problem solving. In addition to pure linear programs, ALPS can solve for integer, mixed integer, and binary type problems. Pure linear programs are solved with the revised simplex method. Integer or mixed integer programs are solved initially with the revised simplex, and the completed using the branch-and-bound technique. Binary programs are solved with the method of implicit enumeration. This manual describes how to use ALPS to create, edit, and solve linear programming problems. Instructions for installing ALPS on a PC compatible computer are included in the appendices along with a general introduction to linear programming. A programmers guide is also included for assistance in modifying and maintaining the program.

  17. Adaptive nearly optimal control for a class of continuous-time nonaffine nonlinear systems with inequality constraints.

    PubMed

    Fan, Quan-Yong; Yang, Guang-Hong

    2017-01-01

    The state inequality constraints have been hardly considered in the literature on solving the nonlinear optimal control problem based the adaptive dynamic programming (ADP) method. In this paper, an actor-critic (AC) algorithm is developed to solve the optimal control problem with a discounted cost function for a class of state-constrained nonaffine nonlinear systems. To overcome the difficulties resulting from the inequality constraints and the nonaffine nonlinearities of the controlled systems, a novel transformation technique with redesigned slack functions and a pre-compensator method are introduced to convert the constrained optimal control problem into an unconstrained one for affine nonlinear systems. Then, based on the policy iteration (PI) algorithm, an online AC scheme is proposed to learn the nearly optimal control policy for the obtained affine nonlinear dynamics. Using the information of the nonlinear model, novel adaptive update laws are designed to guarantee the convergence of the neural network (NN) weights and the stability of the affine nonlinear dynamics without the requirement for the probing signal. Finally, the effectiveness of the proposed method is validated by simulation studies. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

  18. Classifying 50 years of Bell inequalities

    NASA Astrophysics Data System (ADS)

    Rosset, Denis; Bancal, Jean-Daniel; Gisin, Nicolas

    2014-10-01

    Since John S Bell demonstrated the interest of studying linear combinations of probabilities in relation with the EPR paradox in 1964, Bell inequalities have lead to numerous developments. Unfortunately, the description of Bell inequalities is subject to several degeneracies, which make any exchange of information about them unnecessarily hard. Here, we analyze these degeneracies and propose a decomposition for Bell-like inequalities based on a set of reference expressions which is not affected by them. These reference expressions set a common ground for comparing Bell inequalities. We provide algorithms based on finite group theory to compute this decomposition. Implementing these algorithms allows us to set up a compendium of reference Bell-like inequalities, available online at www.faacets.com. This website constitutes a platform where registered Bell-like inequalities can be explored, new inequalities can be compared to previously-known ones and relevant information on Bell inequalities can be added in a collaborative manner. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘50 years of Bell’s theorem’.

  19. Rising U.S. income inequality, gender and individual self-rated health, 1972-2004.

    PubMed

    Zheng, Hui

    2009-11-01

    The effect of income inequality on health has been a contested topic among social scientists. Most previous research is based on cross-sectional comparisons rather than temporal comparisons. Using data from the General Social Survey and the U.S. Census Bureau, this study examines how rising income inequality affects individual self-rated health in the U.S. from 1972 to 2004. Data are analyzed using hierarchical generalized linear models. The findings suggest a significant association between income inequality and individual self-rated health. The dramatic increase in income inequality from 1972 to 2004 increases the odds of worse self-rated health by 9.4 percent. These findings hold for three measures of income inequality: the Gini coefficient, the Atkinson Index, and the Theil entropy index. Results also suggest that overall income inequality and gender-specific income inequality harm men's, but not women's, self-rated health. These findings also hold for the three measures of income inequality. These findings suggest that inattention to gender composition may explain apparent discrepancies across previous studies.

  20. The use of Lyapunov differential inequalities for estimating the transients of mechanical systems

    NASA Astrophysics Data System (ADS)

    Alyshev, A. S.; Dudarenko, N. A.; Melnikov, V. G.; Melnikov, G. I.

    2018-05-01

    In this paper we consider an autonomous mechanical system in a finite neighborhood of the zero of the phase space of states. The system is given as a matrix differential equation in the Cauchy form with the right-hand side of the polynomial structure. We propose a method for constructing a sequence of linear inhomogeneous differential inequalities for Lyapunov functions. As a result, we obtain estimates of transient processes in the form of functional inequalities.

  1. Hoeffding Type Inequalities and their Applications in Statistics and Operations Research

    NASA Astrophysics Data System (ADS)

    Daras, Tryfon

    2007-09-01

    Large Deviation theory is the branch of Probability theory that deals with rare events. Sometimes, these events can be described by the sum of random variables that deviates from its mean more than a "normal" amount. A precise calculation of the probabilities of such events turns out to be crucial in a variety of different contents (e.g. in Probability Theory, Statistics, Operations Research, Statistical Physics, Financial Mathematics e.t.c.). Recent applications of the theory deal with random walks in random environments, interacting diffusions, heat conduction, polymer chains [1]. In this paper we prove an inequality of exponential type, namely theorem 2.1, which gives a large deviation upper bound for a specific sequence of r.v.s. Inequalities of this type have many applications in Combinatorics [2]. The inequality generalizes already proven results of this type, in the case of symmetric probability measures. We get as consequences to the inequality: (a) large deviations upper bounds for exchangeable Bernoulli sequences of random variables, generalizing results proven for independent and identically distributed Bernoulli sequences of r.v.s. and (b) a general form of Bernstein's inequality. We compare the inequality with large deviation results already proven by the author and try to see its advantages. Finally, using the inequality, we solve one of the basic problems of Operations Research (bin packing problem) in the case of exchangeable r.v.s.

  2. Modeling the Origin and Possible Control of the Wealth Inequality Surge

    PubMed Central

    Berman, Yonatan; Shapira, Yoash; Ben-Jacob, Eshel

    2015-01-01

    The rapid increase of wealth inequality in the past few decades is a most disturbing social and economic issue of our time. In order to control, and even reverse that surge, its origin and underlying mechanisms should be revealed. One of the challenges in studying these mechanisms is to incorporate realistic individual dynamics in the population level in a self-consistent manner. Our theoretical approach meets the challenge by using interacting multi-agent master-equations to model the dynamics of wealth inequality. The model is solved using stochastic multi-agent iterated maps. Taking into account growth rate, return on capital, private savings and economic mobility, we were able to capture the historical dynamics of wealth inequality in the United States during the course of the 20th century. We show that the fraction of capital income in the national income and the fraction of private savings are the critical factors that govern the wealth inequality dynamics. In addition, we found that economic mobility plays a crucial role in wealth accumulation. Notably, we found that the major decrease in private savings since the 1980s could be associated primarily with the recent surge in wealth inequality and if nothing changes in this respect we predict further increase in wealth inequality in the future. However, the 2007–08 financial crisis brought an opportunity to restrain the wealth inequality surge by increasing private savings. If this trend continues, it may lead to prevention, and even reversing, of the ongoing inequality surge. PMID:26107388

  3. Modeling the Origin and Possible Control of the Wealth Inequality Surge.

    PubMed

    Berman, Yonatan; Shapira, Yoash; Ben-Jacob, Eshel

    2015-01-01

    The rapid increase of wealth inequality in the past few decades is a most disturbing social and economic issue of our time. In order to control, and even reverse that surge, its origin and underlying mechanisms should be revealed. One of the challenges in studying these mechanisms is to incorporate realistic individual dynamics in the population level in a self-consistent manner. Our theoretical approach meets the challenge by using interacting multi-agent master-equations to model the dynamics of wealth inequality. The model is solved using stochastic multi-agent iterated maps. Taking into account growth rate, return on capital, private savings and economic mobility, we were able to capture the historical dynamics of wealth inequality in the United States during the course of the 20th century. We show that the fraction of capital income in the national income and the fraction of private savings are the critical factors that govern the wealth inequality dynamics. In addition, we found that economic mobility plays a crucial role in wealth accumulation. Notably, we found that the major decrease in private savings since the 1980s could be associated primarily with the recent surge in wealth inequality and if nothing changes in this respect we predict further increase in wealth inequality in the future. However, the 2007-08 financial crisis brought an opportunity to restrain the wealth inequality surge by increasing private savings. If this trend continues, it may lead to prevention, and even reversing, of the ongoing inequality surge.

  4. On supporting students' understanding of solving linear equation by using flowchart

    NASA Astrophysics Data System (ADS)

    Toyib, Muhamad; Kusmayadi, Tri Atmojo; Riyadi

    2017-05-01

    The aim of this study was to support 7th graders to gradually understand the concepts and procedures of solving linear equation. Thirty-two 7th graders of a Junior High School in Surakarta, Indonesia were involved in this study. Design research was used as the research approach to achieve the aim. A set of learning activities in solving linear equation with one unknown were designed based on Realistic Mathematics Education (RME) approach. The activities were started by playing LEGO to find a linear equation then solve the equation by using flowchart. The results indicate that using the realistic problems, playing LEGO could stimulate students to construct linear equation. Furthermore, Flowchart used to encourage students' reasoning and understanding on the concepts and procedures of solving linear equation with one unknown.

  5. Determination of design and operation parameters for upper atmospheric research instrumentation to yield optimum resolution with deconvolution, appendix 4

    NASA Technical Reports Server (NTRS)

    Ioup, George E.; Ioup, Juliette W.

    1989-01-01

    The power spectrum for a stationary random process can be defined with the Wiener-Khintchine Theorem, which says that the power spectrum and the auto correlation function are a Fourier transform pair. To implement this theorem for signals that are discrete and of finite length we can use the Blackman-Tukey method. Blackman and Tukey (1958) show that a function w(tau), called a lag window, can be applied to the auto correlation estimates to obtain power spectrum estimates that are statistically stable. The Fourier transform of w(r) is called a spectral window. Typical choices for spectral windows show a distinct trade-off between the main lobe width and side lobe strength. A new idea for designing windows by taking linear combinations of the standard windows to produce hybrid windows was introduced by Smith (1985). We implement Smith's idea to obtain spectral windows with narrow main lobes and smaller (compared with typical windows) near side lobes. One of the main contributions of this thesis is that we show that Smith's problem is equivalent to a Quadratic Programming (QP) problem with linear equality and inequality constraints. A computer program was written to produce hybrid windows by setting up and solving the QP problem. We also developed and solved two variations of the original problem. The two variations involved changing the inequality constraints in both cases from non negativity on the combination coefficients to non negativity on the hybrid lag window itself. For the second variation, the window functions used to construct the hybrid window were changed to a frequency-variable set of truncated cosinusoids. A series of tests was run with the three computer programs to investigate the behavior of the hybrid spectral and lag windows. Emphasis was put on obtaining spectral windows with both relatively narrow main lobes and the lowest possible (for these algorithms) near side lobes. Some success was achieved for this goal. A 10 dB peak side lobe reduction over the rectangular spectral window without significant main lobe broadening was achieved. Also, average side lobe levels of -117 dB were reached at a cost of doubling the main lobe width (at the -3 dB point).

  6. Parallel algorithms for the molecular conformation problem

    NASA Astrophysics Data System (ADS)

    Rajan, Kumar

    Given a set of objects, and some of the pairwise distances between them, the problem of identifying the positions of the objects in the Euclidean space is referred to as the molecular conformation problem. This problem is known to be computationally difficult. One of the most important applications of this problem is the determination of the structure of molecules. In the case of molecular structure determination, usually only the lower and upper bounds on some of the interatomic distances are available. The process of obtaining a tighter set of bounds between all pairs of atoms, using the available interatomic distance bounds is referred to as bound-smoothing . One method for bound-smoothing is to use the limits imposed by the triangle inequality. The distance bounds so obtained can often be tightened further by applying the tetrangle inequality---the limits imposed on the six pairwise distances among a set of four atoms (instead of three for the triangle inequalities). The tetrangle inequality is expressed by the Cayley-Menger determinants. The sequential tetrangle-inequality bound-smoothing algorithm considers a quadruple of atoms at a time, and tightens the bounds on each of its six distances. The sequential algorithm is computationally expensive, and its application is limited to molecules with up to a few hundred atoms. Here, we conduct an experimental study of tetrangle-inequality bound-smoothing and reduce the sequential time by identifying the most computationally expensive portions of the process. We also present a simple criterion to determine which of the quadruples of atoms are likely to be tightened the most by tetrangle-inequality bound-smoothing. This test could be used to enhance the applicability of this process to large molecules. We map the problem of parallelizing tetrangle-inequality bound-smoothing to that of generating disjoint packing designs of a certain kind. We map this, in turn, to a regular-graph coloring problem, and present a simple, parallel algorithm for tetrangle-inequality bound-smoothing. We implement the parallel algorithm on the Intel Paragon X/PS, and apply it to real-life molecules. Our results show that with this parallel algorithm, tetrangle inequality can be applied to large molecules in a reasonable amount of time. We extend the regular graph to represent more general packing designs, and present a coloring algorithm for this graph. This can be used to generate constant-weight binary codes in parallel. Once a tighter set of distance bounds is obtained, the molecular conformation problem is usually formulated as a non-linear optimization problem, and a global optimization algorithm is then used to solve the problem. Here we present a parallel, deterministic algorithm for the optimization problem based on Interval Analysis. We implement our algorithm, using dynamic load balancing, on a network of Sun Ultra-Sparc workstations. Our experience with this algorithm shows that its application is limited to small instances of the molecular conformation problem, where the number of measured, pairwise distances is close to the maximum value. However, since the interval method eliminates a substantial portion of the initial search space very quickly, it can be used to prune the search space before any of the more efficient, nondeterministic methods can be applied.

  7. State-constrained booster trajectory solutions via finite elements and shooting

    NASA Technical Reports Server (NTRS)

    Bless, Robert R.; Hodges, Dewey H.; Seywald, Hans

    1993-01-01

    This paper presents an extension of a FEM formulation based on variational principles. A general formulation for handling internal boundary conditions and discontinuities in the state equations is presented, and the general formulation is modified for optimal control problems subject to state-variable inequality constraints. Solutions which only touch the state constraint and solutions which have a boundary arc of finite length are considered. Suitable shape and test functions are chosen for a FEM discretization. All element quadrature (equivalent to one-point Gaussian quadrature over each element) may be done in closed form. The final form of the algebraic equations is then derived. A simple state-constrained problem is solved. Then, for a practical application of the use of the FEM formulation, a launch vehicle subject to a dynamic pressure constraint (a first-order state inequality constraint) is solved. The results presented for the launch-vehicle trajectory have some interesting features, including a touch-point solution.

  8. Estimating kinetic mechanisms with prior knowledge I: Linear parameter constraints.

    PubMed

    Salari, Autoosa; Navarro, Marco A; Milescu, Mirela; Milescu, Lorin S

    2018-02-05

    To understand how ion channels and other proteins function at the molecular and cellular levels, one must decrypt their kinetic mechanisms. Sophisticated algorithms have been developed that can be used to extract kinetic parameters from a variety of experimental data types. However, formulating models that not only explain new data, but are also consistent with existing knowledge, remains a challenge. Here, we present a two-part study describing a mathematical and computational formalism that can be used to enforce prior knowledge into the model using constraints. In this first part, we focus on constraints that enforce explicit linear relationships involving rate constants or other model parameters. We develop a simple, linear algebra-based transformation that can be applied to enforce many types of model properties and assumptions, such as microscopic reversibility, allosteric gating, and equality and inequality parameter relationships. This transformation converts the set of linearly interdependent model parameters into a reduced set of independent parameters, which can be passed to an automated search engine for model optimization. In the companion article, we introduce a complementary method that can be used to enforce arbitrary parameter relationships and any constraints that quantify the behavior of the model under certain conditions. The procedures described in this study can, in principle, be coupled to any of the existing methods for solving molecular kinetics for ion channels or other proteins. These concepts can be used not only to enforce existing knowledge but also to formulate and test new hypotheses. © 2018 Salari et al.

  9. Ecological analysis of teen birth rates: association with community income and income inequality.

    PubMed

    Gold, R; Kawachi, I; Kennedy, B P; Lynch, J W; Connell, F A

    2001-09-01

    To examine whether per capita income and income inequality are independently associated with teen birth rate in populous U.S. counties. This study used 1990 U.S. Census data and National Center for Health Statistics birth data. Income inequality was measured with the 90:10 ratio, a ratio of percent of cumulative income held by the richest and poorest population deciles. Linear regression and analysis of variance were used to assess associations between county-level average income, income inequality, and teen birth rates among counties with population greater than 100,000. Among teens aged 15-17, income inequality and per capita income were independently associated with birth rate; the mean birth rate was 54 per 1,000 in counties with low income and high income inequality, and 19 per 1,000 in counties with high income and low inequality. Among older teens (aged 18-19) only per capita income was significantly associated with birth rate. Although teen childbearing is the result of individual behaviors, these findings suggest that community-level factors such as income and income inequality may contribute significantly to differences in teen birth rates.

  10. Extension of the firefly algorithm and preference rules for solving MINLP problems

    NASA Astrophysics Data System (ADS)

    Costa, M. Fernanda P.; Francisco, Rogério B.; Rocha, Ana Maria A. C.; Fernandes, Edite M. G. P.

    2017-07-01

    An extension of the firefly algorithm (FA) for solving mixed-integer nonlinear programming (MINLP) problems is presented. Although penalty functions are nowadays frequently used to handle integrality conditions and inequality and equality constraints, this paper proposes the implementation within the FA of a simple rounded-based heuristic and four preference rules to find and converge to MINLP feasible solutions. Preliminary numerical experiments are carried out to validate the proposed methodology.

  11. Asymptotic aspect of derivations in Banach algebras.

    PubMed

    Roh, Jaiok; Chang, Ick-Soon

    2017-01-01

    We prove that every approximate linear left derivation on a semisimple Banach algebra is continuous. Also, we consider linear derivations on Banach algebras and we first study the conditions for a linear derivation on a Banach algebra. Then we examine the functional inequalities related to a linear derivation and their stability. We finally take central linear derivations with radical ranges on semiprime Banach algebras and a continuous linear generalized left derivation on a semisimple Banach algebra.

  12. Modelling and Computation in the Valuation of Carbon Derivatives with Stochastic Convenience Yields

    PubMed Central

    Chang, Shuhua; Wang, Xinyu

    2015-01-01

    The anthropogenic greenhouse gas (GHG) emission has risen dramatically during the last few decades, which mainstream researchers believe to be the main cause of climate change, especially the global warming. The mechanism of market-based carbon emission trading is regarded as a policy instrument to deal with global climate change. Although several empirical researches about the carbon allowance and its derivatives price have been made, theoretical results seem to be sparse. In this paper, we theoretically develop a mathematical model to price the CO2 emission allowance derivatives with stochastic convenience yields by the principle of absence of arbitrage opportunities. In the case of American options, we formulate the pricing problem to a linear parabolic variational inequality (VI) in two spatial dimensions and develop a power penalty method to solve it. Then, a fitted finite volume method is designed to solve the nonlinear partial differential equation (PDE) resulting from the power penalty method and governing the futures, European and American option valuation. Moreover, some numerical results are performed to illustrate the efficiency and usefulness of this method. We find that the stochastic convenience yield does effect the valuation of carbon emission derivatives. In addition, some sensitivity analyses are also made to examine the effects of some parameters on the valuation results. PMID:26010900

  13. Modelling and computation in the valuation of carbon derivatives with stochastic convenience yields.

    PubMed

    Chang, Shuhua; Wang, Xinyu

    2015-01-01

    The anthropogenic greenhouse gas (GHG) emission has risen dramatically during the last few decades, which mainstream researchers believe to be the main cause of climate change, especially the global warming. The mechanism of market-based carbon emission trading is regarded as a policy instrument to deal with global climate change. Although several empirical researches about the carbon allowance and its derivatives price have been made, theoretical results seem to be sparse. In this paper, we theoretically develop a mathematical model to price the CO2 emission allowance derivatives with stochastic convenience yields by the principle of absence of arbitrage opportunities. In the case of American options, we formulate the pricing problem to a linear parabolic variational inequality (VI) in two spatial dimensions and develop a power penalty method to solve it. Then, a fitted finite volume method is designed to solve the nonlinear partial differential equation (PDE) resulting from the power penalty method and governing the futures, European and American option valuation. Moreover, some numerical results are performed to illustrate the efficiency and usefulness of this method. We find that the stochastic convenience yield does effect the valuation of carbon emission derivatives. In addition, some sensitivity analyses are also made to examine the effects of some parameters on the valuation results.

  14. Polynomial Monogamy Relations for Entanglement Negativity.

    PubMed

    Allen, Grant W; Meyer, David A

    2017-02-24

    The notion of nonclassical correlations is a powerful contrivance for explaining phenomena exhibited in quantum systems. It is well known, however, that quantum systems are not free to explore arbitrary correlations-the church of the smaller Hilbert space only accepts monogamous congregants. We demonstrate how to characterize the limits of what is quantum mechanically possible with a computable measure, entanglement negativity. We show that negativity only saturates the standard linear monogamy inequality in trivial cases implied by its monotonicity under local operations and classical communication, and derive a necessary and sufficient inequality which, for the first time, is a nonlinear higher degree polynomial. For very large quantum systems, we prove that the negativity can be distributed at least linearly for the tightest constraint and conjecture that it is at most linear.

  15. Polynomial Monogamy Relations for Entanglement Negativity

    NASA Astrophysics Data System (ADS)

    Allen, Grant W.; Meyer, David A.

    2017-02-01

    The notion of nonclassical correlations is a powerful contrivance for explaining phenomena exhibited in quantum systems. It is well known, however, that quantum systems are not free to explore arbitrary correlations—the church of the smaller Hilbert space only accepts monogamous congregants. We demonstrate how to characterize the limits of what is quantum mechanically possible with a computable measure, entanglement negativity. We show that negativity only saturates the standard linear monogamy inequality in trivial cases implied by its monotonicity under local operations and classical communication, and derive a necessary and sufficient inequality which, for the first time, is a nonlinear higher degree polynomial. For very large quantum systems, we prove that the negativity can be distributed at least linearly for the tightest constraint and conjecture that it is at most linear.

  16. Revisiting r > g-The asymptotic dynamics of wealth inequality

    NASA Astrophysics Data System (ADS)

    Berman, Yonatan; Shapira, Yoash

    2017-02-01

    Studying the underlying mechanisms of wealth inequality dynamics is essential for its understanding and for policy aiming to regulate its level. We apply a heterogeneous non-interacting agent-based modeling approach, solved using iterated maps to model the dynamics of wealth inequality based on 3 parameters-the economic output growth rate g, the capital value change rate a and the personal savings rate s and show that for a < g the wealth distribution reaches an asymptotic shape and becomes close to the income distribution. If a > g, the wealth distribution constantly becomes more and more inegalitarian. We also show that when a < g, wealth is asymptotically accumulated at the same rate as the economic output, which also implies that the wealth-disposable income ratio asymptotically converges to s /(g - a) .

  17. Time-domain finite elements in optimal control with application to launch-vehicle guidance. PhD. Thesis

    NASA Technical Reports Server (NTRS)

    Bless, Robert R.

    1991-01-01

    A time-domain finite element method is developed for optimal control problems. The theory derived is general enough to handle a large class of problems including optimal control problems that are continuous in the states and controls, problems with discontinuities in the states and/or system equations, problems with control inequality constraints, problems with state inequality constraints, or problems involving any combination of the above. The theory is developed in such a way that no numerical quadrature is necessary regardless of the degree of nonlinearity in the equations. Also, the same shape functions may be employed for every problem because all strong boundary conditions are transformed into natural or weak boundary conditions. In addition, the resulting nonlinear algebraic equations are very sparse. Use of sparse matrix solvers allows for the rapid and accurate solution of very difficult optimization problems. The formulation is applied to launch-vehicle trajectory optimization problems, and results show that real-time optimal guidance is realizable with this method. Finally, a general problem solving environment is created for solving a large class of optimal control problems. The algorithm uses both FORTRAN and a symbolic computation program to solve problems with a minimum of user interaction. The use of symbolic computation eliminates the need for user-written subroutines which greatly reduces the setup time for solving problems.

  18. Flight control with adaptive critic neural network

    NASA Astrophysics Data System (ADS)

    Han, Dongchen

    2001-10-01

    In this dissertation, the adaptive critic neural network technique is applied to solve complex nonlinear system control problems. Based on dynamic programming, the adaptive critic neural network can embed the optimal solution into a neural network. Though trained off-line, the neural network forms a real-time feedback controller. Because of its general interpolation properties, the neurocontroller has inherit robustness. The problems solved here are an agile missile control for U.S. Air Force and a midcourse guidance law for U.S. Navy. In the first three papers, the neural network was used to control an air-to-air agile missile to implement a minimum-time heading-reverse in a vertical plane corresponding to following conditions: a system without constraint, a system with control inequality constraint, and a system with state inequality constraint. While the agile missile is a one-dimensional problem, the midcourse guidance law is the first test-bed for multiple-dimensional problem. In the fourth paper, the neurocontroller is synthesized to guide a surface-to-air missile to a fixed final condition, and to a flexible final condition from a variable initial condition. In order to evaluate the adaptive critic neural network approach, the numerical solutions for these cases are also obtained by solving two-point boundary value problem with a shooting method. All of the results showed that the adaptive critic neural network could solve complex nonlinear system control problems.

  19. Impact of income and income inequality on infant health outcomes in the United States.

    PubMed

    Olson, Maren E; Diekema, Douglas; Elliott, Barbara A; Renier, Colleen M

    2010-12-01

    The goal was to investigate the relationships of income and income inequality with neonatal and infant health outcomes in the United States. The 2000-2004 state data were extracted from the Kids Count Data Center. Health indicators included proportion of preterm births (PTBs), proportion of infants with low birth weight (LBW), proportion of infants with very low birth weight (VLBW), and infant mortality rate (IMR). Income was evaluated on the basis of median family income and proportion of federal poverty levels; income inequality was measured by using the Gini coefficient. Pearson correlations evaluated associations between the proportion of children living in poverty and the health indicators. Linear regression evaluated predictive relationships between median household income, proportion of children living in poverty, and income inequality for the 4 health indicators. Median family income was negatively correlated with all birth outcomes (PTB, r = -0.481; LBW, r = -0.295; VLBW, r = -0.133; IMR, r = -0.432), and the Gini coefficient was positively correlated (PTB, r = 0.339; LBW, r = 0.398; VLBW, r = 0.460; IMR, r = 0.114). The Gini coefficient explained a significant proportion of the variance in rate for each outcome in linear regression models with median family income. Among children living in poverty, the role of income decreased as the degree of poverty decreased, whereas the role of income inequality increased. Both income and income inequality affect infant health outcomes in the United States. The health of the poorest infants was affected more by absolute wealth than relative wealth.

  20. Non-Asymptotic Oracle Inequalities for the High-Dimensional Cox Regression via Lasso.

    PubMed

    Kong, Shengchun; Nan, Bin

    2014-01-01

    We consider finite sample properties of the regularized high-dimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. The summands in the negative log partial likelihood function for censored survival data, however, are neither iid nor Lipschitz.We first approximate the negative log partial likelihood function by a sum of iid non-Lipschitz terms, then derive the non-asymptotic oracle inequalities for the lasso penalized Cox regression using pointwise arguments to tackle the difficulties caused by lacking iid Lipschitz losses.

  1. Non-Asymptotic Oracle Inequalities for the High-Dimensional Cox Regression via Lasso

    PubMed Central

    Kong, Shengchun; Nan, Bin

    2013-01-01

    We consider finite sample properties of the regularized high-dimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. The summands in the negative log partial likelihood function for censored survival data, however, are neither iid nor Lipschitz.We first approximate the negative log partial likelihood function by a sum of iid non-Lipschitz terms, then derive the non-asymptotic oracle inequalities for the lasso penalized Cox regression using pointwise arguments to tackle the difficulties caused by lacking iid Lipschitz losses. PMID:24516328

  2. Horizontal Inequity in Health Care Utilization among the Middle-Aged and Elderly in China.

    PubMed

    Li, Chaofan; Dou, Lei; Wang, Haipeng; Jing, Shanshan; Yin, Aitian

    2017-07-26

    Equitable utilization of health care is a primary goal of the Chinese health system. This study aimed to examine horizontal inequity in health care utilization and identify the factors resulting in inequity among the middle-aged and elderly in China. The data were obtained from the China Health and Retirement Longitudinal Study (CHARLS). We employed the concentration index (CI) and horizontal inequity (HI) to measure inequity in health care utilization. Non-linear regression models were used to decompose the CI into the contribution of each factor. The CIs for the probability of and total number of outpatient visits were 0.0642 and 0.0780, respectively, and those for inpatient visits were 0.1418 and 0.1471, respectively. The HIs were also significantly positive. Living standard was the most important contributor. The contribution of health insurance varied between plans. This study supported the presence of pro-rich inequity in health care utilization for both probability and frequency among the middle-aged and elderly in China. Narrowing the living standard gap and improving the health insurance benefit package for the elderly should help to resolve these inequities.

  3. Income inequality and high blood pressure in Colombia: a multilevel analysis.

    PubMed

    Lucumi, Diego I; Schulz, Amy J; Roux, Ana V Diez; Grogan-Kaylor, Andrew

    2017-11-21

    The objective of this research was to examine the association between income inequality and high blood pressure in Colombia. Using a nationally representative Colombian sample of adults, and data from departments and municipalities, we fit sex-stratified linear and logistic multilevel models with blood pressure as a continuous and binary variable, respectively. In adjusted models, women living in departments with the highest quintile of income inequality in 1997 had higher systolic blood pressure than their counterparts living in the lowest quintile of income inequality (mean difference 4.42mmHg; 95%CI: 1.46, 7.39). Women living in departments that were at the fourth and fifth quintile of income inequality in 1994 were more likely to have hypertension than those living in departments at the first quintile in the same year (OR: 1.56 and 1.48, respectively). For men, no associations of income inequality with either systolic blood pressure or hypertension were observed. Our findings are consistent with the hypothesis that income inequality is associated with increased risk of high blood pressure for women. Future studies to analyze pathways linking income inequality to high blood pressure in Colombia are needed.

  4. Exploring the joint measurability using an information-theoretic approach

    NASA Astrophysics Data System (ADS)

    Hsu, Li-Yi

    2016-12-01

    We explore the legal purity parameters for the joint measurements. Instead of direct unsharpening the measurements, we perform the quantum cloning before the sharp measurements. The necessary fuzziness in the unsharp measurements is equivalently introduced in the imperfect cloning process. Based on the information causality and the consequent noisy nonlocal computation, one can derive the information-theoretic quadratic inequalities that must be satisfied by any physical theory. On the other hand, to guarantee the classicality, the linear Bell-type inequalities deduced by these quadratic ones must be obeyed. As for the joint measurability, the purity parameters must be chosen to obey both types of inequalities. Finally, the quadratic inequalities for purity parameters in the joint measurability region are derived.

  5. PIAAC Skills and Economic Inequality

    ERIC Educational Resources Information Center

    Pena, Anita Alves

    2016-01-01

    Mixed findings characterize the literature on skills and economic distributions within and across countries. The Programme for the International Assessment of Adult Competencies (PIAAC) offers new, internationally comparable data on literacy, numeracy, and digital problem-solving skills that can be combined with wage information. This paper…

  6. The intelligence of dual simplex method to solve linear fractional fuzzy transportation problem.

    PubMed

    Narayanamoorthy, S; Kalyani, S

    2015-01-01

    An approach is presented to solve a fuzzy transportation problem with linear fractional fuzzy objective function. In this proposed approach the fractional fuzzy transportation problem is decomposed into two linear fuzzy transportation problems. The optimal solution of the two linear fuzzy transportations is solved by dual simplex method and the optimal solution of the fractional fuzzy transportation problem is obtained. The proposed method is explained in detail with an example.

  7. A problem in non-linear Diophantine approximation

    NASA Astrophysics Data System (ADS)

    Harrap, Stephen; Hussain, Mumtaz; Kristensen, Simon

    2018-05-01

    In this paper we obtain the Lebesgue and Hausdorff measure results for the set of vectors satisfying infinitely many fully non-linear Diophantine inequalities. The set is associated with a class of linear inhomogeneous partial differential equations whose solubility depends on a certain Diophantine condition. The failure of the Diophantine condition guarantees the existence of a smooth solution.

  8. Solving constrained minimum-time robot problems using the sequential gradient restoration algorithm

    NASA Technical Reports Server (NTRS)

    Lee, Allan Y.

    1991-01-01

    Three constrained minimum-time control problems of a two-link manipulator are solved using the Sequential Gradient and Restoration Algorithm (SGRA). The inequality constraints considered are reduced via Valentine-type transformations to nondifferential path equality constraints. The SGRA is then used to solve these transformed problems with equality constraints. The results obtained indicate that at least one of the two controls is at its limits at any instant in time. The remaining control then adjusts itself so that none of the system constraints is violated. Hence, the minimum-time control is either a pure bang-bang control or a combined bang-bang/singular control.

  9. Multigrid approaches to non-linear diffusion problems on unstructured meshes

    NASA Technical Reports Server (NTRS)

    Mavriplis, Dimitri J.; Bushnell, Dennis M. (Technical Monitor)

    2001-01-01

    The efficiency of three multigrid methods for solving highly non-linear diffusion problems on two-dimensional unstructured meshes is examined. The three multigrid methods differ mainly in the manner in which the nonlinearities of the governing equations are handled. These comprise a non-linear full approximation storage (FAS) multigrid method which is used to solve the non-linear equations directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based on a non-linear FAS multigrid scheme, but employs a linear solver on each level as a smoother. Results indicate that all methods are equally effective at converging the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.

  10. Chosen interval methods for solving linear interval systems with special type of matrix

    NASA Astrophysics Data System (ADS)

    Szyszka, Barbara

    2013-10-01

    The paper is devoted to chosen direct interval methods for solving linear interval systems with special type of matrix. This kind of matrix: band matrix with a parameter, from finite difference problem is obtained. Such linear systems occur while solving one dimensional wave equation (Partial Differential Equations of hyperbolic type) by using the central difference interval method of the second order. Interval methods are constructed so as the errors of method are enclosed in obtained results, therefore presented linear interval systems contain elements that determining the errors of difference method. The chosen direct algorithms have been applied for solving linear systems because they have no errors of method. All calculations were performed in floating-point interval arithmetic.

  11. The Intelligence of Dual Simplex Method to Solve Linear Fractional Fuzzy Transportation Problem

    PubMed Central

    Narayanamoorthy, S.; Kalyani, S.

    2015-01-01

    An approach is presented to solve a fuzzy transportation problem with linear fractional fuzzy objective function. In this proposed approach the fractional fuzzy transportation problem is decomposed into two linear fuzzy transportation problems. The optimal solution of the two linear fuzzy transportations is solved by dual simplex method and the optimal solution of the fractional fuzzy transportation problem is obtained. The proposed method is explained in detail with an example. PMID:25810713

  12. Investigations in Mathematics Education, Vol. 10, No. 3.

    ERIC Educational Resources Information Center

    Osborne, Alan R., Ed.

    Eighteen research reports related to mathematics education are abstracted and analyzed in this publication. Three of the reports deal with aspects of learning theory, seven with topics in mathematics instruction (problem solving, weight, quadratic inequalities, probability and statistics, area and volume conservation, cardinality), five with…

  13. Assessing environmental inequalities in ambient air pollution across urban Australia.

    PubMed

    Knibbs, Luke D; Barnett, Adrian G

    2015-04-01

    Identifying inequalities in air pollution levels across population groups can help address environmental justice concerns. We were interested in assessing these inequalities across major urban areas in Australia. We used a land-use regression model to predict ambient nitrogen dioxide (NO2) levels and sought the best socio-economic and population predictor variables. We used a generalised least squares model that accounted for spatial correlation in NO2 levels to examine the associations between the variables. We found that the best model included the index of economic resources (IER) score as a non-linear variable and the percentage of non-Indigenous persons as a linear variable. NO2 levels decreased with increasing IER scores (higher scores indicate less disadvantage) in almost all major urban areas, and NO2 also decreased slightly as the percentage of non-Indigenous persons increased. However, the magnitude of differences in NO2 levels was small and may not translate into substantive differences in health. Copyright © 2015 Elsevier Ltd. All rights reserved.

  14. Robust state estimation for uncertain fuzzy bidirectional associative memory networks with time-varying delays

    NASA Astrophysics Data System (ADS)

    Vadivel, P.; Sakthivel, R.; Mathiyalagan, K.; Arunkumar, A.

    2013-09-01

    This paper addresses the issue of robust state estimation for a class of fuzzy bidirectional associative memory (BAM) neural networks with time-varying delays and parameter uncertainties. By constructing the Lyapunov-Krasovskii functional, which contains the triple-integral term and using the free-weighting matrix technique, a set of sufficient conditions are derived in terms of linear matrix inequalities (LMIs) to estimate the neuron states through available output measurements such that the dynamics of the estimation error system is robustly asymptotically stable. In particular, we consider a generalized activation function in which the traditional assumptions on the boundedness, monotony and differentiability of the activation functions are removed. More precisely, the design of the state estimator for such BAM neural networks can be obtained by solving some LMIs, which are dependent on the size of the time derivative of the time-varying delays. Finally, a numerical example with simulation result is given to illustrate the obtained theoretical results.

  15. Decentralized Fuzzy MPC on Spatial Power Control of a Large PHWR

    NASA Astrophysics Data System (ADS)

    Liu, Xiangjie; Jiang, Di; Lee, Kwang Y.

    2016-08-01

    Reliable power control for stabilizing the spatial oscillations is quite important for ensuring the safe operation of a modern pressurized heavy water reactor (PHWR), since these spatial oscillations can cause “flux tilting” in the reactor core. In this paper, a decentralized fuzzy model predictive control (DFMPC) is proposed for spatial control of PHWR. Due to the load dependent dynamics of the nuclear power plant, fuzzy modeling is used to approximate the nonlinear process. A fuzzy Lyapunov function and “quasi-min-max” strategy is utilized in designing the DFMPC, to reduce the conservatism. The plant-wide stability is achieved by the asymptotically positive realness constraint (APRC) for this decentralized MPC. The solving optimization problem is based on a receding horizon scheme involving the linear matrix inequalities (LMIs) technique. Through dynamic simulations, it is demonstrated that the designed DFMPC can effectively suppress spatial oscillations developed in PHWR, and further, shows the advantages over the typical parallel distributed compensation (PDC) control scheme.

  16. Cloud-based shaft torque estimation for electric vehicle equipped with integrated motor-transmission system

    NASA Astrophysics Data System (ADS)

    Zhu, Xiaoyuan; Zhang, Hui; Yang, Bo; Zhang, Guichen

    2018-01-01

    In order to improve oscillation damping control performance as well as gear shift quality of electric vehicle equipped with integrated motor-transmission system, a cloud-based shaft torque estimation scheme is proposed in this paper by using measurable motor and wheel speed signals transmitted by wireless network. It can help reduce computational burden of onboard controllers and also relief network bandwidth requirement of individual vehicle. Considering possible delays during signal wireless transmission, delay-dependent full-order observer design is proposed to estimate the shaft torque in cloud server. With these random delays modeled by using homogenous Markov chain, robust H∞ performance is adopted to minimize the effect of wireless network-induced delays, signal measurement noise as well as system modeling uncertainties on shaft torque estimation error. Observer parameters are derived by solving linear matrix inequalities, and simulation results using acceleration test and tip-in, tip-out test demonstrate the effectiveness of proposed shaft torque observer design.

  17. Identification of optimal feedback control rules from micro-quadrotor and insect flight trajectories.

    PubMed

    Faruque, Imraan A; Muijres, Florian T; Macfarlane, Kenneth M; Kehlenbeck, Andrew; Humbert, J Sean

    2018-06-01

    This paper presents "optimal identification," a framework for using experimental data to identify the optimality conditions associated with the feedback control law implemented in the measurements. The technique compares closed loop trajectory measurements against a reduced order model of the open loop dynamics, and uses linear matrix inequalities to solve an inverse optimal control problem as a convex optimization that estimates the controller optimality conditions. In this study, the optimal identification technique is applied to two examples, that of a millimeter-scale micro-quadrotor with an engineered controller on board, and the example of a population of freely flying Drosophila hydei maneuvering about forward flight. The micro-quadrotor results show that the performance indices used to design an optimal flight control law for a micro-quadrotor may be recovered from the closed loop simulated flight trajectories, and the Drosophila results indicate that the combined effect of the insect longitudinal flight control sensing and feedback acts principally to regulate pitch rate.

  18. Robust preview control for a class of uncertain discrete-time systems with time-varying delay.

    PubMed

    Li, Li; Liao, Fucheng

    2018-02-01

    This paper proposes a concept of robust preview tracking control for uncertain discrete-time systems with time-varying delay. Firstly, a model transformation is employed for an uncertain discrete system with time-varying delay. Then, the auxiliary variables related to the system state and input are introduced to derive an augmented error system that includes future information on the reference signal. This leads to the tracking problem being transformed into a regulator problem. Finally, for the augmented error system, a sufficient condition of asymptotic stability is derived and the preview controller design method is proposed based on the scaled small gain theorem and linear matrix inequality (LMI) technique. The method proposed in this paper not only solves the difficulty problem of applying the difference operator to the time-varying matrices but also simplifies the structure of the augmented error system. The numerical simulation example also illustrates the effectiveness of the results presented in the paper. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

  19. Stability analysis of nonlinear Roesser-type two-dimensional systems via a homogenous polynomial technique

    NASA Astrophysics Data System (ADS)

    Zhang, Tie-Yan; Zhao, Yan; Xie, Xiang-Peng

    2012-12-01

    This paper is concerned with the problem of stability analysis of nonlinear Roesser-type two-dimensional (2D) systems. Firstly, the fuzzy modeling method for the usual one-dimensional (1D) systems is extended to the 2D case so that the underlying nonlinear 2D system can be represented by the 2D Takagi—Sugeno (TS) fuzzy model, which is convenient for implementing the stability analysis. Secondly, a new kind of fuzzy Lyapunov function, which is a homogeneous polynomially parameter dependent on fuzzy membership functions, is developed to conceive less conservative stability conditions for the TS Roesser-type 2D system. In the process of stability analysis, the obtained stability conditions approach exactness in the sense of convergence by applying some novel relaxed techniques. Moreover, the obtained result is formulated in the form of linear matrix inequalities, which can be easily solved via standard numerical software. Finally, a numerical example is also given to demonstrate the effectiveness of the proposed approach.

  20. Clutch pressure estimation for a power-split hybrid transmission using nonlinear robust observer

    NASA Astrophysics Data System (ADS)

    Zhou, Bin; Zhang, Jianwu; Gao, Ji; Yu, Haisheng; Liu, Dong

    2018-06-01

    For a power-split hybrid transmission, using the brake clutch to realize the transition from electric drive mode to hybrid drive mode is an available strategy. Since the pressure information of the brake clutch is essential for the mode transition control, this research designs a nonlinear robust reduced-order observer to estimate the brake clutch pressure. Model uncertainties or disturbances are considered as additional inputs, thus the observer is designed in order that the error dynamics is input-to-state stable. The nonlinear characteristics of the system are expressed as the lookup tables in the observer. Moreover, the gain matrix of the observer is solved by two optimization procedures under the constraints of the linear matrix inequalities. The proposed observer is validated by offline simulation and online test, the results have shown that the observer achieves significant performance during the mode transition, as the estimation error is within a reasonable range, more importantly, it is asymptotically stable.

  1. Convergence of neural networks for programming problems via a nonsmooth Lojasiewicz inequality.

    PubMed

    Forti, Mauro; Nistri, Paolo; Quincampoix, Marc

    2006-11-01

    This paper considers a class of neural networks (NNs) for solving linear programming (LP) problems, convex quadratic programming (QP) problems, and nonconvex QP problems where an indefinite quadratic objective function is subject to a set of affine constraints. The NNs are characterized by constraint neurons modeled by ideal diodes with vertical segments in their characteristic, which enable to implement an exact penalty method. A new method is exploited to address convergence of trajectories, which is based on a nonsmooth Lojasiewicz inequality for the generalized gradient vector field describing the NN dynamics. The method permits to prove that each forward trajectory of the NN has finite length, and as a consequence it converges toward a singleton. Furthermore, by means of a quantitative evaluation of the Lojasiewicz exponent at the equilibrium points, the following results on convergence rate of trajectories are established: (1) for nonconvex QP problems, each trajectory is either exponentially convergent, or convergent in finite time, toward a singleton belonging to the set of constrained critical points; (2) for convex QP problems, the same result as in (1) holds; moreover, the singleton belongs to the set of global minimizers; and (3) for LP problems, each trajectory converges in finite time to a singleton belonging to the set of global minimizers. These results, which improve previous results obtained via the Lyapunov approach, are true independently of the nature of the set of equilibrium points, and in particular they hold even when the NN possesses infinitely many nonisolated equilibrium points.

  2. [Income-related health inequalities in France in 2004: Decomposition and explanations].

    PubMed

    Tubeuf, S

    2009-10-01

    This analysis supplements existing work on social health inequalities at two levels: the measurement of health and the measurement of inequalities. Firstly, individual health status was measured using a subjective health indicator corrected within a promising cardinalisation method which had not yet been carried out on French data. Secondly, this study used an innovative methodology to measure income-related health inequalities, to understand the relationships between income, income inequality, various social determinants, and health. The analysis was based on a sample of working-age adults from the 2004 Health and Health Insurance Survey. The methodology used in the study measures the total income-related health inequality using the concentration index. This index is based on a linear model explaining health according to several individual characteristics, such as age, sex, and various socioeconomic characteristics. The method thus takes into account both the causal relationships between the various explicative factors introduced in the model and their relationship with health. Furthermore, it concretely measures the contribution of the social determinants to income-related health inequalities. The results show an income-related health inequality favouring individuals with a higher income. Moreover, income level, supplementary private health insurance, education level, and social class account for the main contributions to inequality. Therefore, the decomposition method highlights population groups that policies should target. The study suggests that reducing income inequality is not sufficient to lower income-related health inequalities in France in 2004 and needs to be supplemented with the reduction of the relationship between income and health and the reduction of income inequality over socioeconomic status.

  3. Design of Linear Quadratic Regulators and Kalman Filters

    NASA Technical Reports Server (NTRS)

    Lehtinen, B.; Geyser, L.

    1986-01-01

    AESOP solves problems associated with design of controls and state estimators for linear time-invariant systems. Systems considered are modeled in state-variable form by set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are linear quadratic regulator (LQR) design problem and steady-state Kalman filter design problem. AESOP is interactive. User solves design problems and analyzes solutions in single interactive session. Both numerical and graphical information available to user during the session.

  4. Solving a mixture of many random linear equations by tensor decomposition and alternating minimization.

    DOT National Transportation Integrated Search

    2016-09-01

    We consider the problem of solving mixed random linear equations with k components. This is the noiseless setting of mixed linear regression. The goal is to estimate multiple linear models from mixed samples in the case where the labels (which sample...

  5. Socioeconomic Status and Health: A New Approach to the Measurement of Bivariate Inequality.

    PubMed

    Erreygers, Guido; Kessels, Roselinde

    2017-06-23

    We suggest an alternative way to construct a family of indices of socioeconomic inequality of health. Our indices belong to the broad category of linear indices. In contrast to rank-dependent indices, which are defined in terms of the ranks of the socioeconomic variable and the levels of the health variable, our indices are based on the levels of both the socioeconomic and the health variable. We also indicate how the indices can be modified in order to introduce sensitivity to inequality in the socioeconomic distribution and to inequality in the health distribution. As an empirical illustration, we make a comparative study of the relation between income and well-being in 16 European countries using data from the Survey of Health, Ageing and Retirement in Europe (SHARE) Wave 4.

  6. ADM For Solving Linear Second-Order Fredholm Integro-Differential Equations

    NASA Astrophysics Data System (ADS)

    Karim, Mohd F.; Mohamad, Mahathir; Saifullah Rusiman, Mohd; Che-Him, Norziha; Roslan, Rozaini; Khalid, Kamil

    2018-04-01

    In this paper, we apply Adomian Decomposition Method (ADM) as numerically analyse linear second-order Fredholm Integro-differential Equations. The approximate solutions of the problems are calculated by Maple package. Some numerical examples have been considered to illustrate the ADM for solving this equation. The results are compared with the existing exact solution. Thus, the Adomian decomposition method can be the best alternative method for solving linear second-order Fredholm Integro-Differential equation. It converges to the exact solution quickly and in the same time reduces computational work for solving the equation. The result obtained by ADM shows the ability and efficiency for solving these equations.

  7. Math 3011--College Algebra and Trigonometry. Course Outline.

    ERIC Educational Resources Information Center

    New York Inst. of Tech., Old Westbury.

    This document contains the course syllabus and 12 independent practice modules for a college level mathematics course designed to provide the necessary foundation for success in calculus, develop logical thinking skills, and enhance analytic skills through problem solving. Topics include relations and functions; inequalities; complex numbers;…

  8. Discrete-time neural network for fast solving large linear L1 estimation problems and its application to image restoration.

    PubMed

    Xia, Youshen; Sun, Changyin; Zheng, Wei Xing

    2012-05-01

    There is growing interest in solving linear L1 estimation problems for sparsity of the solution and robustness against non-Gaussian noise. This paper proposes a discrete-time neural network which can calculate large linear L1 estimation problems fast. The proposed neural network has a fixed computational step length and is proved to be globally convergent to an optimal solution. Then, the proposed neural network is efficiently applied to image restoration. Numerical results show that the proposed neural network is not only efficient in solving degenerate problems resulting from the nonunique solutions of the linear L1 estimation problems but also needs much less computational time than the related algorithms in solving both linear L1 estimation and image restoration problems.

  9. Encouraging Students to Think Strategically when Learning to Solve Linear Equations

    ERIC Educational Resources Information Center

    Robson, Daphne; Abell, Walt; Boustead, Therese

    2012-01-01

    Students who are preparing to study science and engineering need to understand equation solving but adult students returning to study can find this difficult. In this paper, the design of an online resource, Equations2go, for helping students learn to solve linear equations is investigated. Students learning to solve equations need to consider…

  10. Income inequality and obesity prevalence among OECD countries.

    PubMed

    Su, Dejun; Esqueda, Omar A; Li, Lifeng; Pagán, José A

    2012-07-01

    Using recent pooled data from the World Health Organization Global Infobase and the World Factbook compiled by the Central Intelligence Agency of the United States, this study assesses the relation between income inequality and obesity prevalence among 31 OECD countries through a series of bivariate and multivariate linear regressions. The United States and Mexico well lead OECD countries in both obesity prevalence and income inequality. A sensitivity analysis suggests that the inclusion or exclusion of these two extreme cases can fundamentally change the findings. When the two countries are included, the results reveal a positive correlation between income inequality and obesity prevalence. This correlation is more salient among females than among males. Income inequality alone is associated with 16% and 35% of the variations in male and female obesity rates, respectively, across OECD countries in 2010. Higher levels of income inequality in the 2005-2010 period were associated with a more rapid increase in obesity prevalence from 2002 to 2010. These associations, however, virtually disappear when the US and Mexico have been excluded from the analysis. Findings from this study underscore the importance of assessing the impact of extreme cases on the relation between income inequality and health outcomes. The potential pathways from income inequality to the alarmingly high rates of obesity in the cases of the US and Mexico warrant further research.

  11. European health inequality through the 'Great Recession': social policy matters.

    PubMed

    van der Wel, Kjetil A; Saltkjel, Therese; Chen, Wen-Hao; Dahl, Espen; Halvorsen, Knut

    2018-05-01

    This paper investigates the association between the Great Recession and educational inequalities in self-rated general health in 25 European countries. We investigate four different indicators related to economic recession: GDP; unemployment; austerity and a 'crisis' indicator signifying severe simultaneous drops in GDP and welfare generosity. We also assess the extent to which health inequality changes can be attributed to changes in the economic conditions and social capital in the European populations. The paper uses data from the European Social Survey (2002-2014). The analyses include both cross-sectional and lagged associations using multilevel linear regression models with country fixed effects. This approach allows us to identify health inequality changes net of all time-invariant differences between countries. GDP drops and increasing unemployment were associated with decreasing health inequalities. Austerity, however, was related to increasing health inequalities, an association that grew stronger with time. The strongest increase in health inequality was found for the more robust 'crisis' indicator. Changes in trust, social relationships and in the experience of economic hardship of the populations accounted for much of the increase in health inequality. The paper concludes that social policy has an important role in the development of health inequalities, particularly during times of economic crisis. © 2018 The Authors. Sociology of Health & Illness published by John Wiley & Sons Ltd on behalf of Foundation for SHIL.

  12. Discrete Applied Mathematics

    DTIC Science & Technology

    1993-05-31

    program. In paper [28], we give a brief and elementary proof of a result of Hoffman [1952) about approximate solutions to systems, of linear inequalities...UCLA, Vestvood, CA, February 1993. " Linear Problems: Formulation and Solution," International Linear Algebra Society, Pensacola, FL, May 1993. Denise S...thresAold If there is a number h and a linear k-separator w assigning a real number to each vertex so that for any subset S of vertices, the sum of w

  13. Parallel Optimization of Polynomials for Large-scale Problems in Stability and Control

    NASA Astrophysics Data System (ADS)

    Kamyar, Reza

    In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a trade off between accuracy and complexity. In particular, we develop a sequence of tractable optimization problems --- in the form of Linear Programs (LPs) and/or Semi-Definite Programs (SDPs) --- whose solutions converge to the exact solution of the NP-hard problem. However, the computational and memory complexity of these LPs and SDPs grow exponentially with the progress of the sequence - meaning that improving the accuracy of the solutions requires solving SDPs with tens of thousands of decision variables and constraints. Setting up and solving such problems is a significant challenge. The existing optimization algorithms and software are only designed to use desktop computers or small cluster computers --- machines which do not have sufficient memory for solving such large SDPs. Moreover, the speed-up of these algorithms does not scale beyond dozens of processors. This in fact is the reason we seek parallel algorithms for setting-up and solving large SDPs on large cluster- and/or super-computers. We propose parallel algorithms for stability analysis of two classes of systems: 1) Linear systems with a large number of uncertain parameters; 2) Nonlinear systems defined by polynomial vector fields. First, we develop a distributed parallel algorithm which applies Polya's and/or Handelman's theorems to some variants of parameter-dependent Lyapunov inequalities with parameters defined over the standard simplex. The result is a sequence of SDPs which possess a block-diagonal structure. We then develop a parallel SDP solver which exploits this structure in order to map the computation, memory and communication to a distributed parallel environment. Numerical tests on a supercomputer demonstrate the ability of the algorithm to efficiently utilize hundreds and potentially thousands of processors, and analyze systems with 100+ dimensional state-space. Furthermore, we extend our algorithms to analyze robust stability over more complicated geometries such as hypercubes and arbitrary convex polytopes. Our algorithms can be readily extended to address a wide variety of problems in control such as Hinfinity synthesis for systems with parametric uncertainty and computing control Lyapunov functions.

  14. Experimental quantum computing to solve systems of linear equations.

    PubMed

    Cai, X-D; Weedbrook, C; Su, Z-E; Chen, M-C; Gu, Mile; Zhu, M-J; Li, Li; Liu, Nai-Le; Lu, Chao-Yang; Pan, Jian-Wei

    2013-06-07

    Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time proportional to the number of variables N. A recently proposed quantum algorithm shows that quantum computers could solve linear systems in a time scale of order log(N), giving an exponential speedup over classical computers. Here we realize the simplest instance of this algorithm, solving 2×2 linear equations for various input vectors on a quantum computer. We use four quantum bits and four controlled logic gates to implement every subroutine required, demonstrating the working principle of this algorithm.

  15. To what extent does immigration affect inequality?

    NASA Astrophysics Data System (ADS)

    Berman, Yonatan; Aste, Tomaso

    2016-11-01

    The current surge in income and wealth inequality in most western countries, along with the continuous immigration to those countries demand a quantitative analysis of the effect immigration has on economic inequality. This paper presents a quantitative analysis framework providing a way to calculate this effect. It shows that in most cases, the effect of immigration on wealth and income inequality is limited, mainly due to the relative small scale of immigration waves. For a large scale flow of immigrants, such as the immigration to the US, the UK and Australia in the past few decades, we estimate that 10 % ÷ 15 % of the wealth and income inequality increase can be attributed to immigration. The results demonstrate that immigration could possibly decrease inequality substantially, if the characteristics of the immigrants resemble the characteristics of the destination middle class population in terms of wealth or income. We empirically found that the simple linear relation ΔS = 0.18 ρ roughly describes the increase in the wealth share of the top 10 % due to immigration of a fraction ρ of the population.

  16. Students’ difficulties in solving linear equation problems

    NASA Astrophysics Data System (ADS)

    Wati, S.; Fitriana, L.; Mardiyana

    2018-03-01

    A linear equation is an algebra material that exists in junior high school to university. It is a very important material for students in order to learn more advanced mathematics topics. Therefore, linear equation material is essential to be mastered. However, the result of 2016 national examination in Indonesia showed that students’ achievement in solving linear equation problem was low. This fact became a background to investigate students’ difficulties in solving linear equation problems. This study used qualitative descriptive method. An individual written test on linear equation tasks was administered, followed by interviews. Twenty-one sample students of grade VIII of SMPIT Insan Kamil Karanganyar did the written test, and 6 of them were interviewed afterward. The result showed that students with high mathematics achievement donot have difficulties, students with medium mathematics achievement have factual difficulties, and students with low mathematics achievement have factual, conceptual, operational, and principle difficulties. Based on the result there is a need of meaningfulness teaching strategy to help students to overcome difficulties in solving linear equation problems.

  17. Semilinear programming: applications and implementation

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Mohan, S.

    Semilinear programming is a method of solving optimization problems with linear constraints where the non-negativity restrictions on the variables are dropped and the objective function coefficients can take on different values depending on whether the variable is positive or negative. The simplex method for linear programming is modified in this thesis to solve general semilinear and piecewise linear programs efficiently without having to transform them into equivalent standard linear programs. Several models in widely different areas of optimization such as production smoothing, facility locations, goal programming and L/sub 1/ estimation are presented first to demonstrate the compact formulation that arisesmore » when such problems are formulated as semilinear programs. A code SLP is constructed using the semilinear programming techniques. Problems in aggregate planning and L/sub 1/ estimation are solved using SLP and equivalent linear programs using a linear programming simplex code. Comparisons of CPU times and number iterations indicate SLP to be far superior. The semilinear programming techniques are extended to piecewise linear programming in the implementation of the code PLP. Piecewise linear models in aggregate planning are solved using PLP and equivalent standard linear programs using a simple upper bounded linear programming code SUBLP.« less

  18. Have we left some behind? Trends in socio-economic inequalities in breastfeeding initiation: a population-based epidemiological surveillance study.

    PubMed

    Nickel, Nathan C; Martens, Patricia J; Chateau, Dan; Brownell, Marni D; Sarkar, Joykrishna; Goh, Chun Yan; Burland, Elaine; Taylor, Carole; Katz, Alan

    2014-07-31

    Breastfeeding is associated with improved health. Surveillance data show that breastfeeding initiation rates have increased; however, limited work has examined trends in socio-economic inequalities in initiation. The study's research question was whether socio-economic inequalities in breastfeeding initiation have changed over the past 20 years. This population-based study is a project within PATHS Equity for Children. Analyses used hospital discharge data for Manitoba mother-infant dyads with live births, 1988-2011 (n=316,027). Income quintiles were created, each with ~20% of dyads. Three-year, overall and by-quintile breastfeeding initiation rates were estimated for Manitoba and two hospitals. Age-adjusted rates were estimated for Manitoba. Rates were modelled using generalized linear models. Three measures, rate ratios (RRs), rate differences (RDs) and concentration indices, assessed inequality at each time point. We also compared concentration indices with Gini coefficients to assess breastfeeding inequality vis-à-vis income inequality. Trend analyses tested for changes over time. Manitoba and Hospital A initiation rates increased; Hospital B rates did not change. Significant inequalities existed in nearly every period, across all three measures: RRs, RDs and concentration indices. RRs and concentration indices suggested little to no change in inequality from 1988 to 2011. RDs for Manitoba (comparing initiation in the highest to lowest income quintiles) did not change significantly over time. RDs decreased for Hospital A, suggesting decreasing socio-economic inequalities in breastfeeding; RDs increased for Hospital B. Income inequality increased significantly in Manitoba during the study period. Overall breastfeeding initiation rates can improve while inequality persists or worsens.

  19. Storytelling in community intervention research: lessons learned from the walk your heart to health intervention.

    PubMed

    LeBron, Alana M; Schulz, Amy J; Bernal, Cristina; Gamboa, Cindy; Wright, Conja; Sand, Sharon; Valerio, Melissa; Caver, Deanna

    2014-01-01

    Contextually and culturally congruent interventions are urgently needed to reduce racial, ethnic, and socioeconomic inequities in physical activity and cardiovascular disease. To examine a community-based participatory research (CBPR) process that incorporated storytelling into a physical activity intervention, and consider implications for reducing health inequities. We used a CBPR process to incorporate storytelling in an existing walking group intervention. Stories conveyed social support and problem-solving intervention themes designed to maintain increases in physical activity over time, and were adapted to the walking group context, group dynamics, challenges, and traditions. After describing of the CBPR process used to adapt stories to walking group sites, we discuss challenges and lessons learned regarding the adaptation and implementation of stories to convey key intervention themes. A CBPR approach to incorporating storytelling to convey intervention themes offers an innovative and flexible strategy to promote health toward the elimination of health inequities.

  20. The Performing School: The Effects of Market & Accountability Policies

    ERIC Educational Resources Information Center

    Falabella, Alejandra

    2014-01-01

    Market and accountability educational reforms have proliferated around the globe, along with high expectations of solving countries' school quality deficits and inequities. In this paper I develop an analytical framework from a critical sociology angle for analyzing the effects of these policies within schools. First I discuss conceptually the…

  1. Easy Absolute Values? Absolutely

    ERIC Educational Resources Information Center

    Taylor, Sharon E.; Mittag, Kathleen Cage

    2015-01-01

    The authors teach a problem-solving course for preservice middle-grades education majors that includes concepts dealing with absolute-value computations, equations, and inequalities. Many of these students like mathematics and plan to teach it, so they are adept at symbolic manipulations. Getting them to think differently about a concept that they…

  2. An efficient method for generalized linear multiplicative programming problem with multiplicative constraints.

    PubMed

    Zhao, Yingfeng; Liu, Sanyang

    2016-01-01

    We present a practical branch and bound algorithm for globally solving generalized linear multiplicative programming problem with multiplicative constraints. To solve the problem, a relaxation programming problem which is equivalent to a linear programming is proposed by utilizing a new two-phase relaxation technique. In the algorithm, lower and upper bounds are simultaneously obtained by solving some linear relaxation programming problems. Global convergence has been proved and results of some sample examples and a small random experiment show that the proposed algorithm is feasible and efficient.

  3. Absolute and relative educational inequalities in obesity among adults in Tehran: Findings from the Urban HEART study-2.

    PubMed

    Kiadaliri, Aliasghar A; Asadi-Lari, Mohsen; Kalantari, Naser; Jafari, Mehdi; Vaez Mahdavi, Mohammad Reza; Faghihzadeh, Soghrat

    2016-09-01

    The prevalence of obesity is increasing in Iran. Previous studies showed mixed results in relation to association between socioeconomic status and obesity in the country. The current study aimed to examine educational inequalities among adults in Tehran in 2011. Data on 90,435 persons 18 years and older from Urban Health Equity Assessment and Response Tool (Urban HEART-2) were analyzed. The Slope Index of Inequality (SII) and the Relative Index of Inequality (RII) were used for assessing educational inequalities in obesity. These measures were quantified using generalized linear models for the binomial family adjusted for sex and age. Subgroup analysis was conducted across sex, age groups and the 22 districts of Tehran. Both SII and RII showed substantial educational inequalities in obesity in favour of more educated adults [RII and SII (95% CI were equal to 2.91 (2.71-3.11) and 0.12 (0.12-0.13)), respectively]. These educational inequalities were persistent even after adjusting for employment, marital status and smoking. Subgroup analysis revealed that educational inequalities were more profound among women. While among men educational inequalities were generally increasing with age, an inverse trend was observed among women. Educational inequalities were observed within all 22 districts of Tehran and generally there were no statistically significant differences between districts. An inverse association between education and obesity was observed in the current study. To decrease educational inequalities in Tehran, priority should be given to younger women and older men. Further analyses are needed to explain these inequalities. Copyright © 2015 Asia Oceania Association for the Study of Obesity. Published by Elsevier Ltd. All rights reserved.

  4. Socioeconomic Status and Health: A New Approach to the Measurement of Bivariate Inequality

    PubMed Central

    Kessels, Roselinde

    2017-01-01

    We suggest an alternative way to construct a family of indices of socioeconomic inequality of health. Our indices belong to the broad category of linear indices. In contrast to rank-dependent indices, which are defined in terms of the ranks of the socioeconomic variable and the levels of the health variable, our indices are based on the levels of both the socioeconomic and the health variable. We also indicate how the indices can be modified in order to introduce sensitivity to inequality in the socioeconomic distribution and to inequality in the health distribution. As an empirical illustration, we make a comparative study of the relation between income and well-being in 16 European countries using data from the Survey of Health, Ageing and Retirement in Europe (SHARE) Wave 4. PMID:28644405

  5. Passivity of memristive BAM neural networks with leakage and additive time-varying delays

    NASA Astrophysics Data System (ADS)

    Wang, Weiping; Wang, Meiqi; Luo, Xiong; Li, Lixiang; Zhao, Wenbing; Liu, Linlin; Ping, Yuan

    2018-02-01

    This paper investigates the passivity of memristive bidirectional associate memory neural networks (MBAMNNs) with leakage and additive time-varying delays. Based on some useful inequalities and appropriate Lyapunov-Krasovskii functionals (LKFs), several delay-dependent conditions for passivity performance are obtained in linear matrix inequalities (LMIs). Moreover, the leakage delays as well as additive delays are considered separately. Finally, numerical simulations are provided to demonstrate the feasibility of the theoretical results.

  6. Global exponential stability of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays.

    PubMed

    Huang, Haiying; Du, Qiaosheng; Kang, Xibing

    2013-11-01

    In this paper, a class of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays is investigated. The jumping parameters are modeled as a continuous-time finite-state Markov chain. At first, the existence of equilibrium point for the addressed neural networks is studied. By utilizing the Lyapunov stability theory, stochastic analysis theory and linear matrix inequality (LMI) technique, new delay-dependent stability criteria are presented in terms of linear matrix inequalities to guarantee the neural networks to be globally exponentially stable in the mean square. Numerical simulations are carried out to illustrate the main results. © 2013 ISA. Published by ISA. All rights reserved.

  7. Solving the Problem of Linear Viscoelasticity for Piecewise-Homogeneous Anisotropic Plates

    NASA Astrophysics Data System (ADS)

    Kaloerov, S. A.; Koshkin, A. A.

    2017-11-01

    An approximate method for solving the problem of linear viscoelasticity for thin anisotropic plates subject to transverse bending is proposed. The method of small parameter is used to reduce the problem to a sequence of boundary problems of applied theory of bending of plates solved using complex potentials. The general form of complex potentials in approximations and the boundary conditions for determining them are obtained. Problems for a plate with elliptic elastic inclusions are solved as an example. The numerical results for a plate with one, two elliptical (circular), and linear inclusions are analyzed.

  8. Dimensionality and R4P: A Health Equity Framework for Research Planning and Evaluation in African American Populations.

    PubMed

    Hogan, Vijaya; Rowley, Diane L; White, Stephanie Baker; Faustin, Yanica

    2018-02-01

    Introduction Existing health disparities frameworks do not adequately incorporate unique interacting contributing factors leading to health inequities among African Americans, resulting in public health stakeholders' inability to translate these frameworks into practice. Methods We developed dimensionality and R4P to integrate multiple theoretical perspectives into a framework of action to eliminate health inequities experienced by African Americans. Results The dimensional framework incorporates Critical Race Theory and intersectionality, and includes dimensions of time-past, present and future. Dimensionality captures the complex linear and non-linear array of influences that cause health inequities, but these pathways do not lend themselves to approaches to developing empirically derived programs, policies and interventions to promote health equity. R4P provides a framework for addressing the scope of actions needed. The five components of R4P are (1) Remove, (2) Repair, (3) Remediate, (4) Restructure and (5) Provide. Conclusion R4P is designed to translate complex causality into a public health equity planning, assessment, evaluation and research tool.

  9. Income inequality and cardiovascular disease risk factors in a highly unequal country: a fixed-effects analysis from South Africa.

    PubMed

    Adjaye-Gbewonyo, Kafui; Kawachi, Ichiro; Subramanian, S V; Avendano, Mauricio

    2018-03-06

    Chronic stress associated with high income inequality has been hypothesized to increase CVD risk and other adverse health outcomes. However, most evidence comes from high-income countries, and there is limited evidence on the link between income inequality and biomarkers of chronic stress and risk for CVD. This study examines how changes in income inequality over recent years relate to changes in CVD risk factors in South Africa, home to some of the highest levels of income inequality globally. We linked longitudinal data from 9356 individuals interviewed in the 2008 and 2012 National Income Dynamics Study to district-level Gini coefficients estimated from census and survey data. We investigated whether subnational district income inequality was associated with several modifiable risk factors for cardiovascular disease (CVD) in South Africa, including body mass index (BMI), waist circumference, blood pressure, physical inactivity, smoking, and high alcohol consumption. We ran individual fixed-effects models to examine the association between changes in income inequality and changes in CVD risk factors over time. Linear models were used for continuous metabolic outcomes while conditional Poisson models were used to estimate risk ratios for dichotomous behavioral outcomes. Both income inequality and prevalence of most CVD risk factors increased over the period of study. In longitudinal fixed-effects models, changes in district Gini coefficients were not significantly associated with changes in CVD risk factors. Our findings do not support the hypothesis that subnational district income inequality is associated with CVD risk factors within the high-inequality setting of South Africa.

  10. Community Social Capital, Built Environment, and Income-Based Inequality in Depressive Symptoms Among Older People in Japan: An Ecological Study From the JAGES Project.

    PubMed

    Haseda, Maho; Kondo, Naoki; Ashida, Toyo; Tani, Yukako; Takagi, Daisuke; Kondo, Katsunori

    2018-03-05

    Although reducing socioeconomic inequalities in depression is necessary, their associated factors have rarely been studied. This study aimed to screen the potential contextual factors associated with income-based inequality in older adults' depression. Using data from the Japan Gerontological Evaluation Study (JAGES) of 2013, we conducted an ecological study covering 77 communities in Japan. Our measures of socioeconomic inequalities in depression were the slope index of inequalities (SII) and the relative index of inequalities (RII) of the prevalence of depressive symptoms across three income levels. We categorized available community-level factors, including socio-demographic factors, social participation, social relationships, subjective changes in the residential area, and the built environment. These indicators were aggregated from individual responses of 51,962 and 52,958 physically independent men and women, respectively, aged 65 years or more. We performed multiple linear regression analyses to explore factors with statistical significance of a two-tailed P-value less than 0.05. Factors associated with shallower gradients in depression for men included higher participation in local activities and reception or provision of social support, which did not show significant association among women. Perceived increases in unemployment and economic inequalities were positively associated with larger inequalities in both genders (P < 0.05). The built environment did not indicate any significant association. A community environment fostering social activities and relationships might be associated with smaller income-based inequalities in depression. There is a need for more deterministic studies for planning of effective community interventions to address socioeconomic inequalities in depression.

  11. No association between gender inequality and peak HIV prevalence in developing countries - an ecological study.

    PubMed

    Kenyon, Chris R; Buyze, Jozefien

    2015-01-01

    The prevalence of both gender inequality and HIV prevalence vary considerably both within all developing countries and within those in sub-Saharan Africa. We test the hypothesis that the extent of gender inequality is associated with national peak HIV prevalence. Linear regression was used to test the association between national peak HIV prevalence and three markers of gender equality - the gender-related development index (GDI), the gender empowerment measure (GEM), and the gender inequality index (GII). No evidence was found of a positive relationship between gender inequality and HIV prevalence, either in the analyses of all developing countries or those limited to Africa. In the bivariate analyses limited to Africa, there was a positive association between the two measures of gender "equality" and peak HIV prevalence (GDI: coefficient 28, 95% confidence interval (CI) 9.1-46.8; GEM: coefficient 54.8, 95% CI 20.5-89.1). There was also a negative association between the marker of gender "inequality" and peak HIV prevalence (GII: coefficient -66.9, 95% CI -112.8 to -21.0). These associations all disappeared on multivariate analyses. We could not find any evidence to support the hypothesis that variations in the extent of gender inequality explain variations in HIV prevalence in developing countries.

  12. Educational inequality in the occurrence of abdominal obesity: Pró-Saúde Study

    PubMed Central

    Alves, Ronaldo Fernandes Santos; Faerstein, Eduardo

    2015-01-01

    OBJECTIVE To estimate the degree of educational inequality in the occurrence of abdominal obesity in a population of non-faculty civil servants at university campi. METHODS In this cross-sectional study, we used data from 3,117 subjects of both genders aged 24 to 65-years old, regarding the baseline of Pró-Saúde Study, 1999-2001. Abdominal obesity was defined according to abdominal circumference thresholds of 88 cm for women and 102 cm for men. A multi-dimensional, self-administered questionnaire was used to evaluate education levels and demographic variables. Slope and relative indices of inequality, and Chi-squared test for linear trend were used in the data analysis. All analyses were stratified by genders, and the indices of inequality were standardized by age. RESULTS Abdominal obesity was the most prevalent among women (43.5%; 95%CI 41.2;45.9), as compared to men (24.3%; 95%CI 22.1;26.7), in all educational strata and age ranges. The association between education levels and abdominal obesity was an inverse one among women (p < 0.001); it was not statistically significant among men (p = 0.436). The educational inequality regarding abdominal obesity in the female population, in absolute terms (slope index of inequality), was 24.0% (95%CI 15.5;32.6). In relative terms (relative index of inequality), it was 2.8 (95%CI 1.9;4.1), after the age adjustment. CONCLUSIONS Gender inequality in the prevalence of abdominal obesity increases with older age and lower education. The slope and relative indices of inequality summarize the strictly monotonous trend between education levels and abdominal obesity, and it described educational inequality regarding abdominal obesity among women. Such indices provide relevant quantitative estimates for monitoring abdominal obesity and dealing with health inequalities. PMID:26465669

  13. Geometric and Algebraic Approaches in the Concept of Complex Numbers

    ERIC Educational Resources Information Center

    Panaoura, A.; Elia, I.; Gagatsis, A.; Giatilis, G.-P.

    2006-01-01

    This study explores pupils' performance and processes in tasks involving equations and inequalities of complex numbers requiring conversions from a geometric representation to an algebraic representation and conversions in the reverse direction, and also in complex numbers problem solving. Data were collected from 95 pupils of the final grade from…

  14. Using, Seeing, Feeling, and Doing Absolute Value for Deeper Understanding

    ERIC Educational Resources Information Center

    Ponce, Gregorio A.

    2008-01-01

    Using sticky notes and number lines, a hands-on activity is shared that anchors initial student thinking about absolute value. The initial point of reference should help students successfully evaluate numeric problems involving absolute value. They should also be able to solve absolute value equations and inequalities that are typically found in…

  15. Development of Intellectual Activity in Solving Exponential Inequalities

    ERIC Educational Resources Information Center

    Alpyssov, Akan; Mukanova, Zhazira; Kireyeva, Assel; Sakenov, Janat; Kervenev, Kabylgazy

    2016-01-01

    The article describes the possibilities and the main directions of development of intellectual activity in teaching mathematics in school. The aims and specific features of application of international comparative TIMSS and PISA studies, as well as their results in the field of mathematics education in relation to the pupils in Kazakhstan are…

  16. Antisocial and Human Capital Pathways to Socioeconomic Exclusion: A 42-Year Prospective Study

    ERIC Educational Resources Information Center

    Savolainen, Jukka; Mason, W. Alex; Lyyra, Anna-Liisa; Pulkkinen, Lea; Kokko, Katja

    2017-01-01

    Nordic welfare states have been very successful at reducing poverty and inequality among their citizens. However, the presence of a strong social safety net in these countries has not solved the problem of "socioeconomic exclusion", manifesting in such outcomes as chronic unemployment and welfare dependency. In an effort to understand…

  17. Shared Space, Liminal Space: Five Years into a Community-University Place-Based Experiment

    ERIC Educational Resources Information Center

    Barajas, Heidi Lasley; Martin, Lauren

    2016-01-01

    This article explores shared space at the University of Minnesota's Robert J. Jones Urban Research and Outreach Engagement Center (UROC), located four miles off campus in a community strong in assets, but facing inequality, disinvestment and racism. UROC's mission promotes university-community collaboration to solve critical urban challenges. We…

  18. Solving the Achievement Gap: Overcoming the Structure of School Inequality

    ERIC Educational Resources Information Center

    Yeh, Stuart S.

    2017-01-01

    This book examines the cause of the student achievement gap, suggesting that the prevailing emphasis on socioeconomic factors, sociocultural influences, and teacher quality is misplaced. The cause of the achievement gap is not differences in parenting styles, or the economic advantages of middle-class parents, or differences in the quality of…

  19. Peace Keepers: Colleges as Teachers of Peace and Conflict Resolution

    ERIC Educational Resources Information Center

    Smith, David

    2010-01-01

    Americans increasingly are looking to community colleges to solve some of the most pressing problems facing this country--not necessarily a surprising revelation. Community colleges have long been in the business of making communities stronger and more vibrant, minimizing economic and social inequities, and instilling hope in those who need it…

  20. Dogs Don't Need Calculus

    ERIC Educational Resources Information Center

    Bolt, Mike

    2010-01-01

    Many optimization problems can be solved without resorting to calculus. This article develops a new variational method for optimization that relies on inequalities. The method is illustrated by four examples, the last of which provides a completely algebraic solution to the problem of minimizing the time it takes a dog to retrieve a thrown ball,…

  1. Optimization of an auto-thermal ammonia synthesis reactor using cyclic coordinate method

    NASA Astrophysics Data System (ADS)

    A-N Nguyen, T.; Nguyen, T.-A.; Vu, T.-D.; Nguyen, K.-T.; K-T Dao, T.; P-H Huynh, K.

    2017-06-01

    The ammonia synthesis system is an important chemical process used in the manufacture of fertilizers, chemicals, explosives, fibers, plastics, refrigeration. In the literature, many works approaching the modeling, simulation and optimization of an auto-thermal ammonia synthesis reactor can be found. However, they just focus on the optimization of the reactor length while keeping the others parameters constant. In this study, the other parameters are also considered in the optimization problem such as the temperature of feed gas enters the catalyst zone, the initial nitrogen proportion. The optimal problem requires the maximization of an objective function which is multivariable function and subject to a number of equality constraints involving the solution of coupled differential equations and also inequality constraint. The cyclic coordinate search was applied to solve the multivariable-optimization problem. In each coordinate, the golden section method was applied to find the maximum value. The inequality constraints were treated using penalty method. The coupled differential equations system was solved using Runge-Kutta 4th order method. The results obtained from this study are also compared to the results from the literature.

  2. Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel

    ERIC Educational Resources Information Center

    El-Gebeily, M.; Yushau, B.

    2008-01-01

    In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…

  3. Decreasing the temporal complexity for nonlinear, implicit reduced-order models by forecasting

    DOE PAGES

    Carlberg, Kevin; Ray, Jaideep; van Bloemen Waanders, Bart

    2015-02-14

    Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves. Most model-reduction techniques for nonlinear ODEs exploit knowledge of system's spatial behavior to reduce the computational complexity of each linear-system solve. However, the number of linear-system solves for the reduced-order simulation often remains roughly the same as that for the full-order simulation. We propose exploiting knowledge of the model's temporal behavior to (1) forecast the unknown variable of the reduced-order system of nonlinear equationsmore » at future time steps, and (2) use this forecast as an initial guess for the Newton-like solver during the reduced-order-model simulation. To compute the forecast, we propose using the Gappy POD technique. As a result, the goal is to generate an accurate initial guess so that the Newton solver requires many fewer iterations to converge, thereby decreasing the number of linear-system solves in the reduced-order-model simulation.« less

  4. National Income, Inequality and Global Patterns of Cigarette Use

    PubMed Central

    Pampel, Fred

    2011-01-01

    Declining tobacco use in high-income nations and rising tobacco use in low- and middle-income nations raises questions about the sources of worldwide patterns of smoking. Theories posit a curvilinear influence of national income based on the balance of affordability and health-cost effects. In addition, however, economic inequality, gender inequality and government policies may moderate the rise and fall in smoking prevalence with national income. This study tests these arguments using aggregate data for 145 nations and measures of smoking prevalence circa 2000. The results show nonlinear effects of national income for males that take the form of an inverted U, but show linear effects for females. They also show non-additive effects of economic inequality for males that moderate both the rise and decline of smoking with national income and non-additive effects of gender equality for females that moderate the positive effect of national income. PMID:21874072

  5. Randomness Amplification under Minimal Fundamental Assumptions on the Devices

    NASA Astrophysics Data System (ADS)

    Ramanathan, Ravishankar; Brandão, Fernando G. S. L.; Horodecki, Karol; Horodecki, Michał; Horodecki, Paweł; Wojewódka, Hanna

    2016-12-01

    Recently, the physically realistic protocol amplifying the randomness of Santha-Vazirani sources producing cryptographically secure random bits was proposed; however, for reasons of practical relevance, the crucial question remained open regarding whether this can be accomplished under the minimal conditions necessary for the task. Namely, is it possible to achieve randomness amplification using only two no-signaling components and in a situation where the violation of a Bell inequality only guarantees that some outcomes of the device for specific inputs exhibit randomness? Here, we solve this question and present a device-independent protocol for randomness amplification of Santha-Vazirani sources using a device consisting of two nonsignaling components. We show that the protocol can amplify any such source that is not fully deterministic into a fully random source while tolerating a constant noise rate and prove the composable security of the protocol against general no-signaling adversaries. Our main innovation is the proof that even the partial randomness certified by the two-party Bell test [a single input-output pair (u* , x* ) for which the conditional probability P (x*|u*) is bounded away from 1 for all no-signaling strategies that optimally violate the Bell inequality] can be used for amplification. We introduce the methodology of a partial tomographic procedure on the empirical statistics obtained in the Bell test that ensures that the outputs constitute a linear min-entropy source of randomness. As a technical novelty that may be of independent interest, we prove that the Santha-Vazirani source satisfies an exponential concentration property given by a recently discovered generalized Chernoff bound.

  6. Solving the Nonlocality Riddle by Conformal Quantum Geometrodynamics

    NASA Astrophysics Data System (ADS)

    Santamato, Enrico; de Martini, Francesco

    2012-01-01

    Since the 1935 proposal by Einstein, Podolsky and Rosen the riddle of nonlocality, today demonstrated by the violation of Bell's inequalities within innumerable experiments, has been a cause of concern and confusion within the debate over the foundations of quantum mechanics. The present paper tackles the problem by a nonrelativistic approach based on conformal differential geometry applied to the solution of the dynamical problem of two entangled spin 1/2 particles. It is found that the quantum nonlocality may be understood on the basis of a conformal quantum geometrodynamics acting necessarily on the full "configuration space" of the entangled particles. At the end, the violation of the Bell inequalities is demonstrated without making recourse to the common nonlocality paradigm.

  7. New Galerkin operational matrices for solving Lane-Emden type equations

    NASA Astrophysics Data System (ADS)

    Abd-Elhameed, W. M.; Doha, E. H.; Saad, A. S.; Bassuony, M. A.

    2016-04-01

    Lane-Emden type equations model many phenomena in mathematical physics and astrophysics, such as thermal explosions. This paper is concerned with introducing third and fourth kind Chebyshev-Galerkin operational matrices in order to solve such problems. The principal idea behind the suggested algorithms is based on converting the linear or nonlinear Lane-Emden problem, through the application of suitable spectral methods, into a system of linear or nonlinear equations in the expansion coefficients, which can be efficiently solved. The main advantage of the proposed algorithm in the linear case is that the resulting linear systems are specially structured, and this of course reduces the computational effort required to solve such systems. As an application, we consider the solar model polytrope with n=3 to show that the suggested solutions in this paper are in good agreement with the numerical results.

  8. Another short and elementary proof of strong subadditivity of quantum entropy

    NASA Astrophysics Data System (ADS)

    Ruskai, Mary Beth

    2007-08-01

    A short and elementary proof of the joint convexity of relative entropy is presented, using nothing beyond linear algebra. The key ingredients are an easily verified integral representation and the strategy used to prove the Cauchy-Schwarz inequality in elementary courses. Several consequences are proved in a way which allows an elementary proof of strong subadditivity in a few more lines. Some expository material on Schwarz inequalities for operators and the Holevo bound for partial measurements is also included.

  9. Community Social Capital, Built Environment, and Income-Based Inequality in Depressive Symptoms Among Older People in Japan: An Ecological Study From the JAGES Project

    PubMed Central

    Takagi, Daisuke; Kondo, Katsunori

    2018-01-01

    Background Although reducing socioeconomic inequalities in depression is necessary, their associated factors have rarely been studied. This study aimed to screen the potential contextual factors associated with income-based inequality in older adults’ depression. Methods Using data from the Japan Gerontological Evaluation Study (JAGES) of 2013, we conducted an ecological study covering 77 communities in Japan. Our measures of socioeconomic inequalities in depression were the slope index of inequalities (SII) and the relative index of inequalities (RII) of the prevalence of depressive symptoms across three income levels. We categorized available community-level factors, including socio-demographic factors, social participation, social relationships, subjective changes in the residential area, and the built environment. These indicators were aggregated from individual responses of 51,962 and 52,958 physically independent men and women, respectively, aged 65 years or more. We performed multiple linear regression analyses to explore factors with statistical significance of a two-tailed P-value less than 0.05. Results Factors associated with shallower gradients in depression for men included higher participation in local activities and reception or provision of social support, which did not show significant association among women. Perceived increases in unemployment and economic inequalities were positively associated with larger inequalities in both genders (P < 0.05). The built environment did not indicate any significant association. Conclusions A community environment fostering social activities and relationships might be associated with smaller income-based inequalities in depression. There is a need for more deterministic studies for planning of effective community interventions to address socioeconomic inequalities in depression. PMID:29093358

  10. Income inequality within urban settings and depressive symptoms among adolescents.

    PubMed

    Pabayo, Roman; Dunn, Erin C; Gilman, Stephen E; Kawachi, Ichiro; Molnar, Beth E

    2016-10-01

    Although recent evidence has shown that area-level income inequality is related to increased risk for depression among adults, few studies have tested this association among adolescents. We analysed the cross-sectional data from a sample of 1878 adolescents living in 38 neighbourhoods participating in the 2008 Boston Youth Survey. Using multilevel linear regression modelling, we: (1) estimated the association between neighbourhood income inequality and depressive symptoms, (2) tested for cross-level interactions between sex and neighbourhood income inequality and (3) examined neighbourhood social cohesion as a mediator of the relationship between income inequality and depressive symptoms. The association between neighbourhood income inequality and depressive symptoms varied significantly by sex, with girls in higher income inequality neighbourhood reporting higher depressive symptom scores, but not boys. Among girls, a unit increase in Gini Z-score was associated with more depressive symptoms (β=0.38, 95% CI 0.28 to 0.47, p=0.01) adjusting for nativity, neighbourhood income, social cohesion, crime and social disorder. There was no evidence that the association between income inequality and depressive symptoms was due to neighbourhood-level differences in social cohesion. The distribution of incomes within an urban area adversely affects adolescent girls' mental health; future work is needed to understand why, as well as to examine in greater depth the potential consequences of inequality for males, which may have been difficult to detect here. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/

  11. Regional income inequality model based on theil index decomposition and weighted variance coeficient

    NASA Astrophysics Data System (ADS)

    Sitepu, H. R.; Darnius, O.; Tambunan, W. N.

    2018-03-01

    Regional income inequality is an important issue in the study on economic development of a certain region. Rapid economic development may not in accordance with people’s per capita income. The method of measuring the regional income inequality has been suggested by many experts. This research used Theil index and weighted variance coefficient in order to measure the regional income inequality. Regional income decomposition which becomes the productivity of work force and their participation in regional income inequality, based on Theil index, can be presented in linear relation. When the economic assumption in j sector, sectoral income value, and the rate of work force are used, the work force productivity imbalance can be decomposed to become the component in sectors and in intra-sectors. Next, weighted variation coefficient is defined in the revenue and productivity of the work force. From the quadrate of the weighted variation coefficient result, it was found that decomposition of regional revenue imbalance could be analyzed by finding out how far each component contribute to regional imbalance which, in this research, was analyzed in nine sectors of economic business.

  12. Robust control of integrated motor-transmission powertrain system over controller area network for automotive applications

    NASA Astrophysics Data System (ADS)

    Zhu, Xiaoyuan; Zhang, Hui; Cao, Dongpu; Fang, Zongde

    2015-06-01

    Integrated motor-transmission (IMT) powertrain system with directly coupled motor and gearbox is a good choice for electric commercial vehicles (e.g., pure electric buses) due to its potential in motor size reduction and energy efficiency improvement. However, the controller design for powertrain oscillation damping becomes challenging due to the elimination of damping components. On the other hand, as controller area network (CAN) is commonly adopted in modern vehicle system, the network-induced time-varying delays that caused by bandwidth limitation will further lead to powertrain vibration or even destabilize the powertrain control system. Therefore, in this paper, a robust energy-to-peak controller is proposed for the IMT powertrain system to address the oscillation damping problem and also attenuate the external disturbance. The control law adopted here is based on a multivariable PI control, which ensures the applicability and performance of the proposed controller in engineering practice. With the linearized delay uncertainties characterized by polytopic inclusions, a delay-free closed-loop augmented system is established for the IMT powertrain system under discrete-time framework. The proposed controller design problem is then converted to a static output feedback (SOF) controller design problem where the feedback control gains are obtained by solving a set of linear matrix inequalities (LMIs). The effectiveness as well as robustness of the proposed controller is demonstrated by comparing its performance against that of a conventional PI controller.

  13. Stationary bound-state massive scalar field configurations supported by spherically symmetric compact reflecting stars

    NASA Astrophysics Data System (ADS)

    Hod, Shahar

    2017-12-01

    It has recently been demonstrated that asymptotically flat neutral reflecting stars are characterized by an intriguing no-hair property. In particular, it has been proved that these horizonless compact objects cannot support spatially regular static matter configurations made of scalar (spin-0) fields, vector (spin-1) fields and tensor (spin-2) fields. In the present paper we shall explicitly prove that spherically symmetric compact reflecting stars can support stationary (rather than static) bound-state massive scalar fields in their exterior spacetime regions. To this end, we solve analytically the Klein-Gordon wave equation for a linearized scalar field of mass μ and proper frequency ω in the curved background of a spherically symmetric compact reflecting star of mass M and radius R_{ {s}}. It is proved that the regime of existence of these stationary composed star-field configurations is characterized by the simple inequalities 1-2M/R_{ {s}}<(ω /μ )^2<1. Interestingly, in the regime M/R_{ {s}}≪ 1 of weakly self-gravitating stars we derive a remarkably compact analytical equation for the discrete spectrum {ω (M,R_{ {s}},μ )}^{n=∞}_{n=1} of resonant oscillation frequencies which characterize the stationary composed compact-reflecting-star-linearized-massive-scalar-field configurations. Finally, we verify the accuracy of the analytically derived resonance formula of the composed star-field configurations with direct numerical computations.

  14. Early-life income inequality and adolescent health and well-being.

    PubMed

    Elgar, Frank J; Gariépy, Geneviève; Torsheim, Torbjørn; Currie, Candace

    2017-02-01

    A prevailing hypothesis about the association between income inequality and poor health is that inequality intensifies social hierarchies, increases stress, erodes social and material resources that support health, and subsequently harms health. However, the evidence in support of this hypothesis is limited by cross-sectional, ecological studies and a scarcity of developmental studies. To address this limitation, we used pooled, multilevel data from the Health Behaviour in School-aged Children study to examine lagged, cumulative, and trajectory associations between early-life income inequality and adolescent health and well-being. Psychosomatic symptoms and life satisfaction were assessed in surveys of 11- to 15-year-olds in 40 countries between 1994 and 2014. We linked these data to national Gini indices of income inequality for every life year from 1979 to 2014. The results showed that exposure to income inequality from 0 to 4 years predicted psychosomatic symptoms and lower life satisfaction in females after controlling lifetime mean income inequality, national per capita income, family affluence, age, and cohort and period effects. The cumulative income inequality exposure in infancy and childhood (i.e., average Gini index from birth to age 10) related to lower life satisfaction in female adolescents but not to symptoms. Finally, individual trajectories in early-life inequality (i.e., linear slopes in Gini indices from birth to 10 years) related to fewer symptoms and higher life satisfaction in females, indicating that earlier exposures mattered more to predicting health and wellbeing. No such associations with early-life income inequality were found in males. These results help to establish the antecedent-consequence conditions in the association between income inequality and health and suggest that both the magnitude and timing of income inequality in early life have developmental consequences that manifest in reduced health and well-being in adolescent girls. Copyright © 2016 Elsevier Ltd. All rights reserved.

  15. Finite-time stability of neutral-type neural networks with random time-varying delays

    NASA Astrophysics Data System (ADS)

    Ali, M. Syed; Saravanan, S.; Zhu, Quanxin

    2017-11-01

    This paper is devoted to the finite-time stability analysis of neutral-type neural networks with random time-varying delays. The randomly time-varying delays are characterised by Bernoulli stochastic variable. This result can be extended to analysis and design for neutral-type neural networks with random time-varying delays. On the basis of this paper, we constructed suitable Lyapunov-Krasovskii functional together and established a set of sufficient linear matrix inequalities approach to guarantee the finite-time stability of the system concerned. By employing the Jensen's inequality, free-weighting matrix method and Wirtinger's double integral inequality, the proposed conditions are derived and two numerical examples are addressed for the effectiveness of the developed techniques.

  16. Exponential H(infinity) synchronization of general discrete-time chaotic neural networks with or without time delays.

    PubMed

    Qi, Donglian; Liu, Meiqin; Qiu, Meikang; Zhang, Senlin

    2010-08-01

    This brief studies exponential H(infinity) synchronization of a class of general discrete-time chaotic neural networks with external disturbance. On the basis of the drive-response concept and H(infinity) control theory, and using Lyapunov-Krasovskii (or Lyapunov) functional, state feedback controllers are established to not only guarantee exponential stable synchronization between two general chaotic neural networks with or without time delays, but also reduce the effect of external disturbance on the synchronization error to a minimal H(infinity) norm constraint. The proposed controllers can be obtained by solving the convex optimization problems represented by linear matrix inequalities. Most discrete-time chaotic systems with or without time delays, such as Hopfield neural networks, cellular neural networks, bidirectional associative memory networks, recurrent multilayer perceptrons, Cohen-Grossberg neural networks, Chua's circuits, etc., can be transformed into this general chaotic neural network to be H(infinity) synchronization controller designed in a unified way. Finally, some illustrated examples with their simulations have been utilized to demonstrate the effectiveness of the proposed methods.

  17. An LMI approach to design H(infinity) controllers for discrete-time nonlinear systems based on unified models.

    PubMed

    Liu, Meiqin; Zhang, Senlin

    2008-10-01

    A unified neural network model termed standard neural network model (SNNM) is advanced. Based on the robust L(2) gain (i.e. robust H(infinity) performance) analysis of the SNNM with external disturbances, a state-feedback control law is designed for the SNNM to stabilize the closed-loop system and eliminate the effect of external disturbances. The control design constraints are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms (e.g. interior-point algorithms) to determine the control law. Most discrete-time recurrent neural network (RNNs) and discrete-time nonlinear systems modelled by neural networks or Takagi and Sugeno (T-S) fuzzy models can be transformed into the SNNMs to be robust H(infinity) performance analyzed or robust H(infinity) controller synthesized in a unified SNNM's framework. Finally, some examples are presented to illustrate the wide application of the SNNMs to the nonlinear systems, and the proposed approach is compared with related methods reported in the literature.

  18. Adaptive nonlinear robust relative pose control of spacecraft autonomous rendezvous and proximity operations.

    PubMed

    Sun, Liang; Huo, Wei; Jiao, Zongxia

    2017-03-01

    This paper studies relative pose control for a rigid spacecraft with parametric uncertainties approaching to an unknown tumbling target in disturbed space environment. State feedback controllers for relative translation and relative rotation are designed in an adaptive nonlinear robust control framework. The element-wise and norm-wise adaptive laws are utilized to compensate the parametric uncertainties of chaser and target spacecraft, respectively. External disturbances acting on two spacecraft are treated as a lumped and bounded perturbation input for system. To achieve the prescribed disturbance attenuation performance index, feedback gains of controllers are designed by solving linear matrix inequality problems so that lumped disturbance attenuation with respect to the controlled output is ensured in the L 2 -gain sense. Moreover, in the absence of lumped disturbance input, asymptotical convergence of relative pose are proved by using the Lyapunov method. Numerical simulations are performed to show that position tracking and attitude synchronization are accomplished in spite of the presence of couplings and uncertainties. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

  19. Switching control of an R/C hovercraft: stabilization and smooth switching.

    PubMed

    Tanaka, K; Iwasaki, M; Wang, H O

    2001-01-01

    This paper presents stable switching control of an radio-controlled (R/C) hovercraft that is a nonholonomic (nonlinear) system. To exactly represent its nonlinear dynamics, more importantly, to maintain controllability of the system, we newly propose a switching fuzzy model that has locally Takagi-Sugeno (T-S) fuzzy models and switches them according to states, external variables, and/or time. A switching fuzzy controller is constructed by mirroring the rule structure of the switching fuzzy model of an R/C hovercraft. We derive linear matrix inequality (LMI) conditions for ensuring the stability of the closed-loop system consisting of a switching fuzzy model and controller. Furthermore, to guarantee smooth switching of control input at switching boundaries, we also derive a smooth switching condition represented in terms of LMIs. A stable switching fuzzy controller satisfying the smooth switching condition is designed by simultaneously solving both of the LMIs. The simulation and experimental results for the trajectory control of an R/C hovercraft show the validity of the switching fuzzy model and controller design, particularly, the smooth switching condition.

  20. Quadcopter Path Following Control Design Using Output Feedback with Command Generator Tracker LOS Based At Square Path

    NASA Astrophysics Data System (ADS)

    Nugraha, A. T.; Agustinah, T.

    2018-01-01

    Quadcopter an unstable system, underactuated and nonlinear in quadcopter control research developments become an important focus of attention. In this study, following the path control method for position on the X and Y axis, used structure-Generator Tracker Command (CGT) is tested. Attitude control and position feedback quadcopter is compared using the optimal output. The addition of the H∞ performance optimal output feedback control is used to maintain the stability and robustness of quadcopter. Iterative numerical techniques Linear Matrix Inequality (LMI) is used to find the gain controller. The following path control problems is solved using the method of LQ regulators with output feedback. Simulations show that the control system can follow the paths that have been defined in the form of a reference signal square shape. The result of the simulation suggest that the method which used can bring the yaw angle at the expected value algorithm. Quadcopter can do automatically following path with cross track error mean X=0.5 m and Y=0.2 m.

  1. Robust iterative learning control for multi-phase batch processes: an average dwell-time method with 2D convergence indexes

    NASA Astrophysics Data System (ADS)

    Wang, Limin; Shen, Yiteng; Yu, Jingxian; Li, Ping; Zhang, Ridong; Gao, Furong

    2018-01-01

    In order to cope with system disturbances in multi-phase batch processes with different dimensions, a hybrid robust control scheme of iterative learning control combined with feedback control is proposed in this paper. First, with a hybrid iterative learning control law designed by introducing the state error, the tracking error and the extended information, the multi-phase batch process is converted into a two-dimensional Fornasini-Marchesini (2D-FM) switched system with different dimensions. Second, a switching signal is designed using the average dwell-time method integrated with the related switching conditions to give sufficient conditions ensuring stable running for the system. Finally, the minimum running time of the subsystems and the control law gains are calculated by solving the linear matrix inequalities. Meanwhile, a compound 2D controller with robust performance is obtained, which includes a robust extended feedback control for ensuring the steady-state tracking error to converge rapidly. The application on an injection molding process displays the effectiveness and superiority of the proposed strategy.

  2. Dilemma over the Issue of Inequality: A Strategy against Political Apathy ("Politikverdrossenheit")

    ERIC Educational Resources Information Center

    Schnebel, Karin

    2016-01-01

    Politics is inseparable from conflict. But we often have the idea that the political process has to simply "solve" conflicts and in so doing make the conflict disappear. And because the politicians are not able to do this and instead simply continue arguing, we get the impression that we have incompetent politicians, whom we cannot…

  3. An evolution infinity Laplace equation modelling dynamic elasto-plastic torsion

    NASA Astrophysics Data System (ADS)

    Messelmi, Farid

    2017-12-01

    We consider in this paper a parabolic partial differential equation involving the infinity Laplace operator and a Leray-Lions operator with no coercitive assumption. We prove the existence and uniqueness of the corresponding approached problem and we show that at the limit the solution solves the parabolic variational inequality arising in the elasto-plastic torsion problem.

  4. Sensitivities to Early Exchange in Synchronous Computer-Supported Collaborative Learning (CSCL) Groups

    ERIC Educational Resources Information Center

    Kapur, Manu; Voiklis, John; Kinzer, Charles K.

    2008-01-01

    This study reports the impact of high sensitivity to early exchange in 11th-grade, CSCL triads solving well- and ill-structured problems in Newtonian Kinematics. A mixed-method analysis of the evolution of participation inequity (PI) in group discussions suggested that participation levels tended to get locked-in relatively early on in the…

  5. Can violations of Bell's inequalities be considered as a final proof of quantum physics?

    NASA Astrophysics Data System (ADS)

    Hénault, François

    2013-10-01

    Nowadays, it is commonly admitted that the experimental violation of Bell's inequalities that was successfully demonstrated in the last decades by many experimenters, are indeed the ultimate proof of quantum physics and of its ability to describe the whole microscopic world and beyond. But the historical and scientific story may not be envisioned so clearly: it starts with the original paper of Einstein, Podolsky and Rosen (EPR) aiming at demonstrating that the formalism of quantum theory is incomplete. It then goes through the works of D. Bohm, to finally proceed to the famous John Bell's relationships providing an experimental setup to solve the EPR paradox. In this communication is proposed an alternative reading of this history, showing that modern experiments based on correlations between light polarizations significantly deviate from the original spirit of the EPR paper. It is concluded that current experimental violations of Bell's inequalities cannot be considered as an ultimate proof of the completeness of quantum physics models.

  6. Storytelling in Community Intervention Research: Lessons Learned From the Walk Your Heart to Health Intervention

    PubMed Central

    LeBron, Alana M. W.; Schulz, Amy J.; Bernal, Cristina; Gamboa, Cindy; Wright, Conja; Sand, Sharon; Valerio, Melissa; Caver, Deanna

    2015-01-01

    Background Contextually and culturally congruent interventions are urgently needed to reduce racial, ethnic, and socio economic inequities in physical activity and cardiovascular disease. Objectives To examine a community-based participatory research (CBPR) process that incorporated storytelling into a physical activity intervention, and consider implications for reducing health inequities. Methods We used a CBPR process to incorporate storytelling in an existing walking group intervention. Stories conveyed social support and problem-solving intervention themes designed to maintain increases in physical activity over time, and were adapted to the walking group context, group dynamics, challenges, and traditions. Lessons Learned After describing of the CBPR process used to adapt stories to walking group sites, we discuss challenges and lessons learned regarding the adaptation and implementation of stories to convey key intervention themes. Conclusions A CBPR approach to incorporating storytelling to convey intervention themes offers an innovative and flexible strategy to promote health toward the elimination of health inequities. PMID:25727980

  7. Impact of income inequality on life expectancy in a highly unequal developing country: the case of Brazil.

    PubMed

    Rasella, Davide; Aquino, Rosana; Barreto, Mauricio Lima

    2013-08-01

    Few studies have analysed the effects of income inequality on health in developing countries, particularly during economic growth, reduction of social disparities and reinforcement of the welfare and healthcare system. We evaluated the association between income inequality and life expectancy in Brazil, including the effect of social and health interventions, in the period 2000-2009. A panel dataset was created for the 27 Brazilian states over the referred time period. Multivariable linear regressions were performed using fixed-effects estimation with heteroscedasticity and serial correlation robust SEs. Models were fitted for life expectancy as a dependent variable, using the Gini index or a percentile income dispersion ratio as the main independent variable, and for demographic, socioeconomic and healthcare-related determinants as covariates. The Gini index, as the other measure of income inequality, was negatively associated with life expectancy (p<0.05), even after adjustment for all the socioeconomic and health-related covariates. The Family Health Program, the main primary healthcare (PHC) programme of the country, was positively associated with life expectancy (p<0.05). In recent years, effective social policies have enabled Brazil to partially reduce absolute poverty and income inequality, contributing-together with PHC-to decreasing death rates in the population. Reducing income inequality may represent an important step towards improving health and increasing life expectancy, particularly in developing countries where inequalities are high.

  8. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Gearhart, Jared Lee; Adair, Kristin Lynn; Durfee, Justin David.

    When developing linear programming models, issues such as budget limitations, customer requirements, or licensing may preclude the use of commercial linear programming solvers. In such cases, one option is to use an open-source linear programming solver. A survey of linear programming tools was conducted to identify potential open-source solvers. From this survey, four open-source solvers were tested using a collection of linear programming test problems and the results were compared to IBM ILOG CPLEX Optimizer (CPLEX) [1], an industry standard. The solvers considered were: COIN-OR Linear Programming (CLP) [2], [3], GNU Linear Programming Kit (GLPK) [4], lp_solve [5] and Modularmore » In-core Nonlinear Optimization System (MINOS) [6]. As no open-source solver outperforms CPLEX, this study demonstrates the power of commercial linear programming software. CLP was found to be the top performing open-source solver considered in terms of capability and speed. GLPK also performed well but cannot match the speed of CLP or CPLEX. lp_solve and MINOS were considerably slower and encountered issues when solving several test problems.« less

  9. Geochemical mole-balance modeling with uncertain data

    USGS Publications Warehouse

    Parkhurst, David L.

    1997-01-01

    Geochemical mole-balance models are sets of chemical reactions that quantitatively account for changes in the chemical and isotopic composition of water along a flow path. A revised mole-balance formulation that includes an uncertainty term for each chemical and isotopic datum is derived. The revised formulation is comprised of mole-balance equations for each element or element redox state, alkalinity, electrons, solvent water, and each isotope; a charge-balance equation and an equation that relates the uncertainty terms for pH, alkalinity, and total dissolved inorganic carbon for each aqueous solution; inequality constraints on the size of the uncertainty terms; and inequality constraints on the sign of the mole transfer of reactants. The equations and inequality constraints are solved by a modification of the simplex algorithm combined with an exhaustive search for unique combinations of aqueous solutions and reactants for which the equations and inequality constraints can be solved and the uncertainty terms minimized. Additional algorithms find only the simplest mole-balance models and determine the ranges of mixing fractions for each solution and mole transfers for each reactant that are consistent with specified limits on the uncertainty terms. The revised formulation produces simpler and more robust mole-balance models and allows the significance of mixing fractions and mole transfers to be evaluated. In an example from the central Oklahoma aquifer, inclusion of up to 5% uncertainty in the chemical data can reduce the number of reactants in mole-balance models from seven or more to as few as three, these being cation exchange, dolomite dissolution, and silica precipitation. In another example from the Madison aquifer, inclusion of the charge-balance constraint requires significant increases in the mole transfers of calcite, dolomite, and organic matter, which reduce the estimated maximum carbon 14 age of the sample by about 10,000 years, from 22,700 years to 12,600 years.

  10. Basic Research in the Mathematical Foundations of Stability Theory, Control Theory and Numerical Linear Algebra.

    DTIC Science & Technology

    1979-09-01

    without determinantal divisors, Linear and Multilinear Algebra 7(1979), 107-109. 4. The use of integral operators in number theory (with C. Ryavec and...Gersgorin revisited, to appear in Letters in Linear Algebra. 15. A surprising determinantal inequality for real matrices (with C.R. Johnson), to appear in...Analysis: An Essay Concerning the Limitations of Some Mathematical Methods in the Social , Political and Biological Sciences, David Berlinski, MIT Press

  11. EZLP: An Interactive Computer Program for Solving Linear Programming Problems. Final Report.

    ERIC Educational Resources Information Center

    Jarvis, John J.; And Others

    Designed for student use in solving linear programming problems, the interactive computer program described (EZLP) permits the student to input the linear programming model in exactly the same manner in which it would be written on paper. This report includes a brief review of the development of EZLP; narrative descriptions of program features,…

  12. Optimization-Based Robust Nonlinear Control

    DTIC Science & Technology

    2006-08-01

    ABSTRACT New control algorithms were developed for robust stabilization of nonlinear dynamical systems . Novel, linear matrix inequality-based synthesis...was to further advance optimization-based robust nonlinear control design, for general nonlinear systems (especially in discrete time ), for linear...Teel, IEEE Transactions on Control Systems Technology, vol. 14, no. 3, p. 398-407, May 2006. 3. "A unified framework for input-to-state stability in

  13. Robust scalable stabilisability conditions for large-scale heterogeneous multi-agent systems with uncertain nonlinear interactions: towards a distributed computing architecture

    NASA Astrophysics Data System (ADS)

    Manfredi, Sabato

    2016-06-01

    Large-scale dynamic systems are becoming highly pervasive in their occurrence with applications ranging from system biology, environment monitoring, sensor networks, and power systems. They are characterised by high dimensionality, complexity, and uncertainty in the node dynamic/interactions that require more and more computational demanding methods for their analysis and control design, as well as the network size and node system/interaction complexity increase. Therefore, it is a challenging problem to find scalable computational method for distributed control design of large-scale networks. In this paper, we investigate the robust distributed stabilisation problem of large-scale nonlinear multi-agent systems (briefly MASs) composed of non-identical (heterogeneous) linear dynamical systems coupled by uncertain nonlinear time-varying interconnections. By employing Lyapunov stability theory and linear matrix inequality (LMI) technique, new conditions are given for the distributed control design of large-scale MASs that can be easily solved by the toolbox of MATLAB. The stabilisability of each node dynamic is a sufficient assumption to design a global stabilising distributed control. The proposed approach improves some of the existing LMI-based results on MAS by both overcoming their computational limits and extending the applicative scenario to large-scale nonlinear heterogeneous MASs. Additionally, the proposed LMI conditions are further reduced in terms of computational requirement in the case of weakly heterogeneous MASs, which is a common scenario in real application where the network nodes and links are affected by parameter uncertainties. One of the main advantages of the proposed approach is to allow to move from a centralised towards a distributed computing architecture so that the expensive computation workload spent to solve LMIs may be shared among processors located at the networked nodes, thus increasing the scalability of the approach than the network size. Finally, a numerical example shows the applicability of the proposed method and its advantage in terms of computational complexity when compared with the existing approaches.

  14. Socioeconomic Inequalities in Health and Perceived Unmet Needs for Healthcare among the Elderly in Germany

    PubMed Central

    Rommel, Alexander; Schröder, Sara Lena; Fuchs, Judith; Nowossadeck, Enno; Lampert, Thomas

    2017-01-01

    Research into health inequalities in the elderly population of Germany is relatively scarce. This study examines socioeconomic inequalities in health and perceived unmet needs for healthcare and explores the dynamics of health inequalities with age among elderly people in Germany. Data were derived from the Robert Koch Institute’s cross-sectional German Health Update study. The sample was restricted to participants aged 50–85 years (n = 11,811). Socioeconomic status (SES) was measured based on education, (former) occupation, and income. Odds ratios and prevalence differences were estimated using logistic regression and linear probability models, respectively. Our results show that self-reported health problems were more prevalent among men and women with lower SES. The extent of SES-related health inequalities decreased at older ages, predominantly among men. Although the prevalence of perceived unmet needs for healthcare was low overall, low SES was associated with higher perceptions of unmet needs in both sexes and for several kinds of health services. In conclusion, socioeconomic inequalities in health exist in a late working age and early retirement but may narrow at older ages, particularly among men. Socially disadvantaged elderly people perceive greater barriers to accessing healthcare services than those who are better off. PMID:28954436

  15. Can Linear Superiorization Be Useful for Linear Optimization Problems?

    PubMed Central

    Censor, Yair

    2017-01-01

    Linear superiorization considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not necessarily minimal) target function values. The two questions that we set out to explore experimentally are (i) Does linear superiorization provide a feasible point whose linear target function value is lower than that obtained by running the same feasibility-seeking algorithm without superiorization under identical conditions? and (ii) How does linear superiorization fare in comparison with the Simplex method for solving linear programming problems? Based on our computational experiments presented here, the answers to these two questions are: “yes” and “very well”, respectively. PMID:29335660

  16. Krylov subspace methods - Theory, algorithms, and applications

    NASA Technical Reports Server (NTRS)

    Sad, Youcef

    1990-01-01

    Projection methods based on Krylov subspaces for solving various types of scientific problems are reviewed. The main idea of this class of methods when applied to a linear system Ax = b, is to generate in some manner an approximate solution to the original problem from the so-called Krylov subspace span. Thus, the original problem of size N is approximated by one of dimension m, typically much smaller than N. Krylov subspace methods have been very successful in solving linear systems and eigenvalue problems and are now becoming popular for solving nonlinear equations. The main ideas in Krylov subspace methods are shown and their use in solving linear systems, eigenvalue problems, parabolic partial differential equations, Liapunov matrix equations, and nonlinear system of equations are discussed.

  17. Educational inequalities in subjective health in Germany from 1994 to 2014: a trend analysis using the German Socio-Economic Panel study (GSOEP).

    PubMed

    Moor, Irene; Günther, Sebastian; Knöchelmann, Anja; Hoebel, Jens; Pförtner, Timo-Kolja; Lampert, Thomas; Richter, Matthias

    2018-06-08

    As trend studies have shown, health inequalities by income and occupation have widened or remained stable. However, research on time trends in educational inequalities in health in Germany is scarce. The aim of this study is to analyse how educational inequalities in health evolved over a period of 21 years in the middle-aged population in Germany, and whether the trends differ by gender. Data were obtained from the German Socio-Economic Panel covering the period from 1994 to 2014. In total, n=16 339 participants (106 221 person years) aged 30-49 years were included in the study sample. Educational level was measured based on the 'Comparative Analysis of Social Mobility in Industrial Nations' (CASMIN) classification. Health outcomes were self-rated health (SRH) as well as (mental and physical) health-related quality of life (HRQOL, SF-12v2). Absolute Index of Inequality (Slope Index of Inequality (SII)) and Relative Index of Inequality (RII) were calculated using linear and logarithmic regression analyses with robust SEs. Significant educational inequalities in SRH and physical HRQOL were found for almost every survey year from 1994 to 2014. Relative inequalities in SRH ranged from 1.50 to 2.10 in men and 1.25 to 1.87 in women (RII). Regarding physical HRQOL, the lowest educational group yielded 4.5 to 6.6 points (men) and 3.3 to 6.1 points (women) lower scores (SII). Although educational level increased over time, absolute and relative health inequalities remained largely stable over the last 21 years. For mental HRQOL, only few educational inequalities were found. This study found persistent educational inequalities in SRH and physical HRQOL among adults in Germany from 1994 to 2014. Our findings highlight the need to intensify efforts in social and health policies to tackle these persistent inequalities. © Article author(s) (or their employer(s) unless otherwise stated in the text of the article) 2018. All rights reserved. No commercial use is permitted unless otherwise expressly granted.

  18. DOE Office of Scientific and Technical Information (OSTI.GOV)

    Burchett, Deon L.; Chen, Richard Li-Yang; Phillips, Cynthia A.

    This report summarizes the work performed under the project project Next-Generation Algo- rithms for Assessing Infrastructure Vulnerability and Optimizing System Resilience. The goal of the project was to improve mathematical programming-based optimization technology for in- frastructure protection. In general, the owner of a network wishes to design a network a network that can perform well when certain transportation channels are inhibited (e.g. destroyed) by an adversary. These are typically bi-level problems where the owner designs a system, an adversary optimally attacks it, and then the owner can recover by optimally using the remaining network. This project funded three years ofmore » Deon Burchett's graduate research. Deon's graduate advisor, Professor Jean-Philippe Richard, and his Sandia advisors, Richard Chen and Cynthia Phillips, supported Deon on other funds or volunteer time. This report is, therefore. essentially a replication of the Ph.D. dissertation it funded [12] in a format required for project documentation. The thesis had some general polyhedral research. This is the study of the structure of the feasi- ble region of mathematical programs, such as integer programs. For example, an integer program optimizes a linear objective function subject to linear constraints, and (nonlinear) integrality con- straints on the variables. The feasible region without the integrality constraints is a convex polygon. Careful study of additional valid constraints can significantly improve computational performance. Here is the abstract from the dissertation: We perform a polyhedral study of a multi-commodity generalization of variable upper bound flow models. In particular, we establish some relations between facets of single- and multi- commodity models. We then introduce a new family of inequalities, which generalizes traditional flow cover inequalities to the multi-commodity context. We present encouraging numerical results. We also consider the directed edge-failure resilient network design problem (DRNDP). This problem entails the design of a directed multi-commodity flow network that is capable of fulfilling a specified percentage of demands in the event that any G arcs are destroyed, where G is a constant parameter. We present a formulation of DRNDP and solve it in a branch-column-cut framework. We present computational results.« less

  19. Unequal distribution of health human resource in mainland China: what are the determinants from a comprehensive perspective?

    PubMed

    Li, Dan; Zhou, Zhongliang; Si, Yafei; Xu, Yongjian; Shen, Chi; Wang, Yiyang; Wang, Xiao

    2018-02-27

    The inequality of health human resource is a worldwide problem, and solving it also is one of the major goals of China's recent health system reform. Yet there is a huge disparity among cities in mainland China. The aim of this study is to analyze the distribution inequality of the health human resource in 322 prefecture-level cities of mainland China in 2014, and to reveal the facets and causes of the inequalities. The data for this study were acquired from the provincial and municipal Health Statistics Yearbook (2014) and Statistical Yearbook (2014), the municipal National Economic Bulletin (2014), and the official websites of municipal governments, involving 322 prefecture-level cities. Meanwhile, Concentration Index was used to measure the magnitude of the unequal distribution of health human resource. A decomposition analysis was employed to quantify the contribution of each determinant to the total inequality. The overall concentration index of doctors and nurses in mainland China in 2014 was 0.1038 (95% CI = 0.0208, 0.1865) and 0.0785 (95% CI =0.0018, 0.1561). Decomposition of the concentration index revealed that economic status was the primary contributor (58.5% and 57%) to the inequality of doctors and nurses, followed by the Southwest China (19.1% and 18.6%), urbanization level (- 13.1% and - 12.8%), and revenue (8.0% and 7.8%). Party secretaries with Master degree (7.0%, 6.8%), mayors who were 60 years old or above (6.3%, 6.1%) also were proved to be a major contributor to the inequality of health human resource. There was inequality of health human resource distribution which was pro-rich in mainland China in 2014. Economic status of the cities accounted for most of the existing inequality, followed by the Southwest China, urbanization level, revenue, party secretaries with Master degree, and mayors who were 60 years old or above in respective importance. Besides, the party secretaries and mayors also had certain influence on the allocation of health human resource. The tough issue of HHR inequality should be addressed by comprehensive measures from a multidisciplinary perspective.

  20. Income inequality among American states and the incidence of major depression.

    PubMed

    Pabayo, Roman; Kawachi, Ichiro; Gilman, Stephen E

    2014-02-01

    Although cross-sectional and ecological studies have shown that higher area-level income inequality is related to increased risk for depression, few longitudinal studies have been conducted. This investigation examines the relationship between state-level income inequality and major depression among adults participating in a population-based, representative longitudinal study. We used data from the National Epidemiologic Survey on Alcohol and Related Conditions (n=34 653). Respondents completed structured diagnostic interviews at baseline (2001-2002) and follow-up (2004-2005). Weighted multilevel modelling was used to determine if U.S. state-level income inequality (measured by the Gini coefficient) was a significant predictor of depression at baseline and at follow-up, while controlling for individual-level and state-level covariates. We also repeated the longitudinal analyses, excluding those who had a history of depression or at baseline, in order to test whether income inequality was related to incident depression. State-level inequality was associated with increased incidence of depression among women but not men. In comparison to women residing in states belonging to the lowest quintile of income inequality, women were at increased risk for depression in the second (OR=1.18, 95% CI 0.86 to 1.62), third (OR=1.22, 95% CI 0.91 to 1.62), fourth (OR=1.37, 95% CI 1.03 to 1.82) and fifth (OR=1.50, 95% CI 1.14 to 1.96) quintiles at follow-up (p<0.05 for the linear trend). Living in a state with higher income inequality increases the risk for the development of depression among women.

  1. Discrimination, perceived social inequity, and mental health among rural-to-urban migrants in China.

    PubMed

    Lin, Danhua; Li, Xiaoming; Wang, Bo; Hong, Yan; Fang, Xiaoyi; Qin, Xiong; Stanton, Bonita

    2011-04-01

    Status-based discrimination and inequity have been associated with the process of migration, especially with economics-driven internal migration. However, their association with mental health among economy-driven internal migrants in developing countries is rarely assessed. This study examines discriminatory experiences and perceived social inequity in relation to mental health status among rural-to-urban migrants in China. Cross-sectional data were collected from 1,006 rural-to-urban migrants in 2004-2005 in Beijing, China. Participants reported their perceptions and experiences of being discriminated in daily life in urban destination and perceived social inequity. Mental health was measured using the symptom checklist-90 (SCL-90). Multivariate analyses using general linear model were performed to test the effect of discriminatory experience and perceived social inequity on mental health. Experience of discrimination was positively associated with male gender, being married at least once, poorer health status, shorter duration of migration, and middle range of personal income. Likewise, perceived social inequity was associated with poorer health status, higher education attainment, and lower personal income. Multivariate analyses indicate that both experience of discrimination and perceived social inequity were strongly associated with mental health problems of rural-to-urban migrants. Experience of discrimination in daily life and perceived social inequity have a significant influence on mental health among rural-to-urban migrants. The findings underscore the needs to reduce public or societal discrimination against rural-to-urban migrants, to eliminate structural barriers (i.e., dual household registrations) for migrants to fully benefit from the urban economic development, and to create a positive atmosphere to improve migrant's psychological well-being.

  2. Entanglement criteria via the uncertainty relations in su(2) and su(1,1) algebras: Detection of non-Gaussian entangled states

    NASA Astrophysics Data System (ADS)

    Nha, Hyunchul; Kim, Jaewan

    2006-07-01

    We derive a class of inequalities, from the uncertainty relations of the su(1,1) and the su(2) algebra in conjunction with partial transposition, that must be satisfied by any separable two-mode states. These inequalities are presented in terms of the su(2) operators Jx=(a†b+ab†)/2 , Jy=(a†b-ab†)/2i , and the total photon number ⟨Na+Nb⟩ . They include as special cases the inequality derived by Hillery and Zubairy [Phys. Rev. Lett. 96, 050503 (2006)], and the one by Agarwal and Biswas [New J. Phys. 7, 211 (2005)]. In particular, optimization over the whole inequalities leads to the criterion obtained by Agarwal and Biswas. We show that this optimal criterion can detect entanglement for a broad class of non-Gaussian entangled states, i.e., the su(2) minimum-uncertainty states. Experimental schemes to test the optimal criterion are also discussed, especially the one using linear optical devices and photodetectors.

  3. Live Broadcast Classroom: A Feasible Solution for Chinese Rural Weak Education

    ERIC Educational Resources Information Center

    Zhou, Yuxia; Xiong, Ying

    2017-01-01

    Inequity between urban and rural education prevalently exists in China. A lack of qualified teachers is the main reason for disadvantaged education in rural areas. In order to solve this problem, Live Broadcast Classroom was adopted for use in grade 5 English classes. 90 students and 3 teachers of 3 classes from two primary schools in Yunnan…

  4. Solving the "Rural School Problem": New State Aid, Standards, and Supervision of Local Schools, 1900-1933

    ERIC Educational Resources Information Center

    Steffes, Tracy L.

    2008-01-01

    In 1918, Minnesota county superintendent Julius Arp argued that the greatest educational problem facing the American people was the Rural School Problem, saying: "There is no defect more glaring today than the inequality that exists between the educational facilities of the urban and rural communities. Rural education in the United States has…

  5. A duality approach for solving bounded linear programming problems with fuzzy variables based on ranking functions and its application in bounded transportation problems

    NASA Astrophysics Data System (ADS)

    Ebrahimnejad, Ali

    2015-08-01

    There are several methods, in the literature, for solving fuzzy variable linear programming problems (fuzzy linear programming in which the right-hand-side vectors and decision variables are represented by trapezoidal fuzzy numbers). In this paper, the shortcomings of some existing methods are pointed out and to overcome these shortcomings a new method based on the bounded dual simplex method is proposed to determine the fuzzy optimal solution of that kind of fuzzy variable linear programming problems in which some or all variables are restricted to lie within lower and upper bounds. To illustrate the proposed method, an application example is solved and the obtained results are given. The advantages of the proposed method over existing methods are discussed. Also, one application of this algorithm in solving bounded transportation problems with fuzzy supplies and demands is dealt with. The proposed method is easy to understand and to apply for determining the fuzzy optimal solution of bounded fuzzy variable linear programming problems occurring in real-life situations.

  6. Strengthened MILP formulation for certain gas turbine unit commitment problems

    DOE PAGES

    Pan, Kai; Guan, Yongpei; Watson, Jean -Paul; ...

    2015-05-22

    In this study, we derive a strengthened MILP formulation for certain gas turbine unit commitment problems, in which the ramping rates are no smaller than the minimum generation amounts. This type of gas turbines can usually start-up faster and have a larger ramping rate, as compared to the traditional coal-fired power plants. Recently, the number of this type of gas turbines increases significantly due to affordable gas prices and their scheduling flexibilities to accommodate intermittent renewable energy generation. In this study, several new families of strong valid inequalities are developed to help reduce the computational time to solve these typesmore » of problems. Meanwhile, the validity and facet-defining proofs are provided for certain inequalities. Finally, numerical experiments on a modified IEEE 118-bus system and the power system data based on recent studies verify the effectiveness of applying our formulation to model and solve this type of gas turbine unit commitment problems, including reducing the computational time to obtain an optimal solution or obtaining a much smaller optimality gap, as compared to the default CPLEX, when the time limit is reached with no optimal solutions obtained.« less

  7. A Simple Algorithm for the Metric Traveling Salesman Problem

    NASA Technical Reports Server (NTRS)

    Grimm, M. J.

    1984-01-01

    An algorithm was designed for a wire list net sort problem. A branch and bound algorithm for the metric traveling salesman problem is presented for this. The algorithm is a best bound first recursive descent where the bound is based on the triangle inequality. The bounded subsets are defined by the relative order of the first K of the N cities (i.e., a K city subtour). When K equals N, the bound is the length of the tour. The algorithm is implemented as a one page subroutine written in the C programming language for the VAX 11/750. Average execution times for randomly selected planar points using the Euclidean metric are 0.01, 0.05, 0.42, and 3.13 seconds for ten, fifteen, twenty, and twenty-five cities, respectively. Maximum execution times for a hundred cases are less than eleven times the averages. The speed of the algorithms is due to an initial ordering algorithm that is a N squared operation. The algorithm also solves the related problem where the tour does not return to the starting city and the starting and/or ending cities may be specified. It is possible to extend the algorithm to solve a nonsymmetric problem satisfying the triangle inequality.

  8. Contextual Fraction as a Measure of Contextuality.

    PubMed

    Abramsky, Samson; Barbosa, Rui Soares; Mansfield, Shane

    2017-08-04

    We consider the contextual fraction as a quantitative measure of contextuality of empirical models, i.e., tables of probabilities of measurement outcomes in an experimental scenario. It provides a general way to compare the degree of contextuality across measurement scenarios; it bears a precise relationship to violations of Bell inequalities; its value, and a witnessing inequality, can be computed using linear programing; it is monotonic with respect to the "free" operations of a resource theory for contextuality; and it measures quantifiable advantages in informatic tasks, such as games and a form of measurement-based quantum computing.

  9. Contextual Fraction as a Measure of Contextuality

    NASA Astrophysics Data System (ADS)

    Abramsky, Samson; Barbosa, Rui Soares; Mansfield, Shane

    2017-08-01

    We consider the contextual fraction as a quantitative measure of contextuality of empirical models, i.e., tables of probabilities of measurement outcomes in an experimental scenario. It provides a general way to compare the degree of contextuality across measurement scenarios; it bears a precise relationship to violations of Bell inequalities; its value, and a witnessing inequality, can be computed using linear programing; it is monotonic with respect to the "free" operations of a resource theory for contextuality; and it measures quantifiable advantages in informatic tasks, such as games and a form of measurement-based quantum computing.

  10. Chemical Equation Balancing.

    ERIC Educational Resources Information Center

    Blakley, G. R.

    1982-01-01

    Reviews mathematical techniques for solving systems of homogeneous linear equations and demonstrates that the algebraic method of balancing chemical equations is a matter of solving a system of homogeneous linear equations. FORTRAN programs using this matrix method to chemical equation balancing are available from the author. (JN)

  11. Symbolic Solution of Linear Differential Equations

    NASA Technical Reports Server (NTRS)

    Feinberg, R. B.; Grooms, R. G.

    1981-01-01

    An algorithm for solving linear constant-coefficient ordinary differential equations is presented. The computational complexity of the algorithm is discussed and its implementation in the FORMAC system is described. A comparison is made between the algorithm and some classical algorithms for solving differential equations.

  12. On Solving Linear Recurrences

    ERIC Educational Resources Information Center

    Dobbs, David E.

    2013-01-01

    A direct method is given for solving first-order linear recurrences with constant coefficients. The limiting value of that solution is studied as "n to infinity." This classroom note could serve as enrichment material for the typical introductory course on discrete mathematics that follows a calculus course.

  13. Country-level economic disparity and child mortality related to housing and injuries: a study in 26 European countries.

    PubMed

    Sengoelge, Mathilde; Elling, Berty; Laflamme, Lucie; Hasselberg, Marie

    2013-10-01

    Adverse living standards are associated with poorer child health and safety. This study investigates whether adverse housing and neighbourhood conditions contribute to explain country-level associations between a country's economic level and income inequality and child mortality, specifically injury mortality. Ecological, cross-sectional study. Twenty-six European countries were grouped according to two country-level economic measures from Eurostat: gross domestic product (GDP) and income inequality. Adverse country-level housing and neighbourhood conditions were assessed using data from the 2006 European Union Income Social Inclusion and Living Conditions Database (n=203 000). Child mortality incidence rates were derived for children aged 1-14 years for all causes, all injuries, road traffic injuries and unintentional injuries excluding road traffic. Linear regression analysis was applied to measure whether housing or neighbourhood conditions have a significant association with child mortality and whether a strain modified the association between GDP/income inequality and mortality. Country-level income inequality and GDP demonstrated a significant association with child mortality for all outcomes. A significant association was also found between housing strain and all child mortality outcomes, but not for neighbourhood strain. Housing strain partially modified the relationship between income inequality and GDP and all child mortality outcomes, with the exception of income inequality and road traffic injury mortality showing full mediation by housing strain. Adverse housing conditions are a likely pathway in the country-level association between income inequality and economic GDP and child injury mortality.

  14. The Use of Sparse Direct Solver in Vector Finite Element Modeling for Calculating Two Dimensional (2-D) Magnetotelluric Responses in Transverse Electric (TE) Mode

    NASA Astrophysics Data System (ADS)

    Yihaa Roodhiyah, Lisa’; Tjong, Tiffany; Nurhasan; Sutarno, D.

    2018-04-01

    The late research, linear matrices of vector finite element in two dimensional(2-D) magnetotelluric (MT) responses modeling was solved by non-sparse direct solver in TE mode. Nevertheless, there is some weakness which have to be improved especially accuracy in the low frequency (10-3 Hz-10-5 Hz) which is not achieved yet and high cost computation in dense mesh. In this work, the solver which is used is sparse direct solver instead of non-sparse direct solverto overcome the weaknesses of solving linear matrices of vector finite element metod using non-sparse direct solver. Sparse direct solver will be advantageous in solving linear matrices of vector finite element method because of the matrix properties which is symmetrical and sparse. The validation of sparse direct solver in solving linear matrices of vector finite element has been done for a homogen half-space model and vertical contact model by analytical solution. Thevalidation result of sparse direct solver in solving linear matrices of vector finite element shows that sparse direct solver is more stable than non-sparse direct solver in computing linear problem of vector finite element method especially in low frequency. In the end, the accuracy of 2D MT responses modelling in low frequency (10-3 Hz-10-5 Hz) has been reached out under the efficient allocation memory of array and less computational time consuming.

  15. Ethics and governance of global health inequalities

    PubMed Central

    Ruger, J P

    2006-01-01

    Background A world divided by health inequalities poses ethical challenges for global health. International and national responses to health disparities must be rooted in ethical values about health and its distribution; this is because ethical claims have the power to motivate, delineate principles, duties and responsibilities, and hold global and national actors morally responsible for achieving common goals. Theories of justice are necessary to define duties and obligations of institutions and actors in reducing inequalities. The problem is the lack of a moral framework for solving problems of global health justice. Aim To study why global health inequalities are morally troubling, why efforts to reduce them are morally justified, how they should be measured and evaluated; how much priority disadvantaged groups should receive; and to delineate roles and responsibilities of national and international actors and institutions. Discussion and conclusions Duties and obligations of international and state actors in reducing global health inequalities are outlined. The ethical principles endorsed include the intrinsic value of health to well‐being and equal respect for all human life, the importance of health for individual and collective agency, the concept of a shortfall from the health status of a reference group, and the need for a disproportionate effort to help disadvantaged groups. This approach does not seek to find ways in which global and national actors address global health inequalities by virtue of their self‐interest, national interest, collective security or humanitarian assistance. It endorses the more robust concept of “human flourishing” and the desire to live in a world where all people have the capability to be healthy. Unlike cosmopolitan theory, this approach places the role of the nation‐state in the forefront with primary, though not sole, moral responsibility. Rather shared health governance is essential for delivering health equity on a global scale. PMID:17053290

  16. Are some areas more equal than others? Socioeconomic inequality in potentially avoidable emergency hospital admissions within English local authority areas.

    PubMed

    Sheringham, Jessica; Asaria, Miqdad; Barratt, Helen; Raine, Rosalind; Cookson, Richard

    2017-04-01

    Objectives Reducing health inequalities is an explicit goal of England's health system. Our aim was to compare the performance of English local administrative areas in reducing socioeconomic inequality in emergency hospital admissions for ambulatory care sensitive chronic conditions. Methods We used local authority area as a stable proxy for health and long-term care administrative geography between 2004/5 and 2011/12. We linked inpatient hospital activity, deprivation, primary care, and population data to small area neighbourhoods (typical population 1500) within administrative areas (typical population 250,000). We measured absolute inequality gradients nationally and within each administrative area using neighbourhood-level linear models of the relationship between national deprivation and age-sex-adjusted emergency admission rates. We assessed local equity performance by comparing local inequality against national inequality to identify areas significantly more or less equal than expected; evaluated stability over time; and identified where equity performance was steadily improving or worsening. We then examined associations between change in socioeconomic inequalities and change in within-area deprivation (gentrification). Finally, we used administrative area-level random and fixed effects models to examine the contribution of primary care to inequalities in admissions. Results Data on 316 administrative areas were included in the analysis. Local inequalities were fairly stable between consecutive years, but 32 areas (10%) showed steadily improving or worsening equity. In the 21 improving areas, the gap between most and least deprived fell by 3.9 admissions per 1000 (six times the fall nationally) between 2004/5 and 2011/12, while in the 11 areas worsening, the gap widened by 2.4. There was no indication that measured improvements in local equity were an artefact of gentrification or that changes in primary care supply or quality contributed to changes in inequality. Conclusions Local equity performance in reducing inequality in emergency admissions varies both geographically and over time. Identifying this variation could provide insights into which local delivery strategies are most effective in reducing such inequalities.

  17. Identifying Determinants of Socioeconomic Inequality in Health Service Utilization among Patients with Chronic Non-Communicable Diseases in China

    PubMed Central

    Wu, Qunhong; Hao, Yanhua; Ning, Ning; Xu, Ling; Liu, Chaojie; Li, Ye; Kang, Zheng; Liu, Guoxiang

    2014-01-01

    Background People with chronic non-communicable diseases (NCD) are particularly vulnerable to socioeconomic inequality due to their long-term expensive health needs. This study aimed to assess socioeconomic-related inequality in health service utilization among NCD patients in China and to analyze factors associated with this disparity. Methods Data were taken from the 2008 Chinese National Health Survey, in which a multiple stage stratified random sampling method was employed to survey 56,456 households. We analyzed the distribution of actual use, need-expected use, and need-standardized usage of outpatient services (over a two-week period) and inpatient services (over one-year) across different income groups in 27,233 adult respondents who reported as having a NCD. We used a concentration index to measure inequality in the distribution of health services, which was expressed as HI (Horizontal Inequity Index) for need-standardized use of services. A non-linear probit regression model was employed to detect inequality across socio-economic groups. Results Pro-rich inequity in health services among NCD patients was more substantial than the average population. A higher degree of pro-rich inequity (HI = 0.253) was found in inpatient services compared to outpatient services (HI = 0.089). Despite a greater need for health services amongst those of lower socio-economic status, their actual use is much less than their more affluent counterparts. Health service underuse by the poor and overuse by the affluent are evident. Household income disparity was the greatest inequality factor in NCD service use for both outpatients (71.3%) and inpatients (108%), more so than health insurance policies. Some medical insurance schemes, such as the MIUE, actually made a pro-rich contribution to health service inequality (16.1% for outpatient and 12.1% for inpatient). Conclusions Inequality in health services amongst NCD patients in China remains largely determined by patient financial capability. The current insurance schemes are insufficient to address this inequity. A comprehensive social policy that encompasses a more progressive taxation package and redistribution of social capital as well as pro-poor welfare is needed. PMID:24960168

  18. Identifying determinants of socioeconomic inequality in health service utilization among patients with chronic non-communicable diseases in China.

    PubMed

    Xie, Xin; Wu, Qunhong; Hao, Yanhua; Yin, Hui; Fu, Wenqi; Ning, Ning; Xu, Ling; Liu, Chaojie; Li, Ye; Kang, Zheng; He, Changzhi; Liu, Guoxiang

    2014-01-01

    People with chronic non-communicable diseases (NCD) are particularly vulnerable to socioeconomic inequality due to their long-term expensive health needs. This study aimed to assess socioeconomic-related inequality in health service utilization among NCD patients in China and to analyze factors associated with this disparity. Data were taken from the 2008 Chinese National Health Survey, in which a multiple stage stratified random sampling method was employed to survey 56,456 households. We analyzed the distribution of actual use, need-expected use, and need-standardized usage of outpatient services (over a two-week period) and inpatient services (over one-year) across different income groups in 27,233 adult respondents who reported as having a NCD. We used a concentration index to measure inequality in the distribution of health services, which was expressed as HI (Horizontal Inequity Index) for need-standardized use of services. A non-linear probit regression model was employed to detect inequality across socio-economic groups. Pro-rich inequity in health services among NCD patients was more substantial than the average population. A higher degree of pro-rich inequity (HI = 0.253) was found in inpatient services compared to outpatient services (HI = 0.089). Despite a greater need for health services amongst those of lower socio-economic status, their actual use is much less than their more affluent counterparts. Health service underuse by the poor and overuse by the affluent are evident. Household income disparity was the greatest inequality factor in NCD service use for both outpatients (71.3%) and inpatients (108%), more so than health insurance policies. Some medical insurance schemes, such as the MIUE, actually made a pro-rich contribution to health service inequality (16.1% for outpatient and 12.1% for inpatient). Inequality in health services amongst NCD patients in China remains largely determined by patient financial capability. The current insurance schemes are insufficient to address this inequity. A comprehensive social policy that encompasses a more progressive taxation package and redistribution of social capital as well as pro-poor welfare is needed.

  19. Are some areas more equal than others? Socioeconomic inequality in potentially avoidable emergency hospital admissions within English local authority areas

    PubMed Central

    Asaria, Miqdad; Barratt, Helen; Raine, Rosalind; Cookson, Richard

    2016-01-01

    Objectives Reducing health inequalities is an explicit goal of England’s health system. Our aim was to compare the performance of English local administrative areas in reducing socioeconomic inequality in emergency hospital admissions for ambulatory care sensitive chronic conditions. Methods We used local authority area as a stable proxy for health and long-term care administrative geography between 2004/5 and 2011/12. We linked inpatient hospital activity, deprivation, primary care, and population data to small area neighbourhoods (typical population 1500) within administrative areas (typical population 250,000). We measured absolute inequality gradients nationally and within each administrative area using neighbourhood-level linear models of the relationship between national deprivation and age–sex-adjusted emergency admission rates. We assessed local equity performance by comparing local inequality against national inequality to identify areas significantly more or less equal than expected; evaluated stability over time; and identified where equity performance was steadily improving or worsening. We then examined associations between change in socioeconomic inequalities and change in within-area deprivation (gentrification). Finally, we used administrative area-level random and fixed effects models to examine the contribution of primary care to inequalities in admissions. Results Data on 316 administrative areas were included in the analysis. Local inequalities were fairly stable between consecutive years, but 32 areas (10%) showed steadily improving or worsening equity. In the 21 improving areas, the gap between most and least deprived fell by 3.9 admissions per 1000 (six times the fall nationally) between 2004/5 and 2011/12, while in the 11 areas worsening, the gap widened by 2.4. There was no indication that measured improvements in local equity were an artefact of gentrification or that changes in primary care supply or quality contributed to changes in inequality. Conclusions Local equity performance in reducing inequality in emergency admissions varies both geographically and over time. Identifying this variation could provide insights into which local delivery strategies are most effective in reducing such inequalities. PMID:28429977

  20. A review on classification methods for solving fully fuzzy linear systems

    NASA Astrophysics Data System (ADS)

    Daud, Wan Suhana Wan; Ahmad, Nazihah; Aziz, Khairu Azlan Abd

    2015-12-01

    Fully Fuzzy Linear System (FFLS) exists when there are fuzzy numbers on both sides of the linear systems. This system is quite significant today since most of the linear systems play with uncertainties of parameters especially in mathematics, engineering and finance. Many researchers and practitioners used the FFLS to model their problem and they apply various methods to solve it. In this paper, we present the outcome of a comprehensive review that we have done on various methods used for solving the FFLS. We classify our findings based on parameters' type used for the FFLS either restricted or unrestricted. We also discuss some of the methods by illustrating numerical examples and identify the differences between the methods. Ultimately, we summarize all findings in a table. We hope this study will encourage researchers to appreciate the use of this method and with that it will be easier for them to choose the right method or to propose any new method for solving the FFLS.

  1. Impact of Income Inequality on the Nation's Health.

    PubMed

    López, Diego B; Loehrer, Andrew P; Chang, David C

    2016-10-01

    Income inequality in the United States has been increasing in recent decades. It is unclear whether income inequality has an independent effect on health outcomes, or whether it simply correlates with increasing levels of poverty. The goal of this study was to evaluate whether income inequality is significantly associated with US county health care expenditures and health care use. Cross-sectional analysis of county health expenditure data from the Health Resources and Services Administration's Area Resources File, county income inequality measures (Gini coefficient) from the Census' American Community Survey, and estimates of potentially preventable admissions and potentially discretionary procedures from the Nationwide Inpatient Sample (1998 to 2011). Datasets were linked via county Federal Information Processing Standard codes. Multivariable linear and Poisson regression analyses were performed at the county level adjusting for county characteristics. A total of 1,237 counties (of 3,144) were included. Income inequality was associated with higher health care expenditures, with each 1 percentage-point increase in county Gini coefficient associated with a US$40,008 increase in annual county Medicare cost (p = 0.003), and an increase of 174.7 total county Medicare inpatient days per year (p < 0.001). Even after accounting for poverty level and county characteristics, counties with higher inequality had higher potentially preventable admission (eg 4.86 rate ratio for low-birth-weight hospital admissions in the top income inequality quartile compared with bottom quartile; p < 0.001) and a higher incidence of potentially discretionary procedures (eg 1.79 rate ratio for prostatectomy for benign prostatic hyperplasia in the top income inequality quartile compared with bottom quartile; p < 0.001). Income inequality is independently associated with higher health care expenditures and more health care use, with increases in both potentially discretionary procedures and in potentially preventable admissions. Copyright © 2016 American College of Surgeons. Published by Elsevier Inc. All rights reserved.

  2. Obesity in Scotland: a persistent inequality.

    PubMed

    Tod, Elaine; Bromley, Catherine; Millard, Andrew D; Boyd, Allan; Mackie, Phil; McCartney, Gerry

    2017-07-27

    Obesity is a health problem in its own right and a risk factor for other conditions such as cardiovascular disease. The prevalence of overweight and obesity increased in Scotland between 1995 and 2008 with socio-economic inequalities persisting in adults over time and increasing in children. This paper explores changes in the underlying distribution of body mass index (BMI) which is less well understood. Using data from the Scottish Health Survey (SHeS) between 1995 and 2014 for adults aged 18-64 years, we calculated population distributions for BMI for the population overall, and for age, sex and deprivation strata. We used SHeS data for children aged 2-15 years between 1998 and 2014, in addition to data from the Child Health Systems Programme (CHSP) collected from primary one (P1) children in participating local authorities, to describe the overall trends and to compare trends in inequalities by deprivation strata. Amongst adults, the BMI distribution shifted upwards, with a large proportion of the population gaining a small amount of weight between 1995 and 2008 before subsequently stabilising across the distribution. In men the prevalence of obesity showed a linear deprivation gradient in 1995 but over time obesity declined in the least deprived quintile while the remaining four quintiles converged (and stabilised). In contrast, a persistent and generally linear gradient is evident among women for most of the 1995-2014 period. For those aged 2-15 years, obesity increased between 1998 and 2014 for the most deprived 40% of children contrasted with stable trends for the least deprived. The surveillance data for P1 children in Scotland showed a persistent inequality between 2005/06 and 2014/15 though it was less clear if this is widening. The BMI distribution for adults increased between 1995 and 2008 with a large proportion of the population gaining a small amount of weight before stabilising across the distribution. Inequalities in obesity persist for adults (with different underlying patterns evident for men and women), and may be widening for children. Actions to reduce the obesogenic environment, including structural changes not dependent on individual agency, are urgently needed if the long-term health, social and inequality consequences of obesity are to be reduced.

  3. Can linear superiorization be useful for linear optimization problems?

    NASA Astrophysics Data System (ADS)

    Censor, Yair

    2017-04-01

    Linear superiorization (LinSup) considers linear programming problems but instead of attempting to solve them with linear optimization methods it employs perturbation resilient feasibility-seeking algorithms and steers them toward reduced (not necessarily minimal) target function values. The two questions that we set out to explore experimentally are: (i) does LinSup provide a feasible point whose linear target function value is lower than that obtained by running the same feasibility-seeking algorithm without superiorization under identical conditions? (ii) How does LinSup fare in comparison with the Simplex method for solving linear programming problems? Based on our computational experiments presented here, the answers to these two questions are: ‘yes’ and ‘very well’, respectively.

  4. Using the Multiplicative Schwarz Alternating Algorithm (MSAA) for Solving the Large Linear System of Equations Related to Global Gravity Field Recovery up to Degree and Order 120

    NASA Astrophysics Data System (ADS)

    Safari, A.; Sharifi, M. A.; Amjadiparvar, B.

    2010-05-01

    The GRACE mission has substantiated the low-low satellite-to-satellite tracking (LL-SST) concept. The LL-SST configuration can be combined with the previously realized high-low SST concept in the CHAMP mission to provide a much higher accuracy. The line of sight (LOS) acceleration difference between the GRACE satellite pair is the mostly used observable for mapping the global gravity field of the Earth in terms of spherical harmonic coefficients. In this paper, mathematical formulae for LOS acceleration difference observations have been derived and the corresponding linear system of equations has been set up for spherical harmonic up to degree and order 120. The total number of unknowns is 14641. Such a linear equation system can be solved with iterative solvers or direct solvers. However, the runtime of direct methods or that of iterative solvers without a suitable preconditioner increases tremendously. This is the reason why we need a more sophisticated method to solve the linear system of problems with a large number of unknowns. Multiplicative variant of the Schwarz alternating algorithm is a domain decomposition method, which allows it to split the normal matrix of the system into several smaller overlaped submatrices. In each iteration step the multiplicative variant of the Schwarz alternating algorithm solves linear systems with the matrices obtained from the splitting successively. It reduces both runtime and memory requirements drastically. In this paper we propose the Multiplicative Schwarz Alternating Algorithm (MSAA) for solving the large linear system of gravity field recovery. The proposed algorithm has been tested on the International Association of Geodesy (IAG)-simulated data of the GRACE mission. The achieved results indicate the validity and efficiency of the proposed algorithm in solving the linear system of equations from accuracy and runtime points of view. Keywords: Gravity field recovery, Multiplicative Schwarz Alternating Algorithm, Low-Low Satellite-to-Satellite Tracking

  5. Novel methods for Solving Economic Dispatch of Security-Constrained Unit Commitment Based on Linear Programming

    NASA Astrophysics Data System (ADS)

    Guo, Sangang

    2017-09-01

    There are two stages in solving security-constrained unit commitment problems (SCUC) within Lagrangian framework: one is to obtain feasible units’ states (UC), the other is power economic dispatch (ED) for each unit. The accurate solution of ED is more important for enhancing the efficiency of the solution to SCUC for the fixed feasible units’ statues. Two novel methods named after Convex Combinatorial Coefficient Method and Power Increment Method respectively based on linear programming problem for solving ED are proposed by the piecewise linear approximation to the nonlinear convex fuel cost functions. Numerical testing results show that the methods are effective and efficient.

  6. On a new iterative method for solving linear systems and comparison results

    NASA Astrophysics Data System (ADS)

    Jing, Yan-Fei; Huang, Ting-Zhu

    2008-10-01

    In Ujevic [A new iterative method for solving linear systems, Appl. Math. Comput. 179 (2006) 725-730], the author obtained a new iterative method for solving linear systems, which can be considered as a modification of the Gauss-Seidel method. In this paper, we show that this is a special case from a point of view of projection techniques. And a different approach is established, which is both theoretically and numerically proven to be better than (at least the same as) Ujevic's. As the presented numerical examples show, in most cases, the convergence rate is more than one and a half that of Ujevic.

  7. Inequalities in premature mortality in Britain: observational study from 1921 to 2007.

    PubMed

    Thomas, Bethan; Dorling, Danny; Smith, George Davey

    2010-07-22

    To report on the extent of inequality in premature mortality as measured between geographical areas in Britain. Observational study of routinely collected mortality data and public records. Population subdivided by age, sex, and geographical area (parliamentary constituencies from 1991 to2007, pre-1974 local authorities over a longer time span). Great Britain. Entire population aged under 75 from 1990 to 2007, and entire population aged under 65 in the periods 1921-39, 1950-3, 1959-63, 1969-73, and 1981-2007. Relative index of inequality (RII) and ratios of inequality in age-sex standardised mortality ratios under ages 75 and 65. The relative index of inequality is the relative rate of mortality for the hypothetically worst-off compared with the hypothetically best-off person in the population, assuming a linear association between socioeconomic position and risk of mortality. The ratio of inequality is the ratio of the standardised mortality ratio of the most deprived 10% to the least deprived 10%. When measured by the relative index of inequality, geographical inequalities in age-sex standardised rates of mortality below age 75 have increased every two years from 1990-1 to 2006-7 without exception. Over this period the relative index of inequality increased from 1.61 (95% confidence interval 1.52 to 1.69) in 1990-1 to 2.14 (2.02 to 2.27) in 2006-7. Simple ratios indicated a brief period around 2001 when a small reduction in inequality was recorded, but this was quickly reversed and inequalities up to the age of 75 have now reached the highest levels reported since at least 1990. Similarly, inequalities in mortality ratios under the age of 65 improved slightly in the early years of this century but the latest figures surpass the most extreme previously reported. Comparison of crudely age-sex standardised rates for those below age 65 from historical records showed that geographical inequalities in mortality are higher in the most recent decade than in any similar time period for which records are available since at least 1921. Inequalities in premature mortality between areas of Britain continued to rise steadily during the first decade of the 21st century. The last time in the long economic record that inequalities were almost as high was in the lead up to the economic crash of 1929 and the economic depression of the 1930s. The economic crash of 2008 might precede even greater inequalities in mortality between areas in Britain.

  8. Impact of national income and inequality on sugar and caries relationship.

    PubMed

    Masood, M; Masood, Y; Newton, T

    2012-01-01

    The aim of this study was to examine the impact that national income and income inequality in high and low income countries have on the relationship between dental caries and sugar consumption. An ecological study design was used in this study of 73 countries. The mean decayed, missing, or filled permanent teeth (DMFT) for 12-year-old children were obtained from the WHO Oral Health Country/Area Profile Programme. United Nations Food and Agricultural Organization data were used for per capita sugar consumption. Gross national incomes per capita based on purchasing power parity and the Gini coefficient were obtained from World Bank data. Bivariate and multivariate linear regression analysis was performed to estimate the associations between mean DMFT and per capita sugar consumption in different income and income inequality countries. Bivariate and multivariate regression analysis showed that countries with a high national income and low income inequality have a strong negative association between sugar consumption and caries (B = -2.80, R2 = 0.17), whereas countries with a low income and high income inequality have a strong positive relationship between DMFT and per capita sugar consumption (B = -0.89, R2 = 0.20). The relationship between per capita consumption of sugar and dental caries is modified by the absolute level of income of the country, but not by the level of income inequality within a country. Copyright © 2012 S. Karger AG, Basel.

  9. What's in a country average? Wealth, gender, and regional inequalities in immunization in India.

    PubMed

    Pande, Rohini P; Yazbeck, Abdo S

    2003-12-01

    Recent attention to Millennium Development Goals by the international development community has led to the formation of targets to measure country-level achievements, including achievements on health status indicators such as childhood immunization. Using the example of immunization in India, this paper demonstrates the importance of disaggregating national averages for a better understanding of social disparities in health. Specifically, the paper uses data from the India National Family Health Survey 1992-93 to analyze socioeconomic, gender, urban-rural and regional inequalities in immunization in India for each of the 17 largest states. Results show that, on average, southern states have better immunization levels and lower immunization inequalities than many northern states. Wealth and regional inequalities are correlated with overall levels of immunization in a non-linear fashion. Gender inequalities persist in most states, including in the south, and seem unrelated to overall immunization or the levels of other inequalities measured here. This suggests that the gender differentials reflect deep-seated societal factors rather than health system issues per se. The disaggregated information and analysis used in this paper allows for setting more meaningful targets than country averages. Additionally, it helps policy makers and planners to understand programmatic constraints and needs by identifying disparities between sub-groups of the population, including strong and weak performers at the state and regional levels.

  10. Trimming and procrastination as inversion techniques

    NASA Astrophysics Data System (ADS)

    Backus, George E.

    1996-12-01

    By examining the processes of truncating and approximating the model space (trimming it), and by committing to neither the objectivist nor the subjectivist interpretation of probability (procrastinating), we construct a formal scheme for solving linear and non-linear geophysical inverse problems. The necessary prior information about the correct model xE can be either a collection of inequalities or a probability measure describing where xE was likely to be in the model space X before the data vector y0 was measured. The results of the inversion are (1) a vector z0 that estimates some numerical properties zE of xE; (2) an estimate of the error δz = z0 - zE. As y0 is finite dimensional, so is z0, and hence in principle inversion cannot describe all of xE. The error δz is studied under successively more specialized assumptions about the inverse problem, culminating in a complete analysis of the linear inverse problem with a prior quadratic bound on xE. Our formalism appears to encompass and provide error estimates for many of the inversion schemes current in geomagnetism, and would be equally applicable in geodesy and seismology if adequate prior information were available there. As an idealized example we study the magnetic field at the core-mantle boundary, using satellite measurements of field elements at sites assumed to be almost uniformly distributed on a single spherical surface. Magnetospheric currents are neglected and the crustal field is idealized as a random process with rotationally invariant statistics. We find that an appropriate data compression diagonalizes the variance matrix of the crustal signal and permits an analytic trimming of the idealized problem.

  11. Generalised Assignment Matrix Methodology in Linear Programming

    ERIC Educational Resources Information Center

    Jerome, Lawrence

    2012-01-01

    Discrete Mathematics instructors and students have long been struggling with various labelling and scanning algorithms for solving many important problems. This paper shows how to solve a wide variety of Discrete Mathematics and OR problems using assignment matrices and linear programming, specifically using Excel Solvers although the same…

  12. Solving the linear inviscid shallow water equations in one dimension, with variable depth, using a recursion formula

    NASA Astrophysics Data System (ADS)

    Hernandez-Walls, R.; Martín-Atienza, B.; Salinas-Matus, M.; Castillo, J.

    2017-11-01

    When solving the linear inviscid shallow water equations with variable depth in one dimension using finite differences, a tridiagonal system of equations must be solved. Here we present an approach, which is more efficient than the commonly used numerical method, to solve this tridiagonal system of equations using a recursion formula. We illustrate this approach with an example in which we solve for a rectangular channel to find the resonance modes. Our numerical solution agrees very well with the analytical solution. This new method is easy to use and understand by undergraduate students, so it can be implemented in undergraduate courses such as Numerical Methods, Lineal Algebra or Differential Equations.

  13. Object matching using a locally affine invariant and linear programming techniques.

    PubMed

    Li, Hongsheng; Huang, Xiaolei; He, Lei

    2013-02-01

    In this paper, we introduce a new matching method based on a novel locally affine-invariant geometric constraint and linear programming techniques. To model and solve the matching problem in a linear programming formulation, all geometric constraints should be able to be exactly or approximately reformulated into a linear form. This is a major difficulty for this kind of matching algorithm. We propose a novel locally affine-invariant constraint which can be exactly linearized and requires a lot fewer auxiliary variables than other linear programming-based methods do. The key idea behind it is that each point in the template point set can be exactly represented by an affine combination of its neighboring points, whose weights can be solved easily by least squares. Errors of reconstructing each matched point using such weights are used to penalize the disagreement of geometric relationships between the template points and the matched points. The resulting overall objective function can be solved efficiently by linear programming techniques. Our experimental results on both rigid and nonrigid object matching show the effectiveness of the proposed algorithm.

  14. Realizing Gender Equality in Higher Education: The Need To Integrate Work/Family Issues. 1991 ASHE-ERIC Higher Education Report 2.

    ERIC Educational Resources Information Center

    Hensel, Nancy

    This monograph examines gender differences and related issues in higher education faculty and proposes steps to change the current climate to resolve gender inequalities, solve the impending shortage of faculty, and improve diversity among faculty. A look at the status of women in academia finds that women are an under-represented group in tenured…

  15. Discrimination, Perceived Social Inequity, and Mental Health Among Rural-to-Urban Migrants in China

    PubMed Central

    Lin, Danhua; Wang, Bo; Hong, Yan; Qin, Xiong; Stanton, Bonita

    2010-01-01

    Status-based discrimination and inequity have been associated with the process of migration, especially with economics-driven internal migration. However, their association with mental health among economy-driven internal migrants in developing countries is rarely assessed. This study examines discriminatory experiences and perceived social inequity in relation to mental health status among rural-to-urban migrants in China. Cross-sectional data were collected from 1,006 rural-to-urban migrants in 2004–2005 in Beijing, China. Participants reported their perceptions and experiences of being discriminated in daily life in urban destination and perceived social inequity. Mental health was measured using the symptom checklist-90 (SCL-90). Multivariate analyses using general linear model were performed to test the effect of discriminatory experience and perceived social inequity on mental health. Experience of discrimination was positively associated with male gender, being married at least once, poorer health status, shorter duration of migration, and middle range of personal income. Likewise, perceived social inequity was associated with poorer health status, higher education attainment, and lower personal income. Multivariate analyses indicate that both experience of discrimination and perceived social inequity were strongly associated with mental health problems of rural-to-urban migrants. Experience of discrimination in daily life and perceived social inequity have a significant influence on mental health among rural-to-urban migrants. The findings underscore the needs to reduce public or societal discrimination against rural-to-urban migrants, to eliminate structural barriers (i.e., dual household registrations) for migrants to fully benefit from the urban economic development, and to create a positive atmosphere to improve migrant's psychological well-being. PMID:20033772

  16. Bayes factors for testing inequality constrained hypotheses: Issues with prior specification.

    PubMed

    Mulder, Joris

    2014-02-01

    Several issues are discussed when testing inequality constrained hypotheses using a Bayesian approach. First, the complexity (or size) of the inequality constrained parameter spaces can be ignored. This is the case when using the posterior probability that the inequality constraints of a hypothesis hold, Bayes factors based on non-informative improper priors, and partial Bayes factors based on posterior priors. Second, the Bayes factor may not be invariant for linear one-to-one transformations of the data. This can be observed when using balanced priors which are centred on the boundary of the constrained parameter space with a diagonal covariance structure. Third, the information paradox can be observed. When testing inequality constrained hypotheses, the information paradox occurs when the Bayes factor of an inequality constrained hypothesis against its complement converges to a constant as the evidence for the first hypothesis accumulates while keeping the sample size fixed. This paradox occurs when using Zellner's g prior as a result of too much prior shrinkage. Therefore, two new methods are proposed that avoid these issues. First, partial Bayes factors are proposed based on transformed minimal training samples. These training samples result in posterior priors that are centred on the boundary of the constrained parameter space with the same covariance structure as in the sample. Second, a g prior approach is proposed by letting g go to infinity. This is possible because the Jeffreys-Lindley paradox is not an issue when testing inequality constrained hypotheses. A simulation study indicated that the Bayes factor based on this g prior approach converges fastest to the true inequality constrained hypothesis. © 2013 The British Psychological Society.

  17. Nonlocal games and optimal steering at the boundary of the quantum set

    NASA Astrophysics Data System (ADS)

    Zhen, Yi-Zheng; Goh, Koon Tong; Zheng, Yu-Lin; Cao, Wen-Fei; Wu, Xingyao; Chen, Kai; Scarani, Valerio

    2016-08-01

    The boundary between classical and quantum correlations is well characterized by linear constraints called Bell inequalities. It is much harder to characterize the boundary of the quantum set itself in the space of no-signaling correlations. For the points on the quantum boundary that violate maximally some Bell inequalities, J. Oppenheim and S. Wehner [Science 330, 1072 (2010), 10.1126/science.1192065] pointed out a complex property: Alice's optimal measurements steer Bob's local state to the eigenstate of an effective operator corresponding to its maximal eigenvalue. This effective operator is the linear combination of Bob's local operators induced by the coefficients of the Bell inequality, and it can be interpreted as defining a fine-grained uncertainty relation. It is natural to ask whether the same property holds for other points on the quantum boundary, using the Bell expression that defines the tangent hyperplane at each point. We prove that this is indeed the case for a large set of points, including some that were believed to provide counterexamples. The price to pay is to acknowledge that the Oppenheim-Wehner criterion does not respect equivalence under the no-signaling constraint: for each point, one has to look for specific forms of writing the Bell expressions.

  18. Stochastic sampled-data control for synchronization of complex dynamical networks with control packet loss and additive time-varying delays.

    PubMed

    Rakkiyappan, R; Sakthivel, N; Cao, Jinde

    2015-06-01

    This study examines the exponential synchronization of complex dynamical networks with control packet loss and additive time-varying delays. Additionally, sampled-data controller with time-varying sampling period is considered and is assumed to switch between m different values in a random way with given probability. Then, a novel Lyapunov-Krasovskii functional (LKF) with triple integral terms is constructed and by using Jensen's inequality and reciprocally convex approach, sufficient conditions under which the dynamical network is exponentially mean-square stable are derived. When applying Jensen's inequality to partition double integral terms in the derivation of linear matrix inequality (LMI) conditions, a new kind of linear combination of positive functions weighted by the inverses of squared convex parameters appears. In order to handle such a combination, an effective method is introduced by extending the lower bound lemma. To design the sampled-data controller, the synchronization error system is represented as a switched system. Based on the derived LMI conditions and average dwell-time method, sufficient conditions for the synchronization of switched error system are derived in terms of LMIs. Finally, numerical example is employed to show the effectiveness of the proposed methods. Copyright © 2015 Elsevier Ltd. All rights reserved.

  19. Global health inequalities and breast cancer: an impending public health problem for developing countries.

    PubMed

    Igene, Helen

    2008-01-01

    The aim of the study was to provide information on the global health inequality pattern produced by the increasing incidence of breast cancer and its relationship with the health expenditure of developing countries with emphasis on sub-Saharan Africa. It examines the difference between the health expenditure of developed and developing countries, and how this affects breast cancer incidence and mortality. The data collected from the World Health Organization and World Bank were examined, using bivariate analysis, through scatter-plots and Pearson's product moment correlation coefficient. Multivariate analysis was carried out by multiple regression analysis. National income, health expenditure affects breast cancer incidence, particularly between the developed and developing countries. However, these factors do not adequately explain variations in mortality rates. The study reveals the risk posed to developing countries to solving the present and predicted burden of breast cancer, currently characterized by late presentation, inadequate health care systems, and high mortality. Findings from this study contribute to the knowledge of the burden of disease in developing countries, especially sub-Saharan Africa, and how that is related to globalization and health inequalities.

  20. Bell's Inequality: Revolution in Quantum Physics or Just AN Inadequate Mathematical Model?

    NASA Astrophysics Data System (ADS)

    Khrennikov, Andrei

    The main aim of this review is to stress the role of mathematical models in physics. The Bell inequality (BI) is often called the "most famous inequality of the 20th century." It is commonly accepted that its violation in corresponding experiments induced a revolution in quantum physics. Unlike "old quantum mechanics" (of Einstein, Schrodinger Bohr, Heisenberg, Pauli, Landau, Fock), "modern quantum mechanics" (of Bell, Aspect, Zeilinger, Shimony, Green-berger, Gisin, Mermin) takes seriously so called quantum non-locality. We will show that the conclusion that one has to give up the realism (i.e., a possibility to assign results of measurements to physical systems) or the locality (i.e., to assume action at a distance) is heavily based on one special mathematical model. This model was invented by A. N. Kolmogorov in 1933. One should pay serious attention to the role of mathematical models in physics. The problems of the realism and locality induced by Bell's argument can be solved by using non-Kolmogorovian probabilistic models. We compare this situation with non-Euclidean geometric models in relativity theory.

  1. Memory feedback PID control for exponential synchronisation of chaotic Lur'e systems

    NASA Astrophysics Data System (ADS)

    Zhang, Ruimei; Zeng, Deqiang; Zhong, Shouming; Shi, Kaibo

    2017-09-01

    This paper studies the problem of exponential synchronisation of chaotic Lur'e systems (CLSs) via memory feedback proportional-integral-derivative (PID) control scheme. First, a novel augmented Lyapunov-Krasovskii functional (LKF) is constructed, which can make full use of the information on time delay and activation function. Second, improved synchronisation criteria are obtained by using new integral inequalities, which can provide much tighter bounds than what the existing integral inequalities can produce. In comparison with existing results, in which only proportional control or proportional derivative (PD) control is used, less conservative results are derived for CLSs by PID control. Third, the desired memory feedback controllers are designed in terms of the solution to linear matrix inequalities. Finally, numerical simulations of Chua's circuit and neural network are provided to show the effectiveness and advantages of the proposed results.

  2. College Algebra I.

    ERIC Educational Resources Information Center

    Benjamin, Carl; And Others

    Presented are student performance objectives, a student progress chart, and assignment sheets with objective and diagnostic measures for the stated performance objectives in College Algebra I. Topics covered include: sets; vocabulary; linear equations; inequalities; real numbers; operations; factoring; fractions; formulas; ratio, proportion, and…

  3. Technology, Linear Equations, and Buying a Car.

    ERIC Educational Resources Information Center

    Sandefur, James T.

    1992-01-01

    Discusses the use of technology in solving compound interest-rate problems that can be modeled by linear relationships. Uses a graphing calculator to solve the specific problem of determining the amount of money that can be borrowed to buy a car for a given monthly payment and interest rate. (MDH)

  4. A reduced successive quadratic programming strategy for errors-in-variables estimation.

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Tjoa, I.-B.; Biegler, L. T.; Carnegie-Mellon Univ.

    Parameter estimation problems in process engineering represent a special class of nonlinear optimization problems, because the maximum likelihood structure of the objective function can be exploited. Within this class, the errors in variables method (EVM) is particularly interesting. Here we seek a weighted least-squares fit to the measurements with an underdetermined process model. Thus, both the number of variables and degrees of freedom available for optimization increase linearly with the number of data sets. Large optimization problems of this type can be particularly challenging and expensive to solve because, for general-purpose nonlinear programming (NLP) algorithms, the computational effort increases atmore » least quadratically with problem size. In this study we develop a tailored NLP strategy for EVM problems. The method is based on a reduced Hessian approach to successive quadratic programming (SQP), but with the decomposition performed separately for each data set. This leads to the elimination of all variables but the model parameters, which are determined by a QP coordination step. In this way the computational effort remains linear in the number of data sets. Moreover, unlike previous approaches to the EVM problem, global and superlinear properties of the SQP algorithm apply naturally. Also, the method directly incorporates inequality constraints on the model parameters (although not on the fitted variables). This approach is demonstrated on five example problems with up to 102 degrees of freedom. Compared to general-purpose NLP algorithms, large improvements in computational performance are observed.« less

  5. A Block-LU Update for Large-Scale Linear Programming

    DTIC Science & Technology

    1990-01-01

    linear programming problems. Results are given from runs on the Cray Y -MP. 1. Introduction We wish to use the simplex method [Dan63] to solve the...standard linear program, minimize cTx subject to Ax = b 1< x <U, where A is an m by n matrix and c, x, 1, u, and b are of appropriate dimension. The simplex...the identity matrix. The basis is used to solve for the search direction y and the dual variables 7r in the following linear systems: Bky = aq (1.2) and

  6. A comparison of Heuristic method and Llewellyn’s rules for identification of redundant constraints

    NASA Astrophysics Data System (ADS)

    Estiningsih, Y.; Farikhin; Tjahjana, R. H.

    2018-03-01

    Important techniques in linear programming is modelling and solving practical optimization. Redundant constraints are consider for their effects on general linear programming problems. Identification and reduce redundant constraints are for avoidance of all the calculations associated when solving an associated linear programming problems. Many researchers have been proposed for identification redundant constraints. This paper a compararison of Heuristic method and Llewellyn’s rules for identification of redundant constraints.

  7. The mediating role of social capital in the association between neighbourhood income inequality and body mass index.

    PubMed

    Mackenbach, Joreintje D; Lakerveld, Jeroen; van Oostveen, Yavanna; Compernolle, Sofie; De Bourdeaudhuij, Ilse; Bárdos, Helga; Rutter, Harry; Glonti, Ketevan; Oppert, Jean-Michel; Charreire, Helene; Brug, Johannes; Nijpels, Giel

    2017-04-01

    Neighbourhood income inequality may contribute to differences in body weight. We explored whether neighbourhood social capital mediated the association of neighbourhood income inequality with individual body mass index (BMI). A total of 4126 adult participants from 48 neighbourhoods in France, Hungary, the Netherlands and the UK provided information on their levels of income, perceptions of neighbourhood social capital and BMI. Factor analysis of the 13-item social capital scale revealed two social capital constructs: social networks and social cohesion. Neighbourhood income inequality was defined as the ratio of the amount of income earned by the top 20% and the bottom 20% in a given neighbourhood. Two single mediation analyses-using multilevel linear regression analyses-with neighbourhood social networks and neighbourhood social cohesion as possible mediators-were conducted using MacKinnon's product-of-coefficients method, adjusted for age, gender, education and absolute household income. Higher neighbourhood income inequality was associated with elevated levels of BMI and lower levels of neighbourhood social networks and neighbourhood social cohesion. High levels of neighbourhood social networks were associated with lower BMI. Results stratified by country demonstrate that social networks fully explained the association between income inequality and BMI in France and the Netherlands. Social cohesion was only a significant mediating variable for Dutch participants. The results suggest that in some European urban regions, neighbourhood social capital plays a large role in the association between neighbourhood income inequality and individual BMI. © The Author 2016. Published by Oxford University Press on behalf of the European Public Health Association. All rights reserved.

  8. Socioeconomic inequalities in the quality of life of older Europeans in different welfare regimes

    PubMed Central

    Katikireddi, Srinivasa Vittal; Pell, Jill P.; Mitchell, Richard

    2014-01-01

    Background: Whether socioeconomic inequalities in health and well-being persist into old age and are narrower in more generous welfare states is debated. We investigated the magnitude of socioeconomic inequality in the quality of life of Europeans in early old age and the influence of the welfare regime type on these relationships. Methods: Data from individuals aged 50–75 years (n = 16 074) residing in 13 European countries were derived from Waves 2 and 3 of the Survey of Health, Ageing and Retirement in Europe. Slope indices of inequality (SIIs) were calculated for the association between socioeconomic position and CASP-12, a measure of positive quality of life. Multilevel linear regression was used to assess the overall relationship between socioeconomic position and quality of life, using interaction terms to investigate the influence of the type of welfare regime (Southern, Scandinavian, Post-communist or Bismarckian). Results: Socioeconomic inequalities in quality of life were narrowest in the Scandinavian and Bismarckian regimes, and were largest by measures of current wealth. Compared with the Scandinavian welfare regime, where narrow inequalities in quality of life by education level were found in both men (SII = 0.02, 95% CI: −1.09 to 1.13) and women (SII = 1.11, 95% CI: 0.05–2.17), the difference in quality of life between the least and most educated was particularly wide in Southern and Post-communist regimes. Conclusion: Individuals in more generous welfare regimes experienced higher levels of quality of life, as well as narrower socioeconomic inequalities in quality of life. PMID:24568754

  9. The fastclime Package for Linear Programming and Large-Scale Precision Matrix Estimation in R.

    PubMed

    Pang, Haotian; Liu, Han; Vanderbei, Robert

    2014-02-01

    We develop an R package fastclime for solving a family of regularized linear programming (LP) problems. Our package efficiently implements the parametric simplex algorithm, which provides a scalable and sophisticated tool for solving large-scale linear programs. As an illustrative example, one use of our LP solver is to implement an important sparse precision matrix estimation method called CLIME (Constrained L 1 Minimization Estimator). Compared with existing packages for this problem such as clime and flare, our package has three advantages: (1) it efficiently calculates the full piecewise-linear regularization path; (2) it provides an accurate dual certificate as stopping criterion; (3) it is completely coded in C and is highly portable. This package is designed to be useful to statisticians and machine learning researchers for solving a wide range of problems.

  10. Improved finite difference schemes for transonic potential calculations

    NASA Technical Reports Server (NTRS)

    Hafez, M.; Osher, S.; Whitlow, W., Jr.

    1984-01-01

    Engquist and Osher (1980) have introduced a finite difference scheme for solving the transonic small disturbance equation, taking into account cases in which only compression shocks are admitted. Osher et al. (1983) studied a class of schemes for the full potential equation. It is proved that these schemes satisfy a new discrete 'entropy inequality' which rules out expansion shocks. However, the conducted analysis is restricted to steady two-dimensional flows. The present investigation is concerned with the adoption of a heuristic approach. The full potential equation in conservation form is solved with the aid of a modified artificial density method, based on flux biasing. It is shown that, with the current scheme, expansion shocks are not possible.

  11. A new Newton-like method for solving nonlinear equations.

    PubMed

    Saheya, B; Chen, Guo-Qing; Sui, Yun-Kang; Wu, Cai-Ying

    2016-01-01

    This paper presents an iterative scheme for solving nonline ar equations. We establish a new rational approximation model with linear numerator and denominator which has generalizes the local linear model. We then employ the new approximation for nonlinear equations and propose an improved Newton's method to solve it. The new method revises the Jacobian matrix by a rank one matrix each iteration and obtains the quadratic convergence property. The numerical performance and comparison show that the proposed method is efficient.

  12. An approximately factored incremental strategy for calculating consistent discrete aerodynamic sensitivity derivatives

    NASA Technical Reports Server (NTRS)

    Korivi, V. M.; Taylor, A. C., III; Newman, P. A.; Hou, G. J.-W.; Jones, H. E.

    1992-01-01

    An incremental strategy is presented for iteratively solving very large systems of linear equations, which are associated with aerodynamic sensitivity derivatives for advanced CFD codes. It is shown that the left-hand side matrix operator and the well-known factorization algorithm used to solve the nonlinear flow equations can also be used to efficiently solve the linear sensitivity equations. Two airfoil problems are considered as an example: subsonic low Reynolds number laminar flow and transonic high Reynolds number turbulent flow.

  13. Clauser-Horne-Shimony-Holt violation and the entropy-concurrence plane

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Derkacz, Lukasz; Jakobczyk, Lech

    2005-10-15

    We characterize violation of Clauser-Horne-Shimony-Holt (CHSH) inequalities for mixed two-qubit states by their mixedness and entanglement. The class of states that have maximum degree of CHSH violation for a given linear entropy is also constructed.

  14. The use of Galerkin finite-element methods to solve mass-transport equations

    USGS Publications Warehouse

    Grove, David B.

    1977-01-01

    The partial differential equation that describes the transport and reaction of chemical solutes in porous media was solved using the Galerkin finite-element technique. These finite elements were superimposed over finite-difference cells used to solve the flow equation. Both convection and flow due to hydraulic dispersion were considered. Linear and Hermite cubic approximations (basis functions) provided satisfactory results: however, the linear functions were computationally more efficient for two-dimensional problems. Successive over relaxation (SOR) and iteration techniques using Tchebyschef polynomials were used to solve the sparce matrices generated using the linear and Hermite cubic functions, respectively. Comparisons of the finite-element methods to the finite-difference methods, and to analytical results, indicated that a high degree of accuracy may be obtained using the method outlined. The technique was applied to a field problem involving an aquifer contaminated with chloride, tritium, and strontium-90. (Woodard-USGS)

  15. The Multifaceted Variable Approach: Selection of Method in Solving Simple Linear Equations

    ERIC Educational Resources Information Center

    Tahir, Salma; Cavanagh, Michael

    2010-01-01

    This paper presents a comparison of the solution strategies used by two groups of Year 8 students as they solved linear equations. The experimental group studied algebra following a multifaceted variable approach, while the comparison group used a traditional approach. Students in the experimental group employed different solution strategies,…

  16. Solving rational matrix equations in the state space with applications to computer-aided control-system design

    NASA Technical Reports Server (NTRS)

    Packard, A. K.; Sastry, S. S.

    1986-01-01

    A method of solving a class of linear matrix equations over various rings is proposed, using results from linear geometric control theory. An algorithm, successfully implemented, is presented, along with non-trivial numerical examples. Applications of the method to the algebraic control system design methodology are discussed.

  17. Secondary Pre-Service Teachers' Algebraic Reasoning about Linear Equation Solving

    ERIC Educational Resources Information Center

    Alvey, Christina; Hudson, Rick A.; Newton, Jill; Males, Lorraine M.

    2016-01-01

    This study analyzes the responses of 12 secondary pre-service teachers on two tasks focused on reasoning when solving linear equations. By documenting the choices PSTs made while engaging in these tasks, we gain insight into how new teachers work mathematically, reason algebraically, communicate their thinking, and make pedagogical decisions. We…

  18. Synthesizing Strategies Creatively: Solving Linear Equations

    ERIC Educational Resources Information Center

    Ponce, Gregorio A.; Tuba, Imre

    2015-01-01

    New strategies can ignite teachers' imagination to create new lessons or adapt lessons created by others. In this article, the authors present the experience of an algebra teacher and his students solving linear and literal equations and explain how the use of ideas found in past NCTM journals helped bring this lesson to life. The…

  19. A nearly-linear computational-cost scheme for the forward dynamics of an N-body pendulum

    NASA Technical Reports Server (NTRS)

    Chou, Jack C. K.

    1989-01-01

    The dynamic equations of motion of an n-body pendulum with spherical joints are derived to be a mixed system of differential and algebraic equations (DAE's). The DAE's are kept in implicit form to save arithmetic and preserve the sparsity of the system and are solved by the robust implicit integration method. At each solution point, the predicted solution is corrected to its exact solution within given tolerance using Newton's iterative method. For each iteration, a linear system of the form J delta X = E has to be solved. The computational cost for solving this linear system directly by LU factorization is O(n exp 3), and it can be reduced significantly by exploring the structure of J. It is shown that by recognizing the recursive patterns and exploiting the sparsity of the system the multiplicative and additive computational costs for solving J delta X = E are O(n) and O(n exp 2), respectively. The formulation and solution method for an n-body pendulum is presented. The computational cost is shown to be nearly linearly proportional to the number of bodies.

  20. Experimental entanglement and nonlocality of a two-photon six-qubit cluster state.

    PubMed

    Ceccarelli, Raino; Vallone, Giuseppe; De Martini, Francesco; Mataloni, Paolo; Cabello, Adán

    2009-10-16

    We create a six-qubit linear cluster state by transforming a two-photon hyperentangled state in which three qubits are encoded in each particle, one in the polarization and two in the linear momentum degrees of freedom. For this state, we demonstrate genuine six-qubit entanglement, persistency of entanglement against the loss of qubits, and higher violation than in previous experiments on Bell inequalities of the Mermin type.

  1. A new neural network model for solving random interval linear programming problems.

    PubMed

    Arjmandzadeh, Ziba; Safi, Mohammadreza; Nazemi, Alireza

    2017-05-01

    This paper presents a neural network model for solving random interval linear programming problems. The original problem involving random interval variable coefficients is first transformed into an equivalent convex second order cone programming problem. A neural network model is then constructed for solving the obtained convex second order cone problem. Employing Lyapunov function approach, it is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact satisfactory solution of the original problem. Several illustrative examples are solved in support of this technique. Copyright © 2017 Elsevier Ltd. All rights reserved.

  2. Optimal multi-floor plant layout based on the mathematical programming and particle swarm optimization.

    PubMed

    Lee, Chang Jun

    2015-01-01

    In the fields of researches associated with plant layout optimization, the main goal is to minimize the costs of pipelines and pumping between connecting equipment under various constraints. However, what is the lacking of considerations in previous researches is to transform various heuristics or safety regulations into mathematical equations. For example, proper safety distances between equipments have to be complied for preventing dangerous accidents on a complex plant. Moreover, most researches have handled single-floor plant. However, many multi-floor plants have been constructed for the last decade. Therefore, the proper algorithm handling various regulations and multi-floor plant should be developed. In this study, the Mixed Integer Non-Linear Programming (MINLP) problem including safety distances, maintenance spaces, etc. is suggested based on mathematical equations. The objective function is a summation of pipeline and pumping costs. Also, various safety and maintenance issues are transformed into inequality or equality constraints. However, it is really hard to solve this problem due to complex nonlinear constraints. Thus, it is impossible to use conventional MINLP solvers using derivatives of equations. In this study, the Particle Swarm Optimization (PSO) technique is employed. The ethylene oxide plant is illustrated to verify the efficacy of this study.

  3. Reliable fuzzy H∞ control for active suspension of in-wheel motor driven electric vehicles with dynamic damping

    NASA Astrophysics Data System (ADS)

    Shao, Xinxin; Naghdy, Fazel; Du, Haiping

    2017-03-01

    A fault-tolerant fuzzy H∞ control design approach for active suspension of in-wheel motor driven electric vehicles in the presence of sprung mass variation, actuator faults and control input constraints is proposed. The controller is designed based on the quarter-car active suspension model with a dynamic-damping-in-wheel-motor-driven-system, in which the suspended motor is operated as a dynamic absorber. The Takagi-Sugeno (T-S) fuzzy model is used to model this suspension with possible sprung mass variation. The parallel-distributed compensation (PDC) scheme is deployed to derive a fault-tolerant fuzzy controller for the T-S fuzzy suspension model. In order to reduce the motor wear caused by the dynamic force transmitted to the in-wheel motor, the dynamic force is taken as an additional controlled output besides the traditional optimization objectives such as sprung mass acceleration, suspension deflection and actuator saturation. The H∞ performance of the proposed controller is derived as linear matrix inequalities (LMIs) comprising three equality constraints which are solved efficiently by means of MATLAB LMI Toolbox. The proposed controller is applied to an electric vehicle suspension and its effectiveness is demonstrated through computer simulation.

  4. Estimating the Inertia Matrix of a Spacecraft

    NASA Technical Reports Server (NTRS)

    Acikmese, Behcet; Keim, Jason; Shields, Joel

    2007-01-01

    A paper presents a method of utilizing some flight data, aboard a spacecraft that includes reaction wheels for attitude control, to estimate the inertia matrix of the spacecraft. The required data are digitized samples of (1) the spacecraft attitude in an inertial reference frame as measured, for example, by use of a star tracker and (2) speeds of rotation of the reaction wheels, the moments of inertia of which are deemed to be known. Starting from the classical equations for conservation of angular momentum of a rigid body, the inertia-matrix-estimation problem is formulated as a constrained least-squares minimization problem with explicit bounds on the inertia matrix incorporated as linear matrix inequalities. The explicit bounds reflect physical bounds on the inertia matrix and reduce the volume of data that must be processed to obtain a solution. The resulting minimization problem is a semidefinite optimization problem that can be solved efficiently, with guaranteed convergence to the global optimum, by use of readily available algorithms. In a test case involving a model attitude platform rotating on an air bearing, it is shown that, relative to a prior method, the present method produces better estimates from few data.

  5. Design and Evaluation of a Real-Time Video Conferencing Environment for Support Teaching: An Attempt to Promote Equality of K-12 Education in China

    ERIC Educational Resources Information Center

    Xiong, Caiping; Ge, Jun; Wang, Qiyun; Wang, Xuejun

    2017-01-01

    Imbalanced allocation of teacher resources is a major factor causing inequality in K-12 education in China. Traditional ways to solve this problem, such as on-site support teaching and recorded lectures of quality teachers, have posed many defects. It is suggested that information and communication technology should be employed to deal with the…

  6. Conditions for Stabilizability of Linear Switched Systems

    NASA Astrophysics Data System (ADS)

    Minh, Vu Trieu

    2011-06-01

    This paper investigates some conditions that can provide stabilizability for linear switched systems with polytopic uncertainties via their closed loop linear quadratic state feedback regulator. The closed loop switched systems can stabilize unstable open loop systems or stable open loop systems but in which there is no solution for a common Lyapunov matrix. For continuous time switched linear systems, we show that if there exists solution in an associated Riccati equation for the closed loop systems sharing one common Lyapunov matrix, the switched linear systems are stable. For the discrete time switched systems, we derive a Linear Matrix Inequality (LMI) to calculate a common Lyapunov matrix and solution for the stable closed loop feedback systems. These closed loop linear quadratic state feedback regulators guarantee the global asymptotical stability for any switched linear systems with any switching signal sequence.

  7. The contribution of health selection to occupational status inequality in Germany - differences by gender and between the public and private sectors.

    PubMed

    Kröger, H

    2016-04-01

    Estimating the size of health inequalities between hierarchical levels of job status and the contribution of direct health selection to these inequalities for men and women in the private and public sector in Germany. The study uses prospective data from the Socio-Economic Panel study on 11,788 women and 11,494 men working in the public and private sector in Germany. Direct selection effects of self-rated health on job status are estimated using fixed-effects linear probability models. The contribution of health selection to overall health-related inequalities between high and low status jobs is calculated. Women in the private sector who report very good health have a 1.9 [95% CI: 0.275; 3.507] percentage point higher probability of securing a high status job than women in poor self-rated health. This direct selection effect constitutes 20.12% of total health inequalities between women in high and low status jobs. For men in the private and men and women in the public sector no relevant health selection effects were identified. The contribution of health selection to total health inequalities between high and low status jobs varies with gender and public versus private sector. Women in the private sector in Germany experience the strongest health selection. Possible explanations are general occupational disadvantages that women have to overcome to secure high status jobs. Copyright © 2015 The Royal Society for Public Health. Published by Elsevier Ltd. All rights reserved.

  8. Enhanced robust finite-time passivity for Markovian jumping discrete-time BAM neural networks with leakage delay.

    PubMed

    Sowmiya, C; Raja, R; Cao, Jinde; Rajchakit, G; Alsaedi, Ahmed

    2017-01-01

    This paper is concerned with the problem of enhanced results on robust finite-time passivity for uncertain discrete-time Markovian jumping BAM delayed neural networks with leakage delay. By implementing a proper Lyapunov-Krasovskii functional candidate, the reciprocally convex combination method together with linear matrix inequality technique, several sufficient conditions are derived for varying the passivity of discrete-time BAM neural networks. An important feature presented in our paper is that we utilize the reciprocally convex combination lemma in the main section and the relevance of that lemma arises from the derivation of stability by using Jensen's inequality. Further, the zero inequalities help to propose the sufficient conditions for finite-time boundedness and passivity for uncertainties. Finally, the enhancement of the feasible region of the proposed criteria is shown via numerical examples with simulation to illustrate the applicability and usefulness of the proposed method.

  9. MM Algorithms for Geometric and Signomial Programming

    PubMed Central

    Lange, Kenneth; Zhou, Hua

    2013-01-01

    This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates. PMID:24634545

  10. MM Algorithms for Geometric and Signomial Programming.

    PubMed

    Lange, Kenneth; Zhou, Hua

    2014-02-01

    This paper derives new algorithms for signomial programming, a generalization of geometric programming. The algorithms are based on a generic principle for optimization called the MM algorithm. In this setting, one can apply the geometric-arithmetic mean inequality and a supporting hyperplane inequality to create a surrogate function with parameters separated. Thus, unconstrained signomial programming reduces to a sequence of one-dimensional minimization problems. Simple examples demonstrate that the MM algorithm derived can converge to a boundary point or to one point of a continuum of minimum points. Conditions under which the minimum point is unique or occurs in the interior of parameter space are proved for geometric programming. Convergence to an interior point occurs at a linear rate. Finally, the MM framework easily accommodates equality and inequality constraints of signomial type. For the most important special case, constrained quadratic programming, the MM algorithm involves very simple updates.

  11. A feasible DY conjugate gradient method for linear equality constraints

    NASA Astrophysics Data System (ADS)

    LI, Can

    2017-09-01

    In this paper, we propose a feasible conjugate gradient method for solving linear equality constrained optimization problem. The method is an extension of the Dai-Yuan conjugate gradient method proposed by Dai and Yuan to linear equality constrained optimization problem. It can be applied to solve large linear equality constrained problem due to lower storage requirement. An attractive property of the method is that the generated direction is always feasible and descent direction. Under mild conditions, the global convergence of the proposed method with exact line search is established. Numerical experiments are also given which show the efficiency of the method.

  12. Polynomial elimination theory and non-linear stability analysis for the Euler equations

    NASA Technical Reports Server (NTRS)

    Kennon, S. R.; Dulikravich, G. S.; Jespersen, D. C.

    1986-01-01

    Numerical methods are presented that exploit the polynomial properties of discretizations of the Euler equations. It is noted that most finite difference or finite volume discretizations of the steady-state Euler equations produce a polynomial system of equations to be solved. These equations are solved using classical polynomial elimination theory, with some innovative modifications. This paper also presents some preliminary results of a new non-linear stability analysis technique. This technique is applicable to determining the stability of polynomial iterative schemes. Results are presented for applying the elimination technique to a one-dimensional test case. For this test case, the exact solution is computed in three iterations. The non-linear stability analysis is applied to determine the optimal time step for solving Burgers' equation using the MacCormack scheme. The estimated optimal time step is very close to the time step that arises from a linear stability analysis.

  13. Homotopy approach to optimal, linear quadratic, fixed architecture compensation

    NASA Technical Reports Server (NTRS)

    Mercadal, Mathieu

    1991-01-01

    Optimal linear quadratic Gaussian compensators with constrained architecture are a sensible way to generate good multivariable feedback systems meeting strict implementation requirements. The optimality conditions obtained from the constrained linear quadratic Gaussian are a set of highly coupled matrix equations that cannot be solved algebraically except when the compensator is centralized and full order. An alternative to the use of general parameter optimization methods for solving the problem is to use homotopy. The benefit of the method is that it uses the solution to a simplified problem as a starting point and the final solution is then obtained by solving a simple differential equation. This paper investigates the convergence properties and the limitation of such an approach and sheds some light on the nature and the number of solutions of the constrained linear quadratic Gaussian problem. It also demonstrates the usefulness of homotopy on an example of an optimal decentralized compensator.

  14. On flows of viscoelastic fluids under threshold-slip boundary conditions

    NASA Astrophysics Data System (ADS)

    Baranovskii, E. S.

    2018-03-01

    We investigate a boundary-value problem for the steady isothermal flow of an incompressible viscoelastic fluid of Oldroyd type in a 3D bounded domain with impermeable walls. We use the Fujita threshold-slip boundary condition. This condition states that the fluid can slip along a solid surface when the shear stresses reach a certain critical value; otherwise the slipping velocity is zero. Assuming that the flow domain is not rotationally symmetric, we prove an existence theorem for the corresponding slip problem in the framework of weak solutions. The proof uses methods for solving variational inequalities with pseudo-monotone operators and convex functionals, the method of introduction of auxiliary viscosity, as well as a passage-to-limit procedure based on energy estimates of approximate solutions, Korn’s inequality, and compactness arguments. Also, some properties and estimates of weak solutions are established.

  15. Bayesian Optimization Under Mixed Constraints with A Slack-Variable Augmented Lagrangian

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Picheny, Victor; Gramacy, Robert B.; Wild, Stefan M.

    An augmented Lagrangian (AL) can convert a constrained optimization problem into a sequence of simpler (e.g., unconstrained) problems, which are then usually solved with local solvers. Recently, surrogate-based Bayesian optimization (BO) sub-solvers have been successfully deployed in the AL framework for a more global search in the presence of inequality constraints; however, a drawback was that expected improvement (EI) evaluations relied on Monte Carlo. Here we introduce an alternative slack variable AL, and show that in this formulation the EI may be evaluated with library routines. The slack variables furthermore facilitate equality as well as inequality constraints, and mixtures thereof.more » We show our new slack “ALBO” compares favorably to the original. Its superiority over conventional alternatives is reinforced on several mixed constraint examples.« less

  16. Socio-economic factors associated with infant mortality in Italy: an ecological study.

    PubMed

    Dallolio, Laura; Di Gregori, Valentina; Lenzi, Jacopo; Franchino, Giuseppe; Calugi, Simona; Domenighetti, Gianfranco; Fantini, Maria Pia

    2012-08-16

    One issue that continues to attract the attention of public health researchers is the possible relationship in high-income countries between income, income inequality and infant mortality (IM). The aim of this study was to assess the associations between IM and major socio-economic determinants in Italy. Associations between infant mortality rates in the 20 Italian regions (2006-2008) and the Gini index of income inequality, mean household income, percentage of women with at least 8 years of education, and percentage of unemployed aged 15-64 years were assessed using Pearson correlation coefficients. Univariate linear regression and multiple stepwise linear regression analyses were performed to determine the magnitude and direction of the effect of the four socio-economic variables on IM. The Gini index and the total unemployment rate showed a positive strong correlation with IM (r = 0.70; p < 0.001 and r = 0.84; p < 0.001 respectively), mean household income showed a strong negative correlation (r = -0.78; p < 0.001), while female educational attainment presented a weak negative correlation (r = -0.45; p < 0.05). Using a multiple stepwise linear regression model, only unemployment rate was independently associated with IM (b = 0.15, p < 0.001). In Italy, a high-income country where health care is universally available, variations in IM were strongly associated with relative and absolute income and unemployment rate. These results suggest that in Italy IM is not only related to income distribution, as demonstrated for other developed countries, but also to economic factors such as absolute income and unemployment. In order to reduce IM and the existing inequalities, the challenge for Italian decision makers is to promote economic growth and enhance employment levels.

  17. Household income, income inequality, and health-related quality of life measured by the EQ-5D in Shaanxi, China: a cross-sectional study.

    PubMed

    Tan, Zhijun; Shi, Fuyan; Zhang, Haiyue; Li, Ning; Xu, Yongyong; Liang, Ying

    2018-03-14

    In advanced economies, economic factors have been found to be associated with many health outcomes, including health-related quality of life (HRQL), and people's health is affected more by income inequality than by absolute income. However, few studies have examined the association of income inequality and absolute income with HRQL in transitional economies using individual data. This paper focuses on the effects of county or district income inequality and absolute income on the HRQL measured by EQ-5D and the differences between rural and urban regions in Shaanxi province, China. Data were collected from the 2008 National Health Service Survey conducted in Shaanxi, China. The EQ-5D index based on Japanese weights was employed as a health indicator. The income inequality was calculated on the basis of self-reported income. The special requirements for complex survey data analysis were considered in the bivariate analysis and linear regression models. The mean of the EQ-5D index was 94.6. The EQ-5D index of people with low income was lower than that in the high-income group (for people in the rural region: 93.2 v 96.1, P < 0.01; for people in the urban region: 95.5 v 96.8, P < 0.01). Compared with people with moderate inequality, the EQ-5D index of those with high inequality was relatively lower (for people living in the rural region: 91.1 v 95.8, P < 0.01; for people living in the urban region: 95.6 v 97.3, P < 0.01). Adjusted by age, gender, education, marital status, employment, medical insurance, and chronic disease, all the coefficients of the low-income group and high income inequality were significantly negative. After stratifying by income group, all the effects of high income inequality remained negative in both income groups. However, the coefficients of the models in the high income group were not statistically significant. Income inequality has damaging effects on HRQL in Shaanxi, China, especially for people with low income. In addition, people living in rural regions were more vulnerable to economic factors.

  18. Insights into the School Mathematics Tradition from Solving Linear Equations

    ERIC Educational Resources Information Center

    Buchbinder, Orly; Chazan, Daniel; Fleming, Elizabeth

    2015-01-01

    In this article, we explore how the solving of linear equations is represented in English­-language algebra text books from the early nineteenth century when schooling was becoming institutionalized, and then survey contemporary teachers. In the text books, we identify the increasing presence of a prescribed order of steps (a canonical method) for…

  19. Instructional Supports for Representational Fluency in Solving Linear Equations with Computer Algebra Systems and Paper-and-Pencil

    ERIC Educational Resources Information Center

    Fonger, Nicole L.; Davis, Jon D.; Rohwer, Mary Lou

    2018-01-01

    This research addresses the issue of how to support students' representational fluency--the ability to create, move within, translate across, and derive meaning from external representations of mathematical ideas. The context of solving linear equations in a combined computer algebra system (CAS) and paper-and-pencil classroom environment is…

  20. Investigating High-School Students' Reasoning Strategies when They Solve Linear Equations

    ERIC Educational Resources Information Center

    Huntley, Mary Ann; Marcus, Robin; Kahan, Jeremy; Miller, Jane Lincoln

    2007-01-01

    A cross-curricular structured-probe task-based clinical interview study with 44 pairs of third-year high-school mathematics students, most of whom were high achieving, was conducted to investigate their approaches to a variety of algebra problems. This paper presents results from one problem that involved solving a set of three linear equations of…

  1. General purpose computer programs for numerically analyzing linear ac electrical and electronic circuits for steady-state conditions

    NASA Technical Reports Server (NTRS)

    Egebrecht, R. A.; Thorbjornsen, A. R.

    1967-01-01

    Digital computer programs determine steady-state performance characteristics of active and passive linear circuits. The ac analysis program solves the basic circuit parameters. The compiler program solves these circuit parameters and in addition provides a more versatile program by allowing the user to perform mathematical and logical operations.

  2. Solving large-scale fixed cost integer linear programming models for grid-based location problems with heuristic techniques

    NASA Astrophysics Data System (ADS)

    Noor-E-Alam, Md.; Doucette, John

    2015-08-01

    Grid-based location problems (GBLPs) can be used to solve location problems in business, engineering, resource exploitation, and even in the field of medical sciences. To solve these decision problems, an integer linear programming (ILP) model is designed and developed to provide the optimal solution for GBLPs considering fixed cost criteria. Preliminary results show that the ILP model is efficient in solving small to moderate-sized problems. However, this ILP model becomes intractable in solving large-scale instances. Therefore, a decomposition heuristic is proposed to solve these large-scale GBLPs, which demonstrates significant reduction of solution runtimes. To benchmark the proposed heuristic, results are compared with the exact solution via ILP. The experimental results show that the proposed method significantly outperforms the exact method in runtime with minimal (and in most cases, no) loss of optimality.

  3. Global Trends in Adolescent Fertility, 1990-2012, in Relation to National Wealth, Income Inequalities, and Educational Expenditures.

    PubMed

    Santelli, John S; Song, Xiaoyu; Garbers, Samantha; Sharma, Vinit; Viner, Russell M

    2017-02-01

    National wealth, income inequalities, and expenditures on education can profoundly influence the health of a nation's women, children, and adolescents. We explored the association of trends in national socioeconomic status (SES) indicators with trends in adolescent birth rates (ABRs), by nation and region. An ecologic research design was employed using national-level data from the World Bank on birth rates per 1,000 women aged 15-19 years, national wealth (per capita gross domestic product or GDP), income inequality (Gini index), and expenditures on education as a percentage of GDP (EduExp). Data were available for 142 countries and seven regions for 1990-2012. Multiple linear regression for repeated measures with generalized estimating equations was used to examine independent associations. ABRs in 2012 varied >200-fold-with the highest rates in Sub-Saharan Africa and lowest rates in the Western Europe/Central Asia region. The median national ABR fell 40% from 72.4/1,000 in 1990 to 43.6/1,000 in 2012. The largest regional declines in ABR occurred in South Asia (70%), Europe/Central Asia (63%), and the Middle East/North Africa (53%)-regions with lower income inequality. In multivariable analyses considering change over time, ABRs were negatively associated with GDP and EduExp and positively associated with greater income inequality. ABRs have declined globally since 1990. Declines closely followed rising socioeconomic status and were greater where income inequalities were lower in 1990. Reducing poverty and income inequalities and increasing investments in education should be essential components of national policies to prevent adolescent childbearing. Copyright © 2016 Society for Adolescent Health and Medicine. Published by Elsevier Inc. All rights reserved.

  4. The association between life course socioeconomic position and life satisfaction in different welfare states: European comparative study of individuals in early old age

    PubMed Central

    Niedzwiedz, Claire L.; Katikireddi, Srinivasa Vittal; Pell, Jill P.; Mitchell, Richard

    2014-01-01

    Background: whether socioeconomic position over the life course influences the wellbeing of older people similarly in different societies is not known. Objective: to investigate the magnitude of socioeconomic inequalities in life satisfaction among individuals in early old age and the influence of the welfare state regime on the associations. Design: comparative study using data from Wave 2 and SHARELIFE, the retrospective Wave of the Survey of Health, Ageing, and Retirement in Europe (SHARE), collected during 2006–07 and 2008–09, respectively. Setting: thirteen European countries representing four welfare regimes (Southern, Scandinavian, Post-communist and Bismarckian). Subjects: a total of 17,697 individuals aged 50–75 years. Methods: slope indices of inequality (SIIs) were calculated for the association between life course socioeconomic position (measured by the number of books in childhood, education level and current wealth) and life satisfaction. Single level linear regression models stratified by welfare regime and multilevel regression models, containing interaction terms between socioeconomic position and welfare regime type, were calculated. Results: socioeconomic inequalities in life satisfaction were present in all welfare regimes. Educational inequalities in life satisfaction were narrowest in Scandinavian and Bismarckian regimes among both genders. Post-communist and Southern countries experienced both lower life satisfaction and larger socioeconomic inequalities in life satisfaction, using most measures of socioeconomic position. Current wealth was associated with large inequalities in life satisfaction across all regimes. Conclusions: Scandinavian and Bismarckian countries exhibited narrower socioeconomic inequalities in life satisfaction. This suggests that more generous welfare states help to produce a more equitable distribution of wellbeing among older people. PMID:24476800

  5. The Use of Iterative Linear-Equation Solvers in Codes for Large Systems of Stiff IVPs (Initial-Value Problems) for ODEs (Ordinary Differential Equations).

    DTIC Science & Technology

    1984-04-01

    numerical solution, of sstem ot stiff Wh-f Cr ODs. Fro- qontl. a substantial portia of the total computationskwok and cooap required! to solve stiff...exep, possl- bly, foreciadalms of problem. That is% a syste of linewat o nonlinear algebrac equa- tion mumt be solved at auk step of the numerical ...onjugate gradient method [431 is a mall-know ezuze, have prove to be particularly -2- efecti for solving the linear stwem that &ise in the numerical

  6. A scalable parallel algorithm for multiple objective linear programs

    NASA Technical Reports Server (NTRS)

    Wiecek, Malgorzata M.; Zhang, Hong

    1994-01-01

    This paper presents an ADBASE-based parallel algorithm for solving multiple objective linear programs (MOLP's). Job balance, speedup and scalability are of primary interest in evaluating efficiency of the new algorithm. Implementation results on Intel iPSC/2 and Paragon multiprocessors show that the algorithm significantly speeds up the process of solving MOLP's, which is understood as generating all or some efficient extreme points and unbounded efficient edges. The algorithm gives specially good results for large and very large problems. Motivation and justification for solving such large MOLP's are also included.

  7. Same Old Problem, New Name? Alerting Students to the Nature of the Problem-Solving Process

    ERIC Educational Resources Information Center

    Yerushalmi, Edit; Magen, Esther

    2006-01-01

    Students frequently misconceive the process of problem-solving, expecting the linear process required for solving an exercise, rather than the convoluted search process required to solve a genuine problem. In this paper we present an activity designed to foster in students realization and appreciation of the nature of the problem-solving process,…

  8. Measuring the global information society - explaining digital inequality by economic level and education standard

    NASA Astrophysics Data System (ADS)

    Ünver, H.

    2017-02-01

    A main focus of this research paper is to investigate on the explanation of the ‘digital inequality’ or ‘digital divide’ by economic level and education standard of about 150 countries worldwide. Inequality regarding GDP per capita, literacy and the so-called UN Education Index seem to be important factors affecting ICT usage, in particular Internet penetration, mobile phone usage and also mobile Internet services. Empirical methods and (multivariate) regression analysis with linear and non-linear functions are useful methods to measure some crucial factors of a country or culture towards becoming information and knowledge based society. Overall, the study concludes that the convergence regarding ICT usage proceeds worldwide faster than the convergence in terms of economic wealth and education in general. The results based on a large data analysis show that the digital divide is declining over more than a decade between 2000 and 2013, since more people worldwide use mobile phones and the Internet. But a high digital inequality explained to a significant extent by the functional relation between technology penetration rates, education level and average income still exists. Furthermore it supports the actions of countries at UN/G20/OECD level for providing ICT access to all people for a more balanced world in context of sustainable development by postulating that policymakers need to promote comprehensive education worldwide by means of using ICT.

  9. Inequalities in out-of-pocket payments for health care services among elderly Germans – results of a population-based cross-sectional study

    PubMed Central

    2014-01-01

    Introduction In order to limit rising publicly-financed health expenditure, out-of-pocket payments for health care services (OOPP) have been raised in many industrialized countries. However, higher health-related OOPP may burden social subgroups unequally. In Germany, inequalities in OOPP have rarely been analyzed. The aim of this study was to examine OOPP of the German elderly population in the different sectors of the health care system. Socio-economic and morbidity-related determinants of inequalities in OOPP were analyzed. Methods This cross-sectional analysis used data of N = 3,124 subjects aged 57 to 84 years from a population-based prospective cohort study (ESTHER study) collected in the Saarland, Germany, from 2008 to 2010. Subjects passed a geriatric assessment, including a questionnaire for health care utilization and OOPP covering a period of three months in the following sectors: inpatient care, outpatient physician and non-physician services, medical supplies, pharmaceuticals, dental prostheses and nursing care. Determinants of OOPP were analyzed by a two-part model. The financial burden of OOPP for certain social subgroups (measured by the OOPP-income-ratio) was investigated by a generalized linear model for the binomial family. Results Mean OOPP during three months amounted to €119, with 34% for medical supplies, 22% for dental prostheses, 21% for pharmaceuticals, 17% for outpatient physician and non-physician services, 5% for inpatient care and 1% for nursing care. The two-part model showed a significant positive association between income (square root equivalence scale) and total OOPP. Increasing morbidity was associated with significantly higher total OOPP, and in particular with higher OOPP for pharmaceuticals. Total OOPP amounted to about 3% of disposable income. The generalized linear model for the binomial family showed a significantly lower financial burden for the wealthiest quintile as compared to the poorest one. Conclusions This is the first study providing evidence of inequalities in OOPP in the German elderly population. Socio-economic and morbidity-related inequalities in OOPP and the resulting financial burden could be identified. The results of this study may contribute to the discussion about the mechanisms causing the observed inequalities and can thus help decision makers to consider them when adapting future regulations on OOPP. PMID:24397544

  10. Adaptive tracking control of leader-following linear multi-agent systems with external disturbances

    NASA Astrophysics Data System (ADS)

    Lin, Hanquan; Wei, Qinglai; Liu, Derong; Ma, Hongwen

    2016-10-01

    In this paper, the consensus problem for leader-following linear multi-agent systems with external disturbances is investigated. Brownian motions are used to describe exogenous disturbances. A distributed tracking controller based on Riccati inequalities with an adaptive law for adjusting coupling weights between neighbouring agents is designed for leader-following multi-agent systems under fixed and switching topologies. In traditional distributed static controllers, the coupling weights depend on the communication graph. However, coupling weights associated with the feedback gain matrix in our method are updated by state errors between neighbouring agents. We further present the stability analysis of leader-following multi-agent systems with stochastic disturbances under switching topology. Most traditional literature requires the graph to be connected all the time, while the communication graph is only assumed to be jointly connected in this paper. The design technique is based on Riccati inequalities and algebraic graph theory. Finally, simulations are given to show the validity of our method.

  11. Synchronization of an Inertial Neural Network With Time-Varying Delays and Its Application to Secure Communication.

    PubMed

    Lakshmanan, Shanmugam; Prakash, Mani; Lim, Chee Peng; Rakkiyappan, Rajan; Balasubramaniam, Pagavathigounder; Nahavandi, Saeid

    2018-01-01

    In this paper, synchronization of an inertial neural network with time-varying delays is investigated. Based on the variable transformation method, we transform the second-order differential equations into the first-order differential equations. Then, using suitable Lyapunov-Krasovskii functionals and Jensen's inequality, the synchronization criteria are established in terms of linear matrix inequalities. Moreover, a feedback controller is designed to attain synchronization between the master and slave models, and to ensure that the error model is globally asymptotically stable. Numerical examples and simulations are presented to indicate the effectiveness of the proposed method. Besides that, an image encryption algorithm is proposed based on the piecewise linear chaotic map and the chaotic inertial neural network. The chaotic signals obtained from the inertial neural network are utilized for the encryption process. Statistical analyses are provided to evaluate the effectiveness of the proposed encryption algorithm. The results ascertain that the proposed encryption algorithm is efficient and reliable for secure communication applications.

  12. Measuring correlations in non-separable vector beams using projective measurements

    NASA Astrophysics Data System (ADS)

    Subramanian, Keerthan; Viswanathan, Nirmal K.

    2017-09-01

    Doubts regarding the completeness of quantum mechanics as raised by Einstein, Podolsky and Rosen(EPR) have predominantly been resolved by resorting to a measurement of correlations between entangled photons which clearly demonstrate violation of Bell's inequality. This article is an attempt to reconcile incompatibility of hidden variable theories with reality by demonstrating experimentally a violation of Bell's inequality in locally correlated systems whose two degrees of freedom, the spin and orbital angular momentum, are maximally correlated. To this end we propose and demonstrate a linear, achromatic modified Sagnac interferometer to project orbital angular momentum states which we combine with spin projections to measure correlations.

  13. Community mobilisation in the 21st century: updating our theory of social change?

    PubMed

    Campbell, Catherine

    2014-01-01

    The article explores the Freirian theory of social change underpinning health-related community mobilisation in poor and marginalised communities. Highlighting potential shortcomings of its essentialist understandings of power and identity, and linear notions of change, it examines how lessons from the 'new left', and burgeoning global protest movements, can rejuvenate the field given the growing complexity of 21st-century social inequalities. It suggests the need for a pastiche of approaches to accommodate health struggles in different times and places. However, while needing some updating, Freire's profound and actionable understandings of the symbolic and material dimensions of social inequalities remain a powerful starting point for activism.

  14. Parameter estimation of Monod model by the Least-Squares method for microalgae Botryococcus Braunii sp

    NASA Astrophysics Data System (ADS)

    See, J. J.; Jamaian, S. S.; Salleh, R. M.; Nor, M. E.; Aman, F.

    2018-04-01

    This research aims to estimate the parameters of Monod model of microalgae Botryococcus Braunii sp growth by the Least-Squares method. Monod equation is a non-linear equation which can be transformed into a linear equation form and it is solved by implementing the Least-Squares linear regression method. Meanwhile, Gauss-Newton method is an alternative method to solve the non-linear Least-Squares problem with the aim to obtain the parameters value of Monod model by minimizing the sum of square error ( SSE). As the result, the parameters of the Monod model for microalgae Botryococcus Braunii sp can be estimated by the Least-Squares method. However, the estimated parameters value obtained by the non-linear Least-Squares method are more accurate compared to the linear Least-Squares method since the SSE of the non-linear Least-Squares method is less than the linear Least-Squares method.

  15. Improving Shaping Efforts in Africa’s Maghreb and Sahel

    DTIC Science & Technology

    2011-03-21

    threat in North Africa to U.S. interests? Al Qaeda in the Islamic Maghreb (AQIM) is a relatively new franchise of Al Qaeda. Upon declaring allegiance...trafficking to finance their operations. Should a West African franchise of Al Qaeda, or any other terrorist organization with local grievances and/or global...solve issues like desertification, poverty, unemployment , social inequalities, and so on. By adapting to this new environment and by reallocating

  16. Linear SFM: A hierarchical approach to solving structure-from-motion problems by decoupling the linear and nonlinear components

    NASA Astrophysics Data System (ADS)

    Zhao, Liang; Huang, Shoudong; Dissanayake, Gamini

    2018-07-01

    This paper presents a novel hierarchical approach to solving structure-from-motion (SFM) problems. The algorithm begins with small local reconstructions based on nonlinear bundle adjustment (BA). These are then joined in a hierarchical manner using a strategy that requires solving a linear least squares optimization problem followed by a nonlinear transform. The algorithm can handle ordered monocular and stereo image sequences. Two stereo images or three monocular images are adequate for building each initial reconstruction. The bulk of the computation involves solving a linear least squares problem and, therefore, the proposed algorithm avoids three major issues associated with most of the nonlinear optimization algorithms currently used for SFM: the need for a reasonably accurate initial estimate, the need for iterations, and the possibility of being trapped in a local minimum. Also, by summarizing all the original observations into the small local reconstructions with associated information matrices, the proposed Linear SFM manages to preserve all the information contained in the observations. The paper also demonstrates that the proposed problem formulation results in a sparse structure that leads to an efficient numerical implementation. The experimental results using publicly available datasets show that the proposed algorithm yields solutions that are very close to those obtained using a global BA starting with an accurate initial estimate. The C/C++ source code of the proposed algorithm is publicly available at https://github.com/LiangZhaoPKUImperial/LinearSFM.

  17. A 2D systems approach to iterative learning control for discrete linear processes with zero Markov parameters

    NASA Astrophysics Data System (ADS)

    Hladowski, Lukasz; Galkowski, Krzysztof; Cai, Zhonglun; Rogers, Eric; Freeman, Chris T.; Lewin, Paul L.

    2011-07-01

    In this article a new approach to iterative learning control for the practically relevant case of deterministic discrete linear plants with uniform rank greater than unity is developed. The analysis is undertaken in a 2D systems setting that, by using a strong form of stability for linear repetitive processes, allows simultaneous consideration of both trial-to-trial error convergence and along the trial performance, resulting in design algorithms that can be computed using linear matrix inequalities (LMIs). Finally, the control laws are experimentally verified on a gantry robot that replicates a pick and place operation commonly found in a number of applications to which iterative learning control is applicable.

  18. A systematic linear space approach to solving partially described inverse eigenvalue problems

    NASA Astrophysics Data System (ADS)

    Hu, Sau-Lon James; Li, Haujun

    2008-06-01

    Most applications of the inverse eigenvalue problem (IEP), which concerns the reconstruction of a matrix from prescribed spectral data, are associated with special classes of structured matrices. Solving the IEP requires one to satisfy both the spectral constraint and the structural constraint. If the spectral constraint consists of only one or few prescribed eigenpairs, this kind of inverse problem has been referred to as the partially described inverse eigenvalue problem (PDIEP). This paper develops an efficient, general and systematic approach to solve the PDIEP. Basically, the approach, applicable to various structured matrices, converts the PDIEP into an ordinary inverse problem that is formulated as a set of simultaneous linear equations. While solving simultaneous linear equations for model parameters, the singular value decomposition method is applied. Because of the conversion to an ordinary inverse problem, other constraints associated with the model parameters can be easily incorporated into the solution procedure. The detailed derivation and numerical examples to implement the newly developed approach to symmetric Toeplitz and quadratic pencil (including mass, damping and stiffness matrices of a linear dynamic system) PDIEPs are presented. Excellent numerical results for both kinds of problem are achieved under the situations that have either unique or infinitely many solutions.

  19. Reifying human difference: the debate on genetics, race, and health.

    PubMed

    Braun, Lundy

    2006-01-01

    The causes of racial and ethnic inequalities in health and the most appropriate categories to use to address health inequality have been the subject of heated debate in recent years. At the same time, genetic explanations for racial disparities have figured prominently in the scientific and popular press since the announcement of the sequencing of the human genome. To understand how such explanations assumed prominence, this essay analyzes the circulation of ideas about race and genetics and the rhetorical strategies used by authors of key texts to shape the debate. The authority of genetic accounts for racial and ethnic difference in disease, the author argues, is rooted in a broad cultural faith in the promise of genetics to solve problems of human disease and the inner truth of human beings that is intertwined with historical meanings attached to race. Such accounts are problematic for a variety of reasons. Importantly, they produce, reify, and naturalize notions of racial difference, provide a scientific rationale for racially targeted medical care, and distract attention from research that probes the complex ways in which political, economic, social, and biological factors, especially those of inequality and racism, cause health disparities.

  20. Solving Fuzzy Optimization Problem Using Hybrid Ls-Sa Method

    NASA Astrophysics Data System (ADS)

    Vasant, Pandian

    2011-06-01

    Fuzzy optimization problem has been one of the most and prominent topics inside the broad area of computational intelligent. It's especially relevant in the filed of fuzzy non-linear programming. It's application as well as practical realization can been seen in all the real world problems. In this paper a large scale non-linear fuzzy programming problem has been solved by hybrid optimization techniques of Line Search (LS), Simulated Annealing (SA) and Pattern Search (PS). As industrial production planning problem with cubic objective function, 8 decision variables and 29 constraints has been solved successfully using LS-SA-PS hybrid optimization techniques. The computational results for the objective function respect to vagueness factor and level of satisfaction has been provided in the form of 2D and 3D plots. The outcome is very promising and strongly suggests that the hybrid LS-SA-PS algorithm is very efficient and productive in solving the large scale non-linear fuzzy programming problem.

  1. Towards lexicographic multi-objective linear programming using grossone methodology

    NASA Astrophysics Data System (ADS)

    Cococcioni, Marco; Pappalardo, Massimo; Sergeyev, Yaroslav D.

    2016-10-01

    Lexicographic Multi-Objective Linear Programming (LMOLP) problems can be solved in two ways: preemptive and nonpreemptive. The preemptive approach requires the solution of a series of LP problems, with changing constraints (each time the next objective is added, a new constraint appears). The nonpreemptive approach is based on a scalarization of the multiple objectives into a single-objective linear function by a weighted combination of the given objectives. It requires the specification of a set of weights, which is not straightforward and can be time consuming. In this work we present both mathematical and software ingredients necessary to solve LMOLP problems using a recently introduced computational methodology (allowing one to work numerically with infinities and infinitesimals) based on the concept of grossone. The ultimate goal of such an attempt is an implementation of a simplex-like algorithm, able to solve the original LMOLP problem by solving only one single-objective problem and without the need to specify finite weights. The expected advantages are therefore obvious.

  2. Variance approach for multi-objective linear programming with fuzzy random of objective function coefficients

    NASA Astrophysics Data System (ADS)

    Indarsih, Indrati, Ch. Rini

    2016-02-01

    In this paper, we define variance of the fuzzy random variables through alpha level. We have a theorem that can be used to know that the variance of fuzzy random variables is a fuzzy number. We have a multi-objective linear programming (MOLP) with fuzzy random of objective function coefficients. We will solve the problem by variance approach. The approach transform the MOLP with fuzzy random of objective function coefficients into MOLP with fuzzy of objective function coefficients. By weighted methods, we have linear programming with fuzzy coefficients and we solve by simplex method for fuzzy linear programming.

  3. A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation

    NASA Technical Reports Server (NTRS)

    Diosady, Laslo T.; Murman, Scott M.

    2018-01-01

    A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.

  4. Psychosocial work exposures among European employees: explanations for occupational inequalities in mental health.

    PubMed

    Schütte, Stefanie; Chastang, Jean-François; Parent-Thirion, Agnès; Vermeylen, Greet; Niedhammer, Isabelle

    2015-09-01

    Social inequalities in mental health have been demonstrated but understanding the mechanisms remains unclear. This study aims at exploring the role of psychosocial work factors in explaining occupational inequalities in mental health among European employees. The study sample covered 33,443 employees coming from the European Working Conditions Survey 2010. Mental health was measured by the WHO-5 well-being index and socioeconomic position by occupation. Twenty-five psychosocial work factors were constructed including job demands, job influence and development, role stressors, social support, quality of leadership, discrimination, violence at work, working hours, job promotion, job insecurity and work-life imbalance. Multilevel linear regressions and bootstrap analyses were performed. Occupational differences were observed for poor mental health and almost all psychosocial work factors. Factors related to job demands, influence and development at work, social relationships and leadership, working hours and other factors contributed to explain the occupational inequalities in mental health. In particular, factors related to influence and development contributed substantially. Among men, workplace violences were found to contribute little whereas among women these factors did not play a role. Future prevention interventions should have a broad and comprehensive focus in order to reduce social inequalities in mental health. © The Author 2015. Published by Oxford University Press on behalf of Faculty of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

  5. Quantum cryptography using single-particle entanglement

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Lee, Jae-Weon; Lee, Eok Kyun; Chung, Yong Wook

    2003-07-01

    A quantum cryptography scheme based on entanglement between a single-particle state and a vacuum state is proposed. The scheme utilizes linear optics devices to detect the superposition of the vacuum and single-particle states. Existence of an eavesdropper can be detected by using a variant of Bell's inequality.

  6. Projective-Dual Method for Solving Systems of Linear Equations with Nonnegative Variables

    NASA Astrophysics Data System (ADS)

    Ganin, B. V.; Golikov, A. I.; Evtushenko, Yu. G.

    2018-02-01

    In order to solve an underdetermined system of linear equations with nonnegative variables, the projection of a given point onto its solutions set is sought. The dual of this problem—the problem of unconstrained maximization of a piecewise-quadratic function—is solved by Newton's method. The problem of unconstrained optimization dual of the regularized problem of finding the projection onto the solution set of the system is considered. A connection of duality theory and Newton's method with some known algorithms of projecting onto a standard simplex is shown. On the example of taking into account the specifics of the constraints of the transport linear programming problem, the possibility to increase the efficiency of calculating the generalized Hessian matrix is demonstrated. Some examples of numerical calculations using MATLAB are presented.

  7. Linear solver performance in elastoplastic problem solution on GPU cluster

    NASA Astrophysics Data System (ADS)

    Khalevitsky, Yu. V.; Konovalov, A. V.; Burmasheva, N. V.; Partin, A. S.

    2017-12-01

    Applying the finite element method to severe plastic deformation problems involves solving linear equation systems. While the solution procedure is relatively hard to parallelize and computationally intensive by itself, a long series of large scale systems need to be solved for each problem. When dealing with fine computational meshes, such as in the simulations of three-dimensional metal matrix composite microvolume deformation, tens and hundreds of hours may be needed to complete the whole solution procedure, even using modern supercomputers. In general, one of the preconditioned Krylov subspace methods is used in a linear solver for such problems. The method convergence highly depends on the operator spectrum of a problem stiffness matrix. In order to choose the appropriate method, a series of computational experiments is used. Different methods may be preferable for different computational systems for the same problem. In this paper we present experimental data obtained by solving linear equation systems from an elastoplastic problem on a GPU cluster. The data can be used to substantiate the choice of the appropriate method for a linear solver to use in severe plastic deformation simulations.

  8. High profile students’ growth of mathematical understanding in solving linier programing problems

    NASA Astrophysics Data System (ADS)

    Utomo; Kusmayadi, TA; Pramudya, I.

    2018-04-01

    Linear program has an important role in human’s life. This linear program is learned in senior high school and college levels. This material is applied in economy, transportation, military and others. Therefore, mastering linear program is useful for provision of life. This research describes a growth of mathematical understanding in solving linear programming problems based on the growth of understanding by the Piere-Kieren model. Thus, this research used qualitative approach. The subjects were students of grade XI in Salatiga city. The subjects of this study were two students who had high profiles. The researcher generally chose the subjects based on the growth of understanding from a test result in the classroom; the mark from the prerequisite material was ≥ 75. Both of the subjects were interviewed by the researcher to know the students’ growth of mathematical understanding in solving linear programming problems. The finding of this research showed that the subjects often folding back to the primitive knowing level to go forward to the next level. It happened because the subjects’ primitive understanding was not comprehensive.

  9. Robust synchronization control scheme of a population of nonlinear stochastic synthetic genetic oscillators under intrinsic and extrinsic molecular noise via quorum sensing.

    PubMed

    Chen, Bor-Sen; Hsu, Chih-Yuan

    2012-10-26

    Collective rhythms of gene regulatory networks have been a subject of considerable interest for biologists and theoreticians, in particular the synchronization of dynamic cells mediated by intercellular communication. Synchronization of a population of synthetic genetic oscillators is an important design in practical applications, because such a population distributed over different host cells needs to exploit molecular phenomena simultaneously in order to emerge a biological phenomenon. However, this synchronization may be corrupted by intrinsic kinetic parameter fluctuations and extrinsic environmental molecular noise. Therefore, robust synchronization is an important design topic in nonlinear stochastic coupled synthetic genetic oscillators with intrinsic kinetic parameter fluctuations and extrinsic molecular noise. Initially, the condition for robust synchronization of synthetic genetic oscillators was derived based on Hamilton Jacobi inequality (HJI). We found that if the synchronization robustness can confer enough intrinsic robustness to tolerate intrinsic parameter fluctuation and extrinsic robustness to filter the environmental noise, then robust synchronization of coupled synthetic genetic oscillators is guaranteed. If the synchronization robustness of a population of nonlinear stochastic coupled synthetic genetic oscillators distributed over different host cells could not be maintained, then robust synchronization could be enhanced by external control input through quorum sensing molecules. In order to simplify the analysis and design of robust synchronization of nonlinear stochastic synthetic genetic oscillators, the fuzzy interpolation method was employed to interpolate several local linear stochastic coupled systems to approximate the nonlinear stochastic coupled system so that the HJI-based synchronization design problem could be replaced by a simple linear matrix inequality (LMI)-based design problem, which could be solved with the help of LMI toolbox in MATLAB easily. If the synchronization robustness criterion, i.e. the synchronization robustness ≥ intrinsic robustness + extrinsic robustness, then the stochastic coupled synthetic oscillators can be robustly synchronized in spite of intrinsic parameter fluctuation and extrinsic noise. If the synchronization robustness criterion is violated, external control scheme by adding inducer can be designed to improve synchronization robustness of coupled synthetic genetic oscillators. The investigated robust synchronization criteria and proposed external control method are useful for a population of coupled synthetic networks with emergent synchronization behavior, especially for multi-cellular, engineered networks.

  10. Robust synchronization control scheme of a population of nonlinear stochastic synthetic genetic oscillators under intrinsic and extrinsic molecular noise via quorum sensing

    PubMed Central

    2012-01-01

    Background Collective rhythms of gene regulatory networks have been a subject of considerable interest for biologists and theoreticians, in particular the synchronization of dynamic cells mediated by intercellular communication. Synchronization of a population of synthetic genetic oscillators is an important design in practical applications, because such a population distributed over different host cells needs to exploit molecular phenomena simultaneously in order to emerge a biological phenomenon. However, this synchronization may be corrupted by intrinsic kinetic parameter fluctuations and extrinsic environmental molecular noise. Therefore, robust synchronization is an important design topic in nonlinear stochastic coupled synthetic genetic oscillators with intrinsic kinetic parameter fluctuations and extrinsic molecular noise. Results Initially, the condition for robust synchronization of synthetic genetic oscillators was derived based on Hamilton Jacobi inequality (HJI). We found that if the synchronization robustness can confer enough intrinsic robustness to tolerate intrinsic parameter fluctuation and extrinsic robustness to filter the environmental noise, then robust synchronization of coupled synthetic genetic oscillators is guaranteed. If the synchronization robustness of a population of nonlinear stochastic coupled synthetic genetic oscillators distributed over different host cells could not be maintained, then robust synchronization could be enhanced by external control input through quorum sensing molecules. In order to simplify the analysis and design of robust synchronization of nonlinear stochastic synthetic genetic oscillators, the fuzzy interpolation method was employed to interpolate several local linear stochastic coupled systems to approximate the nonlinear stochastic coupled system so that the HJI-based synchronization design problem could be replaced by a simple linear matrix inequality (LMI)-based design problem, which could be solved with the help of LMI toolbox in MATLAB easily. Conclusion If the synchronization robustness criterion, i.e. the synchronization robustness ≥ intrinsic robustness + extrinsic robustness, then the stochastic coupled synthetic oscillators can be robustly synchronized in spite of intrinsic parameter fluctuation and extrinsic noise. If the synchronization robustness criterion is violated, external control scheme by adding inducer can be designed to improve synchronization robustness of coupled synthetic genetic oscillators. The investigated robust synchronization criteria and proposed external control method are useful for a population of coupled synthetic networks with emergent synchronization behavior, especially for multi-cellular, engineered networks. PMID:23101662

  11. Social inequalities in depression and suicidal ideation among older primary care patients

    PubMed Central

    Gilman, Stephen E.; Bruce, Martha L.; Have, Thomas Ten; Alexopoulos, George S.; Mulsant, Benoit H.; Reynolds, Charles F.; Cohen, Alex

    2012-01-01

    Purpose Depression and suicide are major public health concerns, and are often unrecognized among the elderly. This study investigated social inequalities in depressive symptoms and suicidal ideation among older adults. Methods Data come from 1,226 participants in PROSPECT (Prevention of Suicide in Primary Care Elderly: Collaborative Trial), a large primary care-based intervention trial for late-life depression. Linear and logistic regressions were used to analyze depressive symptoms and suicidal ideation over the two-year follow-up period. Results Mean Hamilton Depression Rating Scale (HDRS) scores were significantly higher among participants in financial strain (regression coefficient (b)=1.78, 95% confidence interval (CI)=0.67–2.89) and with annual incomes below $20,000 (b=1.67, CI=0.34–3.00). Financial strain was also associated with a higher risk of suicidal ideation (odds ratio=2.35, CI=1.38–3.98). Conclusions There exist marked social inequalities in depressive symptoms and suicidal ideation among older adults attending primary care practices, the setting in which depression is most commonly treated. Our results justify continued efforts to understand the mechanisms generating such inequalities, and to recognize and provide effective treatments for depression among high-risk populations. PMID:22948560

  12. On the Convenience of Using the Complete Linearization Method in Modelling the BLR of AGN

    NASA Astrophysics Data System (ADS)

    Patriarchi, P.; Perinotto, M.

    The Complete Linearization Method (Mihalas, 1978) consists in the determination of the radiation field (at a set of frequency points), atomic level populations, temperature, electron density etc., by resolving the system of radiative transfer, thermal equilibrium, statistical equilibrium equations simultaneously and self-consistently. Since the system is not linear, it must be solved by iteration after linearization, using a perturbative method, starting from an initial guess solution. Of course the Complete Linearization Method is more time consuming than the previous one. But how great can this disadvantage be in the age of supercomputers? It is possible to approximately evaluate the CPU time needed to run a model by computing the number of multiplications necessary to solve the system.

  13. Modification of 2-D Time-Domain Shallow Water Wave Equation using Asymptotic Expansion Method

    NASA Astrophysics Data System (ADS)

    Khairuman, Teuku; Nasruddin, MN; Tulus; Ramli, Marwan

    2018-01-01

    Generally, research on the tsunami wave propagation model can be conducted by using a linear model of shallow water theory, where a non-linear side on high order is ignored. In line with research on the investigation of the tsunami waves, the Boussinesq equation model underwent a change aimed to obtain an improved quality of the dispersion relation and non-linearity by increasing the order to be higher. To solve non-linear sides at high order is used a asymptotic expansion method. This method can be used to solve non linear partial differential equations. In the present work, we found that this method needs much computational time and memory with the increase of the number of elements.

  14. Contribution of working conditions to occupational inequalities in depressive symptoms: results from the national French SUMER survey.

    PubMed

    Niedhammer, Isabelle; Lesuffleur, Thomas; Coutrot, Thomas; Chastang, Jean-François

    2016-08-01

    Social inequalities in mental health have been observed, but explanations are still lacking. The objectives were to evaluate the contribution of a large set of psychosocial work factors and other occupational exposures to social inequalities in mental health in a national representative sample of employees. The sample from the cross-sectional national French survey SUMER 2010 included 46,962 employees: 26,883 men and 20,079 women. Anxiety and depression symptoms were measured using the Hospital Anxiety and Depression scale. Occupation was used as a marker of social position. Psychosocial work factors included various variables related to the classical job strain model, psychological demands, decision latitude, social support, and other understudied variables related to reward, job insecurity, job promotion, esteem, working time/hours, and workplace violence. Other occupational exposures of chemical, biological, physical, and biomechanical nature were also studied. Weighted age-adjusted linear regression analyses were performed. Occupational gradients were found in the exposure to most psychosocial work factors and other occupational exposures. Occupational inequalities were observed for depressive symptoms, but not for anxiety symptoms. The factors related to decision latitude (and its sub-dimensions, skill discretion, and decision authority), social support, and reward (and its sub-dimensions, job promotion, job insecurity, and esteem) contributed to explain occupational inequalities in depressive symptoms. Decision latitude played a major role in the explanation. Workplace violence variables contributed among men only. Other exposures of physical and biomechanical nature also displayed significant contributions. Comprehensive prevention policies at the workplace may help to reduce social inequalities in mental health in the working population.

  15. Linear and Non-Linear Visual Feature Learning in Rat and Humans

    PubMed Central

    Bossens, Christophe; Op de Beeck, Hans P.

    2016-01-01

    The visual system processes visual input in a hierarchical manner in order to extract relevant features that can be used in tasks such as invariant object recognition. Although typically investigated in primates, recent work has shown that rats can be trained in a variety of visual object and shape recognition tasks. These studies did not pinpoint the complexity of the features used by these animals. Many tasks might be solved by using a combination of relatively simple features which tend to be correlated. Alternatively, rats might extract complex features or feature combinations which are nonlinear with respect to those simple features. In the present study, we address this question by starting from a small stimulus set for which one stimulus-response mapping involves a simple linear feature to solve the task while another mapping needs a well-defined nonlinear combination of simpler features related to shape symmetry. We verified computationally that the nonlinear task cannot be trivially solved by a simple V1-model. We show how rats are able to solve the linear feature task but are unable to acquire the nonlinear feature. In contrast, humans are able to use the nonlinear feature and are even faster in uncovering this solution as compared to the linear feature. The implications for the computational capabilities of the rat visual system are discussed. PMID:28066201

  16. A linear programming manual

    NASA Technical Reports Server (NTRS)

    Tuey, R. C.

    1972-01-01

    Computer solutions of linear programming problems are outlined. Information covers vector spaces, convex sets, and matrix algebra elements for solving simultaneous linear equations. Dual problems, reduced cost analysis, ranges, and error analysis are illustrated.

  17. Ultrametric properties of the attractor spaces for random iterated linear function systems

    NASA Astrophysics Data System (ADS)

    Buchovets, A. G.; Moskalev, P. V.

    2018-03-01

    We investigate attractors of random iterated linear function systems as independent spaces embedded in the ordinary Euclidean space. The introduction on the set of attractor points of a metric that satisfies the strengthened triangle inequality makes this space ultrametric. Then inherent in ultrametric spaces the properties of disconnectedness and hierarchical self-similarity make it possible to define an attractor as a fractal. We note that a rigorous proof of these properties in the case of an ordinary Euclidean space is very difficult.

  18. On the boundedness and integration of non-oscillatory solutions of certain linear differential equations of second order.

    PubMed

    Tunç, Cemil; Tunç, Osman

    2016-01-01

    In this paper, certain system of linear homogeneous differential equations of second-order is considered. By using integral inequalities, some new criteria for bounded and [Formula: see text]-solutions, upper bounds for values of improper integrals of the solutions and their derivatives are established to the considered system. The obtained results in this paper are considered as extension to the results obtained by Kroopnick (2014) [1]. An example is given to illustrate the obtained results.

  19. Trends in Health Disparities, Health Inequity, and Social Determinants of Health Research: A 17-Year Analysis of NINR, NCI, NHLBI, and NIMHD Funding.

    PubMed

    Kneipp, Shawn M; Schwartz, Todd A; Drevdahl, Denise J; Canales, Mary K; Santacroce, Sheila; Santos, Hudson P; Anderson, Ruth

    The theoretical landscape of health disparities research now emphasizes health inequities and the role that social determinants of health (SDOH) play in creating and perpetuating them. Whether National Institutes of Health (NIH) funding patterns reflect this theoretical shift is unknown. The aim of this study was to examine the National Institute of Nursing Research's (NINR) funding for research focused on health disparities, health inequities, and SDOH, relative to other key NIH institutes. Data on 32,968 projects funded by NINR, the National Cancer Institute, the National Heart, Lung, and Blood Institute, and the National Institute of Minority Health and Health Disparities (NIMHD) during the years 2000 through 2016 were downloaded from NIH RePORTER; those with health disparities, health inequity, or SDOH terms used in the abstract were identified. Descriptive statistics and a general linear model approach were used to assess differences in cumulative project counts and funding proportions, and funding trends over time. Overall, funding for health disparities projects was 14-19 times greater than for health inequity and SDOH projects and was more concentrated in centers and institutional training than in individual research projects. NINR's proportion of funding for disparities projects was consistently greater than that of the National Cancer Institute and the National Heart, Lung, and Blood Institute, but not for inequities and SDOH projects. NIMHD's proportion of funding for disparities, and inequities and SDOH projects (combined) was 2-30 times greater than that of other institutes. Over the 16-year period, funding for disparities, inequity, and SDOH projects each increased (all ps < .05); however, growth in inequities and SDOH funding was not evident in more recent years. Funding for projects focused on health equities and the SDOH lag behind theoretical shifts in the broader health disparities research arena. With the exception of NIMHD, there is a disconnect between funding for projects with a disparities orientation in institutional training and center projects relative to individual research projects. These trends have implications for nurse scientists seeking NIH funding to support health equity-oriented research.

  20. Investigating maternal risk factors as potential targets of intervention to reduce socioeconomic inequality in small for gestational age: a population-based study.

    PubMed

    Hayward, Irene; Malcoe, Lorraine Halinka; Cleathero, Lesley A; Janssen, Patricia A; Lanphear, Bruce P; Hayes, Michael V; Mattman, Andre; Pampalon, Robert; Venners, Scott A

    2012-06-13

    The major aim of this study was to investigate whether maternal risk factors associated with socioeconomic status and small for gestational age (SGA) might be viable targets of interventions to reduce differential risk of SGA by socioeconomic status (socioeconomic SGA inequality) in the metropolitan area of Vancouver, Canada. This study included 59,039 live, singleton births in the Vancouver Census Metropolitan Area (Vancouver) from January 1, 2006 to September 17, 2009. To identify an indicator of socioeconomic SGA inequality, we used hierarchical logistic regression to model SGA by area-level variables from the Canadian census. We then modelled SGA by area-level average income plus established maternal risk factors for SGA and calculated population attributable SGA risk percentages (PAR%) for each variable. Associations of maternal risk factors for SGA with average income were investigated to identify those that might contribute to SGA inequality. Finally, we estimated crude reductions in the percentage and absolute differences in SGA risks between highest and lowest average income quintiles that would result if interventions on maternal risk factors successfully equalized them across income levels or eliminated them altogether. Average income produced the most linear and statistically significant indicator of socioeconomic SGA inequality with 8.9% prevalence of SGA in the lowest income quintile compared to 5.6% in the highest. The adjusted PAR% of SGA for variables were: bottom four quintiles of height (51%), first birth (32%), bottom four quintiles of average income (14%), oligohydramnios (7%), underweight or hypertension, (6% each), smoking (3%) and placental disorder (1%). Shorter height, underweight and smoking during pregnancy had higher prevalence in lower income groups. Crude models assuming equalization of risk factors across income levels or elimination altogether indicated little potential change in relative socioeconomic SGA inequality and reduction in absolute SGA inequality for shorter height only. Our findings regarding maternal height may indicate trans-generational aetiology for socioeconomic SGA inequalities and/or that adult height influences social mobility. Conditions affecting foetal and childhood growth might be viable targets to reduce absolute socioeconomic SGA inequality in future generations, but more research is needed to determine whether such an approach is appropriate.

  1. History-Dependent Problems with Applications to Contact Models for Elastic Beams

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Bartosz, Krzysztof; Kalita, Piotr; Migórski, Stanisław

    We prove an existence and uniqueness result for a class of subdifferential inclusions which involve a history-dependent operator. Then we specialize this result in the study of a class of history-dependent hemivariational inequalities. Problems of such kind arise in a large number of mathematical models which describe quasistatic processes of contact. To provide an example we consider an elastic beam in contact with a reactive obstacle. The contact is modeled with a new and nonstandard condition which involves both the subdifferential of a nonconvex and nonsmooth function and a Volterra-type integral term. We derive a variational formulation of the problemmore » which is in the form of a history-dependent hemivariational inequality for the displacement field. Then, we use our abstract result to prove its unique weak solvability. Finally, we consider a numerical approximation of the model, solve effectively the approximate problems and provide numerical simulations.« less

  2. Not Just "Study Drugs" for the Rich: Stimulants as Moral Tools for Creating Opportunities for Socially Disadvantaged Students.

    PubMed

    Ray, Keisha Shantel

    2016-06-01

    An argument in the cognitive enhancement literature is that using stimulants in populations of healthy but socially disadvantaged individuals mistakenly attributes pathology to nonpathological individuals who experience social inequalities. As the argument goes, using stimulants as cognitive-enhancing drugs to solve the social problem of poorly educated students in inadequate schools misattributes the problem as an individual medical problem, when it is really a collective sociopolitical problem. I challenge this argument on the grounds that not all types of enhancement have to be explained in medical terms, but rather at least one conception of enhancement can be explained in social terms-opportunity maintenance. Therefore, I propose that as a moral requirement we ought to explore whether stimulants could be a means of remedying underprivileged children's experiences of social inequalities that are borne from inadequate schools for the sake of increasing their chances for opportunities and well-being.

  3. Some Issues about the Introduction of First Concepts in Linear Algebra during Tutorial Sessions at the Beginning of University

    ERIC Educational Resources Information Center

    Grenier-Boley, Nicolas

    2014-01-01

    Certain mathematical concepts were not introduced to solve a specific open problem but rather to solve different problems with the same tools in an economic formal way or to unify several approaches: such concepts, as some of those of linear algebra, are presumably difficult to introduce to students as they are potentially interwoven with many…

  4. Switched periodic systems in discrete time: stability and input-output norms

    NASA Astrophysics Data System (ADS)

    Bolzern, Paolo; Colaneri, Patrizio

    2013-07-01

    This paper deals with the analysis of stability and the characterisation of input-output norms for discrete-time periodic switched linear systems. Such systems consist of a network of time-periodic linear subsystems sharing the same state vector and an exogenous switching signal that triggers the jumps between the subsystems. The overall system exhibits a complex dynamic behaviour due to the interplay between the time periodicity of the subsystem parameters and the switching signal. Both arbitrary switching signals and signals satisfying a dwell-time constraint are considered. Linear matrix inequality conditions for stability and guaranteed H2 and H∞ performances are provided. The results heavily rely on the merge of the theory of linear periodic systems and recent developments on switched linear time-invariant systems.

  5. Contextual Effects on Kindergarten Teachers' Intention to Report Child Abuse

    ERIC Educational Resources Information Center

    Feng, Jui-Ying; Wu, Yow-Wu B.; Fetzer, Susan; Chang, Hsin-Yi

    2012-01-01

    Child abuse is underreported for children with socioeconomic inequalities. The impact of geographic location combined with sociocultural characteristics on teachers' reports of child abuse remains unclear. A national survey of 572 kindergarten teachers from 79 schools in Taiwan used hierarchical linear modeling to investigate the contribution of…

  6. Social Inequality and Labor Force Participation.

    ERIC Educational Resources Information Center

    King, Jonathan

    The labor force participation rates of whites, blacks, and Spanish-Americans, grouped by sex, are explained in a linear regression model fitted with 1970 U. S. Census data on Standard Metropolitan Statistical Area (SMSA). The explanatory variables are: average age, average years of education, vocational training rate, disabled rate, unemployment…

  7. UCSMP Algebra. What Works Clearinghouse Intervention Report

    ERIC Educational Resources Information Center

    What Works Clearinghouse, 2007

    2007-01-01

    "University of Chicago School Mathematics Project (UCSMP) Algebra," designed to increase students' skills in algebra, is appropriate for students in grades 7-10, depending on the students' incoming knowledge. This one-year course highlights applications, uses statistics and geometry to develop the algebra of linear equations and inequalities, and…

  8. Unpacking the Inequality among Turkish Schools: Findings from PISA 2006

    ERIC Educational Resources Information Center

    Alacaci, Cengiz; Erbas, Ayhan Kursat

    2010-01-01

    The study investigates the effects of certain school characteristics on students' mathematics performances in Turkey in the PISA 2006 while controlling for family background and demographic characteristics. Three models of Hierarchical Linear Modeling (HLM) are constructed. The results reveal that 55% of the variance is attributable to…

  9. Higher Order Time Integration Schemes for the Unsteady Navier-Stokes Equations on Unstructured Meshes

    NASA Technical Reports Server (NTRS)

    Jothiprasad, Giridhar; Mavriplis, Dimitri J.; Caughey, David A.; Bushnell, Dennis M. (Technical Monitor)

    2002-01-01

    The efficiency gains obtained using higher-order implicit Runge-Kutta schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier-Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each timestep are presented. The first algorithm (NMG) is a pseudo-time-stepping scheme which employs a non-linear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on Inexact Newton's methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson's iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the Generalized Minimal Residual method. Results demonstrating the relative superiority of these Newton's methods based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes with the more efficient nonlinear solvers.

  10. ELECTRONIC DIGITAL COMPUTER

    DOEpatents

    Stone, J.J. Jr.; Bettis, E.S.; Mann, E.R.

    1957-10-01

    The electronic digital computer is designed to solve systems involving a plurality of simultaneous linear equations. The computer can solve a system which converges rather rapidly when using Von Seidel's method of approximation and performs the summations required for solving for the unknown terms by a method of successive approximations.

  11. Fast, Nonlinear, Fully Probabilistic Inversion of Large Geophysical Problems

    NASA Astrophysics Data System (ADS)

    Curtis, A.; Shahraeeni, M.; Trampert, J.; Meier, U.; Cho, G.

    2010-12-01

    Almost all Geophysical inverse problems are in reality nonlinear. Fully nonlinear inversion including non-approximated physics, and solving for probability distribution functions (pdf’s) that describe the solution uncertainty, generally requires sampling-based Monte-Carlo style methods that are computationally intractable in most large problems. In order to solve such problems, physical relationships are usually linearized leading to efficiently-solved, (possibly iterated) linear inverse problems. However, it is well known that linearization can lead to erroneous solutions, and in particular to overly optimistic uncertainty estimates. What is needed across many Geophysical disciplines is a method to invert large inverse problems (or potentially tens of thousands of small inverse problems) fully probabilistically and without linearization. This talk shows how very large nonlinear inverse problems can be solved fully probabilistically and incorporating any available prior information using mixture density networks (driven by neural network banks), provided the problem can be decomposed into many small inverse problems. In this talk I will explain the methodology, compare multi-dimensional pdf inversion results to full Monte Carlo solutions, and illustrate the method with two applications: first, inverting surface wave group and phase velocities for a fully-probabilistic global tomography model of the Earth’s crust and mantle, and second inverting industrial 3D seismic data for petrophysical properties throughout and around a subsurface hydrocarbon reservoir. The latter problem is typically decomposed into 104 to 105 individual inverse problems, each solved fully probabilistically and without linearization. The results in both cases are sufficiently close to the Monte Carlo solution to exhibit realistic uncertainty, multimodality and bias. This provides far greater confidence in the results, and in decisions made on their basis.

  12. A spatial domain decomposition approach to distributed H ∞ observer design of a linear unstable parabolic distributed parameter system with spatially discrete sensors

    NASA Astrophysics Data System (ADS)

    Wang, Jun-Wei; Liu, Ya-Qiang; Hu, Yan-Yan; Sun, Chang-Yin

    2017-12-01

    This paper discusses the design problem of distributed H∞ Luenberger-type partial differential equation (PDE) observer for state estimation of a linear unstable parabolic distributed parameter system (DPS) with external disturbance and measurement disturbance. Both pointwise measurement in space and local piecewise uniform measurement in space are considered; that is, sensors are only active at some specified points or applied at part thereof of the spatial domain. The spatial domain is decomposed into multiple subdomains according to the location of the sensors such that only one sensor is located at each subdomain. By using Lyapunov technique, Wirtinger's inequality at each subdomain, and integration by parts, a Lyapunov-based design of Luenberger-type PDE observer is developed such that the resulting estimation error system is exponentially stable with an H∞ performance constraint, and presented in terms of standard linear matrix inequalities (LMIs). For the case of local piecewise uniform measurement in space, the first mean value theorem for integrals is utilised in the observer design development. Moreover, the problem of optimal H∞ observer design is also addressed in the sense of minimising the attenuation level. Numerical simulation results are presented to show the satisfactory performance of the proposed design method.

  13. Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Yang, Xiaofeng, E-mail: xfyang@math.sc.edu; Han, Daozhi, E-mail: djhan@iu.edu

    2017-02-01

    In this paper, we develop a series of linear, unconditionally energy stable numerical schemes for solving the classical phase field crystal model. The temporal discretizations are based on the first order Euler method, the second order backward differentiation formulas (BDF2) and the second order Crank–Nicolson method, respectively. The schemes lead to linear elliptic equations to be solved at each time step, and the induced linear systems are symmetric positive definite. We prove that all three schemes are unconditionally energy stable rigorously. Various classical numerical experiments in 2D and 3D are performed to validate the accuracy and efficiency of the proposedmore » schemes.« less

  14. Health inequalities between employed and unemployed in northern Sweden: a decomposition analysis of social determinants for mental health.

    PubMed

    Brydsten, Anna; Hammarström, Anne; San Sebastian, Miguel

    2018-05-16

    Even though population health is strongly influenced by employment and working conditions, public health research has to a lesser extent explored the social determinants of health inequalities between people in different positions on the labour market, and whether these social determinants vary across the life course. This study analyses mental health inequalities between unemployed and employed in three age groups (youth, adulthood and mid-life), and identifies the extent to which social determinants explain the mental health gap between employed and unemployed in northern Sweden. The Health on Equal Terms survey of 2014 was used, with self-reported employment (unemployed or employed) as exposure and the General Health Questionnaire (GHQ-12) as mental health outcome. The social determinants of health inequalities were grouped into four dimensions: socioeconomic status, economic resources, social network and trust in institutional systems. The non-linear Oaxaca decomposition analysis was applied, stratified by gender and age groups. Mental health inequality was found in all age groups among women and men (difference in GHQ varying between 0.12 and 0.20). The decomposition analysis showed that the social determinants included in the model accounted for 43-51% of the inequalities among youths, 42-98% of the inequalities among adults and 60-65% among middle-aged. The main contributing factors were shown to vary between age groups: cash margin (among youths and middle-aged men), financial strain (among adults and middle-aged women), income (among men in adulthood), along with trust in others (all age groups), practical support (young women) and social support (middle-aged men); stressing how the social determinants of health inequalities vary across the life course. The health gap between employed and unemployed was explained by the difference in access to economic and social resources, and to a smaller extent in the trust in the institutional systems. Findings from this study corroborate that much of the mental health inequality in the Swedish labour market is socially and politically produced and potentially avoidable. Greater attention from researchers, policy makers on unemployment and public health should be devoted to the social and economic deprivation of unemployment from a life course perspective to prevent mental health inequality.

  15. Impulsive synchronization of stochastic reaction-diffusion neural networks with mixed time delays.

    PubMed

    Sheng, Yin; Zeng, Zhigang

    2018-07-01

    This paper discusses impulsive synchronization of stochastic reaction-diffusion neural networks with Dirichlet boundary conditions and hybrid time delays. By virtue of inequality techniques, theories of stochastic analysis, linear matrix inequalities, and the contradiction method, sufficient criteria are proposed to ensure exponential synchronization of the addressed stochastic reaction-diffusion neural networks with mixed time delays via a designed impulsive controller. Compared with some recent studies, the neural network models herein are more general, some restrictions are relaxed, and the obtained conditions enhance and generalize some published ones. Finally, two numerical simulations are performed to substantiate the validity and merits of the developed theoretical analysis. Copyright © 2018 Elsevier Ltd. All rights reserved.

  16. Investigating the impact of the English health inequalities strategy: time trend analysis.

    PubMed

    Barr, Ben; Higgerson, James; Whitehead, Margaret

    2017-07-26

    Objective  To investigate whether the English health inequalities strategy was associated with a decline in geographical health inequalities, compared with trends before and after the strategy. Design  Time trend analysis. Setting  Two groups of lower tier local authorities in England. The most deprived, bottom fifth and the rest of England. Intervention  The English health inequalities strategy-a cross government strategy implemented between 1997 and 2010 to reduce health inequalities in England. Trends in geographical health inequalities were assessed before (1983-2003), during (2004-12), and after (2013-15) the strategy using segmented linear regression. Main outcome measure  Geographical health inequalities measured as the relative and absolute differences in male and female life expectancy at birth between the most deprived local authorities in England and the rest of the country. Results  Before the strategy the gap in male and female life expectancy between the most deprived local authorities in England and the rest of the country increased at a rate of 0.57 months each year (95% confidence interval 0.40 to 0.74 months) and 0.30 months each year (0.12 to 0.48 months). During the strategy period this trend reversed and the gap in life expectancy for men reduced by 0.91 months each year (0.54 to 1.27 months) and for women by 0.50 months each year (0.15 to 0.86 months). Since the end of the strategy period the inequality gap has increased again at a rate of 0.68 months each year (-0.20 to 1.56 months) for men and 0.31 months each year (-0.26 to 0.88) for women. By 2012 the gap in male life expectancy was 1.2 years smaller (95% confidence interval 0.8 to 1.5 years smaller) and the gap in female life expectancy was 0.6 years smaller (0.3 to 1.0 years smaller) than it would have been if the trends in inequalities before the strategy had continued. Conclusion  The English health inequalities strategy was associated with a decline in geographical inequalities in life expectancy, reversing a previously increasing trend. Since the strategy ended, inequalities have started to increase again. The strategy may have reduced geographical health inequalities in life expectancy, and future approaches should learn from this experience. The concerns are that current policies are reversing the achievements of the strategy. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://group.bmj.com/group/rights-licensing/permissions.

  17. A reciprocal theorem for a mixture theory. [development of linearized theory of interacting media

    NASA Technical Reports Server (NTRS)

    Martin, C. J.; Lee, Y. M.

    1972-01-01

    A dynamic reciprocal theorem for a linearized theory of interacting media is developed. The constituents of the mixture are a linear elastic solid and a linearly viscous fluid. In addition to Steel's field equations, boundary conditions and inequalities on the material constants that have been shown by Atkin, Chadwick and Steel to be sufficient to guarantee uniqueness of solution to initial-boundary value problems are used. The elements of the theory are given and two different boundary value problems are considered. The reciprocal theorem is derived with the aid of the Laplace transform and the divergence theorem and this section is concluded with a discussion of the special cases which arise when one of the constituents of the mixture is absent.

  18. Decentralized event-triggered synchronization of uncertain Markovian jumping neutral-type neural networks with mixed delays.

    PubMed

    Senan, Sibel; Syed Ali, M; Vadivel, R; Arik, Sabri

    2017-02-01

    In this study, we present an approach for the decentralized event-triggered synchronization of Markovian jumping neutral-type neural networks with mixed delays. We present a method for designing decentralized event-triggered synchronization, which only utilizes locally available information, in order to determine the time instants for transmission from sensors to a central controller. By applying a novel Lyapunov-Krasovskii functional, as well as using the reciprocal convex combination method and some inequality techniques such as Jensen's inequality, we obtain several sufficient conditions in terms of a set of linear matrix inequalities (LMIs) under which the delayed neural networks are stochastically stable in terms of the error systems. Finally, we conclude that the drive systems synchronize stochastically with the response systems. We show that the proposed stability criteria can be verified easily using the numerically efficient Matlab LMI toolbox. The effectiveness and feasibility of the results obtained are verified by numerical examples. Copyright © 2016 Elsevier Ltd. All rights reserved.

  19. Stability analysis of switched cellular neural networks: A mode-dependent average dwell time approach.

    PubMed

    Huang, Chuangxia; Cao, Jie; Cao, Jinde

    2016-10-01

    This paper addresses the exponential stability of switched cellular neural networks by using the mode-dependent average dwell time (MDADT) approach. This method is quite different from the traditional average dwell time (ADT) method in permitting each subsystem to have its own average dwell time. Detailed investigations have been carried out for two cases. One is that all subsystems are stable and the other is that stable subsystems coexist with unstable subsystems. By employing Lyapunov functionals, linear matrix inequalities (LMIs), Jessen-type inequality, Wirtinger-based inequality, reciprocally convex approach, we derived some novel and less conservative conditions on exponential stability of the networks. Comparing to ADT, the proposed MDADT show that the minimal dwell time of each subsystem is smaller and the switched system stabilizes faster. The obtained results extend and improve some existing ones. Moreover, the validness and effectiveness of these results are demonstrated through numerical simulations. Copyright © 2016 Elsevier Ltd. All rights reserved.

  20. Unequal views of inequality: Cross-national support for redistribution 1985-2011.

    PubMed

    VanHeuvelen, Tom

    2017-05-01

    This research examines public views on government responsibility to reduce income inequality, support for redistribution. While individual-level correlates of support for redistribution are relatively well understood, many questions remain at the country-level. Therefore, I examine how country-level characteristics affect aggregate support for redistribution. I test explanations of aggregate support using a unique dataset combining 18 waves of the International Social Survey Programme and European Social Survey. Results from mixed-effects logistic regression and fixed-effects linear regression models show two primary and contrasting effects. States that reduce inequality through bundles of tax and transfer policies are rewarded with more supportive publics. In contrast, economic development has a seemingly equivalent and dampening effect on public support. Importantly, the effect of economic development grows at higher levels of development, potentially overwhelming the amplifying effect of state redistribution. My results therefore suggest a fundamental challenge to proponents of egalitarian politics. Copyright © 2016 Elsevier Inc. All rights reserved.

  1. Quasi-projective synchronization of fractional-order complex-valued recurrent neural networks.

    PubMed

    Yang, Shuai; Yu, Juan; Hu, Cheng; Jiang, Haijun

    2018-08-01

    In this paper, without separating the complex-valued neural networks into two real-valued systems, the quasi-projective synchronization of fractional-order complex-valued neural networks is investigated. First, two new fractional-order inequalities are established by using the theory of complex functions, Laplace transform and Mittag-Leffler functions, which generalize traditional inequalities with the first-order derivative in the real domain. Additionally, different from hybrid control schemes given in the previous work concerning the projective synchronization, a simple and linear control strategy is designed in this paper and several criteria are derived to ensure quasi-projective synchronization of the complex-valued neural networks with fractional-order based on the established fractional-order inequalities and the theory of complex functions. Moreover, the error bounds of quasi-projective synchronization are estimated. Especially, some conditions are also presented for the Mittag-Leffler synchronization of the addressed neural networks. Finally, some numerical examples with simulations are provided to show the effectiveness of the derived theoretical results. Copyright © 2018 Elsevier Ltd. All rights reserved.

  2. Adapting iterative algorithms for solving large sparse linear systems for efficient use on the CDC CYBER 205

    NASA Technical Reports Server (NTRS)

    Kincaid, D. R.; Young, D. M.

    1984-01-01

    Adapting and designing mathematical software to achieve optimum performance on the CYBER 205 is discussed. Comments and observations are made in light of recent work done on modifying the ITPACK software package and on writing new software for vector supercomputers. The goal was to develop very efficient vector algorithms and software for solving large sparse linear systems using iterative methods.

  3. Enhanced algorithms for stochastic programming

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Krishna, Alamuru S.

    1993-09-01

    In this dissertation, we present some of the recent advances made in solving two-stage stochastic linear programming problems of large size and complexity. Decomposition and sampling are two fundamental components of techniques to solve stochastic optimization problems. We describe improvements to the current techniques in both these areas. We studied different ways of using importance sampling techniques in the context of Stochastic programming, by varying the choice of approximation functions used in this method. We have concluded that approximating the recourse function by a computationally inexpensive piecewise-linear function is highly efficient. This reduced the problem from finding the mean ofmore » a computationally expensive functions to finding that of a computationally inexpensive function. Then we implemented various variance reduction techniques to estimate the mean of a piecewise-linear function. This method achieved similar variance reductions in orders of magnitude less time than, when we directly applied variance-reduction techniques directly on the given problem. In solving a stochastic linear program, the expected value problem is usually solved before a stochastic solution and also to speed-up the algorithm by making use of the information obtained from the solution of the expected value problem. We have devised a new decomposition scheme to improve the convergence of this algorithm.« less

  4. Krylov Subspace Methods for Complex Non-Hermitian Linear Systems. Thesis

    NASA Technical Reports Server (NTRS)

    Freund, Roland W.

    1991-01-01

    We consider Krylov subspace methods for the solution of large sparse linear systems Ax = b with complex non-Hermitian coefficient matrices. Such linear systems arise in important applications, such as inverse scattering, numerical solution of time-dependent Schrodinger equations, underwater acoustics, eddy current computations, numerical computations in quantum chromodynamics, and numerical conformal mapping. Typically, the resulting coefficient matrices A exhibit special structures, such as complex symmetry, or they are shifted Hermitian matrices. In this paper, we first describe a Krylov subspace approach with iterates defined by a quasi-minimal residual property, the QMR method, for solving general complex non-Hermitian linear systems. Then, we study special Krylov subspace methods designed for the two families of complex symmetric respectively shifted Hermitian linear systems. We also include some results concerning the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.

  5. Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach

    NASA Astrophysics Data System (ADS)

    Nasiri, Alireza; Nguang, Sing Kiong; Swain, Akshya; Almakhles, Dhafer

    2018-02-01

    This paper deals with the problem of designing a controller for a class of discrete-time nonlinear systems which is represented by discrete-time polynomial fuzzy model. Most of the existing control design methods for discrete-time fuzzy polynomial systems cannot guarantee their Lyapunov function to be a radially unbounded polynomial function, hence the global stability cannot be assured. The proposed control design in this paper guarantees a radially unbounded polynomial Lyapunov functions which ensures global stability. In the proposed design, state feedback structure is considered and non-convexity problem is solved by incorporating an integrator into the controller. Sufficient conditions of stability are derived in terms of polynomial matrix inequalities which are solved via SOSTOOLS in MATLAB. A numerical example is presented to illustrate the effectiveness of the proposed controller.

  6. Optimal blood glucose control in diabetes mellitus treatment using dynamic programming based on Ackerman’s linear model

    NASA Astrophysics Data System (ADS)

    Pradanti, Paskalia; Hartono

    2018-03-01

    Determination of insulin injection dose in diabetes mellitus treatment can be considered as an optimal control problem. This article is aimed to simulate optimal blood glucose control for patient with diabetes mellitus. The blood glucose regulation of diabetic patient is represented by Ackerman’s Linear Model. This problem is then solved using dynamic programming method. The desired blood glucose level is obtained by minimizing the performance index in Lagrange form. The results show that dynamic programming based on Ackerman’s Linear Model is quite good to solve the problem.

  7. Program for the solution of multipoint boundary value problems of quasilinear differential equations

    NASA Technical Reports Server (NTRS)

    1973-01-01

    Linear equations are solved by a method of superposition of solutions of a sequence of initial value problems. For nonlinear equations and/or boundary conditions, the solution is iterative and in each iteration a problem like the linear case is solved. A simple Taylor series expansion is used for the linearization of both nonlinear equations and nonlinear boundary conditions. The perturbation method of solution is used in preference to quasilinearization because of programming ease, and smaller storage requirements; and experiments indicate that the desired convergence properties exist although no proof or convergence is given.

  8. An efficient parallel algorithm for the solution of a tridiagonal linear system of equations

    NASA Technical Reports Server (NTRS)

    Stone, H. S.

    1971-01-01

    Tridiagonal linear systems of equations are solved on conventional serial machines in a time proportional to N, where N is the number of equations. The conventional algorithms do not lend themselves directly to parallel computations on computers of the ILLIAC IV class, in the sense that they appear to be inherently serial. An efficient parallel algorithm is presented in which computation time grows as log sub 2 N. The algorithm is based on recursive doubling solutions of linear recurrence relations, and can be used to solve recurrence relations of all orders.

  9. Some Applications of Algebraic System Solving

    ERIC Educational Resources Information Center

    Roanes-Lozano, Eugenio

    2011-01-01

    Technology and, in particular, computer algebra systems, allows us to change both the way we teach mathematics and the mathematical curriculum. Curiously enough, unlike what happens with linear system solving, algebraic system solving is not widely known. The aim of this paper is to show that, although the theory lying behind the "exact…

  10. Coupled variational formulations of linear elasticity and the DPG methodology

    NASA Astrophysics Data System (ADS)

    Fuentes, Federico; Keith, Brendan; Demkowicz, Leszek; Le Tallec, Patrick

    2017-11-01

    This article presents a general approach akin to domain-decomposition methods to solve a single linear PDE, but where each subdomain of a partitioned domain is associated to a distinct variational formulation coming from a mutually well-posed family of broken variational formulations of the original PDE. It can be exploited to solve challenging problems in a variety of physical scenarios where stability or a particular mode of convergence is desired in a part of the domain. The linear elasticity equations are solved in this work, but the approach can be applied to other equations as well. The broken variational formulations, which are essentially extensions of more standard formulations, are characterized by the presence of mesh-dependent broken test spaces and interface trial variables at the boundaries of the elements of the mesh. This allows necessary information to be naturally transmitted between adjacent subdomains, resulting in coupled variational formulations which are then proved to be globally well-posed. They are solved numerically using the DPG methodology, which is especially crafted to produce stable discretizations of broken formulations. Finally, expected convergence rates are verified in two different and illustrative examples.

  11. Summer Proceedings 2016: The Center for Computing Research at Sandia National Laboratories

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Carleton, James Brian; Parks, Michael L.

    Solving sparse linear systems from the discretization of elliptic partial differential equations (PDEs) is an important building block in many engineering applications. Sparse direct solvers can solve general linear systems, but are usually slower and use much more memory than effective iterative solvers. To overcome these two disadvantages, a hierarchical solver (LoRaSp) based on H2-matrices was introduced in [22]. Here, we have developed a parallel version of the algorithm in LoRaSp to solve large sparse matrices on distributed memory machines. On a single processor, the factorization time of our parallel solver scales almost linearly with the problem size for three-dimensionalmore » problems, as opposed to the quadratic scalability of many existing sparse direct solvers. Moreover, our solver leads to almost constant numbers of iterations, when used as a preconditioner for Poisson problems. On more than one processor, our algorithm has significant speedups compared to sequential runs. With this parallel algorithm, we are able to solve large problems much faster than many existing packages as demonstrated by the numerical experiments.« less

  12. Train repathing in emergencies based on fuzzy linear programming.

    PubMed

    Meng, Xuelei; Cui, Bingmou

    2014-01-01

    Train pathing is a typical problem which is to assign the train trips on the sets of rail segments, such as rail tracks and links. This paper focuses on the train pathing problem, determining the paths of the train trips in emergencies. We analyze the influencing factors of train pathing, such as transferring cost, running cost, and social adverse effect cost. With the overall consideration of the segment and station capability constraints, we build the fuzzy linear programming model to solve the train pathing problem. We design the fuzzy membership function to describe the fuzzy coefficients. Furthermore, the contraction-expansion factors are introduced to contract or expand the value ranges of the fuzzy coefficients, coping with the uncertainty of the value range of the fuzzy coefficients. We propose a method based on triangular fuzzy coefficient and transfer the train pathing (fuzzy linear programming model) to a determinate linear model to solve the fuzzy linear programming problem. An emergency is supposed based on the real data of the Beijing-Shanghai Railway. The model in this paper was solved and the computation results prove the availability of the model and efficiency of the algorithm.

  13. Socioeconomic Inequalities Persist Despite Declining Stunting Prevalence in Low- and Middle-Income Countries.

    PubMed

    da Silva, Inácio Crochemore M; França, Giovanny V; Barros, Aluisio J D; Amouzou, Agbessi; Krasevec, Julia; Victora, Cesar G

    2018-02-01

    Global stunting prevalence has been nearly halved between 1990 and 2016, but it remains unclear whether this decline has benefited poor and rural populations within low- and middle-income countries (LMICs). We assessed time trends in stunting among children <5 y of age (under-5) according to household wealth and place of residence in 67 LMICs. Stunting prevalence was analyzed in 217 nationally representative Demographic and Health Surveys and Multiple Indicator Cluster Surveys from 67 countries with ≥2 surveys between 1993 and 2014. National estimates were stratified by wealth and area of residence, comparing the poorest 40% with the wealthiest 60%, and those residing in urban and rural areas. Time trends were calculated for LMICs by using multilevel regression models weighted by under-5 population, with stratification by wealth and by residence. Trends in absolute (slope index of inequality; SII) and relative (concentration index; CIX) inequalities were calculated. Mean prevalences in 1993 were 53.7% in low-income and 48.2% in middle-income countries, with annual average linear declines of 0.76 and 0.72 percentage points (pp), respectively. Although similar slopes of declines were observed for the poorest 40% and wealthiest 60% groups in all countries (0.78 and 0.74 pp, respectively), absolute and relative inequalities increased over time in low-income countries (SII increased from -19.3% in 1993 to -23.7% in 2014 and CIX increased from -6.2% to -10.8% in the same period). In middle-income countries, socioeconomic inequalities remained stable. Overall, stunting prevalence decreased more rapidly among rural than for urban children (0.78 and 0.55 pp, respectively). The prevalence of stunting is decreasing. Poor-rich gaps are stable in middle-income countries and slightly increasing in low-income countries. Rural-urban inequalities are decreasing over time.

  14. School-Based Fluoride Mouth-Rinse Program Dissemination Associated With Decreasing Dental Caries Inequalities Between Japanese Prefectures: An Ecological Study.

    PubMed

    Matsuyama, Yusuke; Aida, Jun; Taura, Katsuhiko; Kimoto, Kazunari; Ando, Yuichi; Aoyama, Hitoshi; Morita, Manabu; Ito, Kanade; Koyama, Shihoko; Hase, Akihiro; Tsuboya, Toru; Osaka, Ken

    2016-11-05

    Dental caries inequalities still severely burden individuals' and society's health, even in countries where fluoride toothpastes are widely used and the incidence of dental caries has been decreasing. School-based fluoride mouth-rinse (S-FMR) programs, a population strategy for dental caries prevention, might decrease dental caries inequalities. This study investigated the association between S-FMR and decreasing dental caries prevalence and caries-related inequalities in 12-year-olds by Japanese prefecture. We conducted an ecological study using multi-year prefecture-level aggregated data of children born between 1994 and 2000 in all 47 Japanese prefectures. Using two-level linear regression analyses (birth year nested within prefecture), the association between S-FMR utilization in each prefecture and 12-year-olds' decayed, missing, or filled permanent teeth (DMFT), which indicates dental caries experience in their permanent teeth, were examined. Variables that could explain DMFT inequalities between prefectures, such as dental caries experience at age 3 years, dentist density, and prefectural socioeconomic circumstances, were also considered. High S-FMR utilization was significantly associated with low DMFT at age 12 (coefficient -0.011; 95% confidence interval, -0.018 to -0.005). S-FMR utilization explained 25.2% of the DMFT variance between prefectures after considering other variables. Interaction between S-FMR and dental caries experience at age 3 years showed that S-FMR was significantly more effective in prefectures where the 3-year-olds had high levels of dental caries experience. S-FMR, administered to children of all socioeconomic statuses, was associated with lower DMFT. Utilization of S-FMR reduced dental caries inequalities via proportionate universalism.

  15. School-Based Fluoride Mouth-Rinse Program Dissemination Associated With Decreasing Dental Caries Inequalities Between Japanese Prefectures: An Ecological Study

    PubMed Central

    Matsuyama, Yusuke; Aida, Jun; Taura, Katsuhiko; Kimoto, Kazunari; Ando, Yuichi; Aoyama, Hitoshi; Morita, Manabu; Ito, Kanade; Koyama, Shihoko; Hase, Akihiro; Tsuboya, Toru; Osaka, Ken

    2016-01-01

    Background Dental caries inequalities still severely burden individuals’ and society’s health, even in countries where fluoride toothpastes are widely used and the incidence of dental caries has been decreasing. School-based fluoride mouth-rinse (S-FMR) programs, a population strategy for dental caries prevention, might decrease dental caries inequalities. This study investigated the association between S-FMR and decreasing dental caries prevalence and caries-related inequalities in 12-year-olds by Japanese prefecture. Methods We conducted an ecological study using multi-year prefecture-level aggregated data of children born between 1994 and 2000 in all 47 Japanese prefectures. Using two-level linear regression analyses (birth year nested within prefecture), the association between S-FMR utilization in each prefecture and 12-year-olds’ decayed, missing, or filled permanent teeth (DMFT), which indicates dental caries experience in their permanent teeth, were examined. Variables that could explain DMFT inequalities between prefectures, such as dental caries experience at age 3 years, dentist density, and prefectural socioeconomic circumstances, were also considered. Results High S-FMR utilization was significantly associated with low DMFT at age 12 (coefficient −0.011; 95% confidence interval, −0.018 to −0.005). S-FMR utilization explained 25.2% of the DMFT variance between prefectures after considering other variables. Interaction between S-FMR and dental caries experience at age 3 years showed that S-FMR was significantly more effective in prefectures where the 3-year-olds had high levels of dental caries experience. Conclusions S-FMR, administered to children of all socioeconomic statuses, was associated with lower DMFT. Utilization of S-FMR reduced dental caries inequalities via proportionate universalism. PMID:27108752

  16. The social income inequality, social integration and health status of internal migrants in China.

    PubMed

    Lin, Yanwei; Zhang, Qi; Chen, Wen; Ling, Li

    2017-08-04

    To examine the interaction between social income inequality, social integration, and health status among internal migrants (IMs) who migrate between regions in China. We used the data from the 2014 Internal Migrant Dynamic Monitoring Survey in China, which sampled 15,999 IMs in eight cities in China. The Gini coefficient at the city level was calculated to measure social income inequality and was categorized into low (0.2 < Gini <= 0.3), medium (0.3 < Gini <= 0.4), high (0.4 < x < = 0.5), and very high (Gini >0.5). Health status was measured based upon self-reported health, subjective well-being, and perceptions of stress and mental health. Social integration was measured from four perspectives (acculturation and integration willingness, social insurance, economy, social communication). Linear mixed models were used to examine the interaction effects between health statuses, social integration, and the Gini coefficient. Factors of social integration, such as economic integration and acculturation and integration willingness, were significantly related to health. Social income inequality had a negative relationship with the health status of IMs. For example, IMs in one city, Qingdao, with a medium income inequality level (Gini = 0.329), had the best health statuses and better social integration. On the other hand, IMs in another city, Shenzhen, who had a large income inequality (Gini = 0.447) were worst in health statues and had worse social integration. Policies or programs targeting IMs should support integration willingness, promote a sense of belonging, and improve economic equality. In the meantime, social activities to facilitate employment and create social trust should also be promoted. At the societal level, structural and policy changes are necessary to promote income equity to promote IMs' general health status.

  17. Algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations with the use of parallel computations

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Moryakov, A. V., E-mail: sailor@orc.ru

    2016-12-15

    An algorithm for solving the linear Cauchy problem for large systems of ordinary differential equations is presented. The algorithm for systems of first-order differential equations is implemented in the EDELWEISS code with the possibility of parallel computations on supercomputers employing the MPI (Message Passing Interface) standard for the data exchange between parallel processes. The solution is represented by a series of orthogonal polynomials on the interval [0, 1]. The algorithm is characterized by simplicity and the possibility to solve nonlinear problems with a correction of the operator in accordance with the solution obtained in the previous iterative process.

  18. Matrix form of Legendre polynomials for solving linear integro-differential equations of high order

    NASA Astrophysics Data System (ADS)

    Kammuji, M.; Eshkuvatov, Z. K.; Yunus, Arif A. M.

    2017-04-01

    This paper presents an effective approximate solution of high order of Fredholm-Volterra integro-differential equations (FVIDEs) with boundary condition. Legendre truncated series is used as a basis functions to estimate the unknown function. Matrix operation of Legendre polynomials is used to transform FVIDEs with boundary conditions into matrix equation of Fredholm-Volterra type. Gauss Legendre quadrature formula and collocation method are applied to transfer the matrix equation into system of linear algebraic equations. The latter equation is solved by Gauss elimination method. The accuracy and validity of this method are discussed by solving two numerical examples and comparisons with wavelet and methods.

  19. [The Common Risk Factor Approach - An Integrated Population- and Evidence-Based Approach for Reducing Social Inequalities in Oral Health].

    PubMed

    Heilmann, A; Sheiham, A; Watt, R G; Jordan, R A

    2016-10-01

    Worldwide, non-communicable diseases including dental caries and periodontal diseases, remain a major public health problem. Moreover, there is a social gradient in health across society that runs from the top to the bottom in a linear, stepwise fashion. Health promoting behaviours become more difficult to sustain further down the social ladder. Oral health inequalities also exist in Germany. Earlier explanations of social inequalities have mainly focused on individual lifestyle factors, ignoring the broader social determinants of health and disease. Until recently, the dominant approaches to general health promotion focused on actions to reduce specific diseases, separating oral health from general health. An alternative approach is the common risk factor approach (CRFA) where risk factors common to a number of major chronic diseases, including diseases of the mouth and teeth, are tackled. The CRFA focuses on the common underlying determinants of health to improve the overall health of populations, thereby reducing social inequalities. The main implication of the CRFA for oral health policies is to work in partnership with a range of other sectors and disciplines. Oral health issues need to be integrated with recommendations to promote general health. Improvements in oral health and a reduction in oral health inequalities are more likely by working in partnership across sectors and disciplines using strategies that focus upstream on the underlying determinants of oral diseases. © Georg Thieme Verlag KG Stuttgart · New York.

  20. Robust pinning control of heterogeneous complex networks with jointly connected topologies and time-varying parametric uncertainty

    NASA Astrophysics Data System (ADS)

    Manfredi, Sabato

    2018-05-01

    The pinning/leader control problems provide the design of the leader or pinning controller in order to guide a complex network to a desired trajectory or target (synchronisation or consensus). Let a time-invariant complex network, pinning/leader control problems include the design of the leader or pinning controller gain and number of nodes to pin in order to guide a network to a desired trajectory (synchronization or consensus). Usually, lower is the number of pinned nodes larger is the pinning gain required to assess network synchronisation. On the other side, realistic application scenario of complex networks is characterised by switching topologies, time-varying node coupling strength and link weight that make hard to solve the pinning/leader control problem. Additionally, the system dynamics at nodes can be heterogeneous. In this paper, we derive robust stabilisation conditions of time-varying heterogeneous complex networks with jointly connected topologies when coupling strength and link weight interactions are affected by time-varying uncertainties. By employing Lyapunov stability theory and linear matrix inequality (LMI) technique, we formulate low computationally demanding stabilisability conditions to design a pinning/leader control gain for robust network synchronisation. The effectiveness of the proposed approach is shown by several design examples applied to a paradigmatic well-known complex network composed of heterogeneous Chua's circuits.

  1. Deterministic methods for multi-control fuel loading optimization

    NASA Astrophysics Data System (ADS)

    Rahman, Fariz B. Abdul

    We have developed a multi-control fuel loading optimization code for pressurized water reactors based on deterministic methods. The objective is to flatten the fuel burnup profile, which maximizes overall energy production. The optimal control problem is formulated using the method of Lagrange multipliers and the direct adjoining approach for treatment of the inequality power peaking constraint. The optimality conditions are derived for a multi-dimensional multi-group optimal control problem via calculus of variations. Due to the Hamiltonian having a linear control, our optimal control problem is solved using the gradient method to minimize the Hamiltonian and a Newton step formulation to obtain the optimal control. We are able to satisfy the power peaking constraint during depletion with the control at beginning of cycle (BOC) by building the proper burnup path forward in time and utilizing the adjoint burnup to propagate the information back to the BOC. Our test results show that we are able to achieve our objective and satisfy the power peaking constraint during depletion using either the fissile enrichment or burnable poison as the control. Our fuel loading designs show an increase of 7.8 equivalent full power days (EFPDs) in cycle length compared with 517.4 EFPDs for the AP600 first cycle.

  2. New Techniques in Numerical Analysis and Their Application to Aerospace Systems.

    DTIC Science & Technology

    1979-01-01

    employment of the sequential gradient-restoration algorithm and the modified quasilineari- zation algorithm in some problems of structural analysis (Refs. 6...and a state inequa - lity constraint. The state inequality constraint is of a special type, namely, it is linear in some or all of the com- ponents of

  3. NEWSUMT: A FORTRAN program for inequality constrained function minimization, users guide

    NASA Technical Reports Server (NTRS)

    Miura, H.; Schmit, L. A., Jr.

    1979-01-01

    A computer program written in FORTRAN subroutine form for the solution of linear and nonlinear constrained and unconstrained function minimization problems is presented. The algorithm is the sequence of unconstrained minimizations using the Newton's method for unconstrained function minimizations. The use of NEWSUMT and the definition of all parameters are described.

  4. Global Inequalities in Cervical Cancer Incidence and Mortality are Linked to Deprivation, Low Socioeconomic Status, and Human Development

    PubMed Central

    Singh, Gopal K.; Azuine, Romuladus E.; Siahpush, Mohammad

    2012-01-01

    Objectives This study examined global inequalities in cervical cancer incidence and mortality rates as a function of cross-national variations in the Human Development Index (HDI), socioeconomic factors, Gender Inequality Index (GII), and healthcare expenditure. Methods Age-adjusted incidence and mortality rates were calculated for women in 184 countries using the 2008 GLOBOCAN database, and incidence and mortality trends were analyzed using the WHO cancer mortality database. Log-linear regression was used to model annual trends, while OLS and Poisson regression models were used to estimate the impact of socioeconomic and human development factors on incidence and mortality rates. Results Cervical cancer incidence and mortality rates varied widely, with many African countries such as Guinea, Zambia, Comoros, Tanzania, and Malawi having at least 10-to-20-fold higher rates than several West Asian, Middle East, and European countries, including Iran, Saudi Arabia, Syria, Egypt, and Switzerland. HDI, GII, poverty rate, health expenditure per capita, urbanization, and literacy rate were all significantly related to cervical cancer incidence and mortality, with HDI and poverty rate each explaining >52% of the global variance in mortality. Both incidence and mortality rates increased in relation to lower human development and higher gender inequality levels. A 0.2 unit increase in HDI was associated with a 20% decrease in cervical cancer risk and a 33% decrease in cervical cancer mortality risk. The risk of a cervical cancer diagnosis increased by 24% and of cervical cancer death by 42% for a 0.2 unit increase in GII. Higher health expenditure levels were independently associated with decreased incidence and mortality risks. Conclusions and Public Health Implications Global inequalities in cervical cancer are clearly linked to disparities in human development, social inequality, and living standards. Reductions in cervical cancer rates are achievable by reducing inequalities in socioeconomic conditions, availability of preventive health services, and women’s social status. PMID:27621956

  5. Disability and ageing in China and India - decomposing the effects of gender and residence. Results from the WHO study on global AGEing and adult health (SAGE).

    PubMed

    Stewart Williams, Jennifer; Norström, Fredrik; Ng, Nawi

    2017-08-31

    China and India are the world's two most populous countries. Although their populations are growing in number and life expectancies are extending they have different trajectories of economic growth, epidemiological transition and social change. Cross-country comparisons can allow national and global insights and provide evidence for policy and decision-making. The aim of this study is to measure and compare disability in men and women, and in urban and rural dwellers in China and India, and assess the extent to which social and other factors contribute to the inequalities. National samples of adults aged 50 to 79 years in China (n = 11,694) and India (n = 6187) from the World Health Organization (WHO) longitudinal Study on global AGEing and adult health (SAGE) Wave 1 were analysed. Stratified multiple linear regressions were undertaken to assess disability differences by sex and residence, controlling for other biological and socioeconomic determinants of disability. Oaxaca-Blinder decomposition partitioned the two-group inequalities into explained and unexplained components. In both countries women and rural residents reported more disability. In India, the gender inequality is attributed to the distribution of the determinants (employment, education and chronic conditions) but in China about half the inequality is attributed to the same. In India, more than half of the urban rural inequality is attributed to the distribution of the determinants (education, household wealth) compared with under 20% in China. Education and employment were important drivers of these measured inequalities. Overall inequalities in disability among older adults in China and India were shaped by gender and residence, suggesting the need for policies that target women and rural residents. There is a need for further research, using both qualitative and quantitative methods, to question and challenge entrenched practices and institutions and grasp the implications of global economic and social changes that are impacting on population health and ageing in China and India.

  6. Global Inequalities in Cervical Cancer Incidence and Mortality are Linked to Deprivation, Low Socioeconomic Status, and Human Development.

    PubMed

    Singh, Gopal K; Azuine, Romuladus E; Siahpush, Mohammad

    2012-01-01

    This study examined global inequalities in cervical cancer incidence and mortality rates as a function of cross-national variations in the Human Development Index (HDI), socioeconomic factors, Gender Inequality Index (GII), and healthcare expenditure. Age-adjusted incidence and mortality rates were calculated for women in 184 countries using the 2008 GLOBOCAN database, and incidence and mortality trends were analyzed using the WHO cancer mortality database. Log-linear regression was used to model annual trends, while OLS and Poisson regression models were used to estimate the impact of socioeconomic and human development factors on incidence and mortality rates. Cervical cancer incidence and mortality rates varied widely, with many African countries such as Guinea, Zambia, Comoros, Tanzania, and Malawi having at least 10-to-20-fold higher rates than several West Asian, Middle East, and European countries, including Iran, Saudi Arabia, Syria, Egypt, and Switzerland. HDI, GII, poverty rate, health expenditure per capita, urbanization, and literacy rate were all significantly related to cervical cancer incidence and mortality, with HDI and poverty rate each explaining >52% of the global variance in mortality. Both incidence and mortality rates increased in relation to lower human development and higher gender inequality levels. A 0.2 unit increase in HDI was associated with a 20% decrease in cervical cancer risk and a 33% decrease in cervical cancer mortality risk. The risk of a cervical cancer diagnosis increased by 24% and of cervical cancer death by 42% for a 0.2 unit increase in GII. Higher health expenditure levels were independently associated with decreased incidence and mortality risks. Global inequalities in cervical cancer are clearly linked to disparities in human development, social inequality, and living standards. Reductions in cervical cancer rates are achievable by reducing inequalities in socioeconomic conditions, availability of preventive health services, and women's social status.

  7. Instantaneous global spatial interaction? Exploring the Gaussian inequality, distance and Internet pings in a global network

    NASA Astrophysics Data System (ADS)

    Baker, R. G. V.

    2005-12-01

    The Internet has been publicly portrayed as a new technological horizon yielding instantaneous interaction to a point where geography no longer matters. This research aims to dispel this impression by applying a dynamic form of trip modelling to investigate pings in a global computer network compiled by the Stanford Linear Accelerator Centre (SLAC) from 1998 to 2004. Internet flows have been predicted to have the same mathematical operators as trips to a supermarket, since they are both periodic and constrained by a distance metric. Both actual and virtual trips are part of a spectrum of origin-destination pairs in the time-space convergence of trip time-lines. Internet interaction is very near to the convergence of these time-lines (at a very small time scale in milliseconds, but with interactions over thousands of kilometres). There is a lag effect and this is formalised by the derivation of Gaussian and gravity inequalities between the time taken (Δ t) and the partitioning of distance (Δ x). This inequality seems to be robust for a regression of Δ t to Δ x in the SLAC data set for each year (1998 to 2004). There is a constant ‘forbidden zone’ in the interaction, underpinned by the fact that pings do not travel faster than the speed of light. Superimposed upon this zone is the network capacity where a linear regression of Δ t to Δ x is a proxy summarising global Internet connectivity for that year. The results suggest that there has been a substantial improvement in connectivity over the period with R 2 increasing steadily from 0.39 to 0.65 from less Gaussian spreading of the ping latencies. Further, the regression line shifts towards the inequality boundary from 1998 to 2004, where the increased slope shows a greater proportional rise in local connectivity over global connectivity. A conclusion is that national geography still does matter in spatial interaction modelling of the Internet.

  8. Investigation of deformation at a centrifugal compressor rotor in process of interference on shaft

    NASA Astrophysics Data System (ADS)

    Shamim, M. R.; Berezhnoi, D. V.

    2016-11-01

    In this paper, according to the finite element method, we had implemented “master- slave” method of contact interaction in elastic deformable bodies, with consider of the friction in the contact zone. We had compiled the orientation of solving extremum problems with inequality restrictions, projection algorithm, which called “the closest point projection algorithm”. Finally, an example, had brought to show the calculation of the rotor nozzle centrifugal compressor on the shaft with interference.

  9. Radar Control Optimal Resource Allocation

    DTIC Science & Technology

    2015-07-13

    other tunable parameters of radars [17, 18]. Such radar resource scheduling usually demands massive computation. Even myopic 14 Distribution A: Approved...reduced validity of the optimal choice of radar resource. In the non- myopic context, the computational problem becomes exponentially more difficult...computed as t? = ασ2 q + σ r √ α q (σ + r + α q) α q2 r − 1ασ q2 + q r2 . (19) We are only interested in t? > 1 and solving the inequality we obtain the

  10. Implementation and Performance Issues in Collaborative Optimization

    NASA Technical Reports Server (NTRS)

    Braun, Robert; Gage, Peter; Kroo, Ilan; Sobieski, Ian

    1996-01-01

    Collaborative optimization is a multidisciplinary design architecture that is well-suited to large-scale multidisciplinary optimization problems. This paper compares this approach with other architectures, examines the details of the formulation, and some aspects of its performance. A particular version of the architecture is proposed to better accommodate the occurrence of multiple feasible regions. The use of system level inequality constraints is shown to increase the convergence rate. A series of simple test problems, demonstrated to challenge related optimization architectures, is successfully solved with collaborative optimization.

  11. AZTEC: A parallel iterative package for the solving linear systems

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Hutchinson, S.A.; Shadid, J.N.; Tuminaro, R.S.

    1996-12-31

    We describe a parallel linear system package, AZTEC. The package incorporates a number of parallel iterative methods (e.g. GMRES, biCGSTAB, CGS, TFQMR) and preconditioners (e.g. Jacobi, Gauss-Seidel, polynomial, domain decomposition with LU or ILU within subdomains). Additionally, AZTEC allows for the reuse of previous preconditioning factorizations within Newton schemes for nonlinear methods. Currently, a number of different users are using this package to solve a variety of PDE applications.

  12. On the equivalence of Gaussian elimination and Gauss-Jordan reduction in solving linear equations

    NASA Technical Reports Server (NTRS)

    Tsao, Nai-Kuan

    1989-01-01

    A novel general approach to round-off error analysis using the error complexity concepts is described. This is applied to the analysis of the Gaussian Elimination and Gauss-Jordan scheme for solving linear equations. The results show that the two algorithms are equivalent in terms of our error complexity measures. Thus the inherently parallel Gauss-Jordan scheme can be implemented with confidence if parallel computers are available.

  13. A globally convergent LCL method for nonlinear optimization.

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Friedlander, M. P.; Saunders, M. A.; Mathematics and Computer Science

    2005-01-01

    For optimization problems with nonlinear constraints, linearly constrained Lagrangian (LCL) methods solve a sequence of subproblems of the form 'minimize an augmented Lagrangian function subject to linearized constraints.' Such methods converge rapidly near a solution but may not be reliable from arbitrary starting points. Nevertheless, the well-known software package MINOS has proved effective on many large problems. Its success motivates us to derive a related LCL algorithm that possesses three important properties: it is globally convergent, the subproblem constraints are always feasible, and the subproblems may be solved inexactly. The new algorithm has been implemented in Matlab, with an optionmore » to use either MINOS or SNOPT (Fortran codes) to solve the linearly constrained subproblems. Only first derivatives are required. We present numerical results on a subset of the COPS, HS, and CUTE test problems, which include many large examples. The results demonstrate the robustness and efficiency of the stabilized LCL procedure.« less

  14. Investigating Integer Restrictions in Linear Programming

    ERIC Educational Resources Information Center

    Edwards, Thomas G.; Chelst, Kenneth R.; Principato, Angela M.; Wilhelm, Thad L.

    2015-01-01

    Linear programming (LP) is an application of graphing linear systems that appears in many Algebra 2 textbooks. Although not explicitly mentioned in the Common Core State Standards for Mathematics, linear programming blends seamlessly into modeling with mathematics, the fourth Standard for Mathematical Practice (CCSSI 2010, p. 7). In solving a…

  15. [Gender inequity in health in contexts of environmental risk from mining and industrial activity in Mexico].

    PubMed

    Catalán-Vázquez, Minerva; Riojas-Rodríguez, Horacio

    2015-06-01

    Analyze how gender inequity manifests in contexts of poverty in different environmental risk scenarios in Mexico. Qualitative design based on six discussion groups and 54 in-depth interviews with women from six exposed communities: two to environmental manganese in a mining district, two in an industrial corridor, and two bordering a sanitary landfill. A document review of environmental and health studies in each area was done to relate them to the women's perspective on the problem. In the three case studies, by gender roles, women stay at home and do housework and, therefore, are subject to intense environmental exposure when carrying out their daily tasks, such as house cleaning. Interview and discussion group results were found to be related to epidemiological study results. In the case of the mining district, women's perceptions are consistent with study comments on adverse cognitive effects of manganese exposure. In all three cases, there are serious limitations on women's political participation in environmental risk management. Due to conditions of inequity, women are highly exposed to environmental health risks and their social participation in solving environmental problems is quite limited. These results have social and environmental policy implications in the areas studied, especially with regard to risk assessment, management, and communication.

  16. On improving linear solver performance: a block variant of GMRES

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Baker, A H; Dennis, J M; Jessup, E R

    2004-05-10

    The increasing gap between processor performance and memory access time warrants the re-examination of data movement in iterative linear solver algorithms. For this reason, we explore and establish the feasibility of modifying a standard iterative linear solver algorithm in a manner that reduces the movement of data through memory. In particular, we present an alternative to the restarted GMRES algorithm for solving a single right-hand side linear system Ax = b based on solving the block linear system AX = B. Algorithm performance, i.e. time to solution, is improved by using the matrix A in operations on groups of vectors.more » Experimental results demonstrate the importance of implementation choices on data movement as well as the effectiveness of the new method on a variety of problems from different application areas.« less

  17. [Income inequality, corruption, and life expectancy at birth in Mexico].

    PubMed

    Idrovo, Alvaro Javier

    2005-01-01

    To ascertain if the effect of income inequality on life expectancy at birth in Mexico is mediated by corruption, used as a proxy of social capital. An ecological study was carried out with the 32 Mexican federative entities. Global and by sex correlations between life expectancy at birth were estimated by federative entity with the Gini coefficient, the Corruption and Good Government Index, the percentage of Catholics, and the percentage of the population speaking indigenous language. Robust linear regressions, with and without instrumental variables, were used to explore if corruption acts as intermediate variable in the studied relationship. Negative correlations with Spearman's rho near to -0.60 (p < 0.05) and greater than -0.66 (p < 0.05) between life expectancy at birth, the Gini coefficient and the population speaking indigenous language, respectively, were observed. Moreover, the Corruption and Good Government Index correlated with men's life expectancy at birth with Spearman's rho -0.3592 (p < 0.05). Regressions with instruments were more consistent than conventional ones and they show a strong negative effect (p < 0.05) of income inequality on life expectancy at birth. This effect was greater among men. The findings suggest a negative effect of income inequality on life expectancy at birth in Mexico, mediated by corruption levels and other related cultural factors.

  18. Newton's method: A link between continuous and discrete solutions of nonlinear problems

    NASA Technical Reports Server (NTRS)

    Thurston, G. A.

    1980-01-01

    Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.

  19. Socio-economic factors associated with infant mortality in Italy: an ecological study

    PubMed Central

    2012-01-01

    Introduction One issue that continues to attract the attention of public health researchers is the possible relationship in high-income countries between income, income inequality and infant mortality (IM). The aim of this study was to assess the associations between IM and major socio-economic determinants in Italy. Methods Associations between infant mortality rates in the 20 Italian regions (2006–2008) and the Gini index of income inequality, mean household income, percentage of women with at least 8 years of education, and percentage of unemployed aged 15–64 years were assessed using Pearson correlation coefficients. Univariate linear regression and multiple stepwise linear regression analyses were performed to determine the magnitude and direction of the effect of the four socio-economic variables on IM. Results The Gini index and the total unemployment rate showed a positive strong correlation with IM (r = 0.70; p < 0.001 and r = 0.84; p < 0.001 respectively), mean household income showed a strong negative correlation (r = −0.78; p < 0.001), while female educational attainment presented a weak negative correlation (r = −0.45; p < 0.05). Using a multiple stepwise linear regression model, only unemployment rate was independently associated with IM (b = 0.15, p < 0.001). Conclusions In Italy, a high-income country where health care is universally available, variations in IM were strongly associated with relative and absolute income and unemployment rate. These results suggest that in Italy IM is not only related to income distribution, as demonstrated for other developed countries, but also to economic factors such as absolute income and unemployment. In order to reduce IM and the existing inequalities, the challenge for Italian decision makers is to promote economic growth and enhance employment levels. PMID:22898293

  20. Optimal Load Shedding and Generation Rescheduling for Overload Suppression in Large Power Systems.

    NASA Astrophysics Data System (ADS)

    Moon, Young-Hyun

    Ever-increasing size, complexity and operation costs in modern power systems have stimulated the intensive study of an optimal Load Shedding and Generator Rescheduling (LSGR) strategy in the sense of a secure and economic system operation. The conventional approach to LSGR has been based on the application of LP (Linear Programming) with the use of an approximately linearized model, and the LP algorithm is currently considered to be the most powerful tool for solving the LSGR problem. However, all of the LP algorithms presented in the literature essentially lead to the following disadvantages: (i) piecewise linearization involved in the LP algorithms requires the introduction of a number of new inequalities and slack variables, which creates significant burden to the computing facilities, and (ii) objective functions are not formulated in terms of the state variables of the adopted models, resulting in considerable numerical inefficiency in the process of computing the optimal solution. A new approach is presented, based on the development of a new linearized model and on the application of QP (Quadratic Programming). The changes in line flows as a result of changes to bus injection power are taken into account in the proposed model by the introduction of sensitivity coefficients, which avoids the mentioned second disadvantages. A precise method to calculate these sensitivity coefficients is given. A comprehensive review of the theory of optimization is included, in which results of the development of QP algorithms for LSGR as based on Wolfe's method and Kuhn -Tucker theory are evaluated in detail. The validity of the proposed model and QP algorithms has been verified and tested on practical power systems, showing the significant reduction of both computation time and memory requirements as well as the expected lower generation costs of the optimal solution as compared with those obtained from computing the optimal solution with LP. Finally, it is noted that an efficient reactive power compensation algorithm is developed to suppress voltage disturbances due to load sheddings, and that a new method for multiple contingency simulation is presented.

  1. Explicit reference governor for linear systems

    NASA Astrophysics Data System (ADS)

    Garone, Emanuele; Nicotra, Marco; Ntogramatzidis, Lorenzo

    2018-06-01

    The explicit reference governor is a constrained control scheme that was originally introduced for generic nonlinear systems. This paper presents two explicit reference governor strategies that are specifically tailored for the constrained control of linear time-invariant systems subject to linear constraints. Both strategies are based on the idea of maintaining the system states within an invariant set which is entirely contained in the constraints. This invariant set can be constructed by exploiting either the Lyapunov inequality or modal decomposition. To improve the performance, we show that the two strategies can be combined by choosing at each time instant the least restrictive set. Numerical simulations illustrate that the proposed scheme achieves performances that are comparable to optimisation-based reference governors.

  2. Robust stability for stochastic bidirectional associative memory neural networks with time delays

    NASA Astrophysics Data System (ADS)

    Shu, H. S.; Lv, Z. W.; Wei, G. L.

    2008-02-01

    In this paper, the asymptotic stability is considered for a class of uncertain stochastic bidirectional associative memory neural networks with time delays and parameter uncertainties. The delays are time-invariant and the uncertainties are norm-bounded that enter into all network parameters. The aim of this paper is to establish easily verifiable conditions under which the delayed neural network is robustly asymptotically stable in the mean square for all admissible parameter uncertainties. By employing a Lyapunov-Krasovskii functional and conducting the stochastic analysis, a linear matrix inequality matrix inequality (LMI) approach is developed to derive the stability criteria. The proposed criteria can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed criteria.

  3. Ambivalent stereotypes link to peace, conflict, and inequality across 38 nations.

    PubMed

    Durante, Federica; Fiske, Susan T; Gelfand, Michele J; Crippa, Franca; Suttora, Chiara; Stillwell, Amelia; Asbrock, Frank; Aycan, Zeynep; Bye, Hege H; Carlsson, Rickard; Björklund, Fredrik; Dagher, Munqith; Geller, Armando; Larsen, Christian Albrekt; Latif, Abdel-Hamid Abdel; Mähönen, Tuuli Anna; Jasinskaja-Lahti, Inga; Teymoori, Ali

    2017-01-24

    A cross-national study, 49 samples in 38 nations (n = 4,344), investigates whether national peace and conflict reflect ambivalent warmth and competence stereotypes: High-conflict societies (Pakistan) may need clearcut, unambivalent group images distinguishing friends from foes. Highly peaceful countries (Denmark) also may need less ambivalence because most groups occupy the shared national identity, with only a few outcasts. Finally, nations with intermediate conflict (United States) may need ambivalence to justify more complex intergroup-system stability. Using the Global Peace Index to measure conflict, a curvilinear (quadratic) relationship between ambivalence and conflict highlights how both extremely peaceful and extremely conflictual countries display lower stereotype ambivalence, whereas countries intermediate on peace-conflict present higher ambivalence. These data also replicated a linear inequality-ambivalence relationship.

  4. Solving Two-Level Optimization Problems with Applications to Robust Design and Energy Markets

    DTIC Science & Technology

    2011-01-01

    additional a transportation system operator (TSO) who manages the congestion and 172 flows. The TSO’s linear program is as follows (where other...were tested are shown in Table 5.11 below. Node 1 Node 2 Producer A Producer B Producer C Producer D Transmission System Operator 174... Systems to Solve Problems that are Not Linear. Operational Research Quarterly , 26, 609–618. 9. Beale, E., & Tomlin, J. (1970). Special Facilities

  5. The application of MINIQUASI to thermal program boundary and initial value problems

    NASA Technical Reports Server (NTRS)

    1974-01-01

    The feasibility of applying the solution techniques of Miniquasi to the set of equations which govern a thermoregulatory model is investigated. For solving nonlinear equations and/or boundary conditions, a Taylor Series expansion is required for linearization of both equations and boundary conditions. The solutions are iterative and in each iteration, a problem like the linear case is solved. It is shown that Miniquasi cannot be applied to the thermoregulatory model as originally planned.

  6. Optimal Artificial Boundary Condition Configurations for Sensitivity-Based Model Updating and Damage Detection

    DTIC Science & Technology

    2010-09-01

    matrix is used in many methods, like Jacobi or Gauss Seidel , for solving linear systems. Also, no partial pivoting is necessary for a strictly column...problems that arise during the procedure, which in general, converges to the solving of a linear system. The most common issue with the solution is the... iterative procedure to find an appropriate subset of parameters that produce an optimal solution commonly known as forward selection. Then, the

  7. AZTEC. Parallel Iterative method Software for Solving Linear Systems

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Hutchinson, S.; Shadid, J.; Tuminaro, R.

    1995-07-01

    AZTEC is an interactive library that greatly simplifies the parrallelization process when solving the linear systems of equations Ax=b where A is a user supplied n X n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. AZTEC is intended as a software tool for users who want to avoid cumbersome parallel programming details but who have large sparse linear systems which require an efficiently utilized parallel processing system. A collection of data transformation tools are provided that allow for easy creation of distributed sparse unstructured matricesmore » for parallel solutions.« less

  8. Graph cuts via l1 norm minimization.

    PubMed

    Bhusnurmath, Arvind; Taylor, Camillo J

    2008-10-01

    Graph cuts have become an increasingly important tool for solving a number of energy minimization problems in computer vision and other fields. In this paper, the graph cut problem is reformulated as an unconstrained l1 norm minimization that can be solved effectively using interior point methods. This reformulation exposes connections between the graph cuts and other related continuous optimization problems. Eventually the problem is reduced to solving a sequence of sparse linear systems involving the Laplacian of the underlying graph. The proposed procedure exploits the structure of these linear systems in a manner that is easily amenable to parallel implementations. Experimental results obtained by applying the procedure to graphs derived from image processing problems are provided.

  9. Application of Nearly Linear Solvers to Electric Power System Computation

    NASA Astrophysics Data System (ADS)

    Grant, Lisa L.

    To meet the future needs of the electric power system, improvements need to be made in the areas of power system algorithms, simulation, and modeling, specifically to achieve a time frame that is useful to industry. If power system time-domain simulations could run in real-time, then system operators would have situational awareness to implement online control and avoid cascading failures, significantly improving power system reliability. Several power system applications rely on the solution of a very large linear system. As the demands on power systems continue to grow, there is a greater computational complexity involved in solving these large linear systems within reasonable time. This project expands on the current work in fast linear solvers, developed for solving symmetric and diagonally dominant linear systems, in order to produce power system specific methods that can be solved in nearly-linear run times. The work explores a new theoretical method that is based on ideas in graph theory and combinatorics. The technique builds a chain of progressively smaller approximate systems with preconditioners based on the system's low stretch spanning tree. The method is compared to traditional linear solvers and shown to reduce the time and iterations required for an accurate solution, especially as the system size increases. A simulation validation is performed, comparing the solution capabilities of the chain method to LU factorization, which is the standard linear solver for power flow. The chain method was successfully demonstrated to produce accurate solutions for power flow simulation on a number of IEEE test cases, and a discussion on how to further improve the method's speed and accuracy is included.

  10. Open-Ended, Problem-Solving Investigations--Getting Started.

    ERIC Educational Resources Information Center

    Lock, Roger

    1991-01-01

    Ways in which linear lesson sequences can be modified to provide increased opportunities for open-ended activities especially with problem solving are considered. Examples drawn from chemistry and plant reproduction, seeds, and germination are given. (KR)

  11. ORACLS: A system for linear-quadratic-Gaussian control law design

    NASA Technical Reports Server (NTRS)

    Armstrong, E. S.

    1978-01-01

    A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.

  12. Engaging with complexity to improve the health of indigenous people: a call for the use of systems thinking to tackle health inequity.

    PubMed

    Hernández, Alison; Ruano, Ana Lorena; Marchal, Bruno; San Sebastián, Miguel; Flores, Walter

    2017-02-21

    The 400 million indigenous people worldwide represent a wealth of linguistic and cultural diversity, as well as traditional knowledge and sustainable practices that are invaluable resources for human development. However, indigenous people remain on the margins of society in high, middle and low-income countries, and they bear a disproportionate burden of poverty, disease, and mortality compared to the general population. These inequalities have persisted, and in some countries have even worsened, despite the overall improvements in health indicators in relation to the 15-year push to meet the Millennium Development Goals. As we enter the Sustainable Development Goals (SDGs) era, there is growing consensus that efforts to achieve Universal Health Coverage (UHC) and promote sustainable development should be guided by the moral imperative to improve equity. To achieve this, we need to move beyond the reductionist tendency to frame indigenous health as a problem of poor health indicators to be solved through targeted service delivery tactics and move towards holistic, integrated approaches that address the causes of inequalities both inside and outside the health sector. To meet the challenge of engaging with the conditions underlying inequalities and promoting transformational change, equity-oriented research and practice in the field of indigenous health requires: engaging power, context-adapted strategies to improve service delivery, and mobilizing networks of collective action. The application of systems thinking approaches offers a pathway for the evolution of equity-oriented research and practice in collaborative, politically informed and mutually enhancing efforts to understand and transform the systems that generate and reproduce inequities in indigenous health. These approaches hold the potential to strengthen practice through the development of more nuanced, context-sensitive strategies for redressing power imbalances, reshaping the service delivery environment and fostering the dynamics of collective action for political reform.

  13. Optimal Control Problems with Switching Points. Ph.D. Thesis, 1990 Final Report

    NASA Technical Reports Server (NTRS)

    Seywald, Hans

    1991-01-01

    The main idea of this report is to give an overview of the problems and difficulties that arise in solving optimal control problems with switching points. A brief discussion of existing optimality conditions is given and a numerical approach for solving the multipoint boundary value problems associated with the first-order necessary conditions of optimal control is presented. Two real-life aerospace optimization problems are treated explicitly. These are altitude maximization for a sounding rocket (Goddard Problem) in the presence of a dynamic pressure limit, and range maximization for a supersonic aircraft flying in the vertical, also in the presence of a dynamic pressure limit. In the second problem singular control appears along arcs with active dynamic pressure limit, which in the context of optimal control, represents a first-order state inequality constraint. An extension of the Generalized Legendre-Clebsch Condition to the case of singular control along state/control constrained arcs is presented and is applied to the aircraft range maximization problem stated above. A contribution to the field of Jacobi Necessary Conditions is made by giving a new proof for the non-optimality of conjugate paths in the Accessory Minimum Problem. Because of its simple and explicit character, the new proof may provide the basis for an extension of Jacobi's Necessary Condition to the case of the trajectories with interior point constraints. Finally, the result that touch points cannot occur for first-order state inequality constraints is extended to the case of vector valued control functions.

  14. Secondary School Advanced Mathematics, Chapter 8, Systems of Equations. Student's Text.

    ERIC Educational Resources Information Center

    Stanford Univ., CA. School Mathematics Study Group.

    This text is the last of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. In this volume the solution of systems of linear and quadratic equations and inequalities in…

  15. Gender Equality and Girls' Education: Investigating Frameworks, Disjunctures and Meanings of Quality Education

    ERIC Educational Resources Information Center

    Aikman, Sheila; Rao, Nitya

    2012-01-01

    The article draws on qualitative educational research across a diversity of low-income countries to examine the gendered inequalities in education as complex, multi-faceted and situated rather than a series of barriers to be overcome through linear input-output processes focused on isolated dimensions of quality. It argues that frameworks for…

  16. Ideologies in the Swedish health sector today: the crisis of the social democracy.

    PubMed

    Diderichsen, F

    1982-01-01

    Sweden has a long tradition of social democracy and corporate cooperation. Social problems are treated as technological questions that always should be solved through rational and neutral means. Today Sweden faces a crisis of economy as well as a crisis of medicine. In the spirit of consensus, the state has proposed a new health reform emphasizing the responsibility of the public health service to prevent disease and provide equal access to care. It is claimed that improved health planning, based on epidemiological knowledge on inequalities, can solve the crisis in medicine within an improved system of primary care and prevention. However, in the context of the current economic crisis, the struggle against health hazards and cuts in public spending has intensified and the gap between the ideology of technological rationalism and reality has widened.

  17. An Introduction to Kristof's Theorem for Solving Least-Square Optimization Problems Without Calculus.

    PubMed

    Waller, Niels

    2018-01-01

    Kristof's Theorem (Kristof, 1970 ) describes a matrix trace inequality that can be used to solve a wide-class of least-square optimization problems without calculus. Considering its generality, it is surprising that Kristof's Theorem is rarely used in statistics and psychometric applications. The underutilization of this method likely stems, in part, from the mathematical complexity of Kristof's ( 1964 , 1970 ) writings. In this article, I describe the underlying logic of Kristof's Theorem in simple terms by reviewing four key mathematical ideas that are used in the theorem's proof. I then show how Kristof's Theorem can be used to provide novel derivations to two cognate models from statistics and psychometrics. This tutorial includes a glossary of technical terms and an online supplement with R (R Core Team, 2017 ) code to perform the calculations described in the text.

  18. A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations

    NASA Astrophysics Data System (ADS)

    Whiteley, J. P.

    2017-10-01

    Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.

  19. On Solving Systems of Equations by Successive Reduction Using 2×2 Matrices

    ERIC Educational Resources Information Center

    Carley, Holly

    2014-01-01

    Usually a student learns to solve a system of linear equations in two ways: "substitution" and "elimination." While the two methods will of course lead to the same answer they are considered different because the thinking process is different. In this paper the author solves a system in these two ways to demonstrate the…

  20. A social gradient in fatal opioids and cocaine related overdoses?

    PubMed

    Origer, Alain; Le Bihan, Etienne; Baumann, Michèle

    2015-01-01

    To determine the existence of a social gradient in fatal overdose cases related to non-prescribed opioids and cocaine use, recorded in Luxembourg between 1994 and 2011. Overdose cases were individually matched with four controls in a nested case-control study design, according to sex, year of birth, drug administration route and duration of drug use. The study sample, composed of 272 cases and 1,056 controls, was stratified according to a Social Inequality Accumulation Score (SIAS), based on educational attainment, employment, income, financial situation of subjects and the professional status of their father or legal guardian. Least squares linear regression analysis on overdose mortality rates and ridit scores were applied to determine the Relative Index of Inequality (RII) of the study sample. A negative linear relationship between the overdose mortality rate and the relative socioeconomic position was observed. We found a difference in mortality of 29.22 overdose deaths per 100 drug users in the lowest socioeconomic group compared to the most advantaged group. In terms of the Relative Inequality Index, the overdose mortality rate of opioid and cocaine users with lowest socioeconomic profiles was 9.88 times as high as that of their peers from the highest socioeconomic group (95% CI 6.49-13.26). Our findings suggest the existence of a marked social gradient in opioids and cocaine related overdose fatalities. Harm reduction services should integrate socially supportive offers, not only because of their general aim of social (re)integration but crucially in order to meet their most important objective, that is to reduce drug-related mortality.

  1. Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

    NASA Astrophysics Data System (ADS)

    Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

    2017-07-01

    This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

  2. A computational algorithm for spacecraft control and momentum management

    NASA Technical Reports Server (NTRS)

    Dzielski, John; Bergmann, Edward; Paradiso, Joseph

    1990-01-01

    Developments in the area of nonlinear control theory have shown how coordinate changes in the state and input spaces of a dynamical system can be used to transform certain nonlinear differential equations into equivalent linear equations. These techniques are applied to the control of a spacecraft equipped with momentum exchange devices. An optimal control problem is formulated that incorporates a nonlinear spacecraft model. An algorithm is developed for solving the optimization problem using feedback linearization to transform to an equivalent problem involving a linear dynamical constraint and a functional approximation technique to solve for the linear dynamics in terms of the control. The original problem is transformed into an unconstrained nonlinear quadratic program that yields an approximate solution to the original problem. Two examples are presented to illustrate the results.

  3. Mathematics Literacy of Secondary Students in Solving Simultanenous Linear Equations

    NASA Astrophysics Data System (ADS)

    Sitompul, R. S. I.; Budayasa, I. K.; Masriyah

    2018-01-01

    This study examines the profile of secondary students’ mathematical literacy in solving simultanenous linear equations problems in terms of cognitive style of visualizer and verbalizer. This research is a descriptive research with qualitative approach. The subjects in this research consist of one student with cognitive style of visualizer and one student with cognitive style of verbalizer. The main instrument in this research is the researcher herself and supporting instruments are cognitive style tests, mathematics skills tests, problem-solving tests and interview guidelines. Research was begun by determining the cognitive style test and mathematics skill test. The subjects chosen were given problem-solving test about simultaneous linear equations and continued with interview. To ensure the validity of the data, the researcher conducted data triangulation; the steps of data reduction, data presentation, data interpretation, and conclusion drawing. The results show that there is a similarity of visualizer and verbalizer-cognitive style in identifying and understanding the mathematical structure in the process of formulating. There are differences in how to represent problems in the process of implementing, there are differences in designing strategies and in the process of interpreting, and there are differences in explaining the logical reasons.

  4. A new implementation of the CMRH method for solving dense linear systems

    NASA Astrophysics Data System (ADS)

    Heyouni, M.; Sadok, H.

    2008-04-01

    The CMRH method [H. Sadok, Methodes de projections pour les systemes lineaires et non lineaires, Habilitation thesis, University of Lille1, Lille, France, 1994; H. Sadok, CMRH: A new method for solving nonsymmetric linear systems based on the Hessenberg reduction algorithm, Numer. Algorithms 20 (1999) 303-321] is an algorithm for solving nonsymmetric linear systems in which the Arnoldi component of GMRES is replaced by the Hessenberg process, which generates Krylov basis vectors which are orthogonal to standard unit basis vectors rather than mutually orthogonal. The iterate is formed from these vectors by solving a small least squares problem involving a Hessenberg matrix. Like GMRES, this method requires one matrix-vector product per iteration. However, it can be implemented to require half as much arithmetic work and less storage. Moreover, numerical experiments show that this method performs accurately and reduces the residual about as fast as GMRES. With this new implementation, we show that the CMRH method is the only method with long-term recurrence which requires not storing at the same time the entire Krylov vectors basis and the original matrix as in the GMRES algorithmE A comparison with Gaussian elimination is provided.

  5. Social determinants of health inequalities: towards a theoretical perspective using systems science.

    PubMed

    Jayasinghe, Saroj

    2015-08-25

    A systems approach offers a novel conceptualization to natural and social systems. In recent years, this has led to perceiving population health outcomes as an emergent property of a dynamic and open, complex adaptive system. The current paper explores these themes further and applies the principles of systems approach and complexity science (i.e. systems science) to conceptualize social determinants of health inequalities. The conceptualization can be done in two steps: viewing health inequalities from a systems approach and extending it to include complexity science. Systems approach views health inequalities as patterns within the larger rubric of other facets of the human condition, such as educational outcomes and economic development. This anlysis requires more sophisticated models such as systems dynamic models. An extension of the approach is to view systems as complex adaptive systems, i.e. systems that are 'open' and adapt to the environment. They consist of dynamic adapting subsystems that exhibit non-linear interactions, while being 'open' to a similarly dynamic environment of interconnected systems. They exhibit emergent properties that cannot be estimated with precision by using the known interactions among its components (such as economic development, political freedom, health system, culture etc.). Different combinations of the same bundle of factors or determinants give rise to similar patterns or outcomes (i.e. property of convergence), and minor variations in the initial condition could give rise to widely divergent outcomes. Novel approaches using computer simulation models (e.g. agent-based models) would shed light on possible mechanisms as to how factors or determinants interact and lead to emergent patterns of health inequalities of populations.

  6. Income inequality, disinvestment in health care and use of dental services.

    PubMed

    Bhandari, Bishal; Newton, Jonathan T; Bernabé, Eduardo

    2015-01-01

    To explore the interrelationships between income inequality, disinvestment in health care, and use of dental services at country level. This study pooled national estimates for use of dental services among adults aged 18 years or older from the 70 countries that participated in the World Health Survey from 2002 to 2004, together with aggregate data on national income (GDP per capita), income inequality (Gini coefficient), and disinvestment in health care (total health expenditure and dentist-to-population ratio) from various international sources. Use of dental services was defined as having had dental problems in the last 12 months and having received any treatment to address those needs. Associations between variables were explored using Pearson correlation coefficients and linear regression. Data from 63 countries representing the six WHO regions were analyzed. Use of dental services was negatively correlated with Gini coefficient (Pearson correlation coefficient -0.48, P < 0.001) and positively correlated with GDP per capita (0.40, P < 0.05), total health expenditure (0.45, P < 0.001), and dentist-to-population ratio (0.67, P < 0.001). The association between Gini coefficient and use of dental services was attenuated but remained significant after adjustments for GDP per capita, total health expenditure, and dentist-to-population ratio (regression coefficient -0.36; 95% CI -0.57, -0.15). This study shows an inverse relationship between income inequality and use of dental services. Of the two indicators of disinvestment in health care assessed, only dentist-to-population ratio was associated with income inequality and use of dental services. © 2014 American Association of Public Health Dentistry.

  7. Sexual orientation health inequality: Evidence from Understanding Society, the UK Longitudinal Household Study.

    PubMed

    Booker, Cara L; Rieger, Gerulf; Unger, Jennifer B

    2017-08-01

    Few studies from the United Kingdom have fully investigated inequalities between members of different sexual minority groups and heterosexuals over range of health outcomes. Using data from over 40,000 individuals, this study explores the health inequalities of sexual minority UK adults. We include respondents who identify as other and those who prefer not to say (PNS). Data come from wave three (2011-2012) of the nationally-representative Understanding Society, the UK Household Longitudinal Study. Sexual orientation was asked in the self-completion portion of the study. Markers of health include physical and mental functioning, minor psychological distress, self-rated health, substance use and disability. Multiple linear and logistic regression analyses tested for differences in markers of health between sexual orientation groups. Overall, heterosexual respondents had the best health while bisexual respondents had the worst. Gay and lesbian respondents reported poorer health than heterosexuals, specifically with regards to mental functioning, distress and illness status. The other and PNS respondents were most similar to each other and generally experienced fewer health inequalities than gay and lesbian respondents; they were less likely to use tobacco or alcohol. In sum, sexual minorities experience health inequality. The inclusion of other and PNS respondents has not been done in other studies and shows that while they may be healthier than gay/lesbian and bisexual respondents they still experiences poorer health than heterosexuals. Health promotion interventions are needed for these other and PNS individuals, who might not participate in interventions targeted toward known sexual minority groups. Copyright © 2017 The Authors. Published by Elsevier Inc. All rights reserved.

  8. Social inequalities in total and cause-specific mortality of a sample of the Italian population, from 1999 to 2007.

    PubMed

    Marinacci, Chiara; Grippo, Francesco; Pappagallo, Marilena; Sebastiani, Gabriella; Demaria, Moreno; Vittori, Patrizia; Caranci, Nicola; Costa, Giuseppe

    2013-08-01

    There is extensive documentation on social inequalities in mortality across Europe, showing heterogeneity among countries. Italy contributed to this comparative research, through longitudinal systems from northern or central cities of the country. This study aims to analyse educational inequalities in general and cause-specific mortality in a sample of the Italian population. Study population was selected within a cohort of 123,056 individuals, followed up for mortality through record linkage with national archive of death certificates for the period 1999-2007. People aged between 25 and 74 years were selected (n = 81,763); relative risks of death by education were estimated through Poisson models, stratified according to sex and adjusted for age and geographic area of residence. Heterogeneity of risks by area of residence was evaluated. Men and women with primary education or less show 79% and 63% higher mortality risks, respectively, compared with graduates. Mortality risks seem to frequently increase with decreasing education, with a significant linear trend among men. For men, social inequalities appear related to mortality due to diseases of the circulatory system and to all neoplasms, whereas for women, they are related to inequalities in cancer mortality. Results from the first follow-up of a national sample highlight that Italy presents significant differences in mortality according to the socio-economic conditions of both men and women. These results not only challenge policies aimed at redistributing resources to individuals and groups, but also those policies that direct programmes and resources for treatment and prevention according to the different health needs.

  9. Metric versus observable operator representation, higher spin models

    NASA Astrophysics Data System (ADS)

    Fring, Andreas; Frith, Thomas

    2018-02-01

    We elaborate further on the metric representation that is obtained by transferring the time-dependence from a Hermitian Hamiltonian to the metric operator in a related non-Hermitian system. We provide further insight into the procedure on how to employ the time-dependent Dyson relation and the quasi-Hermiticity relation to solve time-dependent Hermitian Hamiltonian systems. By solving both equations separately we argue here that it is in general easier to solve the former. We solve the mutually related time-dependent Schrödinger equation for a Hermitian and non-Hermitian spin 1/2, 1 and 3/2 model with time-independent and time-dependent metric, respectively. In all models the overdetermined coupled system of equations for the Dyson map can be decoupled algebraic manipulations and reduces to simple linear differential equations and an equation that can be converted into the non-linear Ermakov-Pinney equation.

  10. New Operational Matrices for Solving Fractional Differential Equations on the Half-Line

    PubMed Central

    2015-01-01

    In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques. PMID:25996369

  11. New operational matrices for solving fractional differential equations on the half-line.

    PubMed

    Bhrawy, Ali H; Taha, Taha M; Alzahrani, Ebraheem O; Alzahrani, Ebrahim O; Baleanu, Dumitru; Alzahrani, Abdulrahim A

    2015-01-01

    In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques.

  12. Solving a class of generalized fractional programming problems using the feasibility of linear programs.

    PubMed

    Shen, Peiping; Zhang, Tongli; Wang, Chunfeng

    2017-01-01

    This article presents a new approximation algorithm for globally solving a class of generalized fractional programming problems (P) whose objective functions are defined as an appropriate composition of ratios of affine functions. To solve this problem, the algorithm solves an equivalent optimization problem (Q) via an exploration of a suitably defined nonuniform grid. The main work of the algorithm involves checking the feasibility of linear programs associated with the interesting grid points. It is proved that the proposed algorithm is a fully polynomial time approximation scheme as the ratio terms are fixed in the objective function to problem (P), based on the computational complexity result. In contrast to existing results in literature, the algorithm does not require the assumptions on quasi-concavity or low-rank of the objective function to problem (P). Numerical results are given to illustrate the feasibility and effectiveness of the proposed algorithm.

  13. Consumer-choice health plan (first of two parts). Inflation and inequity in health care today: alternatives for cost control and an analysis of proposals for national health insurance.

    PubMed

    Enthoven, A C

    1978-03-23

    The financing system for medical costs in this country suffers from severe inflation and inequity. The tax-supported system of fee for service for doctors, third-party intermediaries and cost reimbursement for hospitals produces inflation by rewarding cost-increasing behavior and failing to provide incentives for economy. The system is inequitable because the government pays more on behalf of those who choose more costly systems of care, because tax benefits subsidize the health insurance of the well-to-do, while not helping many low-income people, and because employment health insurance does not guarantee continuity of coverage and is regressive in its financing. Analysis of previous proposals for national health insurance shows none to be capable of solving most of these problems. Direct economic regulation by government will not improve the situation. Cost controls through incentives and regulated competition in the private sector are most likely to be effective.

  14. The American Family in Black and White: A Post-Racial Strategy for Improving Skills to Promote Equality

    PubMed Central

    Heckman, James J.

    2012-01-01

    In contemporary America, racial gaps in achievement are primarily due to gaps in skills. Skill gaps emerge early before children enter school. Families are major producers of those skills. Inequality in performance in school is strongly linked to inequality in family environments. Schools do little to reduce or enlarge the gaps in skills that are present when children enter school. Parenting matters, and the true measure of child advantage and disadvantage is the quality of parenting received. A growing fraction of American children across all race and ethnic groups is being raised in dysfunctional families. Investment in the early lives of children in disadvantaged families will help close achievement gaps. America currently relies too much on schools and adolescent remediation strategies to solve problems that start in the preschool years. Policy should prevent rather than remediate. Voluntary, culturally sensitive support for parenting is a politically and economically palatable strategy that addresses problems common to all racial and ethnic groups. PMID:22605880

  15. Comparing Classic and Interval Analytical Hierarchy Process Methodologies for Measuring Area-Level Deprivation to Analyze Health Inequalities.

    PubMed

    Cabrera-Barona, Pablo; Ghorbanzadeh, Omid

    2018-01-16

    Deprivation indices are useful measures to study health inequalities. Different techniques are commonly applied to construct deprivation indices, including multi-criteria decision methods such as the analytical hierarchy process (AHP). The multi-criteria deprivation index for the city of Quito is an index in which indicators are weighted by applying the AHP. In this research, a variation of this index is introduced that is calculated using interval AHP methodology. Both indices are compared by applying logistic generalized linear models and multilevel models, considering self-reported health as the dependent variable and deprivation and self-reported quality of life as the independent variables. The obtained results show that the multi-criteria deprivation index for the city of Quito is a meaningful measure to assess neighborhood effects on self-reported health and that the alternative deprivation index using the interval AHP methodology more thoroughly represents the local knowledge of experts and stakeholders. These differences could support decision makers in improving health planning and in tackling health inequalities in more deprived areas.

  16. Comparing Classic and Interval Analytical Hierarchy Process Methodologies for Measuring Area-Level Deprivation to Analyze Health Inequalities

    PubMed Central

    Cabrera-Barona, Pablo

    2018-01-01

    Deprivation indices are useful measures to study health inequalities. Different techniques are commonly applied to construct deprivation indices, including multi-criteria decision methods such as the analytical hierarchy process (AHP). The multi-criteria deprivation index for the city of Quito is an index in which indicators are weighted by applying the AHP. In this research, a variation of this index is introduced that is calculated using interval AHP methodology. Both indices are compared by applying logistic generalized linear models and multilevel models, considering self-reported health as the dependent variable and deprivation and self-reported quality of life as the independent variables. The obtained results show that the multi-criteria deprivation index for the city of Quito is a meaningful measure to assess neighborhood effects on self-reported health and that the alternative deprivation index using the interval AHP methodology more thoroughly represents the local knowledge of experts and stakeholders. These differences could support decision makers in improving health planning and in tackling health inequalities in more deprived areas. PMID:29337915

  17. An interior-point method for total variation regularized positron emission tomography image reconstruction

    NASA Astrophysics Data System (ADS)

    Bai, Bing

    2012-03-01

    There has been a lot of work on total variation (TV) regularized tomographic image reconstruction recently. Many of them use gradient-based optimization algorithms with a differentiable approximation of the TV functional. In this paper we apply TV regularization in Positron Emission Tomography (PET) image reconstruction. We reconstruct the PET image in a Bayesian framework, using Poisson noise model and TV prior functional. The original optimization problem is transformed to an equivalent problem with inequality constraints by adding auxiliary variables. Then we use an interior point method with logarithmic barrier functions to solve the constrained optimization problem. In this method, a series of points approaching the solution from inside the feasible region are found by solving a sequence of subproblems characterized by an increasing positive parameter. We use preconditioned conjugate gradient (PCG) algorithm to solve the subproblems directly. The nonnegativity constraint is enforced by bend line search. The exact expression of the TV functional is used in our calculations. Simulation results show that the algorithm converges fast and the convergence is insensitive to the values of the regularization and reconstruction parameters.

  18. An interactive approach based on a discrete differential evolution algorithm for a class of integer bilevel programming problems

    NASA Astrophysics Data System (ADS)

    Li, Hong; Zhang, Li; Jiao, Yong-Chang

    2016-07-01

    This paper presents an interactive approach based on a discrete differential evolution algorithm to solve a class of integer bilevel programming problems, in which integer decision variables are controlled by an upper-level decision maker and real-value or continuous decision variables are controlled by a lower-level decision maker. Using the Karush--Kuhn-Tucker optimality conditions in the lower-level programming, the original discrete bilevel formulation can be converted into a discrete single-level nonlinear programming problem with the complementarity constraints, and then the smoothing technique is applied to deal with the complementarity constraints. Finally, a discrete single-level nonlinear programming problem is obtained, and solved by an interactive approach. In each iteration, for each given upper-level discrete variable, a system of nonlinear equations including the lower-level variables and Lagrange multipliers is solved first, and then a discrete nonlinear programming problem only with inequality constraints is handled by using a discrete differential evolution algorithm. Simulation results show the effectiveness of the proposed approach.

  19. Amesos2 and Belos: Direct and Iterative Solvers for Large Sparse Linear Systems

    DOE PAGES

    Bavier, Eric; Hoemmen, Mark; Rajamanickam, Sivasankaran; ...

    2012-01-01

    Solvers for large sparse linear systems come in two categories: direct and iterative. Amesos2, a package in the Trilinos software project, provides direct methods, and Belos, another Trilinos package, provides iterative methods. Amesos2 offers a common interface to many different sparse matrix factorization codes, and can handle any implementation of sparse matrices and vectors, via an easy-to-extend C++ traits interface. It can also factor matrices whose entries have arbitrary “Scalar” type, enabling extended-precision and mixed-precision algorithms. Belos includes many different iterative methods for solving large sparse linear systems and least-squares problems. Unlike competing iterative solver libraries, Belos completely decouples themore » algorithms from the implementations of the underlying linear algebra objects. This lets Belos exploit the latest hardware without changes to the code. Belos favors algorithms that solve higher-level problems, such as multiple simultaneous linear systems and sequences of related linear systems, faster than standard algorithms. The package also supports extended-precision and mixed-precision algorithms. Together, Amesos2 and Belos form a complete suite of sparse linear solvers.« less

  20. Real-time adaptive finite element solution of time-dependent Kohn-Sham equation

    NASA Astrophysics Data System (ADS)

    Bao, Gang; Hu, Guanghui; Liu, Di

    2015-01-01

    In our previous paper (Bao et al., 2012 [1]), a general framework of using adaptive finite element methods to solve the Kohn-Sham equation has been presented. This work is concerned with solving the time-dependent Kohn-Sham equations. The numerical methods are studied in the time domain, which can be employed to explain both the linear and the nonlinear effects. A Crank-Nicolson scheme and linear finite element space are employed for the temporal and spatial discretizations, respectively. To resolve the trouble regions in the time-dependent simulations, a heuristic error indicator is introduced for the mesh adaptive methods. An algebraic multigrid solver is developed to efficiently solve the complex-valued system derived from the semi-implicit scheme. A mask function is employed to remove or reduce the boundary reflection of the wavefunction. The effectiveness of our method is verified by numerical simulations for both linear and nonlinear phenomena, in which the effectiveness of the mesh adaptive methods is clearly demonstrated.

  1. An extended basis inexact shift-invert Lanczos for the efficient solution of large-scale generalized eigenproblems

    NASA Astrophysics Data System (ADS)

    Rewieński, M.; Lamecki, A.; Mrozowski, M.

    2013-09-01

    This paper proposes a technique, based on the Inexact Shift-Invert Lanczos (ISIL) method with Inexact Jacobi Orthogonal Component Correction (IJOCC) refinement, and a preconditioned conjugate-gradient (PCG) linear solver with multilevel preconditioner, for finding several eigenvalues for generalized symmetric eigenproblems. Several eigenvalues are found by constructing (with the ISIL process) an extended projection basis. Presented results of numerical experiments confirm the technique can be effectively applied to challenging, large-scale problems characterized by very dense spectra, such as resonant cavities with spatial dimensions which are large with respect to wavelengths of the resonating electromagnetic fields. It is also shown that the proposed scheme based on inexact linear solves delivers superior performance, as compared to methods which rely on exact linear solves, indicating tremendous potential of the 'inexact solve' concept. Finally, the scheme which generates an extended projection basis is found to provide a cost-efficient alternative to classical deflation schemes when several eigenvalues are computed.

  2. Solution of two-body relativistic bound state equations with confining plus Coulomb interactions

    NASA Technical Reports Server (NTRS)

    Maung, Khin Maung; Kahana, David E.; Norbury, John W.

    1992-01-01

    Studies of meson spectroscopy have often employed a nonrelativistic Coulomb plus Linear Confining potential in position space. However, because the quarks in mesons move at an appreciable fraction of the speed of light, it is necessary to use a relativistic treatment of the bound state problem. Such a treatment is most easily carried out in momentum space. However, the position space Linear and Coulomb potentials lead to singular kernels in momentum space. Using a subtraction procedure we show how to remove these singularities exactly and thereby solve the Schroedinger equation in momentum space for all partial waves. Furthermore, we generalize the Linear and Coulomb potentials to relativistic kernels in four dimensional momentum space. Again we use a subtraction procedure to remove the relativistic singularities exactly for all partial waves. This enables us to solve three dimensional reductions of the Bethe-Salpeter equation. We solve six such equations for Coulomb plus Confining interactions for all partial waves.

  3. Parallel/distributed direct method for solving linear systems

    NASA Technical Reports Server (NTRS)

    Lin, Avi

    1990-01-01

    A new family of parallel schemes for directly solving linear systems is presented and analyzed. It is shown that these schemes exhibit a near optimal performance and enjoy several important features: (1) For large enough linear systems, the design of the appropriate paralleled algorithm is insensitive to the number of processors as its performance grows monotonically with them; (2) It is especially good for large matrices, with dimensions large relative to the number of processors in the system; (3) It can be used in both distributed parallel computing environments and tightly coupled parallel computing systems; and (4) This set of algorithms can be mapped onto any parallel architecture without any major programming difficulties or algorithmical changes.

  4. Non-linear eigensolver-based alternative to traditional SCF methods

    NASA Astrophysics Data System (ADS)

    Gavin, B.; Polizzi, E.

    2013-05-01

    The self-consistent procedure in electronic structure calculations is revisited using a highly efficient and robust algorithm for solving the non-linear eigenvector problem, i.e., H({ψ})ψ = Eψ. This new scheme is derived from a generalization of the FEAST eigenvalue algorithm to account for the non-linearity of the Hamiltonian with the occupied eigenvectors. Using a series of numerical examples and the density functional theory-Kohn/Sham model, it will be shown that our approach can outperform the traditional SCF mixing-scheme techniques by providing a higher converge rate, convergence to the correct solution regardless of the choice of the initial guess, and a significant reduction of the eigenvalue solve time in simulations.

  5. An efficient finite element technique for sound propagation in axisymmetric hard wall ducts carrying high subsonic Mach number flows

    NASA Technical Reports Server (NTRS)

    Tag, I. A.; Lumsdaine, E.

    1978-01-01

    The general non-linear three-dimensional equation for acoustic potential is derived by using a perturbation technique. The linearized axisymmetric equation is then solved by using a finite element algorithm based on the Galerkin formulation for a harmonic time dependence. The solution is carried out in complex number notation for the acoustic velocity potential. Linear, isoparametric, quadrilateral elements with non-uniform distribution across the duct section are implemented. The resultant global matrix is stored in banded form and solved by using a modified Gauss elimination technique. Sound pressure levels and acoustic velocities are calculated from post element solutions. Different duct geometries are analyzed and compared with experimental results.

  6. Digital program for solving the linear stochastic optimal control and estimation problem

    NASA Technical Reports Server (NTRS)

    Geyser, L. C.; Lehtinen, B.

    1975-01-01

    A computer program is described which solves the linear stochastic optimal control and estimation (LSOCE) problem by using a time-domain formulation. The LSOCE problem is defined as that of designing controls for a linear time-invariant system which is disturbed by white noise in such a way as to minimize a performance index which is quadratic in state and control variables. The LSOCE problem and solution are outlined; brief descriptions are given of the solution algorithms, and complete descriptions of each subroutine, including usage information and digital listings, are provided. A test case is included, as well as information on the IBM 7090-7094 DCS time and storage requirements.

  7. Linear decomposition approach for a class of nonconvex programming problems.

    PubMed

    Shen, Peiping; Wang, Chunfeng

    2017-01-01

    This paper presents a linear decomposition approach for a class of nonconvex programming problems by dividing the input space into polynomially many grids. It shows that under certain assumptions the original problem can be transformed and decomposed into a polynomial number of equivalent linear programming subproblems. Based on solving a series of liner programming subproblems corresponding to those grid points we can obtain the near-optimal solution of the original problem. Compared to existing results in the literature, the proposed algorithm does not require the assumptions of quasi-concavity and differentiability of the objective function, and it differs significantly giving an interesting approach to solving the problem with a reduced running time.

  8. Application of a repetitive process setting to design of monotonically convergent iterative learning control

    NASA Astrophysics Data System (ADS)

    Boski, Marcin; Paszke, Wojciech

    2015-11-01

    This paper deals with the problem of designing an iterative learning control algorithm for discrete linear systems using repetitive process stability theory. The resulting design produces a stabilizing output feedback controller in the time domain and a feedforward controller that guarantees monotonic convergence in the trial-to-trial domain. The results are also extended to limited frequency range design specification. New design procedure is introduced in terms of linear matrix inequality (LMI) representations, which guarantee the prescribed performances of ILC scheme. A simulation example is given to illustrate the theoretical developments.

  9. A diffuse-interface method for two-phase flows with soluble surfactants

    PubMed Central

    Teigen, Knut Erik; Song, Peng; Lowengrub, John; Voigt, Axel

    2010-01-01

    A method is presented to solve two-phase problems involving soluble surfactants. The incompressible Navier–Stokes equations are solved along with equations for the bulk and interfacial surfactant concentrations. A non-linear equation of state is used to relate the surface tension to the interfacial surfactant concentration. The method is based on the use of a diffuse interface, which allows a simple implementation using standard finite difference or finite element techniques. Here, finite difference methods on a block-structured adaptive grid are used, and the resulting equations are solved using a non-linear multigrid method. Results are presented for a drop in shear flow in both 2D and 3D, and the effect of solubility is discussed. PMID:21218125

  10. Machining Chatter Analysis for High Speed Milling Operations

    NASA Astrophysics Data System (ADS)

    Sekar, M.; Kantharaj, I.; Amit Siddhappa, Savale

    2017-10-01

    Chatter in high speed milling is characterized by time delay differential equations (DDE). Since closed form solution exists only for simple cases, the governing non-linear DDEs of chatter problems are solved by various numerical methods. Custom codes to solve DDEs are tedious to build, implement and not error free and robust. On the other hand, software packages provide solution to DDEs, however they are not straight forward to implement. In this paper an easy way to solve DDE of chatter in milling is proposed and implemented with MATLAB. Time domain solution permits the study and model of non-linear effects of chatter vibration with ease. Time domain results are presented for various stable and unstable conditions of cut and compared with stability lobe diagrams.

  11. Socioeconomic and Racial/Ethnic Disparities in Cancer Mortality, Incidence, and Survival in the United States, 1950–2014: Over Six Decades of Changing Patterns and Widening Inequalities

    PubMed Central

    Jemal, Ahmedin

    2017-01-01

    We analyzed socioeconomic and racial/ethnic disparities in US mortality, incidence, and survival rates from all-cancers combined and major cancers from 1950 to 2014. Census-based deprivation indices were linked to national mortality and cancer data for area-based socioeconomic patterns in mortality, incidence, and survival. The National Longitudinal Mortality Study was used to analyze individual-level socioeconomic and racial/ethnic patterns in mortality. Rates, risk-ratios, least squares, log-linear, and Cox regression were used to examine trends and differentials. Socioeconomic patterns in all-cancer, lung, and colorectal cancer mortality changed dramatically over time. Individuals in more deprived areas or lower education and income groups had higher mortality and incidence rates than their more affluent counterparts, with excess risk being particularly marked for lung, colorectal, cervical, stomach, and liver cancer. Education and income inequalities in mortality from all-cancers, lung, prostate, and cervical cancer increased during 1979–2011. Socioeconomic inequalities in cancer mortality widened as mortality in lower socioeconomic groups/areas declined more slowly. Mortality was higher among Blacks and lower among Asian/Pacific Islanders and Hispanics than Whites. Cancer patient survival was significantly lower in more deprived neighborhoods and among most ethnic-minority groups. Cancer mortality and incidence disparities may reflect inequalities in smoking, obesity, physical inactivity, diet, alcohol use, screening, and treatment. PMID:28408935

  12. A generalized Lyapunov theory for robust root clustering of linear state space models with real parameter uncertainty

    NASA Technical Reports Server (NTRS)

    Yedavalli, R. K.

    1992-01-01

    The problem of analyzing and designing controllers for linear systems subject to real parameter uncertainty is considered. An elegant, unified theory for robust eigenvalue placement is presented for a class of D-regions defined by algebraic inequalities by extending the nominal matrix root clustering theory of Gutman and Jury (1981) to linear uncertain time systems. The author presents explicit conditions for matrix root clustering for different D-regions and establishes the relationship between the eigenvalue migration range and the parameter range. The bounds are all obtained by one-shot computation in the matrix domain and do not need any frequency sweeping or parameter gridding. The method uses the generalized Lyapunov theory for getting the bounds.

  13. Internal null controllability of a linear Schrödinger-KdV system on a bounded interval

    NASA Astrophysics Data System (ADS)

    Araruna, Fágner D.; Cerpa, Eduardo; Mercado, Alberto; Santos, Maurício C.

    2016-01-01

    The control of a linear dispersive system coupling a Schrödinger and a linear Korteweg-de Vries equation is studied in this paper. The system can be viewed as three coupled real-valued equations by taking real and imaginary parts in the Schrödinger equation. The internal null controllability is proven by using either one complex-valued control on the Schrödinger equation or two real-valued controls, one on each equation. Notice that the single Schrödinger equation is not known to be controllable with a real-valued control. The standard duality method is used to reduce the controllability property to an observability inequality, which is obtained by means of a Carleman estimates approach.

  14. Transient response of multidegree-of-freedom linear systems to forcing functions with inequality constraints

    NASA Technical Reports Server (NTRS)

    Michalopoulos, C. D.

    1974-01-01

    Optimal control theory is applied to analyze the transient response of discrete linear systems to forcing functions with unknown time dependence but having known bounds. Particular attention is given to forcing functions which include: (1) maximum displacement of any given mass element, (2) maximum relative displacement of any two adjacent masses, and (3) maximum acceleration of a given mass. Linear mechanical systems with an arbitrary number of degrees of freedom and only one forcing function acting are considered. In the general case, the desired forcing function is found to be a function that switches from the upper-to-lower bound and vice-versa at certain moments of time. A general procedure for finding such switching times is set forth.

  15. Linear Parameter Varying Control Synthesis for Actuator Failure, Based on Estimated Parameter

    NASA Technical Reports Server (NTRS)

    Shin, Jong-Yeob; Wu, N. Eva; Belcastro, Christine

    2002-01-01

    The design of a linear parameter varying (LPV) controller for an aircraft at actuator failure cases is presented. The controller synthesis for actuator failure cases is formulated into linear matrix inequality (LMI) optimizations based on an estimated failure parameter with pre-defined estimation error bounds. The inherent conservatism of an LPV control synthesis methodology is reduced using a scaling factor on the uncertainty block which represents estimated parameter uncertainties. The fault parameter is estimated using the two-stage Kalman filter. The simulation results of the designed LPV controller for a HiMXT (Highly Maneuverable Aircraft Technology) vehicle with the on-line estimator show that the desired performance and robustness objectives are achieved for actuator failure cases.

  16. Regional robust stabilisation and domain-of-attraction estimation for MIMO uncertain nonlinear systems with input saturation

    NASA Astrophysics Data System (ADS)

    Azizi, S.; Torres, L. A. B.; Palhares, R. M.

    2018-01-01

    The regional robust stabilisation by means of linear time-invariant state feedback control for a class of uncertain MIMO nonlinear systems with parametric uncertainties and control input saturation is investigated. The nonlinear systems are described in a differential algebraic representation and the regional stability is handled considering the largest ellipsoidal domain-of-attraction (DOA) inside a given polytopic region in the state space. A novel set of sufficient Linear Matrix Inequality (LMI) conditions with new auxiliary decision variables are developed aiming to design less conservative linear state feedback controllers with corresponding larger DOAs, by considering the polytopic description of the saturated inputs. A few examples are presented showing favourable comparisons with recently published similar control design methodologies.

  17. Guided Discovery, Visualization, and Technology Applied to the New Curriculum for Secondary Mathematics.

    ERIC Educational Resources Information Center

    Smith, Karan B.

    1996-01-01

    Presents activities which highlight major concepts of linear programming. Demonstrates how technology allows students to solve linear programming problems using exploration prior to learning algorithmic methods. (DDR)

  18. Direct measurement of nonlinear properties of bipartite quantum states.

    PubMed

    Bovino, Fabio Antonio; Castagnoli, Giuseppe; Ekert, Artur; Horodecki, Paweł; Alves, Carolina Moura; Sergienko, Alexander Vladimir

    2005-12-09

    Nonlinear properties of quantum states, such as entropy or entanglement, quantify important physical resources and are frequently used in quantum-information science. They are usually calculated from a full description of a quantum state, even though they depend only on a small number of parameters that specify the state. Here we extract a nonlocal and a nonlinear quantity, namely, the Renyi entropy, from local measurements on two pairs of polarization-entangled photons. We also introduce a "phase marking" technique which allows the selection of uncorrupted outcomes even with nondeterministic sources of entangled photons. We use our experimental data to demonstrate the violation of entropic inequalities. They are examples of nonlinear entanglement witnesses and their power exceeds all linear tests for quantum entanglement based on all possible Bell-Clauser-Horne-Shimony-Holt inequalities.

  19. Association between social capital and health in women of reproductive age: a population-based study.

    PubMed

    Baheiraei, Azam; Bakouei, Fatemeh; Mohammadi, Eesa; Majdzadeh, Reza; Hosseni, Mostafa

    2016-12-01

    Women's health is a public health priority. The origins of health inequalities are very complex. The present study was conducted to determine the association between social capital and health status in reproductive-age women in Tehran, Iran. In this population-based, cross-sectional study, the Social Capital Integrated Questionnaire, the SF-36 and socio-demographic questionnaires were used. Analysis of data by one-way ANOVA test and stepwise multiple linear regression showed that the manifestation dimensions of social capital (groups and networks, trust and solidarity, collective action and cooperation) can potentially lead to the outcome dimensions of social capital (social cohesion and inclusion, and empowerment and political action), which in turn affect health inequities after controlling for socio-demographic differences. © The Author(s) 2015.

  20. Power-rate synchronization of coupled genetic oscillators with unbounded time-varying delay.

    PubMed

    Alofi, Abdulaziz; Ren, Fengli; Al-Mazrooei, Abdullah; Elaiw, Ahmed; Cao, Jinde

    2015-10-01

    In this paper, a new synchronization problem for the collective dynamics among genetic oscillators with unbounded time-varying delay is investigated. The dynamical system under consideration consists of an array of linearly coupled identical genetic oscillators with each oscillators having unbounded time-delays. A new concept called power-rate synchronization, which is different from both the asymptotical synchronization and the exponential synchronization, is put forward to facilitate handling the unbounded time-varying delays. By using a combination of the Lyapunov functional method, matrix inequality techniques and properties of Kronecker product, we derive several sufficient conditions that ensure the coupled genetic oscillators to be power-rate synchronized. The criteria obtained in this paper are in the form of matrix inequalities. Illustrative example is presented to show the effectiveness of the obtained results.

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