Science.gov

Sample records for indefinite quadratic forms

  1. Indefinitely stable iron(IV) cage complexes formed in water by air oxidation

    NASA Astrophysics Data System (ADS)

    Tomyn, Stefania; Shylin, Sergii I.; Bykov, Dmytro; Ksenofontov, Vadim; Gumienna-Kontecka, Elzbieta; Bon, Volodymyr; Fritsky, Igor O.

    2017-01-01

    In nature, iron, the fourth most abundant element of the Earth's crust, occurs in its stable forms either as the native metal or in its compounds in the +2 or +3 (low-valent) oxidation states. High-valent iron (+4, +5, +6) compounds are not formed spontaneously at ambient conditions, and the ones obtained synthetically appear to be unstable in polar organic solvents, especially aqueous solutions, and this is what limits their studies and use. Here we describe unprecedented iron(IV) hexahydrazide clathrochelate complexes that are assembled in alkaline aqueous media from iron(III) salts, oxalodihydrazide and formaldehyde in the course of a metal-templated reaction accompanied by air oxidation. The complexes can exist indefinitely at ambient conditions without any sign of decomposition in water, nonaqueous solutions and in the solid state. We anticipate that our findings may open a way to aqueous solution and polynuclear high-valent iron chemistry that remains underexplored and presents an important challenge.

  2. Indefinitely stable iron(IV) cage complexes formed in water by air oxidation

    PubMed Central

    Tomyn, Stefania; Shylin, Sergii I.; Bykov, Dmytro; Ksenofontov, Vadim; Gumienna-Kontecka, Elzbieta; Bon, Volodymyr; Fritsky, Igor O.

    2017-01-01

    In nature, iron, the fourth most abundant element of the Earth's crust, occurs in its stable forms either as the native metal or in its compounds in the +2 or +3 (low-valent) oxidation states. High-valent iron (+4, +5, +6) compounds are not formed spontaneously at ambient conditions, and the ones obtained synthetically appear to be unstable in polar organic solvents, especially aqueous solutions, and this is what limits their studies and use. Here we describe unprecedented iron(IV) hexahydrazide clathrochelate complexes that are assembled in alkaline aqueous media from iron(III) salts, oxalodihydrazide and formaldehyde in the course of a metal-templated reaction accompanied by air oxidation. The complexes can exist indefinitely at ambient conditions without any sign of decomposition in water, nonaqueous solutions and in the solid state. We anticipate that our findings may open a way to aqueous solution and polynuclear high-valent iron chemistry that remains underexplored and presents an important challenge. PMID:28102364

  3. Evaluating the Contributions of Individual Variables to a Quadratic Form.

    PubMed

    Garthwaite, Paul H; Koch, Inge

    2016-03-01

    Quadratic forms capture multivariate information in a single number, making them useful, for example, in hypothesis testing. When a quadratic form is large and hence interesting, it might be informative to partition the quadratic form into contributions of individual variables. In this paper it is argued that meaningful partitions can be formed, though the precise partition that is determined will depend on the criterion used to select it. An intuitively reasonable criterion is proposed and the partition to which it leads is determined. The partition is based on a transformation that maximises the sum of the correlations between individual variables and the variables to which they transform under a constraint. Properties of the partition, including optimality properties, are examined. The contributions of individual variables to a quadratic form are less clear-cut when variables are collinear, and forming new variables through rotation can lead to greater transparency. The transformation is adapted so that it has an invariance property under such rotation, whereby the assessed contributions are unchanged for variables that the rotation does not affect directly. Application of the partition to Hotelling's one- and two-sample test statistics, Mahalanobis distance and discriminant analysis is described and illustrated through examples. It is shown that bootstrap confidence intervals for the contributions of individual variables to a partition are readily obtained.

  4. Space Time Clustering and the Permutation Moments of Quadratic Form.

    PubMed

    Zhou, Yi-Hui; Mayhew, Gregory; Sun, Zhibin; Xu, Xiaolin; Zou, Fei; Wright, Fred A

    2013-01-01

    The Mantel and Knox space-time clustering statistics are popular tools to establish transmissibility of a disease and detect outbreaks. The most commonly used null distributional approximations may provide poor fits, and researchers often resort to direct sampling from the permutation distribution. However, the exact first four moments for these statistics are available, and Pearson distributional approximations are often effective. Thus, our first goal is to clarify the literature and to make these tools more widely available. In addition, by rewriting terms in the statistics we obtain the exact first four permutation moments for the most commonly used quadratic form statistics, which need not be positive definite. The extension of this work to quadratic forms greatly expands the utility of density approximations for these problems, including for high-dimensional applications, where the statistics must be extreme in order to exceed stringent testing thresholds. We demonstrate the methods using examples from the investigation of disease transmission in cattle, the association of a gene expression pathway with breast cancer survival, regional genetic association with cystic fibrosis lung disease, and hypothesis testing for smoothed local linear regression.

  5. Two simple approximations to the distributions of quadratic forms.

    PubMed

    Yuan, Ke-Hai; Bentler, Peter M

    2010-05-01

    Many test statistics are asymptotically equivalent to quadratic forms of normal variables, which are further equivalent to T = sigma(d)(i=1) lambda(i)z(i)(2) with z(i) being independent and following N(0,1). Two approximations to the distribution of T have been implemented in popular software and are widely used in evaluating various models. It is important to know how accurate these approximations are when compared to each other and to the exact distribution of T. The paper systematically studies the quality of the two approximations and examines the effect of the lambda(i) and the degrees of freedom d by analysis and Monte Carlo. The results imply that the adjusted distribution for T can be as good as knowing its exact distribution. When the coefficient of variation of the lambda(i) is small, the rescaled statistic T(R) = dT/(sigma(d)(i=1) lambda(i)) is also adequate for practical model inference. But comparing T(R) against chi2(d) will inflate type I errors when substantial differences exist among the lambda(i), especially, when d is also large.

  6. Solution of a fractional transport equation by using the generalized quadratic form

    NASA Astrophysics Data System (ADS)

    Kadem, Abdelouahab; Baleanu, Dumitru

    2011-08-01

    In this manuscript the one dimensional fractional transport equation in which the prescribed source and angular flux are spatially quadratic is investigated within the generalized quadratic form method. It is reported that the angular flux satisfies Fick's law and the corresponding scalar flux satisfies the fractional generalization of the classic diffusion equation.

  7. Effects of MC-Type Carbide Forming and Graphitizing Elements on Thermal Fatigue Behavior of Indefinite Chilled Cast Iron Rolls

    NASA Astrophysics Data System (ADS)

    Ahiale, Godwin Kwame; Choi, Won-Doo; Suh, Yongchan; Lee, Young-Kook; Oh, Yong-Jun

    2015-11-01

    The thermal fatigue behavior of indefinite chilled cast iron rolls with various V+Nb contents and Si/Cr ratios was evaluated. Increasing the ratio of Si/Cr prolonged the life of the rolls by reducing brittle cementites. Higher V+Nb addition also increased the life through the formation of carbides that refined and toughened the martensite matrix and reduced the thermal expansion mismatch in the microstructure.

  8. Overpartitions and class numbers of binary quadratic forms

    PubMed Central

    Bringmann, Kathrin; Lovejoy, Jeremy

    2009-01-01

    We show that the Zagier–Eisenstein series shares its nonholomorphic part with certain weak Maass forms whose holomorphic parts are generating functions for overpartition rank differences. This has a number of consequences, including exact formulas, asymptotics, and congruences for the rank differences as well as q-series identities of the mock theta type. PMID:19336581

  9. Closed-form solutions for a class of optimal quadratic regulator problems with terminal constraints

    NASA Technical Reports Server (NTRS)

    Juang, J.-N.; Turner, J. D.; Chun, H. M.

    1984-01-01

    Closed-form solutions are derived for coupled Riccati-like matrix differential equations describing the solution of a class of optimal finite time quadratic regulator problems with terminal constraints. Analytical solutions are obtained for the feedback gains and the closed-loop response trajectory. A computational procedure is presented which introduces new variables for efficient computation of the terminal control law. Two examples are given to illustrate the validity and usefulness of the theory.

  10. Limiting subdifferentials of indefinite integrals

    NASA Astrophysics Data System (ADS)

    Chieu, Nguyen Huy

    2008-05-01

    We compute the limiting subdifferential of the indefinite integral of the form where f is an essentially bounded measurable function, or a function continuous on an interval containing (except for, possibly, ), or a step-function which has a countable number of steps around . The related problem of computing the Aumann integral of the limiting subdifferential mapping [not partial differential]f([dot operator]), where f is a Lipschitz real function defined on an open set , is also investigated.

  11. Normal forms for germs of vector fields with quadratic leading part. The polynomial first integral case

    NASA Astrophysics Data System (ADS)

    Stróżyna, Ewa

    2015-12-01

    We study the problem of formal classification of the vector fields of the form x ˙ = ax2 + bxy + cy2 + … , y ˙ = dx2 + exy + fy2 + … using formal changes of the coordinates, but not using the changes of the time. We focus on one special case (which is the most complex one): when the quadratic homogeneous part has a polynomial first integral. In the proofs we avoid complicated calculations. The method we use is effective and it is based on the method introduced in our previous work concerning the Bogdanov-Takens singularity.

  12. Efficient Calculation of P-value and Power for Quadratic Form Statistics in Multilocus Association Testing

    PubMed Central

    TONG, LIPING; YANG, JIE; COOPER, RICHARD S.

    2010-01-01

    SUMMARY We address the asymptotic and approximate distributions of a large class of test statistics with quadratic forms used in association studies. The statistics of interest take the general form D = XT AX, where A is a general similarity matrix which may or may not be positive semi-definite, and X follows the multivariate normal distribution with mean μ and variance matrix Σ, where Σ may or may not be singular. We show that D can be written as a linear combination of independent chi-square random variables with a shift. Furthermore, its distribution can be approximated by a chi-square or the difference of two chi-square distributions. In the setting of association testing, our methods are especially useful in two situations. First, when the required significance level is much smaller than 0.05 such as in a genome scan the estimation of p-values using permutation procedures can be challenging. Second, when an EM algorithm is required to infer haplotype frequencies from un-phased genotype data the computation can be intensive for a permutation procedure. In either situation, an efficient and accurate estimation procedure would be useful. Our method can be applied to any quadratic form statistic and therefore should be of general interest. PMID:20529017

  13. Space–time clustering and the permutation moments of quadratic forms

    PubMed Central

    Zhou, Yi-Hui; Mayhew, Gregory; Sun, Zhibin; Xu, Xiaolin; Zou, Fei; Wright, Fred A

    2013-01-01

    The Mantel and Knox space–time clustering statistics are popular tools to establish transmissibility of a disease and detect outbreaks. The most commonly used null distributional approximations may provide poor fits, and researchers often resort to direct sampling from the permutation distribution. However, the exact first four moments for these statistics are available, and Pearson distributional approximations are often effective. Thus, our first goals are to clarify the literature and make these tools more widely available. In addition, by rewriting terms in the statistics, we obtain the exact first four permutation moments for the most commonly used quadratic form statistics, which need not be positive definite. The extension of this work to quadratic forms greatly expands the utility of density approximations for these problems, including for high-dimensional applications, where the statistics must be extreme in order to exceed stringent testing thresholds. We demonstrate the methods using examples from the investigation of disease transmission in cattle, the association of a gene expression pathway with breast cancer survival, regional genetic association with cystic fibrosis lung disease and hypothesis testing for smoothed local linear regression. © The Authors. Stat published by John Wiley & Sons Ltd. PMID:25210205

  14. The use of quadratic forms in the calculation of ground state electronic structures

    SciTech Connect

    Keller, Jaime; Weinberger, Peter

    2006-08-15

    There are many examples in theoretical physics where a fundamental quantity can be considered a quadratic form {rho}={sigma}{sub i}{rho}{sub i}=vertical bar {psi} vertical bar{sup 2} and the corresponding linear form {psi}={sigma}{sub i}{psi}{sub i} is highly relevant for the physical problem under study. This, in particular, is the case of the density and the wave function in quantum mechanics. In the study of N-identical-fermion systems we have the additional feature that {psi} is a function of the 3N configuration space coordinates and {rho} is defined in three-dimensional real space. For many-electron systems in the ground state the wave function and the Hamiltonian are to be expressed in terms of the configuration space (CS), a replica of real space for each electron. Here we present a geometric formulation of the CS, of the wave function, of the density, and of the Hamiltonian to compute the electronic structure of the system. Then, using the new geometric notation and the indistinguishability and equivalence of the electrons, we obtain an alternative computational method for the ground state of the system. We present the method and discuss its usefulness and relation to other approaches.

  15. Quadratic solid-shell elements for nonlinear structural analysis and sheet metal forming simulation

    NASA Astrophysics Data System (ADS)

    Wang, Peng; Chalal, Hocine; Abed-Meraim, Farid

    2017-01-01

    In this paper, two quadratic solid-shell (SHB) elements are proposed for the three-dimensional modeling of thin structures. These consist of a 20-node hexahedral solid-shell element, denoted SHB20, and its 15-node prismatic counterpart, denoted SHB15. The formulation of these elements is extended in this work to include geometric and material nonlinearities, for application to problems involving large displacements and rotations as well as plasticity. For this purpose, the SHB elements are coupled with large-strain anisotropic elasto-plastic constitutive equations for metallic materials. Although based on a purely three-dimensional approach, several modifications are introduced in the formulation of these elements to provide them with interesting shell features. In particular, a special direction is chosen to represent the thickness, along which a user-defined number of integration points are located. Furthermore, for efficiency requirements and for alleviating locking phenomena, an in-plane reduced-integration scheme is adopted. The resulting formulations are implemented into the finite element software ABAQUS/Standard and, to assess their performance, a variety of nonlinear benchmark problems are investigated. Attention is then focused on the simulation of various complex sheet metal forming processes, involving large strain, anisotropic plasticity, and double-sided contact. From all simulation results, it appears that the SHB elements represent an interesting alternative to traditional shell and solid elements, due to their versatility and capability of accurately modeling selective nonlinear benchmark problems as well as complex sheet metal forming processes.

  16. 48 CFR 1552.217-76 - Option to extend the effective period of the contract-indefinite delivery/indefinite quantity...

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 48 Federal Acquisition Regulations System 6 2010-10-01 2010-10-01 true Option to extend the effective period of the contract-indefinite delivery/indefinite quantity contract. 1552.217-76 Section 1552.217-76 Federal Acquisition Regulations System ENVIRONMENTAL PROTECTION AGENCY CLAUSES AND FORMS SOLICITATION PROVISIONS AND CONTRACT CLAUSES...

  17. Quadratic Damping

    ERIC Educational Resources Information Center

    Fay, Temple H.

    2012-01-01

    Quadratic friction involves a discontinuous damping term in equations of motion in order that the frictional force always opposes the direction of the motion. Perhaps for this reason this topic is usually omitted from beginning texts in differential equations and physics. However, quadratic damping is more realistic than viscous damping in many…

  18. Quadratic Damping

    ERIC Educational Resources Information Center

    Fay, Temple H.

    2012-01-01

    Quadratic friction involves a discontinuous damping term in equations of motion in order that the frictional force always opposes the direction of the motion. Perhaps for this reason this topic is usually omitted from beginning texts in differential equations and physics. However, quadratic damping is more realistic than viscous damping in many…

  19. Retrocausation Or Extant Indefinite Reality?

    NASA Astrophysics Data System (ADS)

    Houtkooper, Joop M.

    2006-10-01

    The possibility of retrocausation has been considered to explain the occurrence of anomalous phenomena in which the ostensible effects are preceded by their causes. A scrutiny of both experimental methodology and the experimental data is called for. A review of experimental data reveals the existence of such effects to be a serious possibility. The experimental methodology entails some conceptual difficulties, these depending on the underlying assumptions about the effects. A major point is an ambiguity between anomalous acquisition of information and retrocausation in exerted influences. A unifying theory has been proposed, based upon the fundamental randomness of quantum mechanics. Quantum mechanical randomness may be regarded as a tenacious phenomenon, that apparently is only resolved by the human observer of the random variable in question. This has led to the "observational theory" of anomalous phenomena, which is based upon the assumption that the preference of a motivated observer is able to interact with the extant indefinite random variable that is being observed. This observational theory has led to a novel prediction, which has been corroborated in experiments. Moreover, different classes of anomalous phenomena can be explained by the same basic mechanism. This foregoes retroactive causation, but, instead, requires that macroscopic physical variables remain in a state of indefinite reality and thus remain influenceable by mental efforts until these are observed. More work is needed to discover the relevant psychological and neurophysiological variables involved in effective motivated observation. Besides these practicalities, the fundamentals still have some interesting loose ends.

  20. 48 CFR 652.216-70 - Ordering-Indefinite-Delivery Contract.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ...-Delivery Contract. 652.216-70 Section 652.216-70 Federal Acquisition Regulations System DEPARTMENT OF STATE... Ordering—Indefinite-Delivery Contract. As prescribed in 616.506-70, insert the following clause: Ordering—Indefinite-Delivery Contracts (APR 2004) The Government shall use one of the following forms to issue...

  1. 48 CFR 652.216-70 - Ordering-Indefinite-Delivery Contract.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ...-Delivery Contract. 652.216-70 Section 652.216-70 Federal Acquisition Regulations System DEPARTMENT OF STATE... Ordering—Indefinite-Delivery Contract. As prescribed in 616.506-70, insert the following clause: Ordering—Indefinite-Delivery Contracts (APR 2004) The Government shall use one of the following forms to issue...

  2. 48 CFR 1552.216-73 - Fixed rates for services-indefinite delivery/indefinite quantity contract.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... 48 Federal Acquisition Regulations System 6 2012-10-01 2012-10-01 false Fixed rates for services... Regulations System ENVIRONMENTAL PROTECTION AGENCY CLAUSES AND FORMS SOLICITATION PROVISIONS AND CONTRACT CLAUSES Texts of Provisions and Clauses 1552.216-73 Fixed rates for services—indefinite...

  3. 48 CFR 1552.216-73 - Fixed rates for services-indefinite delivery/indefinite quantity contract.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 48 Federal Acquisition Regulations System 6 2014-10-01 2014-10-01 false Fixed rates for services... Regulations System ENVIRONMENTAL PROTECTION AGENCY CLAUSES AND FORMS SOLICITATION PROVISIONS AND CONTRACT CLAUSES Texts of Provisions and Clauses 1552.216-73 Fixed rates for services—indefinite...

  4. 48 CFR 1552.216-73 - Fixed rates for services-indefinite delivery/indefinite quantity contract.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ...-indefinite delivery/indefinite quantity contract. 1552.216-73 Section 1552.216-73 Federal Acquisition... CLAUSES Texts of Provisions and Clauses 1552.216-73 Fixed rates for services—indefinite delivery... rates for services in indefinite delivery/indefinite quantity contracts. When the contract contains...

  5. On polynomial preconditioning for indefinite Hermitian matrices

    NASA Technical Reports Server (NTRS)

    Freund, Roland W.

    1989-01-01

    The minimal residual method is studied combined with polynomial preconditioning for solving large linear systems (Ax = b) with indefinite Hermitian coefficient matrices (A). The standard approach for choosing the polynomial preconditioners leads to preconditioned systems which are positive definite. Here, a different strategy is studied which leaves the preconditioned coefficient matrix indefinite. More precisely, the polynomial preconditioner is designed to cluster the positive, resp. negative eigenvalues of A around 1, resp. around some negative constant. In particular, it is shown that such indefinite polynomial preconditioners can be obtained as the optimal solutions of a certain two parameter family of Chebyshev approximation problems. Some basic results are established for these approximation problems and a Remez type algorithm is sketched for their numerical solution. The problem of selecting the parameters such that the resulting indefinite polynomial preconditioners speeds up the convergence of minimal residual method optimally is also addressed. An approach is proposed based on the concept of asymptotic convergence factors. Finally, some numerical examples of indefinite polynomial preconditioners are given.

  6. Highly indefinite multigrid for eigenvalue problems

    SciTech Connect

    Borges, L.; Oliveira, S.

    1996-12-31

    Eigenvalue problems are extremely important in understanding dynamic processes such as vibrations and control systems. Large scale eigenvalue problems can be very difficult to solve, especially if a large number of eigenvalues and the corresponding eigenvectors need to be computed. For solving this problem a multigrid preconditioned algorithm is presented in {open_quotes}The Davidson Algorithm, preconditioning and misconvergence{close_quotes}. Another approach for solving eigenvalue problems is by developing efficient solutions for highly indefinite problems. In this paper we concentrate on the use of new highly indefinite multigrid algorithms for the eigenvalue problem.

  7. Partial focusing by indefinite complementary metamaterials

    NASA Astrophysics Data System (ADS)

    Cheng, Qiang; Liu, Ruopeng; Mock, Jack J.; Cui, Tie Jun; Smith, David R.

    2008-09-01

    We have experimentally realized a two-dimensional partial focusing within a planar waveguide using complementary indefinite metamaterials. When the electric fields emitted from the dipole are TE polarized, the focusing condition requires negative magnetic response in the propagation direction of the waveguide, which can be achieved by the complementary electric resonator (CELC) structures. We have carefully designed the experimental configurations and the dimensions for the CELC structures. The experimental result is consistent with the theoretical prediction, which validates the partial focusing phenomenon.

  8. Properties of surjective real quadratic maps

    NASA Astrophysics Data System (ADS)

    Arutyunov, A. V.; Zhukovskiy, S. E.

    2016-09-01

    The properties of surjective real quadratic maps are investigated. Sufficient conditions for the property of surjectivity to be stable under various perturbations are obtained. Examples of surjective quadratic maps whose surjectivity breaks down after an arbitrarily small perturbation are constructed. Sufficient conditions for quadratic maps to have nontrivial zeros are obtained. For a smooth even map in a neighbourhood of the origin an inverse function theorem in terms of the degree of the corresponding quadratic map is obtained. A canonical form of surjective quadratic maps from {R}^3 to {R}^3 is constructed. Bibliography: 27 titles.

  9. The cataphoric use of the indefinite this in spoken narratives

    PubMed Central

    Gernsbacher, Morton Ann; Shroyer, Suzanne

    2015-01-01

    Are concepts that were introduced with the unstressed, indefinite article this, as opposed to the indefinite a/an, more accessible from listeners' mental representations? Subjects heard and then verbally continued each of a series of informal narratives. The last clause of each narrative introduced a new noun phrase that began with either the indefinite this or the indefinite a/an (e.g., this egg or an egg). When the concepts were introduced with the indefinite this, the subjects referred to them more frequently, often within the first clauses that they produced, and typically via pronouns. In contrast, when the concepts were introduced with a/an, the subjects referred to them less frequently and typically via full noun phrases. Thus, concepts introduced with the indefinite this were more accessible; therefore, the indefinite this appears to operate cataphorically to improve referential access. PMID:2796738

  10. Primal-Dual Interior Methods for Quadratic Programming

    NASA Astrophysics Data System (ADS)

    Shustrova, Anna

    Interior methods are a class of computational methods for solving a con- strained optimization problem. Interior methods follow a continuous path to the solution that passes through the interior of the feasible region (i.e., the set of points that satisfy the constraints). Interior-point methods may also be viewed as methods that replace the constrained problem by a sequence of unconstrained problems in which the objective function is augmented by a weighted "barrier" term that is infinite at the boundary of the feasible region. Convergence to a solution of the constrained problem is achieved by solving a sequence of unconstrained problems in which the weight on the barrier term is steadily reduced to zero. This thesis concerns the formulation and analysis of interior methods for the solution of a quadratic programming (QP) problem, which is an optimization problem with a quadratic objective function and linear constraints. The linear constraints may include an arbitrary mixture of equality and inequality constraints, where the inequality constraints may be subject to lower and/or upper bounds. QP problems arise in a wide variety of applications. An important application is in sequential quadratic programming methods for nonlinear optimization, which involve minimizing a sequence of QP subproblems based on a quadratic approximation of the nonlinear objective function and a set of linearized nonlinear constraints. Two new interior methods for QP are proposed. Each is based on the properties of a barrier function defined in terms of both the primal and dual variables. The first method is suitable for a QP with all inequality constraints. At each iteration, the Newton equations for minimizing a quadratic model of the primal-dual barrier function are reformulated in terms of a symmetric indefinite system of equations that is solved using an inertia controlling factorization. This factorization provides an effective method for the detection and convexification of

  11. Self-Replicating Quadratics

    ERIC Educational Resources Information Center

    Withers, Christopher S.; Nadarajah, Saralees

    2012-01-01

    We show that there are exactly four quadratic polynomials, Q(x) = x [superscript 2] + ax + b, such that (x[superscript 2] + ax + b) (x[superscript 2] - ax + b) = (x[superscript 4] + ax[superscript 2] + b). For n = 1, 2, ..., these quadratic polynomials can be written as the product of N = 2[superscript n] quadratic polynomials in x[superscript…

  12. Self-Replicating Quadratics

    ERIC Educational Resources Information Center

    Withers, Christopher S.; Nadarajah, Saralees

    2012-01-01

    We show that there are exactly four quadratic polynomials, Q(x) = x [superscript 2] + ax + b, such that (x[superscript 2] + ax + b) (x[superscript 2] - ax + b) = (x[superscript 4] + ax[superscript 2] + b). For n = 1, 2, ..., these quadratic polynomials can be written as the product of N = 2[superscript n] quadratic polynomials in x[superscript…

  13. Preconditioners for Indefinite Systems Arising in Optimization

    DTIC Science & Technology

    1990-06-01

    Large-Scale Quadratic Programming, Ph.D. Thesis, Computer Science Department, Stanford University, Stanford, CA. [Rut66] H. Rutishauser (1966). The Jacobi ... method for real symmetric matrices, Nuvuc, tu.’h Mathematik 9, 1-10. [Sau791 M. A. Saunders (1979). Fortran code: a modification of SYMMLQ to allow

  14. 48 CFR 716.505-70 - Vetting orders under indefinite delivery contracts.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... 48 Federal Acquisition Regulations System 5 2013-10-01 2013-10-01 false Vetting orders under...-Delivery Contracts 716.505-70 Vetting orders under indefinite delivery contracts. (a) The task order... subject to vetting and when awardees must submit the USAID Partner Information Form. (b) For orders under...

  15. 48 CFR 716.505-70 - Vetting orders under indefinite delivery contracts.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 48 Federal Acquisition Regulations System 5 2014-10-01 2014-10-01 false Vetting orders under...-Delivery Contracts 716.505-70 Vetting orders under indefinite delivery contracts. (a) The task order... subject to vetting and when awardees must submit the USAID Partner Information Form. (b) For orders under...

  16. 48 CFR 716.505-70 - Vetting orders under indefinite delivery contracts.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... 48 Federal Acquisition Regulations System 5 2012-10-01 2012-10-01 false Vetting orders under...-Delivery Contracts 716.505-70 Vetting orders under indefinite delivery contracts. (a) The task order... subject to vetting and when awardees must submit the USAID Partner Information Form. (b) For orders under...

  17. Communication-avoiding symmetric-indefinite factorization

    SciTech Connect

    Ballard, Grey Malone; Becker, Dulcenia; Demmel, James; Dongarra, Jack; Druinsky, Alex; Peled, Inon; Schwartz, Oded; Toledo, Sivan; Yamazaki, Ichitaro

    2014-11-13

    We describe and analyze a novel symmetric triangular factorization algorithm. The algorithm is essentially a block version of Aasen's triangular tridiagonalization. It factors a dense symmetric matrix A as the product A=PLTLTPT where P is a permutation matrix, L is lower triangular, and T is block tridiagonal and banded. The algorithm is the first symmetric-indefinite communication-avoiding factorization: it performs an asymptotically optimal amount of communication in a two-level memory hierarchy for almost any cache-line size. Adaptations of the algorithm to parallel computers are likely to be communication efficient as well; one such adaptation has been recently published. As a result, the current paper describes the algorithm, proves that it is numerically stable, and proves that it is communication optimal.

  18. Communication-avoiding symmetric-indefinite factorization

    DOE PAGES

    Ballard, Grey Malone; Becker, Dulcenia; Demmel, James; ...

    2014-11-13

    We describe and analyze a novel symmetric triangular factorization algorithm. The algorithm is essentially a block version of Aasen's triangular tridiagonalization. It factors a dense symmetric matrix A as the product A=PLTLTPT where P is a permutation matrix, L is lower triangular, and T is block tridiagonal and banded. The algorithm is the first symmetric-indefinite communication-avoiding factorization: it performs an asymptotically optimal amount of communication in a two-level memory hierarchy for almost any cache-line size. Adaptations of the algorithm to parallel computers are likely to be communication efficient as well; one such adaptation has been recently published. As a result,more » the current paper describes the algorithm, proves that it is numerically stable, and proves that it is communication optimal.« less

  19. Students' understanding of quadratic equations

    NASA Astrophysics Data System (ADS)

    López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

    2016-05-01

    Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help students achieve an understanding of quadratic equations with improved interrelation of ideas and more flexible application of solution methods. Semi-structured interviews with eight beginning undergraduate students explored which of the mental constructions conjectured in the genetic decomposition students could do, and which they had difficulty doing. Two of the mental constructions that form part of the genetic decomposition are highlighted and corresponding further data were obtained from the written work of 121 undergraduate science and engineering students taking a multivariable calculus course. The results suggest the importance of explicitly considering these two highlighted mental constructions.

  20. 48 CFR 19.804-6 - Indefinite delivery contracts.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... 48 Federal Acquisition Regulations System 1 2011-10-01 2011-10-01 false Indefinite delivery contracts. 19.804-6 Section 19.804-6 Federal Acquisition Regulations System FEDERAL ACQUISITION REGULATION...) Program) 19.804-6 Indefinite delivery contracts. (a) Separate offers and acceptances must not be made...

  1. 48 CFR 19.804-6 - Indefinite delivery contracts.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 48 Federal Acquisition Regulations System 1 2010-10-01 2010-10-01 false Indefinite delivery contracts. 19.804-6 Section 19.804-6 Federal Acquisition Regulations System FEDERAL ACQUISITION REGULATION...) Program) 19.804-6 Indefinite delivery contracts. (a) Separate offers and acceptances must not be made...

  2. 48 CFR 916.504 - Indefinite-quantity contracts.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... 48 Federal Acquisition Regulations System 5 2012-10-01 2012-10-01 false Indefinite-quantity contracts. 916.504 Section 916.504 Federal Acquisition Regulations System DEPARTMENT OF ENERGY CONTRACTING METHODS AND CONTRACT TYPES TYPES OF CONTRACTS Indefinite-Delivery Contracts 916.504...

  3. 48 CFR 916.504 - Indefinite-quantity contracts.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 48 Federal Acquisition Regulations System 5 2010-10-01 2010-10-01 false Indefinite-quantity contracts. 916.504 Section 916.504 Federal Acquisition Regulations System DEPARTMENT OF ENERGY CONTRACTING METHODS AND CONTRACT TYPES TYPES OF CONTRACTS Indefinite-Delivery Contracts 916.504...

  4. 48 CFR 916.504 - Indefinite-quantity contracts.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 48 Federal Acquisition Regulations System 5 2014-10-01 2014-10-01 false Indefinite-quantity contracts. 916.504 Section 916.504 Federal Acquisition Regulations System DEPARTMENT OF ENERGY CONTRACTING METHODS AND CONTRACT TYPES TYPES OF CONTRACTS Indefinite-Delivery Contracts 916.504...

  5. 48 CFR 916.504 - Indefinite-quantity contracts.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... 48 Federal Acquisition Regulations System 5 2011-10-01 2011-10-01 false Indefinite-quantity contracts. 916.504 Section 916.504 Federal Acquisition Regulations System DEPARTMENT OF ENERGY CONTRACTING METHODS AND CONTRACT TYPES TYPES OF CONTRACTS Indefinite-Delivery Contracts 916.504...

  6. 48 CFR 916.504 - Indefinite-quantity contracts.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... 48 Federal Acquisition Regulations System 5 2013-10-01 2013-10-01 false Indefinite-quantity contracts. 916.504 Section 916.504 Federal Acquisition Regulations System DEPARTMENT OF ENERGY CONTRACTING METHODS AND CONTRACT TYPES TYPES OF CONTRACTS Indefinite-Delivery Contracts 916.504...

  7. Reduplication of Indefinite Direct Objects in Albanian and Modern Greek

    ERIC Educational Resources Information Center

    Kazazis, Kostas; Pentheroudakis, Joseph

    1976-01-01

    Attempts to show that the reduplication of indefinite direct objects is not necessarily ungrammatical but that there are two kinds of indefinite direct objects, specified and non-specified. The former may undergo reduplication, the latter may not. (Author/RM)

  8. Experimental verification of an indefinite causal order

    PubMed Central

    Rubino, Giulia; Rozema, Lee A.; Feix, Adrien; Araújo, Mateus; Zeuner, Jonas M.; Procopio, Lorenzo M.; Brukner, Časlav; Walther, Philip

    2017-01-01

    Investigating the role of causal order in quantum mechanics has recently revealed that the causal relations of events may not be a priori well defined in quantum theory. Although this has triggered a growing interest on the theoretical side, creating processes without a causal order is an experimental task. We report the first decisive demonstration of a process with an indefinite causal order. To do this, we quantify how incompatible our setup is with a definite causal order by measuring a “causal witness.” This mathematical object incorporates a series of measurements that are designed to yield a certain outcome only if the process under examination is not consistent with any well-defined causal order. In our experiment, we perform a measurement in a superposition of causal orders—without destroying the coherence—to acquire information both inside and outside of a “causally nonordered process.” Using this information, we experimentally determine a causal witness, demonstrating by almost 7 SDs that the experimentally implemented process does not have a definite causal order. PMID:28378018

  9. Quadratic eigenvalue problems.

    SciTech Connect

    Walsh, Timothy Francis; Day, David Minot

    2007-04-01

    In this report we will describe some nonlinear eigenvalue problems that arise in the areas of solid mechanics, acoustics, and coupled structural acoustics. We will focus mostly on quadratic eigenvalue problems, which are a special case of nonlinear eigenvalue problems. Algorithms for solving the quadratic eigenvalue problem will be presented, along with some example calculations.

  10. Incomplete block factorization preconditioning for indefinite elliptic problems

    SciTech Connect

    Guo, Chun-Hua

    1996-12-31

    The application of the finite difference method to approximate the solution of an indefinite elliptic problem produces a linear system whose coefficient matrix is block tridiagonal and symmetric indefinite. Such a linear system can be solved efficiently by a conjugate residual method, particularly when combined with a good preconditioner. We show that specific incomplete block factorization exists for the indefinite matrix if the mesh size is reasonably small. And this factorization can serve as an efficient preconditioner. Some efforts are made to estimate the eigenvalues of the preconditioned matrix. Numerical results are also given.

  11. Gravitational energy in quadratic-curvature gravities.

    PubMed

    Deser, S; Tekin, Bayram

    2002-09-02

    We define energy (E) and compute its values for gravitational systems involving terms quadratic in curvature. There are significant differences, both conceptually and concretely, from Einstein theory. For D=4, all purely quadratic models admit constant curvature vacua with arbitrary Lambda, and E is the "cosmological" Abbott-Deser (AD) expression; instead, E always vanishes in flat, Lambda=0, background. For combined Einstein-quadratic curvature systems without explicit Lambda-term vacuum must be flat space, and E has the usual Arnowitt-Deser-Misner form. A Lambda-term forces unique de Sitter vacuum, with E the sum of contributions from Einstein and quadratic parts to the AD form. We also discuss the effects on energy definition of higher curvature terms and of higher dimension.

  12. Uniform convergence of multigrid v-cycle iterations for indefinite and nonsymmetric problems

    SciTech Connect

    Bramble, J.H. . Dept. of Mathematics); Kwak, D.Y. . Dept. of Mathematics); Pasciak, J.E. . Dept. of Applied Science)

    1994-12-01

    In this paper, an analysis of a multigrid method for nonsymmetric and/or indefinite elliptic problems is presented. In this multigrid method various types of smothers may be used. One type of smoother considered is defined in terms of an associated symmetric problem and includes point and line, Jacobi, and Gauss-Seidel iterations. Smothers based entirely on the original operator are also considered. One smoother is based on the normal form, that is, the product of the operator and its transpose. Other smothers studied include point and line, Jacobi, and Gauss-Seidel. It is shown that the uniform estimates for symmetric positive definite problems carry over to these algorithms. More precisely, the multigrid iteration for the nonsymmetric and/or indefinite problem is shown to converge at a uniform rate provided that the coarsest grid in the multilevel iteration is sufficiently fine (but not dependent on the number of multigrid levels).

  13. Uniform convergence of multigrid V-cycle iterations for indefinite and nonsymmetric problems

    NASA Technical Reports Server (NTRS)

    Bramble, James H.; Kwak, Do Y.; Pasciak, Joseph E.

    1993-01-01

    In this paper, we present an analysis of a multigrid method for nonsymmetric and/or indefinite elliptic problems. In this multigrid method various types of smoothers may be used. One type of smoother which we consider is defined in terms of an associated symmetric problem and includes point and line, Jacobi, and Gauss-Seidel iterations. We also study smoothers based entirely on the original operator. One is based on the normal form, that is, the product of the operator and its transpose. Other smoothers studied include point and line, Jacobi, and Gauss-Seidel. We show that the uniform estimates for symmetric positive definite problems carry over to these algorithms. More precisely, the multigrid iteration for the nonsymmetric and/or indefinite problem is shown to converge at a uniform rate provided that the coarsest grid in the multilevel iteration is sufficiently fine (but not depending on the number of multigrid levels).

  14. Target manifold formation using a quadratic SDF

    NASA Astrophysics Data System (ADS)

    Hester, Charles F.; Risko, Kelly K. D.

    2013-05-01

    Synthetic Discriminant Function (SDF) formulation of correlation filters provides constraints for forming target subspaces for a target set. In this paper we extend the SDF formulation to include quadratic constraints and use this solution to form nonlinear manifolds in the target space. The theory for forming these manifolds will be developed and demonstrated with data.

  15. Quadratic spline subroutine package

    USGS Publications Warehouse

    Rasmussen, Lowell A.

    1982-01-01

    A continuous piecewise quadratic function with continuous first derivative is devised for approximating a single-valued, but unknown, function represented by a set of discrete points. The quadratic is proposed as a treatment intermediate between using the angular (but reliable, easily constructed and manipulated) piecewise linear function and using the smoother (but occasionally erratic) cubic spline. Neither iteration nor the solution of a system of simultaneous equations is necessary to determining the coefficients. Several properties of the quadratic function are given. A set of five short FORTRAN subroutines is provided for generating the coefficients (QSC), finding function value and derivatives (QSY), integrating (QSI), finding extrema (QSE), and computing arc length and the curvature-squared integral (QSK). (USGS)

  16. Some Aspects of Quadratic Generalized White Noise Functionals

    NASA Astrophysics Data System (ADS)

    Si, Si; Hida, Takeyuki

    2009-02-01

    We shall discuss some particular roles of quadratic generalized white noise functionals. First observation is made from the viewpoint of the so-called "la passage du fini à l'infini". We then come to a dual pairing of spaces formed by quadratic generalized white noise functionals. In this line, we can further discuss quadratic forms of differential operators acting on the space of white noise functionals.

  17. Iterative schemes for nonsymmetric and indefinite elliptic boundary value problems

    SciTech Connect

    Bramble, J.H.; Leyk, Z.; Pasciak, J.E.

    1993-01-01

    The purpose of this paper is twofold. The first is to describe some simple and robust iterative schemes for nonsymmetric and indefinite elliptic boundary value problems. The schemes are based in the Sobolev space H ([Omega]) and require minimal hypotheses. The second is to develop algorithms utilizing a coarse-grid approximation. This leads to iteration matrices whose eigenvalues lie in the right half of the complex plane. In fact, for symmetric indefinite problems, the iteration is reduced to a well-conditioned symmetric positive definite system which can be solved by conjugate gradient interation. Applications of the general theory as well as numerical examples are given. 20 refs., 8 tabs.

  18. Black box multigrid solver for definite and indefinite problems

    SciTech Connect

    Shapira, Yair

    1997-02-01

    A two-level analysis method for certain separable problems is introduced. It motivates the definition of improved versions of Black Box Multigrid for diffusion problems with discontinuous coefficients and indefinite Helmholtz equations. For anisotropic problems, it helps in choosing suitable implementations for frequency decomposition multigrid methods. For highly indefinite problems, it provides a way to choose in advance a suitable mesh size for the coarsest grid used. Numerical experiments confirm the analysis and show the advantage of the present methods for several examples.

  19. A Quadratic Spring Equation

    ERIC Educational Resources Information Center

    Fay, Temple H.

    2010-01-01

    Through numerical investigations, we study examples of the forced quadratic spring equation [image omitted]. By performing trial-and-error numerical experiments, we demonstrate the existence of stability boundaries in the phase plane indicating initial conditions yielding bounded solutions, investigate the resonance boundary in the [omega]…

  20. The Mystical "Quadratic Formula."

    ERIC Educational Resources Information Center

    March, Robert H.

    1993-01-01

    Uses projectile motion to explain the two roots found when using the quadratic formula. An example is provided for finding the time of flight for a projectile which has a negative root implying a negative time of flight. This negative time of flight also has a useful physical meaning. (MVL)

  1. The Mystical "Quadratic Formula."

    ERIC Educational Resources Information Center

    March, Robert H.

    1993-01-01

    Uses projectile motion to explain the two roots found when using the quadratic formula. An example is provided for finding the time of flight for a projectile which has a negative root implying a negative time of flight. This negative time of flight also has a useful physical meaning. (MVL)

  2. 29 CFR 4.142 - Contracts in an indefinite amount.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 29 Labor 1 2010-07-01 2010-07-01 true Contracts in an indefinite amount. 4.142 Section 4.142 Labor Office of the Secretary of Labor LABOR STANDARDS FOR FEDERAL SERVICE CONTRACTS Application of the McNamara-O'Hara Service Contract Act Determining Amount of Contract § 4.142 Contracts in an...

  3. A Variable Rule Analysis of the Indefinite Article "An."

    ERIC Educational Resources Information Center

    Terrebonne, Robert A.

    This variable rule analysis of the indefinite article "an" was done by means of a computer program developed by H. Cedergren and D. Sankoff of Montreal. The data was collected from 45-minute interviews with three different groups of college students essentially alike in age: (1) 13 whites from Louisiana, (2) 12 blacks from southwestern Ohio, and…

  4. How Animals Understand the Meaning of Indefinite Information from Environments?

    NASA Astrophysics Data System (ADS)

    Shimizu, H.; Yamaguchi, Y.

    Animals, including human beings, have ability to understand the meaning of indefinite information from environments. Thanks to this ability the animals have flexibility in their behaviors for the environmental changes. Staring from a hypothesis that understanding of the input (Shannonian) information is based on the self-organization of a neuronal representation, that is, a spatio-temporal pattern constituted of coherent activities of neurons encoding a ``figure'', being separated from the ``background'' encoded by incoherent activities, the conditions necessary for the understanding of indefinite information were discussed. The crucial conditions revealed are that the neuronal system is incomplete or indefinite in a sense that its rules for the self-organization of the neuronal activities are completed only after the input of the environmental information and that it has an additional system named "self-specific to relevantly self-organize dynamical ``constraints'' or ``boundary conditions'' for the self-organization of the representation. For the simultaneous self-organizations of the relevant constraints and the representation, a global circulation of activities must be self-organized between these two kinds of neuronal systems. Moreover, for the performance of these functions, a specific kind of synergetic elements, ``holon elements'', are also necessary. By means of a neuronal model, the visual perception of indefinite input signals is demonstrated. The results obtained are consistent with those recently observed in the visual cortex of cats.

  5. Possessives vs. Indefinites: Pragmatic Inference and Determiner Choice.

    ERIC Educational Resources Information Center

    Birner, Betty

    A discussion of pragmatic choice in the use of the possessive pronoun or indefinite article (e.g., "I broke my finger" versus "I broke a finger," and "My leg hurts" versus "A leg hurts") looks at the constructions in the light of a theory of division of pragmatic labor that suggests a binary system of…

  6. Can the periodic table be extended indefinitely?

    NASA Astrophysics Data System (ADS)

    Marshall, Rick

    2014-05-01

    The heaviest naturally occurring element is uranium with Z = 92. Transuranic elements up to Z = 118 have now been synthesized. Is there an upper limit to the number of distinct elements that can exist and could all these new elements actually form atoms?

  7. Quintessence with quadratic coupling to dark matter

    SciTech Connect

    Boehmer, Christian G.; Chan, Nyein; Caldera-Cabral, Gabriela; Lazkoz, Ruth; Maartens, Roy

    2010-04-15

    We introduce a new form of coupling between dark energy and dark matter that is quadratic in their energy densities. Then we investigate the background dynamics when dark energy is in the form of exponential quintessence. The three types of quadratic coupling all admit late-time accelerating critical points, but these are not scaling solutions. We also show that two types of coupling allow for a suitable matter era at early times and acceleration at late times, while the third type of coupling does not admit a suitable matter era.

  8. 48 CFR 452.216-72 - Evaluation Quantities-Indefinite-Delivery Contract.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ...-Indefinite-Delivery Contract. 452.216-72 Section 452.216-72 Federal Acquisition Regulations System DEPARTMENT... Clauses 452.216-72 Evaluation Quantities—Indefinite-Delivery Contract. As prescribed in 416.506(a), insert a provision substantially as follows: Evaluation Quantities—Indefinite-Delivery Contract (FEB...

  9. 48 CFR 716.501-270 - Partner vetting-indefinite-delivery contracts.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... 48 Federal Acquisition Regulations System 5 2013-10-01 2013-10-01 false Partner vetting-indefinite... Contracts 716.501-270 Partner vetting—indefinite-delivery contracts. If a task order or delivery order under an indefinite-delivery contract has the potential to be subject to vetting, then the contract itself...

  10. 48 CFR 716.501-270 - Partner vetting-indefinite-delivery contracts.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 48 Federal Acquisition Regulations System 5 2014-10-01 2014-10-01 false Partner vetting-indefinite... Contracts 716.501-270 Partner vetting—indefinite-delivery contracts. If a task order or delivery order under an indefinite-delivery contract has the potential to be subject to vetting, then the contract itself...

  11. 48 CFR 716.501-270 - Partner vetting-indefinite-delivery contracts.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ... 48 Federal Acquisition Regulations System 5 2012-10-01 2012-10-01 false Partner vetting-indefinite... Contracts 716.501-270 Partner vetting—indefinite-delivery contracts. If a task order or delivery order under an indefinite-delivery contract has the potential to be subject to vetting, then the contract itself...

  12. Requirements and Indefinite Quantity Contracts in Government Procurement

    DTIC Science & Technology

    1990-02-18

    of Master of Laws February 18, 1990 Thesis directed by Ralph Clarke Nash, Jr. and John Cibinic, Jr. Professors of Law 91 2 06 092 TABLE OF CONTENTS...Finally, the Court of Claims had an opportunity co address the Government’s efforts to continue the use of indefinite quantity contracts. In Updike v...Today, it is doubtful such extreme discrepancies would survive scrutiny without a change in circumstances. 201 Womack, Jr. & John R. Vorhies v

  13. Factoring symmetric indefinite matrices on high-performance architectures

    NASA Technical Reports Server (NTRS)

    Jones, Mark T.; Patrick, Merrell L.

    1990-01-01

    The Bunch-Kaufman algorithm is the method of choice for factoring symmetric indefinite matrices in many applications. However, the Bunch-Kaufman algorithm does not take advantage of high-performance architectures such as the Cray Y-MP. Three new algorithms, based on Bunch-Kaufman factorization, that take advantage of such architectures are described. Results from an implementation of the third algorithm are presented.

  14. Curious Consequences of a Miscopied Quadratic

    ERIC Educational Resources Information Center

    Poet, Jeffrey L.; Vestal, Donald L., Jr.

    2005-01-01

    The starting point of this article is a search for pairs of quadratic polynomials x[superscript 2] + bx plus or minus c with the property that they both factor over the integers. The search leads quickly to some number theory in the form of primitive Pythagorean triples, and this paper develops the connection between these two topics.

  15. Curious Consequences of a Miscopied Quadratic

    ERIC Educational Resources Information Center

    Poet, Jeffrey L.; Vestal, Donald L., Jr.

    2005-01-01

    The starting point of this article is a search for pairs of quadratic polynomials x[superscript 2] + bx plus or minus c with the property that they both factor over the integers. The search leads quickly to some number theory in the form of primitive Pythagorean triples, and this paper develops the connection between these two topics.

  16. Quadratic Dynamical Systems and Algebras

    NASA Astrophysics Data System (ADS)

    Kinyon, M. K.; Sagle, A. A.

    1995-03-01

    Quadratic dynamical systems come from differential or discrete systems of the form Ẋ = Q(X) or X(k+1)=Q(X(k)), where Q:Rn→Rn is homogeneous of degree 2; i.e., Q(αX) = α2Q(X) for all α∈R, X∈Rn. Defining a bilinear mapping β:Rn × Rn→Rn by β(X, Y) ≔ {1}/{2}[Q(X+Y)-Q(X)-Q(Y)], we view XY≡β(X, Y) as a multiplication, and thus consider A=(Rn, β) to be a commutative, nonassociative algebra. The quadratic systems are then studied with the general theme that the structure of the algebras helps determine the behavior of the solutions. For example, semisimple algebras give a decoupling of the original system into systems occurring in simple algebras, and solvable algebras give solutions to differential systems via linear differential equations; the general three-dimensional example of the latter phenomenon is described. There are many classical examples and the scope of quadratic systems is large; every polynomial system can be embedded into a higher dimensional quadratic system such that solutions of the original system are obtained from the quadratic system. For differential systems, nilpotents of index 2 (N2=0) are equilibria and idempotents (E2=E) give ray solutions. The origin is never asymptotically stable, and the existence of nonzero idempotents implies that the origin is actually unstable. Nonzero equilibria are not hyperbolic, but can be studied by standard algebra techniques using nondegenerate bilinear forms as Lyapunov functions. Periodic orbits lie on "cones." They cannot occur in dimension 2 or in power-associative algebras. No periodic orbit can be an attractor but "limit cycles" (invariant cones) can exist. Automorphisms of the algebra A leave equilibria, periodic orbits, and domains of attraction invariant. Also, explicit solutions can be given by the action of automorphisms on an initial point; the general three-dimensional example of this is described. Thus if there are sufficient automorphisms, Hilbert‧s sixteenth problem in R3 has

  17. Effects of Classroom Instruction on Students' Understanding of Quadratic Equations

    ERIC Educational Resources Information Center

    Vaiyavutjamai, Pongchawee; Clements, M. A.

    2006-01-01

    Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of…

  18. Analysis of Students' Error in Learning of Quadratic Equations

    ERIC Educational Resources Information Center

    Zakaria, Effandi; Ibrahim; Maat, Siti Mistima

    2010-01-01

    The purpose of the study was to determine the students' error in learning quadratic equation. The samples were 30 form three students from a secondary school in Jambi, Indonesia. Diagnostic test was used as the instrument of this study that included three components: factorization, completing the square and quadratic formula. Diagnostic interview…

  19. The Random Quadratic Assignment Problem

    NASA Astrophysics Data System (ADS)

    Paul, Gerald; Shao, Jia; Stanley, H. Eugene

    2011-11-01

    The quadratic assignment problem, QAP, is one of the most difficult of all combinatorial optimization problems. Here, we use an abbreviated application of the statistical mechanics replica method to study the asymptotic behavior of instances in which the entries of at least one of the two matrices that specify the problem are chosen from a random distribution P. Surprisingly, the QAP has not been studied before using the replica method despite the fact that the QAP was first proposed over 50 years ago and the replica method was developed over 30 years ago. We find simple forms for C min and C max , the costs of the minimal and maximum solutions respectively. Notable features of our results are the symmetry of the results for C min and C max and their dependence on P only through its mean and standard deviation, independent of the details of P.

  20. Bunch-Kaufman factorization for real symmetric indefinite banded matrices

    NASA Technical Reports Server (NTRS)

    Jones, Mark T.; Patrick, Merrell L.

    1989-01-01

    The Bunch-Kaufman algorithm for factoring symmetric indefinite matrices was rejected for banded matrices because it destroys the banded structure of the matrix. Herein, it is shown that for a subclass of real symmetric matrices which arise in solving the generalized eigenvalue problem using Lanczos's method, the Bunch-Kaufman algorithm does not result in major destruction of the bandwidth. Space time complexities of the algorithm are given and used to show that the Bunch-Kaufman algorithm is a significant improvement over LU factorization.

  1. Students' Understanding of Quadratic Equations

    ERIC Educational Resources Information Center

    López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

    2016-01-01

    Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…

  2. Students' Understanding of Quadratic Equations

    ERIC Educational Resources Information Center

    López, Jonathan; Robles, Izraim; Martínez-Planell, Rafael

    2016-01-01

    Action-Process-Object-Schema theory (APOS) was applied to study student understanding of quadratic equations in one variable. This required proposing a detailed conjecture (called a genetic decomposition) of mental constructions students may do to understand quadratic equations. The genetic decomposition which was proposed can contribute to help…

  3. Quadratic algebras for three-dimensional superintegrable systems

    SciTech Connect

    Daskaloyannis, C. Tanoudis, Y.

    2010-02-15

    The three-dimensional superintegrable systems with quadratic integrals of motion have five functionally independent integrals, one among them is the Hamiltonian. Kalnins, Kress, and Miller have proved that in the case of nondegenerate potentials with quadratic integrals of motion there is a sixth quadratic integral, which is linearly independent of the other integrals. The existence of this sixth integral implies that the integrals of motion form a ternary parafermionic-like quadratic Poisson algebra with five generators. In this contribution we investigate the structure of this algebra. We show that in all the nondegenerate cases there is at least one subalgebra of three integrals having a Poisson quadratic algebra structure, which is similar to the two-dimensional case.

  4. On the time-weighted quadratic sum of linear discrete systems

    NASA Technical Reports Server (NTRS)

    Jury, E. I.; Gutman, S.

    1975-01-01

    A method is proposed for obtaining the time-weighted quadratic sum for linear discrete systems. The formula of the weighted quadratic sum is obtained from matrix z-transform formulation. In addition, it is shown that this quadratic sum can be derived in a recursive form for several useful weighted functions. The discussion presented parallels that of MacFarlane (1963) for weighted quadratic integral for linear continuous systems.

  5. A Sequential Quadratically Constrained Quadratic Programming Method of Feasible Directions

    SciTech Connect

    Jian Jinbao Hu Qingjie; Tang Chunming; Zheng Haiyan

    2007-12-15

    In this paper, a sequential quadratically constrained quadratic programming method of feasible directions is proposed for the optimization problems with nonlinear inequality constraints. At each iteration of the proposed algorithm, a feasible direction of descent is obtained by solving only one subproblem which consist of a convex quadratic objective function and simple quadratic inequality constraints without the second derivatives of the functions of the discussed problems, and such a subproblem can be formulated as a second-order cone programming which can be solved by interior point methods. To overcome the Maratos effect, an efficient higher-order correction direction is obtained by only one explicit computation formula. The algorithm is proved to be globally convergent and superlinearly convergent under some mild conditions without the strict complementarity. Finally, some preliminary numerical results are reported.

  6. An alternative method on quadratic programming problems

    NASA Astrophysics Data System (ADS)

    Dasril, Y.; Mohd, I. B.; Mustaffa, I.; Aminuddin, MMM.

    2015-05-01

    In this paper we proposed an alternative approach to find the optimum solution of quadratic programming problems (QPP) in its original form without additional information such as slack variable, surplus variable or artificial variable as done in other favourite methods. This approached is based on the violated constraints by the unconstrained optimum. The optimal solution of QPP obtained by searching from initial point to another point alongside of feasible region.

  7. Quadratic Generalized Scale Invariance

    NASA Astrophysics Data System (ADS)

    Lovejoy, S.; Schertzer, D.; Addor, J. B.

    Nearly twenty years ago, two of us argued that in order to account for the scaling strat- ification of the atmosphere, that an anisotropic "unified scaling model" of the atmo- sphere was required with elliptical dimension 23/9=2.555... "in between" the standard 3-D (small scale) and 2-D large scale model. This model was based on the formal- ism of generalized scale invariance (GSI). Physically, GSI is justified by arguing that various conserved fluxes (energy, buoyancy force variance etc.) should define the ap- propriate notion of scale. In a recent large scale satellite cloud image analysis, we directly confirmed this model by studying the isotropic (angle averaged) horizontal cloud statistics. Mathematically, GSI is based on a a group of scale changing opera- tors and their generators but to date, both analyses (primarily of cloud images) and nu- merical (multifractal) simulations, have been limited to the special case of linear GSI. This has shown that cloud texture can plausibly be associated with local linearizations. However realistic morphologies involve spatially avarying textures; the full non linear GSI is clearly necessary. In this talk, we first show that the observed angle averaged (multi)scaling statistics only give a realtively weak constraint on the nonlinear gner- ator: that the latter can be expressed by self-similar (isotropic) part, and a deviatoric part described (in two dimensions) by an arbitrary scalar potential which contains all the information about the cloud morphology. We then show (using a theorem due to Poincaré) how to reduce nonlinear GSI to linear GSI plus a nonlinear coordinate trans- formation numerically, using this to take multifractal GSI modelling to the next level of approximation: quadratic GSI. We show many examples of the coresponding simu- lations which include transitions from various morphologies (including cyclones) and we discuss the results in relation to satellite cloud images.

  8. Indefinite Plasmonic Beam Engineering by In-plane Holography

    PubMed Central

    Chen, J.; Li, L.; Li, T.; Zhu, S. N.

    2016-01-01

    Recent advances in controlling the optical phase at the sub-wavelength scale by meta-structures offer unprecedented possibilities in the beam engineering, holograms, and even invisible cloaks. In despite of developments of plasmonic beam engineering for definite beams, here, we proposed a new holographic strategy by in-plane diffraction process to access indefinite plasmonic beams, where a counterintuitive oscillating beam was achieved at a free metal surface that is against the common recognition of light traveling. Beyond the conventional hologram, our approach emphasizes on the phase correlation on the target, and casts an in-depth insight into the beam formation as a kind of long depth-of-field object. Moreover, in contrast to previous plasmonic holography with space light as references, our approach is totally fulfilled in a planar dimension that offers a thoroughly compact manipulation of the plasmonic near-field and suggests new possibilities in nanophotonic designs. PMID:27357133

  9. Indefinite Plasmonic Beam Engineering by In-plane Holography

    NASA Astrophysics Data System (ADS)

    Chen, J.; Li, L.; Li, T.; Zhu, S. N.

    2016-06-01

    Recent advances in controlling the optical phase at the sub-wavelength scale by meta-structures offer unprecedented possibilities in the beam engineering, holograms, and even invisible cloaks. In despite of developments of plasmonic beam engineering for definite beams, here, we proposed a new holographic strategy by in-plane diffraction process to access indefinite plasmonic beams, where a counterintuitive oscillating beam was achieved at a free metal surface that is against the common recognition of light traveling. Beyond the conventional hologram, our approach emphasizes on the phase correlation on the target, and casts an in-depth insight into the beam formation as a kind of long depth-of-field object. Moreover, in contrast to previous plasmonic holography with space light as references, our approach is totally fulfilled in a planar dimension that offers a thoroughly compact manipulation of the plasmonic near-field and suggests new possibilities in nanophotonic designs.

  10. Analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems

    SciTech Connect

    Bramble, J.H.; Pasciak, J.E.; Xu, J.

    1988-10-01

    We prove some new estimates for the convergence of multigrid algorithms applied to nonsymmetric and indefinite elliptic boundary value problems. We provide results for the so-called 'symmetric' multigrid schemes. We show that for the variable V-script-cycle and the W-script-cycle schemes, multigrid algorithms with any amount of smoothing on the finest grid converge at a rate that is independent of the number of levels or unknowns, provided that the initial grid is sufficiently fine. We show that the V-script-cycle algorithm also converges (under appropriate assumptions on the coarsest grid) but at a rate which may deteriorate as the number of levels increases. This deterioration for the V-script-cycle may occur even in the case of full elliptic regularity. Finally, the results of numerical experiments are given which illustrate the convergence behavior suggested by the theory.

  11. Equivalence of quadratic performance criteria.

    NASA Technical Reports Server (NTRS)

    Martin, C.

    1973-01-01

    Necessary and sufficient conditions are derived in terms of system parameters and quadratic weighting matrices for two quadratic cost functionals that are defined to be equivalent if they generate the same optimal control law. The derived conditions lie between the conditions of Tanaka and Asai (1971) and those of Kreindler and Hedrick (1970). Sufficient conditions for a vector valued function to attain an infimum are stated.

  12. Experimental investigations of weak definite and weak indefinite noun phrases.

    PubMed

    Klein, Natalie M; Gegg-Harrison, Whitney M; Carlson, Greg N; Tanenhaus, Michael K

    2013-08-01

    Definite noun phrases typically refer to entities that are uniquely identifiable in the speaker and addressee's common ground. Some definite noun phrases (e.g., the hospital in Mary had to go the hospital and John did too) seem to violate this uniqueness constraint. We report six experiments that were motivated by the hypothesis that these "weak definite" interpretations arise in "incorporated" constructions. Experiments 1-3 compared nouns that seem to allow for a weak definite interpretation (e.g., hospital, bank, bus, radio) with those that do not (e.g., farm, concert, car, book). Experiments 1 and 2 used an instruction-following task and picture-judgment task, respectively, to demonstrate that a weak definite need not uniquely refer. In Experiment 3 participants imagined scenarios described by sentences such as The Federal Express driver had to go to the hospital/farm. Scenarios following weak definite noun phrases were more likely to include conventional activities associated with the object, whereas following regular nouns, participants were more likely to imagine scenarios that included typical activities associated with the subject; similar effects were observed with weak indefinites. Experiment 4 found that object-related activities were reduced when the same subject and object were used with a verb that does not license weak definite interpretations. In Experiment 5, a science fiction story introduced an artificial lexicon for novel concepts. Novel nouns that shared conceptual properties with English weak definite nouns were more likely to allow weak reference in a judgment task. Experiment 6 demonstrated that familiarity for definite articles and anti-familiarity for indefinite articles applies to the activity associated with the noun, consistent with predictions made by the incorporation analysis. Copyright © 2013 Elsevier B.V. All rights reserved.

  13. Experimental investigations of weak definite and weak indefinite noun phrases

    PubMed Central

    Klein, Natalie M.; Gegg-Harrison, Whitney M.; Carlson, Greg N.; Tanenhaus, Michael K.

    2013-01-01

    Definite noun phrases typically refer to entities that are uniquely identifiable in the speaker and addressee’s common ground. Some definite noun phrases (e.g. the hospital in Mary had to go the hospital and John did too) seem to violate this uniqueness constraint. We report six experiments that were motivated by the hypothesis that these “weak definite” interpretations arise in “incorporated” constructions. Experiments 1-3 compared nouns that seem to allow for a weak definite interpretation (e.g. hospital, bank, bus, radio) with those that do not (e.g. farm, concert, car, book). Experiments 1 and 2 used an instruction-following task and picture-judgment task, respectively, to demonstrate that a weak definite need not uniquely refer. In Experiment 3 participants imagined scenarios described by sentences such as The Federal Express driver had to go to the hospital/farm. The imagined scenarios following weak definite noun phrases were more likely to include conventional activities associated with the object, whereas following regular nouns, participants were more likely to imagine scenarios that included typical activities associated with the subject; similar effects were observed with weak indefinites. Experiment 4 found that object-related activities were reduced when the same subject and object were used with a verb that does not license weak definite interpretations. In Experiment 5, a science fiction story introduced an artificial lexicon for novel concepts. Novel nouns that shared conceptual properties with English weak definite nouns were more likely to allow weak reference in a judgment task. Experiment 6 demonstrated that familiarity for definite articles and anti- familiarity for indefinite articles applies to the activity associated with the noun, consistent with predictions made by the incorporation analysis. PMID:23685208

  14. The Air Force Processes for Approving Air Force Life Cycle Management Center Single-Award Indefinite-Delivery Indefinite-Quantity Contracts Need Improvement

    DTIC Science & Technology

    2016-04-29

    IDIQ contract may be used to acquire supplies and services when the exact times and quantities of future deliveries are not known at the time of...Force Processes for Approving Air Force Life Cycle Management Center Single‑Award Indefinite‑ Delivery Indefinite‑Quantity Contracts Need...0147.000) │ i Results in Brief The Air Force Processes for Approving Air Force Life Cycle Management Center Single-Award Indefinite- Delivery Indefinite

  15. Linear quadratic output tracking and disturbance rejection

    NASA Astrophysics Data System (ADS)

    Karimi-Ghartemani, Masoud; Khajehoddin, S. Ali; Jain, Praveen; Bakhshai, Alireza

    2011-08-01

    This article introduces the problem of linear quadratic tracking (LQT) where the objective is to design a closed-loop control scheme such that the output signal of the system optimally tracks a given reference signal and rejects a given disturbance. Different performance indices that have been used to address the tracking problem are discussed and an appropriate new form is introduced. It is shown that a solution to the proposed optimality index exists under very mild conditions of stabilisability and detectability of the plant state-space equations. The solution is formulated based on converting the LQT problem to a standard linear quadratic regulation problem. The method is applied to two examples, a first-order plant and a third-order plant, and their simulation results are presented and discussed.

  16. An iteration for indefinite and non-symmetric systems and its application to the Navier-Stokes equations

    SciTech Connect

    Wathen, A.; Golub, G.

    1996-12-31

    A simple fixed point linearisation of the Navier-Stokes equations leads to the Oseen problem which after appropriate discretisation yields large sparse linear systems with coefficient matrices of the form (A B{sup T} B -C). Here A is non-symmetric but its symmetric part is positive definite, and C is symmetric and positive semi-definite. Such systems arise in other situations. In this talk we will describe and present some analysis for an iteration based on an indefinite and symmetric preconditioner of the form (D B{sup T} B -C).

  17. 48 CFR 29.401-1 - Indefinite-delivery contracts for leased equipment.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... 48 Federal Acquisition Regulations System 1 2011-10-01 2011-10-01 false Indefinite-delivery contracts for leased equipment. 29.401-1 Section 29.401-1 Federal Acquisition Regulations System FEDERAL ACQUISITION REGULATION GENERAL CONTRACTING REQUIREMENTS TAXES Contract Clauses 29.401-1 Indefinite-delivery contracts for leased equipment. Insert...

  18. 48 CFR 1352.215-73 - Evaluation quantities-indefinite quantity contract.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... 48 Federal Acquisition Regulations System 5 2014-10-01 2014-10-01 false Evaluation quantities-indefinite quantity contract. 1352.215-73 Section 1352.215-73 Federal Acquisition Regulations System...-570(b)(1), insert the following provision: Evaluation Quantities—Indefinite Quantity Contract (Date...

  19. 48 CFR 29.401-1 - Indefinite-delivery contracts for leased equipment.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... or places of delivery are not known at the time of contracting. ... 48 Federal Acquisition Regulations System 1 2010-10-01 2010-10-01 false Indefinite-delivery... ACQUISITION REGULATION GENERAL CONTRACTING REQUIREMENTS TAXES Contract Clauses 29.401-1 Indefinite-delivery...

  20. The Semantics of Russian Indefinite Pronouns: Scope, Domain Widening, Specificity, and Proportionality and Their Interaction

    ERIC Educational Resources Information Center

    Eremina, Olga

    2012-01-01

    The main goal of this dissertation is to consider the different types of indefinites in Russian as a system and provide a semantic account for each of them that would be able to naturally explain their distribution. The four sets of so-called 'indefinite pronouns' ("-to," "-nibud'," "-libo," and…

  1. 41 CFR 101-25.101-4 - Supply through indefinite quantity requirement contracts.

    Code of Federal Regulations, 2011 CFR

    2011-07-01

    ... following factors requires the maintaining of indefinite quantity requirements contracts— (1) Advantage to... introduced into a supply system), or no advantage accrues doing so; and (b) Industry distribution facilities... can best be served by indefinite quantity requirements contracts. (2) Acute competitive bidding...

  2. 48 CFR 252.247-7005 - Indefinite quantities-no fixed charges.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ... fixed charges. 252.247-7005 Section 252.247-7005 Federal Acquisition Regulations System DEFENSE... CLAUSES Text of Provisions And Clauses 252.247-7005 Indefinite quantities—no fixed charges. As prescribed in 247.270-4(e), use the following clause: Indefinite Quantities—No Fixed Charges (DEC 1991) The...

  3. 48 CFR 252.247-7004 - Indefinite quantities-fixed charges.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ...-fixed charges. 252.247-7004 Section 252.247-7004 Federal Acquisition Regulations System DEFENSE... CLAUSES Text of Provisions And Clauses 252.247-7004 Indefinite quantities—fixed charges. As prescribed in 247.270-4(d), use the following clause: Indefinite Quantities—Fixed Charges (DEC 1991) The amount of...

  4. 48 CFR 252.247-7004 - Indefinite quantities-fixed charges.

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ...-fixed charges. 252.247-7004 Section 252.247-7004 Federal Acquisition Regulations System DEFENSE... CLAUSES Text of Provisions And Clauses 252.247-7004 Indefinite quantities—fixed charges. As prescribed in 247.270-4(d), use the following clause: Indefinite Quantities—Fixed Charges (DEC 1991) The amount of...

  5. 48 CFR 252.247-7004 - Indefinite quantities-fixed charges.

    Code of Federal Regulations, 2014 CFR

    2014-10-01

    ...-fixed charges. 252.247-7004 Section 252.247-7004 Federal Acquisition Regulations System DEFENSE... CLAUSES Text of Provisions And Clauses 252.247-7004 Indefinite quantities—fixed charges. As prescribed in 247.270-4(d), use the following clause: Indefinite Quantities—Fixed Charges (DEC 1991) The amount of...

  6. 48 CFR 252.247-7004 - Indefinite quantities-fixed charges.

    Code of Federal Regulations, 2012 CFR

    2012-10-01

    ...-fixed charges. 252.247-7004 Section 252.247-7004 Federal Acquisition Regulations System DEFENSE... CLAUSES Text of Provisions And Clauses 252.247-7004 Indefinite quantities—fixed charges. As prescribed in 247.270-4(d), use the following clause: Indefinite Quantities—Fixed Charges (DEC 1991) The amount of...

  7. 48 CFR 252.247-7005 - Indefinite quantities-no fixed charges.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ... fixed charges. 252.247-7005 Section 252.247-7005 Federal Acquisition Regulations System DEFENSE... CLAUSES Text of Provisions And Clauses 252.247-7005 Indefinite quantities—no fixed charges. As prescribed in 247.270-4(e), use the following clause: Indefinite Quantities—No Fixed Charges (DEC 1991) The...

  8. 48 CFR 252.247-7004 - Indefinite quantities-fixed charges.

    Code of Federal Regulations, 2011 CFR

    2011-10-01

    ...-fixed charges. 252.247-7004 Section 252.247-7004 Federal Acquisition Regulations System DEFENSE... CLAUSES Text of Provisions And Clauses 252.247-7004 Indefinite quantities—fixed charges. As prescribed in 247.270-4(d), use the following clause: Indefinite Quantities—Fixed Charges (DEC 1991) The amount of...

  9. 48 CFR 252.247-7005 - Indefinite quantities-no fixed charges.

    Code of Federal Regulations, 2013 CFR

    2013-10-01

    ... fixed charges. 252.247-7005 Section 252.247-7005 Federal Acquisition Regulations System DEFENSE... CLAUSES Text of Provisions And Clauses 252.247-7005 Indefinite quantities—no fixed charges. As prescribed in 247.270-4(e), use the following clause: Indefinite Quantities—No Fixed Charges (DEC 1991) The...

  10. Exact solutions to quadratic gravity

    NASA Astrophysics Data System (ADS)

    Pravda, V.; Pravdová, A.; Podolský, J.; Švarc, R.

    2017-04-01

    Since all Einstein spacetimes are vacuum solutions to quadratic gravity in four dimensions, in this paper we study various aspects of non-Einstein vacuum solutions to this theory. Most such known solutions are of traceless Ricci and Petrov type N with a constant Ricci scalar. Thus we assume the Ricci scalar to be constant which leads to a substantial simplification of the field equations. We prove that a vacuum solution to quadratic gravity with traceless Ricci tensor of type N and aligned Weyl tensor of any Petrov type is necessarily a Kundt spacetime. This will considerably simplify the search for new non-Einstein solutions. Similarly, a vacuum solution to quadratic gravity with traceless Ricci type III and aligned Weyl tensor of Petrov type II or more special is again necessarily a Kundt spacetime. Then we study the general role of conformal transformations in constructing vacuum solutions to quadratic gravity. We find that such solutions can be obtained by solving one nonlinear partial differential equation for a conformal factor on any Einstein spacetime or, more generally, on any background with vanishing Bach tensor. In particular, we show that all geometries conformal to Kundt are either Kundt or Robinson-Trautman, and we provide some explicit Kundt and Robinson-Trautman solutions to quadratic gravity by solving the above mentioned equation on certain Kundt backgrounds.

  11. A modified direct preconditioner for indefinite symmetric Toeplitz systems

    SciTech Connect

    Concus, P.; Saylor, P.

    1994-12-31

    A modification is presented of the classical $O(n{sup 2})$ algorithm of Trench for the direct solution of Toeplitz systems of equations. The Trench algorithm can be guaranteed to be stable only for matrices that are (symmetric) positive definite; it is generally unstable otherwise. The modification permits extension of the algorithm to compute an approximate inverse in the indefinite symmetric case, for which the unmodified algorithm breaks down when principal submatrices are singular. As a preconditioner, this approximate inverse has an advantage that only matrix-vector multiplications are required for the solution of a linear system, without forward and backward solves. The approximate inverse so obtained can be sufficiently accurate, moreover that, when it is used as a preconditioner for the applications investigated, subsequent iteration may not even be necessary. Numerical results are given for several test matrices. The perturbation to the original matrix that defines the modification is related to a perturbation in a quantity generated in the Trench algorithm; the associated stability of the Trench algorithm is discussed.

  12. Arrays of indefinitely long uniform nanowires and nanotubes

    NASA Astrophysics Data System (ADS)

    Yaman, Mecit; Khudiyev, Tural; Ozgur, Erol; Kanik, Mehmet; Aktas, Ozan; Ozgur, Ekin O.; Deniz, Hakan; Korkut, Enes; Bayindir, Mehmet

    2011-07-01

    Nanowires are arguably the most studied nanomaterial model to make functional devices and arrays. Although there is remarkable maturity in the chemical synthesis of complex nanowire structures, their integration and interfacing to macro systems with high yields and repeatability still require elaborate aligning, positioning and interfacing and post-synthesis techniques. Top-down fabrication methods for nanowire production, such as lithography and electrospinning, have not enjoyed comparable growth. Here we report a new thermal size-reduction process to produce well-ordered, globally oriented, indefinitely long nanowire and nanotube arrays with different materials. The new technique involves iterative co-drawing of hermetically sealed multimaterials in compatible polymer matrices similar to fibre drawing. Globally oriented, endlessly parallel, axially and radially uniform semiconducting and piezoelectric nanowire and nanotube arrays hundreds of metres long, with nanowire diameters less than 15 nm, are obtained. The resulting nanostructures are sealed inside a flexible substrate, facilitating the handling of and electrical contacting to the nanowires. Inexpensive, high-throughput, multimaterial nanowire arrays pave the way for applications including nanowire-based large-area flexible sensor platforms, phase-changememory, nanostructure-enhanced photovoltaics, semiconductor nanophotonics, dielectric metamaterials,linear and nonlinear photonics and nanowire-enabled high-performance composites.

  13. A modified direct preconditioner for indefinite symmetric Toeplitz systems

    SciTech Connect

    Concus, P. California Univ., Berkeley, CA . Dept. of Mathematics); Saylor, P. . Dept. of Computer Science)

    1992-11-01

    A modification is presented of the classical O(n[sup 2]) algorithm of Trench for the direct solution of Toeplitz systems of equations. The Trench algorithm can be guaranteed to be stable only for matrices that are (symmetric) positive definite; it is generally unstable otherwise. The modification permits extension of the algorithm to compute an approximate inverse in the indefinite symmetric case, for which the unmodified algorithm breaks down when principal submatrices are singular. As a preconditioner, this approximate inverse has an advantage that only matrix-vector multiplications are required for the solution of a linear system, without forward and backward solves. The approximate inverse so obtained can be sufficiently accurate, moreover, that, when it is used as a preconditioner for the applications investigated, subsequent iteration may not even be necessary. Numerical results are given for several test matrices. The perturbation to the original matrix that defines the modification is related to a perturbation in a quantity generated in the Trench algorithm; the associated stability of the Trench algorithm is discussed.

  14. A modified direct preconditioner for indefinite symmetric Toeplitz systems

    SciTech Connect

    Concus, P. |; Saylor, P.

    1992-11-01

    A modification is presented of the classical O(n{sup 2}) algorithm of Trench for the direct solution of Toeplitz systems of equations. The Trench algorithm can be guaranteed to be stable only for matrices that are (symmetric) positive definite; it is generally unstable otherwise. The modification permits extension of the algorithm to compute an approximate inverse in the indefinite symmetric case, for which the unmodified algorithm breaks down when principal submatrices are singular. As a preconditioner, this approximate inverse has an advantage that only matrix-vector multiplications are required for the solution of a linear system, without forward and backward solves. The approximate inverse so obtained can be sufficiently accurate, moreover, that, when it is used as a preconditioner for the applications investigated, subsequent iteration may not even be necessary. Numerical results are given for several test matrices. The perturbation to the original matrix that defines the modification is related to a perturbation in a quantity generated in the Trench algorithm; the associated stability of the Trench algorithm is discussed.

  15. Stabilizing and destabilizing perturbations of PT-symmetric indefinitely damped systems.

    PubMed

    Kirillov, O N

    2013-04-28

    Eigenvalues of a potential dynamical system with damping forces that are described by an indefinite real symmetric matrix can behave as those of a Hamiltonian system when gain and loss are in a perfect balance. This happens when the indefinitely damped system obeys parity-time ( ) symmetry. How do pure imaginary eigenvalues of a stable -symmetric indefinitely damped system behave when variation in the damping and potential forces destroys the symmetry? We establish that it is essentially the tangent cone to the stability domain at the exceptional point corresponding to the Whitney umbrella singularity on the stability boundary that manages transfer of instability between modes.

  16. Concretising Factorisation of Quadratic Expressions

    ERIC Educational Resources Information Center

    Hoong, Leong Yew; Fwe, Yap Sook; Yvonne, Teo Mei Lin; Subramaniam, Thilagam d/o; Zaini, Irni Karen Bte Mohd; Chiew, Quek Eng; Karen, Tan Kang Ling

    2010-01-01

    The way quadratic factorisation was usually taught to students in Bukit View Secondary was through the familiar "cross-method." However, some teachers felt that a significant number of students could not use the method effectively even after careful demonstration through repeated examples. In addition, many secondary mathematics teachers…

  17. Advances in Speedup of the Indefinite One-Sided Block Jacobi Method

    NASA Astrophysics Data System (ADS)

    Singer, Sanja; Singer, Saša; Hari, Vjeran; Bokulić, Krešimir; Davidović, Davor; Jurešić, Marijan; Ušćumlić, Aleksandar

    2007-09-01

    Recent advances in fast implementation of the indefinite one-sided Jacobi method are described. Special attention is devoted to the block pivot strategies and to the column sorting which is embedded in the algorithm.

  18. Exploration of Quadratic Expressions through Multiple Representations for Students with Mathematics Difficulties

    ERIC Educational Resources Information Center

    Strickland, Tricia K.; Maccini, Paula

    2013-01-01

    The current study focuses on the effects of incorporating multiple visual representations on students' conceptual understanding of quadratic expressions embedded within area word problems and students' procedural fluency of transforming quadratic expressions in standard form to factored-form and vice versa. The intervention included the…

  19. Binary Inspiral in Quadratic Gravity

    NASA Astrophysics Data System (ADS)

    Yagi, Kent

    2015-01-01

    Quadratic gravity is a general class of quantum-gravity-inspired theories, where the Einstein-Hilbert action is extended through the addition of all terms quadratic in the curvature tensor coupled to a scalar field. In this article, we focus on the scalar Gauss- Bonnet (sGB) theory and consider the black hole binary inspiral in this theory. By applying the post-Newtonian (PN) formalism, we found that there is a scalar dipole radiation which leads to -1PN correction in the energy flux relative to gravitational radiation in general relativity. From the orbital decay rate of a low-mass X-ray binary A0600-20, we obtain the bound that is six orders of magnitude stronger than the current solar system bound. Furthermore, we show that the excess in the orbital decay rate of XTE J1118+480 can be explained by the scalar radiation in sGB theory.

  20. Orthogonality preserving infinite dimensional quadratic stochastic operators

    SciTech Connect

    Akın, Hasan; Mukhamedov, Farrukh

    2015-09-18

    In the present paper, we consider a notion of orthogonal preserving nonlinear operators. We introduce π-Volterra quadratic operators finite and infinite dimensional settings. It is proved that any orthogonal preserving quadratic operator on finite dimensional simplex is π-Volterra quadratic operator. In infinite dimensional setting, we describe all π-Volterra operators in terms orthogonal preserving operators.

  1. Tuning a fuzzy controller using quadratic response surfaces

    NASA Technical Reports Server (NTRS)

    Schott, Brian; Whalen, Thomas

    1992-01-01

    Response surface methodology, an alternative method to traditional tuning of a fuzzy controller, is described. An example based on a simulated inverted pendulum 'plant' shows that with (only) 15 trial runs, the controller can be calibrated using a quadratic form to approximate the response surface.

  2. Effects of classroom instruction on students' understanding of quadratic equations

    NASA Astrophysics Data System (ADS)

    Vaiyavutjamai, Pongchawee; Clements, M. A. (Ken)

    2006-05-01

    Two hundred and thirty-one students in six Grade 9 classes in two government secondary schools located near Chiang Mai, Thailand, attempted to solve the same 18 quadratic equations before and after participating in 11 lessons on quadratic equations. Data from the students' written responses to the equations, together with data in the form of transcripts of 36 interviews with 18 interviewees (a high performer, a medium performer, and a low performer from each of the six classes), were analysed. Using a rubric for assessing students' understanding, the analysis revealed that at the post-teaching stage students improved their performance on quadratic equations and had a better understanding of associated concepts than they had at the pre-teaching stage. However, many were still confused about the concepts of a variable and of a "solution" to a quadratic equation. After the lessons, most students had acquired neither an instrumental nor a relational understanding of the mathematics associated with solving elementary quadratic equations.

  3. Asymptotic Normality of Quadratic Estimators.

    PubMed

    Robins, James; Li, Lingling; Tchetgen, Eric; van der Vaart, Aad

    2016-12-01

    We prove conditional asymptotic normality of a class of quadratic U-statistics that are dominated by their degenerate second order part and have kernels that change with the number of observations. These statistics arise in the construction of estimators in high-dimensional semi- and non-parametric models, and in the construction of nonparametric confidence sets. This is illustrated by estimation of the integral of a square of a density or regression function, and estimation of the mean response with missing data. We show that estimators are asymptotically normal even in the case that the rate is slower than the square root of the observations.

  4. Factorization method of quadratic template

    NASA Astrophysics Data System (ADS)

    Kotyrba, Martin

    2017-07-01

    Multiplication of two numbers is a one-way function in mathematics. Any attempt to distribute the outcome to its roots is called factorization. There are many methods such as Fermat's factorization, Dixońs method or quadratic sieve and GNFS, which use sophisticated techniques fast factorization. All the above methods use the same basic formula differing only in its use. This article discusses a newly designed factorization method. Effective implementation of this method in programs is not important, it only represents and clearly defines its properties.

  5. Hidden Lessons: How a Focus on Slope-Like Properties of Quadratic Functions Encouraged Unexpected Generalizations

    ERIC Educational Resources Information Center

    Ellis, Amy B.; Grinstead, Paul

    2008-01-01

    This article presents secondary students' generalizations about the connections between algebraic and graphical representations of quadratic functions, focusing specifically on the roles of the parameters a, b, and c in the general form of a quadratic function, y = ax[superscript 2] + bx + c. Students' generalizations about these connections led…

  6. Hidden Lessons: How a Focus on Slope-Like Properties of Quadratic Functions Encouraged Unexpected Generalizations

    ERIC Educational Resources Information Center

    Ellis, Amy B.; Grinstead, Paul

    2008-01-01

    This article presents secondary students' generalizations about the connections between algebraic and graphical representations of quadratic functions, focusing specifically on the roles of the parameters a, b, and c in the general form of a quadratic function, y = ax[superscript 2] + bx + c. Students' generalizations about these connections led…

  7. Polarization Nonlinear Optics of Quadratically Nonlinear Azopolymers

    SciTech Connect

    Konorov, S.O.; Akimov, D.A.; Ivanov, A.A.; Petrov, A.N.; Alfimov, M.V.; Yakimanskii, A.V.; Smirnov, N.N.; Ivanova, V.N.; Kudryavtsev, V.V.; Podshivalov, A.A.; Sokolova, I.M.; Zheltikov, A.M.

    2005-07-15

    The polarization properties of second harmonic and sum-frequency signals generated by femtosecond laser pulses in films of polymers containing covalent groups of an azobenzothiazole chromophore polarized by an external electric field are investigated. It is shown that the methods of polarization nonlinear optics make it possible to determine the structure of oriented molecular dipoles and reveal important properties of the motion of collectivized {pi}electrons in organic molecules with strong optical nonlinearities. The polarization measurements show that the tensor of quadratic nonlinear optical susceptibility of chromophore fragments oriented by an external field in macromolecules of the noted azopolymers has a degenerate form. This is indicative of a predominantly one-dimensional character of motion of collectivized {pi} electrons along an extended group of atoms in such molecules.

  8. Compact stars with quadratic equation of state

    NASA Astrophysics Data System (ADS)

    Ngubelanga, Sifiso A.; Maharaj, Sunil D.; Ray, Subharthi

    2015-05-01

    We provide new exact solutions to the Einstein-Maxwell system of equations for matter configurations with anisotropy and charge. The spacetime is static and spherically symmetric. A quadratic equation of state is utilised for the matter distribution. By specifying a particular form for one of the gravitational potentials and the electric field intensity we obtain new exact solutions in isotropic coordinates. In our general class of models, an earlier model with a linear equation of state is regained. For particular choices of parameters we regain the masses of the stars PSR J1614-2230, 4U 1608-52, PSR J1903+0327, EXO 1745-248 and SAX J1808.4-3658. A comprehensive physical analysis for the star PSR J1903+0327 reveals that our model is reasonable.

  9. Single-photon quadratic optomechanics

    PubMed Central

    Liao, Jie-Qiao; Nori, Franco

    2014-01-01

    We present exact analytical solutions to study the coherent interaction between a single photon and the mechanical motion of a membrane in quadratic optomechanics. We consider single-photon emission and scattering when the photon is initially inside the cavity and in the fields outside the cavity, respectively. Using our solutions, we calculate the single-photon emission and scattering spectra, and find relations between the spectral features and the system's inherent parameters, such as: the optomechanical coupling strength, the mechanical frequency, and the cavity-field decay rate. In particular, we clarify the conditions for the phonon sidebands to be visible. We also study the photon-phonon entanglement for the long-time emission and scattering states. The linear entropy is employed to characterize this entanglement by treating it as a bipartite one between a single mode of phonons and a single photon. PMID:25200128

  10. Large-scale sequential quadratic programming algorithms

    SciTech Connect

    Eldersveld, S.K.

    1992-09-01

    The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to large-scale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasi-Newton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reduced-gradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal null-space basis for large-scale problems. The continuity condition for this choice is proven. 4. The use of incomplete solutions of quadratic programming subproblems. Certain iterates generated by an active-set method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test problems.

  11. Factorising a Quadratic Expression with Geometric Insights

    ERIC Educational Resources Information Center

    Joarder, Anwar H.

    2015-01-01

    An algorithm is presented for factorising a quadratic expression to facilitate instruction and learning. It appeals to elementary geometry which may provide better insights to some students or teachers. There have been many methods for factorising a quadratic expression described in school text books. However, students often seem to struggle with…

  12. An Unexpected Influence on a Quadratic

    ERIC Educational Resources Information Center

    Davis, Jon D.

    2013-01-01

    Using technology to explore the coefficients of a quadratic equation can lead to an unexpected result. This article describes an investigation that involves sliders and dynamically linked representations. It guides students to notice the effect that the parameter "a" has on the graphical representation of a quadratic function in the form…

  13. On Quantization of Quadratic Poisson Structures

    NASA Astrophysics Data System (ADS)

    Manchon, D.; Masmoudi, M.; Roux, A.

    Any classical r-matrix on the Lie algebra of linear operators on a real vector space V gives rise to a quadratic Poisson structure on V which admits a deformation quantization stemming from the construction of V. Drinfel'd [Dr], [Gr]. We exhibit in this article an example of quadratic Poisson structure which does not arise this way.

  14. Preconditioned iterative methods for nonselfadjoint or indefinite elliptic boundary value problems

    SciTech Connect

    Bramble, J.H.; Pasciak, J.E.

    1984-01-01

    We consider a Galerkin-Finite Element approximation to a general linear elliptic boundary value problem which may be nonselfadjoint or indefinite. We show how to precondition the equations so that the resulting systems of linear algebraic equations lead to iteration procedures whose iterative convergence rates are independent of the number of unknowns in the solution.

  15. Risk factors associated with diagnostic discrepancy of gastric indefinite neoplasia: Who need en bloc resection?

    PubMed

    Goo, Ja Jun; Choi, Cheol Woong; Kang, Dae Hwan; Kim, Hyung Wook; Park, Su Bum; Cho, Mong; Hwang, Sun Hwi; Lee, Si Hak

    2015-12-01

    Endoscopic forceps biopsy is insufficient for a definitive diagnosis of dysplastic lesions. It is difficult to decide clinical management of gastric indefinite neoplasia diagnosed by endoscopic forceps biopsy when early gastric cancer (EGC) is macroscopically suspected. The aim of this study was to discuss the final results of gastric indefinite neoplasia and associated clinical factors predictive of early gastric cancer. The medical records of 119 patients who were diagnosed with gastric indefinite neoplasia by index forceps biopsy were retrospectively reviewed. The initial endoscopic findings were analyzed, and predictive factors of EGC were evaluated. The final pathologic diagnoses of 119 patients included early gastric cancer (n = 26, 21.8%), adenoma (n = 6, 5.0%) and non-neoplasm (n = 87, 73.1%). Univariate analysis showed that lesion size greater than 10 mm, surface nodularity and surface redness were associated risk factors. In the multivariate analysis, lesions diameter (p = 0.021, OR 11.401, 95% CI 1.432-90.759) and surface redness (p = 0.014, OR 3.777, 95% CI 1.306-10.923) were significant risk factors. Patients with gastric indefinite neoplasia with larger size (≥10 mm) and surface redness might need further diagnostic investigation rather than simple follow-up endoscopy.

  16. Positive Definiteness via Off-Diagonal Scaling of a Symmetric Indefinite Matrix

    ERIC Educational Resources Information Center

    Bentler, Peter M.; Yuan, Ke-Hai

    2011-01-01

    Indefinite symmetric matrices that are estimates of positive-definite population matrices occur in a variety of contexts such as correlation matrices computed from pairwise present missing data and multinormal based methods for discretized variables. This note describes a methodology for scaling selected off-diagonal rows and columns of such a…

  17. Positive Definiteness via Off-Diagonal Scaling of a Symmetric Indefinite Matrix

    ERIC Educational Resources Information Center

    Bentler, Peter M.; Yuan, Ke-Hai

    2011-01-01

    Indefinite symmetric matrices that are estimates of positive-definite population matrices occur in a variety of contexts such as correlation matrices computed from pairwise present missing data and multinormal based methods for discretized variables. This note describes a methodology for scaling selected off-diagonal rows and columns of such a…

  18. 18 CFR 1304.409 - Indefinite or temporary moorage of recreational vessels.

    Code of Federal Regulations, 2011 CFR

    2011-04-01

    ... 18 Conservation of Power and Water Resources 2 2011-04-01 2011-04-01 false Indefinite or temporary moorage of recreational vessels. 1304.409 Section 1304.409 Conservation of Power and Water Resources TENNESSEE VALLEY AUTHORITY APPROVAL OF CONSTRUCTION IN THE TENNESSEE RIVER SYSTEM AND REGULATION OF...

  19. 18 CFR 1304.409 - Indefinite or temporary moorage of recreational vessels.

    Code of Federal Regulations, 2012 CFR

    2012-04-01

    ... 18 Conservation of Power and Water Resources 2 2012-04-01 2012-04-01 false Indefinite or temporary moorage of recreational vessels. 1304.409 Section 1304.409 Conservation of Power and Water Resources TENNESSEE VALLEY AUTHORITY APPROVAL OF CONSTRUCTION IN THE TENNESSEE RIVER SYSTEM AND REGULATION OF...

  20. 41 CFR 101-39.204 - Obtaining motor vehicles for indefinite assignment.

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 41 Public Contracts and Property Management 2 2010-07-01 2010-07-01 true Obtaining motor vehicles..., TRANSPORTATION, AND MOTOR VEHICLES 39-INTERAGENCY FLEET MANAGEMENT SYSTEMS 39.2-GSA Interagency Fleet Management System Services § 101-39.204 Obtaining motor vehicles for indefinite assignment. Motor vehicles...

  1. 18 CFR 1304.409 - Indefinite or temporary moorage of recreational vessels.

    Code of Federal Regulations, 2010 CFR

    2010-04-01

    ... 18 Conservation of Power and Water Resources 2 2010-04-01 2010-04-01 false Indefinite or temporary moorage of recreational vessels. 1304.409 Section 1304.409 Conservation of Power and Water Resources TENNESSEE VALLEY AUTHORITY APPROVAL OF CONSTRUCTION IN THE TENNESSEE RIVER SYSTEM AND REGULATION...

  2. A new Krylov-subspace method for symmetric indefinite linear systems

    SciTech Connect

    Freund, R.W.; Nachtigal, N.M.

    1994-10-01

    Many important applications involve the solution of large linear systems with symmetric, but indefinite coefficient matrices. For example, such systems arise in incompressible flow computations and as subproblems in optimization algorithms for linear and nonlinear programs. Existing Krylov-subspace iterations for symmetric indefinite systems, such as SYMMLQ and MINRES, require the use of symmetric positive definite preconditioners, which is a rather unnatural restriction when the matrix itself is highly indefinite with both many positive and many negative eigenvalues. In this note, the authors describe a new Krylov-subspace iteration for solving symmetric indefinite linear systems that can be combined with arbitrary symmetric preconditioners. The algorithm can be interpreted as a special case of the quasi-minimal residual method for general non-Hermitian linear systems, and like the latter, it produces iterates defined by a quasi-minimal residual property. The proposed method has the same work and storage requirements per iteration as SYMMLQ or MINRES, however, it usually converges in considerably fewer iterations. Results of numerical experiments are reported.

  3. The Existence of Periodic Orbits and Invariant Tori for Some 3-Dimensional Quadratic Systems

    PubMed Central

    Jiang, Yanan; Han, Maoan; Xiao, Dongmei

    2014-01-01

    We use the normal form theory, averaging method, and integral manifold theorem to study the existence of limit cycles in Lotka-Volterra systems and the existence of invariant tori in quadratic systems in ℝ3. PMID:24982980

  4. The existence of periodic orbits and invariant tori for some 3-dimensional quadratic systems.

    PubMed

    Jiang, Yanan; Han, Maoan; Xiao, Dongmei

    2014-01-01

    We use the normal form theory, averaging method, and integral manifold theorem to study the existence of limit cycles in Lotka-Volterra systems and the existence of invariant tori in quadratic systems in ℝ(3).

  5. Quadratic nonlinear Klein-Gordon equation in one dimension

    NASA Astrophysics Data System (ADS)

    Hayashi, Nakao; Naumkin, Pavel I.

    2012-10-01

    We study the initial value problem for the quadratic nonlinear Klein-Gordon equation vtt + v - vxx = λv2, t ∈ R, x ∈ R, with initial conditions v(0, x) = v0(x), vt(0, x) = v1(x), x ∈ R, where v0 and v1 are real-valued functions, λ ∈ R. Using the method of normal forms of Shatah ["Normal forms and quadratic nonlinear Klein-Gordon equations," Commun. Pure Appl. Math. 38, 685-696 (1985)], we obtain a sharp asymptotic behavior of small solutions without the condition of a compact support on the initial data, which was assumed in the previous work of J.-M. Delort ["Existence globale et comportement asymptotique pour l'équation de Klein-Gordon quasi-linéaire á données petites en dimension 1," Ann. Sci. Ec. Normale Super. 34(4), 1-61 (2001)].

  6. 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.

  7. 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.

  8. Quadratic and Cubic Nonlinear Oscillators with Damping and Their Applications

    NASA Astrophysics Data System (ADS)

    Li, Jibin; Feng, Zhaosheng

    We apply the qualitative theory of dynamical systems to study exact solutions and the dynamics of quadratic and cubic nonlinear oscillators with damping. Under certain parametric conditions, we also consider the van der Waals normal form, Chaffee-Infante equation, compound Burgers-KdV equation and Burgers-KdV equation for explicit representations of kink-profile wave solutions and unbounded traveling wave solutions.

  9. Seven Wonders of the Ancient and Modern Quadratic World.

    ERIC Educational Resources Information Center

    Taylor, Sharon E.; Mittag, Kathleen Cage

    2001-01-01

    Presents four methods for solving a quadratic equation using graphing calculator technology: (1) graphing with the CALC feature; (2) quadratic formula program; (3) table; and (4) solver. Includes a worksheet for a lab activity on factoring quadratic equations. (KHR)

  10. Seven Wonders of the Ancient and Modern Quadratic World.

    ERIC Educational Resources Information Center

    Taylor, Sharon E.; Mittag, Kathleen Cage

    2001-01-01

    Presents four methods for solving a quadratic equation using graphing calculator technology: (1) graphing with the CALC feature; (2) quadratic formula program; (3) table; and (4) solver. Includes a worksheet for a lab activity on factoring quadratic equations. (KHR)

  11. An Analysis of Multiple Award Indefinite Delivery Indefinite Quantity Contracts at the Army Contracting Command -- Aberdeen Proving Ground

    DTIC Science & Technology

    2012-09-01

    quantity of 100 horses/ burros was insufficient to form binding contract. GAO denied the protest on the grounds that historical data indicated that...100 horses/ burros was a number the government was fairly certain to order and that given the multiple award nature of the IDIQ contract there was no...certainty how many horses/ burros each individual contractor would handle over the life of the contract. (Gamboa, 2000) c. B-291185: ABF Freight System’s

  12. Schur Stability Regions for Complex Quadratic Polynomials

    ERIC Educational Resources Information Center

    Cheng, Sui Sun; Huang, Shao Yuan

    2010-01-01

    Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)

  13. A Special Circle for Quadratic Equations.

    ERIC Educational Resources Information Center

    Patterson, Walter M.; Lubecke, Andre M.

    1991-01-01

    Discussed is a method of approximating the roots of a quadratic that allows the discovery of relationships between parabolas and circles and between the use of geometry and algebra. Included are the procedure and justification of the method. (KR)

  14. Linear quadratic optimal control for symmetric systems

    NASA Technical Reports Server (NTRS)

    Lewis, J. H.; Martin, C. F.

    1983-01-01

    Special symmetries are present in many control problems. This paper addresses the problem of determining linear-quadratic optimal control problems whose solutions preserve the symmetry of the initial linear control system.

  15. Schur Stability Regions for Complex Quadratic Polynomials

    ERIC Educational Resources Information Center

    Cheng, Sui Sun; Huang, Shao Yuan

    2010-01-01

    Given a quadratic polynomial with complex coefficients, necessary and sufficient conditions are found in terms of the coefficients such that all its roots have absolute values less than 1. (Contains 3 figures.)

  16. WHAT IS A SATISFACTORY QUADRATIC EQUATION SOLVER?

    DTIC Science & Technology

    The report discusses precise requirements for a satisfactory computer program to solve a quadratic equation with floating - point coefficients. The principal practical problem is coping with overflow and underflow.

  17. Test spaces and characterizations of quadratic spaces

    NASA Astrophysics Data System (ADS)

    Dvurečenskij, Anatolij

    1996-10-01

    We show that a test space consisting of nonzero vectors of a quadratic space E and of the set all maximal orthogonal systems in E is algebraic iff E is Dacey or, equivalently, iff E is orthomodular. In addition, we present another orthomodularity criteria of quadratic spaces, and using the result of Solèr, we show that they can imply that E is a real, complex, or quaternionic Hilbert space.

  18. The convergence rate of the proximal alternating direction method of multipliers with indefinite proximal regularization.

    PubMed

    Sun, Min; Liu, Jing

    2017-01-01

    The proximal alternating direction method of multipliers (P-ADMM) is an efficient first-order method for solving the separable convex minimization problems. Recently, He et al. have further studied the P-ADMM and relaxed the proximal regularization matrix of its second subproblem to be indefinite. This is especially significant in practical applications since the indefinite proximal matrix can result in a larger step size for the corresponding subproblem and thus can often accelerate the overall convergence speed of the P-ADMM. In this paper, without the assumptions that the feasible set of the studied problem is bounded or the objective function's component [Formula: see text] of the studied problem is strongly convex, we prove the worst-case [Formula: see text] convergence rate in an ergodic sense of the P-ADMM with a general Glowinski relaxation factor [Formula: see text], which is a supplement of the previously known results in this area. Furthermore, some numerical results on compressive sensing are reported to illustrate the effectiveness of the P-ADMM with indefinite proximal regularization.

  19. An optimal consumption and investment problem with quadratic utility and negative wealth constraints.

    PubMed

    Roh, Kum-Hwan; Kim, Ji Yeoun; Shin, Yong Hyun

    2017-01-01

    In this paper, we investigate the optimal consumption and portfolio selection problem with negative wealth constraints for an economic agent who has a quadratic utility function of consumption and receives a constant labor income. Due to the property of the quadratic utility function, we separate our problem into two cases and derive the closed-form solutions for each case. We also illustrate some numerical implications of the optimal consumption and portfolio.

  20. The Factorability of Quadratics: Motivation for More Techniques

    ERIC Educational Resources Information Center

    Bosse, Michael J.; Nandakumar, N. R.

    2005-01-01

    Typically, secondary and college algebra students attempt to utilize either completing the square or the quadratic formula as techniques to solve a quadratic equation only after frustration with factoring has arisen. While both completing the square and the quadratic formula are techniques which can determine solutions for all quadratic equations,…

  1. Limit cycles near hyperbolas in quadratic systems

    NASA Astrophysics Data System (ADS)

    Artés, Joan C.; Dumortier, Freddy; Llibre, Jaume

    In this paper we introduce the notion of infinity strip and strip of hyperbolas as organizing centers of limit cycles in polynomial differential systems on the plane. We study a strip of hyperbolas occurring in some quadratic systems. We deal with the cyclicity of the degenerate graphics DI2a from the programme, set up in [F. Dumortier, R. Roussarie, C. Rousseau, Hilbert's 16th problem for quadratic vector fields, J. Differential Equations 110 (1994) 86-133], to solve the finiteness part of Hilbert's 16th problem for quadratic systems. Techniques from geometric singular perturbation theory are combined with the use of the Bautin ideal. We also rely on the theory of Darboux integrability.

  2. Fast Approximate Quadratic Programming for Graph Matching

    PubMed Central

    Vogelstein, Joshua T.; Conroy, John M.; Lyzinski, Vince; Podrazik, Louis J.; Kratzer, Steven G.; Harley, Eric T.; Fishkind, Donniell E.; Vogelstein, R. Jacob; Priebe, Carey E.

    2015-01-01

    Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance. PMID:25886624

  3. Fast approximate quadratic programming for graph matching.

    PubMed

    Vogelstein, Joshua T; Conroy, John M; Lyzinski, Vince; Podrazik, Louis J; Kratzer, Steven G; Harley, Eric T; Fishkind, Donniell E; Vogelstein, R Jacob; Priebe, Carey E

    2015-01-01

    Quadratic assignment problems arise in a wide variety of domains, spanning operations research, graph theory, computer vision, and neuroscience, to name a few. The graph matching problem is a special case of the quadratic assignment problem, and graph matching is increasingly important as graph-valued data is becoming more prominent. With the aim of efficiently and accurately matching the large graphs common in big data, we present our graph matching algorithm, the Fast Approximate Quadratic assignment algorithm. We empirically demonstrate that our algorithm is faster and achieves a lower objective value on over 80% of the QAPLIB benchmark library, compared with the previous state-of-the-art. Applying our algorithm to our motivating example, matching C. elegans connectomes (brain-graphs), we find that it efficiently achieves performance.

  4. Restricted Quadratic Forms, Inertia Theorems and the Schur Complement,

    DTIC Science & Technology

    1985-01-01

    subspace S , the usual orthogonal complement of S. Definition 3.1. For an mxn matrix C, the generalized , or Moore - Penrose , inverse is the unique nym...References D. Carlson, E. Haynsworth and T. Markham (1974); A generalization of the Schur complement by means of the Moore - Penrose Inverse , SIAM 3...A The results of §2 are direct in the sense that they do not Involve any inversion of the matrix A. It will here be shown that when the Moore - Penrose

  5. On the Local Maxima of a Constrained Quadratic Form

    ERIC Educational Resources Information Center

    Bhowmik, Jahar L.

    2006-01-01

    This note presents a brief and partial review of the work of Broom, Cannings and Vickers [1]. It also presents some simple examples of an extension of the their formalism to non-symmetric matrices. (Contains 1 figure.)

  6. Limit Cycles of Planar Quadratic Differential Equations,

    DTIC Science & Technology

    1982-05-01

    A120 71g LIMIT CYCLES OF PLANAR QUADRATIC DIFFERENTIAL EQUATIONS i/i (U) VALE UNIV NEW~ HAVEN CT CENTER FOR SYSTEMS SCIENCE D E KODITSCHE( ET AL...MICROCOPY RESOLUTION TEST CHART ""OftAI IIMEA OF WSTMAIhSIItg0s3a NATIONA BUREAU OF -TANDtMAROga / - -w w w ~ S S S S S S S S LIMIT CYCLES OF PLANAR...pubta rolb=% DW*5UMato UnlIhd ... a.. . . . . . . . . .......- .lu uo . ,aK Limit Cycles of Planar Quadratic Differential Equations D. E. Koditschek

  7. On orthogonality preserving quadratic stochastic operators

    SciTech Connect

    Mukhamedov, Farrukh; Taha, Muhammad Hafizuddin Mohd

    2015-05-15

    A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. In the present paper, we first give a simple characterization of Volterra QSO in terms of absolutely continuity of discrete measures. Further, we introduce a notion of orthogonal preserving QSO, and describe such kind of operators defined on two dimensional simplex. It turns out that orthogonal preserving QSOs are permutations of Volterra QSO. The associativity of genetic algebras generated by orthogonal preserving QSO is studied too.

  8. Guises and disguises of quadratic divergences

    NASA Astrophysics Data System (ADS)

    Cherchiglia, A. L.; Vieira, A. R.; Hiller, Brigitte; Baêta Scarpelli, A. P.; Sampaio, Marcos

    2014-12-01

    In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.

  9. PSQP -- Puzzle Solving by Quadratic Programming.

    PubMed

    Andalo, Fernanda; Taubin, Gabriel; Goldenstein, Siome

    2016-03-25

    In this article we present the first effective global method for the reconstruction of image puzzles comprising rectangle pieces - Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.

  10. PSQP: Puzzle Solving by Quadratic Programming.

    PubMed

    Andalo, Fernanda A; Taubin, Gabriel; Goldenstein, Siome

    2017-02-01

    In this article we present the first effective method based on global optimization for the reconstruction of image puzzles comprising rectangle pieces-Puzzle Solving by Quadratic Programming (PSQP). The proposed novel mathematical formulation reduces the problem to the maximization of a constrained quadratic function, which is solved via a gradient ascent approach. The proposed method is deterministic and can deal with arbitrary identical rectangular pieces. We provide experimental results showing its effectiveness when compared to state-of-the-art approaches. Although the method was developed to solve image puzzles, we also show how to apply it to the reconstruction of simulated strip-shredded documents, broadening its applicability.

  11. Guises and disguises of quadratic divergences

    SciTech Connect

    Cherchiglia, A.L.; Vieira, A.R.; Hiller, Brigitte; Baêta Scarpelli, A.P.; Sampaio, Marcos

    2014-12-15

    In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.

  12. Low Temperature Plasmas Generated and Sustained Indefinitely Using a Focused Microwave Beam

    NASA Astrophysics Data System (ADS)

    Reid, Remington; Hoff, Brad; Lepell, Paul; AFRL Team

    2016-10-01

    The Air Force Research Laboratory has constructed a device that can initiate a plasma discharge in a focused microwave beam and sustain it indefinitely. A 10 kW, 4.5 GHz beam is passed through a vacuum chamber outfitted with pressure windows that are transparent to 4.5 GHz radiation. The pressure windows are large enough in diameter to prevent any interactions between the beam and the metallic chamber. The entire experiment is housed inside an anechoic chamber to minimize reflections. This novel plasma source generates low temperature, low density plasmas that have no contact with the walls which minimizes contamination and sheath formation.

  13. Effects of quadrat size and shape, initial epidemic conditions, and spore dispersal gradient on spatial statistics of plant disease epidemics.

    PubMed

    Xu, X M; Ridout, M S

    2000-07-01

    ABSTRACT The spatiotemporal spread of plant diseases was simulated using a stochastic model to study the effects of initial conditions (number of plants initially infected and their spatial pattern), spore dispersal gradient, and size and shape of sampling quadrats on statistics describing the spatiotemporal dynamics of epidemics. The spatial spread of disease was simulated using a half-Cauchy distribution with median dispersal distance mu (units of distance). A total of 54 different quadrat types, including 23 distinct sizes ranging from 4 to 144 plants, were used to sample the simulated epidemics. A symmetric form of the binary power law with two parameters (alpha, beta) was fitted to the sampled epidemic data using each of the 54 quadrats for each replicate simulation run. The alpha and beta estimates were highly correlated positively with each other, and their estimates were comparable to those estimated from observed epidemics. Intraclass correlation (kappa) was calculated for each quadrat type; kappa decreased exponentially with increasing quadrat size. An asymmetric form of the binary power law with three parameters (alpha (1), beta(1), beta(2)) was used to relate kappa to the disease incidence (p); beta1 was highly correlated to beta: beta1 approximately beta - 1. In general, initial conditions and quadrat size affected alpha, beta, alpha(1), beta(1), and beta(2) greatly. The parameter estimates increased as quadrat size increased, and the relationships were described well by a linear regression model on the logarithm of quadrat size with the slope or intercept parameters dependent on initial conditions and mu. Compared with initial conditions and quadrat size, the overall effects of mu and quadrat shape were generally small, although within each quadrat size and initial condition they could be substantial. Quadrat shape had the greatest effect when the quadrat was long and thin. The relationship of the index of dispersion (D) to p and quadrat size was

  14. Quadratic Gabor correlation filters for object detection

    NASA Astrophysics Data System (ADS)

    Weber, David; Casasent, David P.

    1996-10-01

    We present a new class of quadratic filters that are capable of creating spherical, elliptical, hyperbolic and linear decision surfaces which result in better detection and classification capabilities than the linear decision surfaces obtained from correlation filters. Each filter comprises of a number of separately designed linear basis filters. These filters are linearly combined into several macro filters; the output from these macro filters are passed through a magnitude square operation and are then linearly combined using real weights to achieve the quadratic decision surface. This nonlinear fusion algorithm is called the extended piecewise quadratic neural network (E-PQNN). For detection, the creation of macro filters allows for a substantial computational saving by reducing the number of correlation operations required. In this work, we consider the use of Gabor basis filters; the Gabor filter parameters are separately optimized; the fusion parameters to combine the Gabor filter outputs are optimized using the conjugate gradient method; they and the nonlinear combination of filter outputs are included in our E-PQNN algorithm. We demonstrate methods for selecting the number of macro Gabor filters, the filter parameters and the linear and nonlinear combination coefficients. We prove that our simple E-PQNN architecture is able to generate arbitrary piecewise quadratic decision surfaces. We present preliminary results obtained for an IR vehicle detection problem.

  15. Quadratic Gabor correlation filters for object detection

    NASA Astrophysics Data System (ADS)

    Weber, David; Casasent, David P.

    1997-04-01

    We present a new class of quadratic filters that are capable of creating spherical, elliptical, hyperbolic and linear decision surfaces which result in better detection and classification capabilities than the linear decision surfaces obtained from correlation filters. Each filter comprises of a number of separately designed linear basis filters. These filters are linearly combined into several macro filters; the output from these macro filters are passed through a magnitude square operation and are then linearly combined using real weights to achieve the quadratic decision surface. This non-linear fusion algorithm is called the extended piecewise quadratic neural network (E-PQNN). For detection, the creation of macro filters allows for a substantial computational saving by reducing the number of correlation operations required. In this work, we consider the use of Gabor basis filters; the Gabor filter parameters are separately optimized; the fusion parameters to combine the Gabor filter outputs are optimized using the conjugate gradient method; they and the non-linear combination of filter outputs are included in our E-PQNN algorithm. We demonstrate methods for selecting the number of macro Gabor filters, the filter parameters and the linear and non-linear combination coefficients. We prove that our simple E-PQNN architecture is able to generate arbitrary piecewise quadratic decision surfaces. We present preliminary results obtained for an IR vehicle detection problem.

  16. Integration of the Quadratic Function and Generalization

    ERIC Educational Resources Information Center

    Mitsuma, Kunio

    2011-01-01

    We will first recall useful formulas in integration that simplify the calculation of certain definite integrals with the quadratic function. A main formula relies only on the coefficients of the function. We will then explore a geometric proof of one of these formulas. Finally, we will extend the formulas to more general cases. (Contains 3…

  17. Investigating Students' Mathematical Difficulties with Quadratic Equations

    ERIC Educational Resources Information Center

    O'Connor, Bronwyn Reid; Norton, Stephen

    2016-01-01

    This paper examines the factors that hinder students' success in working with and understanding the mathematics of quadratic equations using a case study analysis of student error patterns. Twenty-five Year 11 students were administered a written test to examine their understanding of concepts and procedures associated with this topic. The…

  18. The use of definite and indefinite articles by children with specific language impairment.

    PubMed

    Polite, Elgustus J; Leonard, Laurence B; Roberts, Felicia D

    2011-08-01

    Among the grammatical limitations seen in English-speaking children with specific language impairment (SLI) is a prolonged period of using articles (e.g., a, the) inconsistently. Most studies documenting this difficulty have focused on article omission and have not made the distinction between definite and indefinite article contexts. In this study, there were 36 participants: 12 5-year-olds with SLI, 12 typically-developing children matched for age, and 12 younger, typically-developing children matched with participants in the SLI group according to mean length of utterance. All 36 children participated in a task requiring indefinite article use, and a task requiring use of the definite article, in which the referent of the noun had already been established in the discourse. The children with SLI showed less use of definite articles in particular, relative to both groups of typically-developing children. Substitutions as well as omissions were seen. The findings suggest that the article limitations of the children with SLI were attributable in part to an incomplete understanding of how definite articles are to be used.

  19. Bôcher and Abstract Contractions of 2nd Order Quadratic Algebras

    NASA Astrophysics Data System (ADS)

    Escobar-Ruiz, Mauricio A.; Kalnins, Ernest G.; Miller, Willar, Jr.; Subag, Eyal

    2017-03-01

    Quadratic algebras are generalizations of Lie algebras which include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical and quantum mechanics. Distinct superintegrable systems and their quadratic algebras can be related by geometric contractions, induced by Bôcher contractions of the conformal Lie algebra {so}(4,C) to itself. In this paper we give a precise definition of Bôcher contractions and show how they can be classified. They subsume well known contractions of {e}(2,C) and {so}(3,C) and have important physical and geometric meanings, such as the derivation of the Askey scheme for obtaining all hypergeometric orthogonal polynomials as limits of Racah/Wilson polynomials. We also classify abstract nondegenerate quadratic algebras in terms of an invariant that we call a canonical form. We describe an algorithm for finding the canonical form of such algebras. We calculate explicitly all canonical forms arising from quadratic algebras of 2D nondegenerate superintegrable systems on constant curvature spaces and Darboux spaces. We further discuss contraction of quadratic algebras, focusing on those coming from superintegrable systems.

  20. Quadratic formula for determining the drop size in pressure-atomized sprays with and without swirl

    SciTech Connect

    Lee, T.-W An, Keju

    2016-06-15

    We use a theoretical framework based on the integral form of the conservation equations, along with a heuristic model of the viscous dissipation, to find a closed-form solution to the liquid atomization problem. The energy balance for the spray renders to a quadratic formula for the drop size as a function, primarily of the liquid velocity. The Sauter mean diameter found using the quadratic formula shows good agreements and physical trends, when compared with experimental observations. This approach is shown to be applicable toward specifying initial drop size in computational fluid dynamics of spray flows.

  1. Quadratic formula for determining the drop size in pressure-atomized sprays with and without swirl

    NASA Astrophysics Data System (ADS)

    Lee, T.-W.; An, Keju

    2016-06-01

    We use a theoretical framework based on the integral form of the conservation equations, along with a heuristic model of the viscous dissipation, to find a closed-form solution to the liquid atomization problem. The energy balance for the spray renders to a quadratic formula for the drop size as a function, primarily of the liquid velocity. The Sauter mean diameter found using the quadratic formula shows good agreements and physical trends, when compared with experimental observations. This approach is shown to be applicable toward specifying initial drop size in computational fluid dynamics of spray flows.

  2. Geometric Approaches to Quadratic Equations from Other Times and Places.

    ERIC Educational Resources Information Center

    Allaire, Patricia R.; Bradley, Robert E.

    2001-01-01

    Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)

  3. Geometric Approaches to Quadratic Equations from Other Times and Places.

    ERIC Educational Resources Information Center

    Allaire, Patricia R.; Bradley, Robert E.

    2001-01-01

    Focuses on geometric solutions of quadratic problems. Presents a collection of geometric techniques from ancient Babylonia, classical Greece, medieval Arabia, and early modern Europe to enhance the quadratic equation portion of an algebra course. (KHR)

  4. Use of quadratic components for buckling calculations

    SciTech Connect

    Dohrmann, C.R.; Segalman, D.J.

    1996-12-31

    A buckling calculation procedure based on the method of quadratic components is presented. Recently developed for simulating the motion of rotating flexible structures, the method of quadratic components is shown to be applicable to buckling problems with either conservative or nonconservative loads. For conservative loads, stability follows from the positive definiteness of the system`s stiffness matrix. For nonconservative loads, stability is determined by solving a nonsymmetric eigenvalue problem, which depends on both the stiffness and mass distribution of the system. Buckling calculations presented for a cantilevered beam are shown to compare favorably with classical results. Although the example problem is fairly simple and well-understood, the procedure can be used in conjunction with a general-purpose finite element code for buckling calculations of more complex systems.

  5. Bifurcations in biparametric quadratic potentials. II.

    PubMed

    Lanchares, V.; Elipe, A.

    1995-09-01

    Quadratic Hamiltonians with the phase space on the S (2) sphere represent numerous dynamical systems. There are only two classes of quadratic Hamiltonians depending on two parameters. We analyze the occurrence of bifurcations and we obtain the bifurcation lines in the parameter plane for one of these classes, thus complementing the work done in a previous paper where the other class was analyzed. As the parameters evolve, the appearance-disappearance of homoclinic orbits in the phase portrait is governed by four types of bifurcations: namely the pitchfork, the butterfly, the oyster and the pentadent bifurcations. We find also values where the system is degenerate, that is, there are nonisolated equilibria. (c) 1995 American Institute of Physics.

  6. Graphical Solution of the Monic Quadratic Equation with Complex Coefficients

    ERIC Educational Resources Information Center

    Laine, A. D.

    2015-01-01

    There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

  7. THE EFFECTIVENESS OF QUADRATS FOR MEASURING VASCULAR PLANT DIVERSITY

    EPA Science Inventory

    Quadrats are widely used for measuring characteristics of vascular plant communities. It is well recognized that quadrat size affects measurements of frequency and cover. The ability of quadrats of varying sizes to adequately measure diversity has not been established. An exha...

  8. Graphical Solution of the Monic Quadratic Equation with Complex Coefficients

    ERIC Educational Resources Information Center

    Laine, A. D.

    2015-01-01

    There are many geometrical approaches to the solution of the quadratic equation with real coefficients. In this article it is shown that the monic quadratic equation with complex coefficients can also be solved graphically, by the intersection of two hyperbolas; one hyperbola being derived from the real part of the quadratic equation and one from…

  9. THE EFFECTIVENESS OF QUADRATS FOR MEASURING VASCULAR PLANT DIVERSITY

    EPA Science Inventory

    Quadrats are widely used for measuring characteristics of vascular plant communities. It is well recognized that quadrat size affects measurements of frequency and cover. The ability of quadrats of varying sizes to adequately measure diversity has not been established. An exha...

  10. Quadratic image destriping. [GOES photograph enhancement

    NASA Technical Reports Server (NTRS)

    Dalton, J. T.; Winkert, G. E.

    1979-01-01

    An algorithm for removing second-order detector banding effects (striping) from digital imagery is described. This quadratic destriping method is basically an extension of a linear method to one higher degree. It provides a nonlinear alternative between the two-parameter linear correction and a multilinear histogram equalization approach. The application of the proposed technique to GOES visible imagery is discussed, and its effectiveness is compared to existing methods.

  11. Monotone and convex quadratic spline interpolation

    NASA Technical Reports Server (NTRS)

    Lam, Maria H.

    1990-01-01

    A method for producing interpolants that preserve the monotonicity and convexity of discrete data is described. It utilizes the quadratic spline proposed by Schumaker (1983) which was subsequently characterized by De Vore and Yan (1986). The selection of first order derivatives at the given data points is essential to this spline. An observation made by De Vore and Yan is generalized, and an improved method to select these derivatives is proposed. The resulting spline is completely local, efficient, and simple to implement.

  12. Communications circuit including a linear quadratic estimator

    DOEpatents

    Ferguson, Dennis D.

    2015-07-07

    A circuit includes a linear quadratic estimator (LQE) configured to receive a plurality of measurements a signal. The LQE is configured to weight the measurements based on their respective uncertainties to produce weighted averages. The circuit further includes a controller coupled to the LQE and configured to selectively adjust at least one data link parameter associated with a communication channel in response to receiving the weighted averages.

  13. Characterization of a Quadratic Function in Rn

    ERIC Educational Resources Information Center

    Xu, Conway

    2010-01-01

    It is proved that a scalar-valued function "f"(x) defined in "n"-dimensional space must be quadratic, if the intersection of tangent planes at x[subscript 1] and x[subscript 2] always contains the midpoint of the line joining x[subscript 1] and x[subscript 2]. This is the converse of a result of Stenlund proved in this JOURNAL in 2001.

  14. Characterization of a Quadratic Function in Rn

    ERIC Educational Resources Information Center

    Xu, Conway

    2010-01-01

    It is proved that a scalar-valued function "f"(x) defined in "n"-dimensional space must be quadratic, if the intersection of tangent planes at x[subscript 1] and x[subscript 2] always contains the midpoint of the line joining x[subscript 1] and x[subscript 2]. This is the converse of a result of Stenlund proved in this JOURNAL in 2001.

  15. Stochastic Linear Quadratic Optimal Control Problems

    SciTech Connect

    Chen, S.; Yong, J.

    2001-07-01

    This paper is concerned with the stochastic linear quadratic optimal control problem (LQ problem, for short) for which the coefficients are allowed to be random and the cost functional is allowed to have a negative weight on the square of the control variable. Some intrinsic relations among the LQ problem, the stochastic maximum principle, and the (linear) forward-backward stochastic differential equations are established. Some results involving Riccati equation are discussed as well.

  16. Optimal Approximation of Quadratic Interval Functions

    NASA Technical Reports Server (NTRS)

    Koshelev, Misha; Taillibert, Patrick

    1997-01-01

    Measurements are never absolutely accurate, as a result, after each measurement, we do not get the exact value of the measured quantity; at best, we get an interval of its possible values, For dynamically changing quantities x, the additional problem is that we cannot measure them continuously; we can only measure them at certain discrete moments of time t(sub 1), t(sub 2), ... If we know that the value x(t(sub j)) at a moment t(sub j) of the last measurement was in the interval [x-(t(sub j)), x + (t(sub j))], and if we know the upper bound D on the rate with which x changes, then, for any given moment of time t, we can conclude that x(t) belongs to the interval [x-(t(sub j)) - D (t - t(sub j)), x + (t(sub j)) + D (t - t(sub j))]. This interval changes linearly with time, an is, therefore, called a linear interval function. When we process these intervals, we get an expression that is quadratic and higher order w.r.t. time t, Such "quadratic" intervals are difficult to process and therefore, it is necessary to approximate them by linear ones. In this paper, we describe an algorithm that gives the optimal approximation of quadratic interval functions by linear ones.

  17. Quadratic optimization in ill-posed problems

    NASA Astrophysics Data System (ADS)

    Ben Belgacem, F.; Kaber, S.-M.

    2008-10-01

    Ill-posed quadratic optimization frequently occurs in control and inverse problems and is not covered by the Lax-Milgram-Riesz theory. Typically, small changes in the input data can produce very large oscillations on the output. We investigate the conditions under which the minimum value of the cost function is finite and we explore the 'hidden connection' between the optimization problem and the least-squares method. Eventually, we address some examples coming from optimal control and data completion, showing how relevant our contribution is in the knowledge of what happens for various ill-posed problems. The results we state bring a substantial improvement to the analysis of the regularization methods applied to the ill-posed quadratic optimization problems. Indeed, for the cost quadratic functions bounded from below the Lavrentiev method is just the Tikhonov regularization for the 'hidden least-squares' problem. As a straightforward result, Lavrentiev's regularization exhibits better regularization and convergence results than expected at first glance.

  18. Quadratic Programming for Allocating Control Effort

    NASA Technical Reports Server (NTRS)

    Singh, Gurkirpal

    2005-01-01

    A computer program calculates an optimal allocation of control effort in a system that includes redundant control actuators. The program implements an iterative (but otherwise single-stage) algorithm of the quadratic-programming type. In general, in the quadratic-programming problem, one seeks the values of a set of variables that minimize a quadratic cost function, subject to a set of linear equality and inequality constraints. In this program, the cost function combines control effort (typically quantified in terms of energy or fuel consumed) and control residuals (differences between commanded and sensed values of variables to be controlled). In comparison with prior control-allocation software, this program offers approximately equal accuracy but much greater computational efficiency. In addition, this program offers flexibility, robustness to actuation failures, and a capability for selective enforcement of control requirements. The computational efficiency of this program makes it suitable for such complex, real-time applications as controlling redundant aircraft actuators or redundant spacecraft thrusters. The program is written in the C language for execution in a UNIX operating system.

  19. Quadratic Gabor filters for object detection.

    PubMed

    Weber, D M; Casasent, D P

    2001-01-01

    We present a new class of quadratic filters that are capable of creating spherical, elliptical, hyperbolic and linear decision surfaces which result in better detection and classification capabilities than the linear decision surfaces obtained from correlation filters. Each filter comprises of a number of separately designed linear basis filters. These filters are linearly combined into several macro filters; the output from these macro filters are passed through a magnitude square operation and are then linearly combined using real weights to achieve the quadratic decision surface. For detection, the creation of macro filters (linear combinations of multiple single filters) allows for a substantial computational saving by reducing the number of correlation operations required. In this work, we consider the use of Gabor basis filters; the Gabor filter parameters are separately optimized. The fusion parameters to combine the Gabor filter outputs are optimized using an extended piecewise quadratic neural network (E-PQNN). We demonstrate methods for selecting the number of macro Gabor filters, the filter parameters and the linear and nonlinear combination coefficients. We present preliminary results obtained for an infrared (IR) vehicle detection problem.

  20. Three-dimensional nanometer-scale optical cavities of indefinite medium

    PubMed Central

    Yao, Jie; Yang, Xiaodong; Yin, Xiaobo; Bartal, Guy; Zhang, Xiang

    2011-01-01

    Miniaturization of optical cavities has numerous advantages for enhancing light–matter interaction in quantum optical devices, low-threshold lasers with minimal power consumption, and efficient integration of optoelectronic devices at large scale. However, the realization of a truly nanometer-scale optical cavity is hindered by the diffraction limit of the nature materials. In addition, the scaling of the photon life time with the cavity size significantly reduces the quality factor of small cavities. Here we theoretically present an approach to achieve ultrasmall optical cavities using indefinite medium with hyperbolic dispersion, which allows propagation of electromagnetic waves with wave vectors much larger than those in vacuum enabling extremely small 3D cavity down to (λ/20)3. These cavities exhibit size-independent resonance frequencies and anomalous scaling of quality factors in contrast to the conventional cavities, resulting in nanocavities with both high Q/Vm ratio and broad bandwidth. PMID:21709266

  1. Principal Eigenvalue Minimization for an Elliptic Problem with Indefinite Weight and Robin Boundary Conditions

    SciTech Connect

    Hintermueller, M.; Kao, C.-Y.; Laurain, A.

    2012-02-15

    This paper focuses on the study of a linear eigenvalue problem with indefinite weight and Robin type boundary conditions. We investigate the minimization of the positive principal eigenvalue under the constraint that the absolute value of the weight is bounded and the total weight is a fixed negative constant. Biologically, this minimization problem is motivated by the question of determining the optimal spatial arrangement of favorable and unfavorable regions for a species to survive. For rectangular domains with Neumann boundary condition, it is known that there exists a threshold value such that if the total weight is below this threshold value then the optimal favorable region is like a section of a disk at one of the four corners; otherwise, the optimal favorable region is a strip attached to the shorter side of the rectangle. Here, we investigate the same problem with mixed Robin-Neumann type boundary conditions and study how this boundary condition affects the optimal spatial arrangement.

  2. 48 CFR 1807.107-70 - Orders against Federal Supply Schedule contracts or other indefinite-delivery contracts awarded...

    Code of Federal Regulations, 2010 CFR

    2010-10-01

    ... 48 Federal Acquisition Regulations System 6 2010-10-01 2010-10-01 true Orders against Federal Supply Schedule contracts or other indefinite-delivery contracts awarded by another agency. 1807.107-70 Section 1807.107-70 Federal Acquisition Regulations System NATIONAL AERONAUTICS AND SPACE ADMINISTRATION COMPETITION AND ACQUISITION...

  3. An Investigation into Undergraduates' Errors in the Use of the Indefinite Article at Omar Al-Mukhtar University

    ERIC Educational Resources Information Center

    Gaibani, Ahmed

    2015-01-01

    The purpose of this study was to examine the use of English articles as well the errors made by the students at Omar Al-Mukhtar University. The research objectives consists of: To identify the types and sources of errors made by Libyan EFL Undergraduates at Omar Al-Mukhtar University in the use of the indefinite article during their written…

  4. "Anything "You" Can Do, "Tu" Can Do Better": "Tu" and "Vous" as Substitutes for Indefinite "On" in French.

    ERIC Educational Resources Information Center

    Coveney, Aidan

    2003-01-01

    Presents a survey of the French indefinite "tu/vous" in in earlier periods and in a range of varieties. Draws on a corpus of French spoken in Picardy in Northern France to investigate the extent to which this use of second person pronouns helps to avoid ambiguity and co-occurs with another grammatical variable. (Author/VWL)

  5. 5 CFR 230.402 - Agency authority to make emergency-indefinite appointments in a national emergency.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ... 5 Administrative Personnel 1 2014-01-01 2014-01-01 false Agency authority to make emergency-indefinite appointments in a national emergency. 230.402 Section 230.402 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT CIVIL SERVICE REGULATIONS ORGANIZATION OF THE GOVERNMENT FOR PERSONNEL MANAGEMENT...

  6. 5 CFR 230.402 - Agency authority to make emergency-indefinite appointments in a national emergency.

    Code of Federal Regulations, 2013 CFR

    2013-01-01

    ... 5 Administrative Personnel 1 2013-01-01 2013-01-01 false Agency authority to make emergency-indefinite appointments in a national emergency. 230.402 Section 230.402 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT CIVIL SERVICE REGULATIONS ORGANIZATION OF THE GOVERNMENT FOR PERSONNEL MANAGEMENT...

  7. 5 CFR 230.402 - Agency authority to make emergency-indefinite appointments in a national emergency.

    Code of Federal Regulations, 2012 CFR

    2012-01-01

    ... 5 Administrative Personnel 1 2012-01-01 2012-01-01 false Agency authority to make emergency-indefinite appointments in a national emergency. 230.402 Section 230.402 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT CIVIL SERVICE REGULATIONS ORGANIZATION OF THE GOVERNMENT FOR PERSONNEL...

  8. 5 CFR 230.402 - Agency authority to make emergency-indefinite appointments in a national emergency.

    Code of Federal Regulations, 2010 CFR

    2010-01-01

    ... 5 Administrative Personnel 1 2010-01-01 2010-01-01 false Agency authority to make emergency-indefinite appointments in a national emergency. 230.402 Section 230.402 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT CIVIL SERVICE REGULATIONS ORGANIZATION OF THE GOVERNMENT FOR PERSONNEL...

  9. 5 CFR 230.402 - Agency authority to make emergency-indefinite appointments in a national emergency.

    Code of Federal Regulations, 2011 CFR

    2011-01-01

    ... 5 Administrative Personnel 1 2011-01-01 2011-01-01 false Agency authority to make emergency-indefinite appointments in a national emergency. 230.402 Section 230.402 Administrative Personnel OFFICE OF PERSONNEL MANAGEMENT CIVIL SERVICE REGULATIONS ORGANIZATION OF THE GOVERNMENT FOR PERSONNEL...

  10. User's guide for SOL/QPSOL: a Fortran package for quadratic programming

    SciTech Connect

    Gill, P.E.; Murray, W.; Saunders, M.A.; Wright, M.H.

    1983-07-01

    This report forms the user's guide for Version 3.1 of SOL/QPSOL, a set of Fortran subroutines designed to locate the minimum value of an arbitrary quadratic function subject to linear constraints and simple upper and lower bounds. If the quadratic function is convex, a global minimum is found; otherwise, a local minimum is found. The method used is most efficient when many constraints or bounds are active at the solution. QPSOL treats the Hessian and general constraints as dense matrices, and hence is not intended for large sparse problems. This document replaces the previous user's guide of June 1982.

  11. Classification of the quantum two-dimensional superintegrable systems with quadratic integrals and the Staeckel transforms

    SciTech Connect

    Daskaloyannis, C. Tanoudis, Y.

    2008-05-15

    The two-dimensional quantum superintegrable systems with quadratic integrals of motion on a manifold are classified by using the quadratic associative algebra of the integrals of motion. There are six general fundamental classes of quantum superintegrable systems corresponding to the classical ones. Analytic formulas for the involved integrals are calculated in all the cases. All the known quantum superintegrable systems with quadratic integrals are classified as special cases of these six general classes. The coefficients of the quadratic associative algebra of integrals are calculated and they are compared to the coefficients of the corresponding coefficients of the Poisson quadratic algebra of the classical systems. The quantum coefficients are similar to the classical ones multiplied by a quantum coefficient -{h_bar}{sup 2} plus a quantum deformation of order {h_bar}{sup 4} and {h_bar}{sup 6}. The systems inside the classes are transformed using Staeckel transforms in the quantum case as in the classical case. The general form of the Staeckel transform between superintegrable systems is discussed.

  12. Diagnostics of the inhomogeneous distribution of quadratic optical susceptibility over parametric scattering spectra

    SciTech Connect

    Kitaeva, G Kh; Penin, A N

    2004-07-31

    A new method is proposed for measuring the spatial distribution of the quadratic susceptibility of inhomogeneous nonlinear media. The method is based on the unique relation of the Fourier harmonics of this distribution with the shape of a signal-radiation line during parametric frequency conversion in a linear regime. The diagnostic possibilities of the method of spontaneous parametric scattering of light are analysed by simulating the spectra of nonlinear diffraction in layered structures with different profiles of variation in the quadratic susceptibility. The cases of step and smoothed variations in the susceptibility of periodically poled regular and irregular superlattices (structures formed by the layers of optically linear and nonlinear media) are considered and the effect of light absorption at an idler frequency is studied. The experimental spectra of periodically poled crystals are presented. Different methods for measuring the one-dimensional dependence of quadratic susceptibility on the coordinate in periodically poled structures and polydomain crystals are proposed. (invited paper)

  13. Theoretical analysis of integral neutron transport equation using collision probability method with quadratic flux approach

    SciTech Connect

    Shafii, Mohammad Ali Meidianti, Rahma Wildian, Fitriyani, Dian; Tongkukut, Seni H. J.; Arkundato, Artoto

    2014-09-30

    Theoretical analysis of integral neutron transport equation using collision probability (CP) method with quadratic flux approach has been carried out. In general, the solution of the neutron transport using the CP method is performed with the flat flux approach. In this research, the CP method is implemented in the cylindrical nuclear fuel cell with the spatial of mesh being conducted into non flat flux approach. It means that the neutron flux at any point in the nuclear fuel cell are considered different each other followed the distribution pattern of quadratic flux. The result is presented here in the form of quadratic flux that is better understanding of the real condition in the cell calculation and as a starting point to be applied in computational calculation.

  14. Quadratic finite elements and incompressible viscous flows.

    SciTech Connect

    Dohrmann, Clark R.; Gartling, David K.

    2005-01-01

    Pressure stabilization methods are applied to higher-order velocity finite elements for application to viscous incompressible flows. Both a standard pressure stabilizing Petrov-Galerkin (PSPG) method and a new polynomial pressure projection stabilization (PPPS) method have been implemented and tested for various quadratic elements in two dimensions. A preconditioner based on relaxing the incompressibility constraint is also tested for the iterative solution of saddle point problems arising from mixed Galerkin finite element approximations to the Navier-Stokes equations. The preconditioner is demonstrated for BB stable elements with discontinuous pressure approximations in two and three dimensions.

  15. Constrained neural approaches to quadratic assignment problems.

    PubMed

    Ishii, S; Sato, M

    1998-08-01

    In this paper, we discuss analog neural approaches to the quadratic assignment problem (QAP). These approaches employ a hard constraints scheme to restrict the domain space, and are able to obtain much improved solutions over conventional neural approaches. Since only a few strong heuristics for QAP have been known to date, our approaches are good alternatives, capable of obtaining fairly good solutions in a short period of time. Some of them can also be applied to large-scale problems, say of size N>/=300.

  16. A quadratic analog-to-digital converter

    NASA Technical Reports Server (NTRS)

    Harrison, D. C.; Staples, M. H.

    1980-01-01

    An analog-to-digital converter with a square root transfer function has been developed for use with a pair of CCD imaging detectors in the White Light Coronagraph/X-ray XUV Telescope experiment to be flown as part of the Internal Solar Polar Mission. It is shown that in background-noise-limited instrumentation systems a quadratic analog-to-digital converter will allow a maximum dynamic range with a fixed number of data bits. Low power dissipation, moderately fast conversion time, and reliability are achieved in the proposed design using standard components and avoiding nonlinear elements.

  17. A quadratic analog-to-digital converter

    NASA Technical Reports Server (NTRS)

    Harrison, D. C.; Staples, M. H.

    1980-01-01

    An analog-to-digital converter with a square root transfer function has been developed for use with a pair of CCD imaging detectors in the White Light Coronagraph/X-ray XUV Telescope experiment to be flown as part of the Internal Solar Polar Mission. It is shown that in background-noise-limited instrumentation systems a quadratic analog-to-digital converter will allow a maximum dynamic range with a fixed number of data bits. Low power dissipation, moderately fast conversion time, and reliability are achieved in the proposed design using standard components and avoiding nonlinear elements.

  18. Using quadratic simplicial elements for hierarchical approximation and visualization

    NASA Astrophysics Data System (ADS)

    Wiley, David F.; Childs, Henry R.; Hamann, Bernd; Joy, Kenneth I.; Max, Nelson

    2002-03-01

    Best quadratic simplicial spline approximations can be computed, using quadratic Bernstein-Bezier basis functions, by identifying and bisecting simplicial elements with largest errors. Our method begins with an initial triangulation of the domain; a best quadratic spline approximation is computed; errors are computed for all simplices; and simplices of maximal error are subdivided. This process is repeated until a user-specified global error tolerance is met. The initial approximations for the unit square and cube are given by two quadratic triangles and five quadratic tetrahedra, respectively. Our more complex triangulation and approximation method that respects field discontinuities and geometrical features allows us to better approximate data. Data is visualized by using the hierarchy of increasingly better quadratic approximations generated by this process. Many visualization problems arise for quadratic elements. First tessellating quadratic elements with smaller linear ones and then rendering the smaller linear elements is one way to visualize quadratic elements. Our results show a significant reduction in the number of simplices required to approximate data sets when using quadratic elements as compared to using linear elements.

  19. BOB CAT: A Large-Scale Review and Delphi Consensus for Management of Barrett’s Esophagus With No Dysplasia, Indefinite for, or Low-Grade Dysplasia

    PubMed Central

    Bennett, Cathy; Moayyedi, Paul; Corley, Douglas A.; DeCaestecker, John; Falck-Ytter, Yngve; Falk, Gary; Vakil, Nimish; Sanders, Scott; Vieth, Michael; Inadomi, John; Aldulaimi, David; Ho, Khek-Yu; Odze, Robert; Meltzer, Stephen J.; Quigley, Eamonn; Gittens, Stuart; Watson, Peter; Zaninotto, Giovanni; Iyer, Prasad G.; Alexandre, Leo; Ang, Yeng; Callaghan, James; Harrison, Rebecca; Singh, Rajvinder; Bhandari, Pradeep; Bisschops, Raf; Geramizadeh, Bita; Kaye, Philip; Krishnadath, Sheila; Fennerty, M. Brian; Manner, Hendrik; Nason, Katie S.; Pech, Oliver; Konda, Vani; Ragunath, Krish; Rahman, Imdadur; Romero, Yvonne; Sampliner, Richard; Siersema, Peter D.; Tack, Jan; Tham, Tony C.K.; Trudgill, Nigel; Weinberg, David S.; Wang, Jean; Wang, Kenneth; Wong, Jennie Y.Y.; Attwood, Stephen; Malfertheiner, Peter; MacDonald, David; Barr, Hugh; Ferguson, Mark K.; Jankowski, Janusz

    2015-01-01

    OBJECTIVES Barrett’s esophagus (BE) is a common premalignant lesion for which surveillance is recommended. This strategy is limited by considerable variations in clinical practice. We conducted an international, multidisciplinary, systematic search and evidence-based review of BE and provided consensus recommendations for clinical use in patients with nondysplastic, indefinite, and low-grade dysplasia (LGD). METHODS We defined the scope, proposed statements, and searched electronic databases, yielding 20,558 publications that were screened, selected online, and formed the evidence base. We used a Delphi consensus process, with an 80% agreement threshold, using GRADE (Grading of Recommendations Assessment, Development and Evaluation) to categorize the quality of evidence and strength of recommendations. RESULTS In total, 80% of respondents agreed with 55 of 127 statements in the final voting rounds. Population endoscopic screening is not recommended and screening should target only very high-risk cases of males aged over 60 years with chronic uncontrolled reflux. A new international definition of BE was agreed upon. For any degree of dysplasia, at least two specialist gastrointestinal (GI) pathologists are required. Risk factors for cancer include male gender, length of BE, and central obesity. Endoscopic resection should be used for visible, nodular areas. Surveillance is not recommended for <5 years of life expectancy. Management strategies for indefinite dysplasia (IND) and LGD were identified, including a de-escalation strategy for lower-risk patients and escalation to intervention with follow-up for higher-risk patients. CONCLUSIONS In this uniquely large consensus process in gastroenterology, we made key clinical recommendations for the escalation/de-escalation of BE in clinical practice. We made strong recommendations for the prioritization of future research. PMID:25869390

  20. BOB CAT: A Large-Scale Review and Delphi Consensus for Management of Barrett's Esophagus With No Dysplasia, Indefinite for, or Low-Grade Dysplasia.

    PubMed

    Bennett, Cathy; Moayyedi, Paul; Corley, Douglas A; DeCaestecker, John; Falck-Ytter, Yngve; Falk, Gary; Vakil, Nimish; Sanders, Scott; Vieth, Michael; Inadomi, John; Aldulaimi, David; Ho, Khek-Yu; Odze, Robert; Meltzer, Stephen J; Quigley, Eamonn; Gittens, Stuart; Watson, Peter; Zaninotto, Giovanni; Iyer, Prasad G; Alexandre, Leo; Ang, Yeng; Callaghan, James; Harrison, Rebecca; Singh, Rajvinder; Bhandari, Pradeep; Bisschops, Raf; Geramizadeh, Bita; Kaye, Philip; Krishnadath, Sheila; Fennerty, M Brian; Manner, Hendrik; Nason, Katie S; Pech, Oliver; Konda, Vani; Ragunath, Krish; Rahman, Imdadur; Romero, Yvonne; Sampliner, Richard; Siersema, Peter D; Tack, Jan; Tham, Tony C K; Trudgill, Nigel; Weinberg, David S; Wang, Jean; Wang, Kenneth; Wong, Jennie Y Y; Attwood, Stephen; Malfertheiner, Peter; MacDonald, David; Barr, Hugh; Ferguson, Mark K; Jankowski, Janusz

    2015-05-01

    Barrett's esophagus (BE) is a common premalignant lesion for which surveillance is recommended. This strategy is limited by considerable variations in clinical practice. We conducted an international, multidisciplinary, systematic search and evidence-based review of BE and provided consensus recommendations for clinical use in patients with nondysplastic, indefinite, and low-grade dysplasia (LGD). We defined the scope, proposed statements, and searched electronic databases, yielding 20,558 publications that were screened, selected online, and formed the evidence base. We used a Delphi consensus process, with an 80% agreement threshold, using GRADE (Grading of Recommendations Assessment, Development and Evaluation) to categorize the quality of evidence and strength of recommendations. In total, 80% of respondents agreed with 55 of 127 statements in the final voting rounds. Population endoscopic screening is not recommended and screening should target only very high-risk cases of males aged over 60 years with chronic uncontrolled reflux. A new international definition of BE was agreed upon. For any degree of dysplasia, at least two specialist gastrointestinal (GI) pathologists are required. Risk factors for cancer include male gender, length of BE, and central obesity. Endoscopic resection should be used for visible, nodular areas. Surveillance is not recommended for <5 years of life expectancy. Management strategies for indefinite dysplasia (IND) and LGD were identified, including a de-escalation strategy for lower-risk patients and escalation to intervention with follow-up for higher-risk patients. In this uniquely large consensus process in gastroenterology, we made key clinical recommendations for the escalation/de-escalation of BE in clinical practice. We made strong recommendations for the prioritization of future research.

  1. Some Randomized Algorithms for Convex Quadratic Programming

    SciTech Connect

    Goldbach, R.

    1999-01-15

    We adapt some randomized algorithms of Clarkson [3] for linear programming to the framework of so-called LP-type problems, which was introduced by Sharir and Welzl [10]. This framework is quite general and allows a unified and elegant presentation and analysis. We also show that LP-type problems include minimization of a convex quadratic function subject to convex quadratic constraints as a special case, for which the algorithms can be implemented efficiently, if only linear constraints are present. We show that the expected running times depend only linearly on the number of constraints, and illustrate this by some numerical results. Even though the framework of LP-type problems may appear rather abstract at first, application of the methods considered in this paper to a given problem of that type is easy and efficient. Moreover, our proofs are in fact rather simple, since many technical details of more explicit problem representations are handled in a uniform manner by our approach. In particular, we do not assume boundedness of the feasible set as required in related methods.

  2. Homogeneous systems with quadratic integrals, Lie-Poisson quasibrackets, and Kovalevskaya's method

    NASA Astrophysics Data System (ADS)

    Bizyaev, I. A.; Kozlov, V. V.

    2015-12-01

    We consider differential equations with quadratic right-hand sides that admit two quadratic first integrals, one of which is a positive-definite quadratic form. We indicate conditions of general nature under which a linear change of variables reduces this system to a certain 'canonical' form. Under these conditions, the system turns out to be divergenceless and can be reduced to a Hamiltonian form, but the corresponding linear Lie-Poisson bracket does not always satisfy the Jacobi identity. In the three-dimensional case, the equations can be reduced to the classical equations of the Euler top, and in four-dimensional space, the system turns out to be superintegrable and coincides with the Euler-Poincaré equations on some Lie algebra. In the five-dimensional case we find a reducing multiplier after multiplying by which the Poisson bracket satisfies the Jacobi identity. In the general case for n>5 we prove the absence of a reducing multiplier. As an example we consider a system of Lotka-Volterra type with quadratic right-hand sides that was studied by Kovalevskaya from the viewpoint of conditions of uniqueness of its solutions as functions of complex time. Bibliography: 38 titles.

  3. Frequency weighted system identification and linear quadratic controller design

    NASA Technical Reports Server (NTRS)

    Horta, Lucas G.; Phan, Minh; Juang, Jer-Nan; Longman, Richard W.; Sulla, Jeffrey L.

    1991-01-01

    Application of filters for frequency weighting of Markov parameters (pulse response functions) is described in relation to system/observer identification. The time domain identification approach recovers a model which has a pulse response weighted according to frequency. The identified model is composed of the original system and filters. The augmented system is in a form which can be used directly for frequency weighted linear quadratic controller design. Data from either single or multiple experiments can be used to recover the Markov parameters. Measured acceleration signals from a truss structure are used for system identification and the model obtained is used for frequency weighted controller design. The procedure makes the identification and controler design complementary problems.

  4. Design and analysis of constrained nonlinear quadratic regulator.

    PubMed

    Ding, BaoCang; Li, ShaoYuan

    2003-04-01

    A suboptimal dual-mode solution to constrained nonlinear quadratic regulator (CNLQR) problem is studied. In a neighborhood of the origin, the controller is formulated as an LQR based on a model obtained by linearizing the original model at the origin. Outside this neighborhood, the control law is obtained by solving a finite horizon optimization problem (FHOP) with additional terminal inequality constraints. The terminal inequality constraints make the terminal states of FHOP be driven into the neighborhood of the origin, which is a specially designed control invariant set with respect to LQR control law. The overall control law is obtained by combining that obtained by solving FHOP and that obtained form LQR. The feasibility aspect is analyzed and asymptotic stability is proven. The effectiveness of this suboptimal controller is demonstrated by simulation studies.

  5. Quadratic trigonometric B-spline for image interpolation using GA

    PubMed Central

    Abbas, Samreen; Irshad, Misbah

    2017-01-01

    In this article, a new quadratic trigonometric B-spline with control parameters is constructed to address the problems related to two dimensional digital image interpolation. The newly constructed spline is then used to design an image interpolation scheme together with one of the soft computing techniques named as Genetic Algorithm (GA). The idea of GA has been formed to optimize the control parameters in the description of newly constructed spline. The Feature SIMilarity (FSIM), Structure SIMilarity (SSIM) and Multi-Scale Structure SIMilarity (MS-SSIM) indices along with traditional Peak Signal-to-Noise Ratio (PSNR) are employed as image quality metrics to analyze and compare the outcomes of approach offered in this work, with three of the present digital image interpolation schemes. The upshots show that the proposed scheme is better choice to deal with the problems associated to image interpolation. PMID:28640906

  6. A quadratic pulse height analyzer for space applications.

    NASA Technical Reports Server (NTRS)

    Burtis, D. W.; Aalami, D.; Evelyn-Veere, R. H.; Sarkady, A. A.

    1972-01-01

    A flight-worthy pulse height analyzer that has a quadratic transfer function is described. This quadratic function permits optimum usage of the entire PHA dynamic range due to the quadratic nature of the gamma ray spectrometer's resolution vs energy. After the theoretical design discussion, the implementation of the design is examined and test results described. The analyzer is part of the University of New Hampshire gamma ray monitor for OSO-H.

  7. A Mathematics Classroom for the Twenty-First Century: Exploring the Complete Story of Turning Points of Quadratics.

    ERIC Educational Resources Information Center

    Olmstead, Eugene

    1995-01-01

    Explores quadratic functions using the graphing calculator. Discoveries are made graphically whereas hypotheses are proven algebraically. Includes traditional quadratics, other algebraic quadratics, nonpolynomial quadratics, transcendental quadratics, and proofs. (MKR)

  8. Existence of nontrivial solution for Schrödinger-Poisson systems with indefinite steep potential well

    NASA Astrophysics Data System (ADS)

    Sun, Juntao; Wu, Tsung-Fang; Wu, Yuanze

    2017-06-01

    In this paper, we study a class of nonlinear Schrödinger-Poisson systems with indefinite steep potential well: -Δ u+V_{λ }(x)u+K(x)φ u=|u|^{p-2}u in R3, -Δ φ =K( x) u2 in R3, where 30 and K(x)≥ 0 for all x\\in R3. We require that a\\in C( R3) is nonnegative and has a potential well Ω a, namely a(x)≡ 0 for x\\in Ω a and a(x)>0 for x\\in R3\\setminus \\overline{Ω a}. Unlike most other papers on this problem, we allow that b\\in C(R3) is unbounded below and sign-changing. By introducing some new hypotheses on the potentials and applying the method of penalized functions, we obtain the existence of nontrivial solutions for λ sufficiently large. Furthermore, the concentration behavior of the nontrivial solution is also described as λ → ∞.

  9. Tailored loss discrimination in indefinite metamaterial-clad hollow-core fibers.

    PubMed

    Tuniz, Alessandro; Zeisberger, Matthias; Schmidt, Markus A

    2016-07-11

    We analyze the modal attenuation properties of silica hollow-core fibers with a gold-wire based indefinite metamaterial cladding at 10.6 µm. We find that by varying the metamaterial feature sizes and core diameter, the loss discrimination can be tailored such that either the HE11, TE01 or TM01 mode has the lowest loss, which is particularly difficult to achieve for the radially polarized mode in commonly used hollow-core fibers. Furthermore, it is possible to tailor the HE11 and TM01 modes in the metamaterial-clad waveguide so that they possess attenuations lower than in hollow tubes composed of the individual constituent materials. We show that S-parameter retrieval techniques in combination with an anisotropic dispersion equation can be used to predict the loss discrimination properties of such fibers. These results pave the way for the design of metamaterial hollow-core fibers with novel guidance properties, in particular for applications demanding cylindrically polarized modes.

  10. The medium is NOT the message or Indefinitely long-term file storage at Leeds University

    NASA Technical Reports Server (NTRS)

    Holdsworth, David

    1996-01-01

    Approximately 3 years ago we implemented an archive file storage system which embodies experiences gained over more than 25 years of using and writing file storage systems. It is the third in-house system that we have written, and all three systems have been adopted by other institutions. This paper discusses the requirements for long-term data storage in a university environment, and describes how our present system is designed to meet these requirements indefinitely. Particular emphasis is laid on experiences from past systems, and their influence on current system design. We also look at the influence of the IEEE-MSS standard. We currently have the system operating in five UK universities. The system operates in a multi-server environment, and is currently operational with UNIX (SunOS4, Solaris2, SGI-IRIX, HP-UX), NetWare3 and NetWare4. PCs logged on to NetWare can also archive and recover files that live on their hard disks.

  11. Toda lattices with indefinite metric II: Topology of the iso-spectral manifolds

    NASA Astrophysics Data System (ADS)

    Kodama, Yuji; Ye, Jian

    1998-10-01

    We consider the iso-spectral real manifolds of tridiagonal Hessenberg matrices with distinct real eigenvalues. The manifolds are described by the iso-spectral flows of indefinite Toda lattice equations introduced by the authors [Physica D 91 (1996) 321-339]. These Toda lattices consist of 2 N-1 different systems with hamiltonians H = {1}/{2} Σ k=1N y k2 + Σ k=1N-1 s ks k+1exp(x k-x k+1) , where sk = ±1, which blow up in finite time except the case with all sksk+1 = 1. We compactify the manifolds by adding infinities according to the Toda flows. The resulting manifolds are shown to be nonorientable for N > 2, and the symmetry group is the semi-direct product of ( Z2) N-1 and the permutation group S n. These properties identify themselves with “small covers” introduced by Davis and Januszkiewicz [Duke Math. J. 62 (1991) 417-451]. As a corollary of our construction, we give a formula for the total number of zeros for a system of exponential polynomials generated as Hankel determinants.

  12. Clinical significance and management of Barrett's esophagus with epithelial changes indefinite for dysplasia.

    PubMed

    Thota, Prashanthi N; Kistangari, Gaurav; Esnakula, Ashwini K; Gonzalo, David Hernandez; Liu, Xiu-Li

    2016-08-06

    Barrett's esophagus (BE) is defined as the extension of salmon-colored mucosa into the tubular esophagus ≥ 1 cm proximal to the gastroesophageal junction with biopsy confirmation of intestinal metaplasia. Patients with BE are at increased risk of esophageal adenocarcinoma (EAC), and undergo endoscopic surveillance biopsies to detect dysplasia or early EAC. Dysplasia in BE is classified as no dysplasia, indefinite for dysplasia (IND), low grade dysplasia (LGD) or high grade dysplasia (HGD). Biopsies are diagnosed as IND when the epithelial abnormalities are not sufficient to diagnose dysplasia or the nature of the epithelial abnormalities is uncertain due to inflammation or technical issues. Specific diagnostic criteria for IND are not well established and its clinical significance and management has not been well studied. Previous studies have focused on HGD in BE and led to changes and improvement in the management of BE with HGD and early EAC. Only recently, IND and LGD in BE have become focus of intense study. This review summarizes the definition, neoplastic risk and clinical management of BE IND.

  13. Clinical significance and management of Barrett’s esophagus with epithelial changes indefinite for dysplasia

    PubMed Central

    Thota, Prashanthi N; Kistangari, Gaurav; Esnakula, Ashwini K; Gonzalo, David Hernandez; Liu, Xiu-Li

    2016-01-01

    Barrett’s esophagus (BE) is defined as the extension of salmon-colored mucosa into the tubular esophagus ≥ 1 cm proximal to the gastroesophageal junction with biopsy confirmation of intestinal metaplasia. Patients with BE are at increased risk of esophageal adenocarcinoma (EAC), and undergo endoscopic surveillance biopsies to detect dysplasia or early EAC. Dysplasia in BE is classified as no dysplasia, indefinite for dysplasia (IND), low grade dysplasia (LGD) or high grade dysplasia (HGD). Biopsies are diagnosed as IND when the epithelial abnormalities are not sufficient to diagnose dysplasia or the nature of the epithelial abnormalities is uncertain due to inflammation or technical issues. Specific diagnostic criteria for IND are not well established and its clinical significance and management has not been well studied. Previous studies have focused on HGD in BE and led to changes and improvement in the management of BE with HGD and early EAC. Only recently, IND and LGD in BE have become focus of intense study. This review summarizes the definition, neoplastic risk and clinical management of BE IND. PMID:27602241

  14. Steller Structure Treatment of Quadratic Gravity

    NASA Astrophysics Data System (ADS)

    Chen, Y.; Shao, C.; Chen, X.

    2001-07-01

    A scheme for considering stellar structure by taking advantage of the quadratic theory of gravitation in four-dimensions is proposed, citing the fact that the possible deviation of gravity in astrophysical systems from the Newtonian inverse square law can be explained through the use of this theory. A modified Lane-Emden equation is derived by making use of the linearized static field equation of quadratic gravity and the polytropic equation of state for a fluid. The influence on stellar structure of the additional force included in quadratic gravity is investigated. It is shown that the additional force can be treated as a perturbation of a bound system by solutions of the modified Lane-Emden equation and an order-of-magnitude analysis. %ZY. Fujii, Nature (London) 234 (1971), 5; Phys. Rev. D9 (1974), 874. D. R. Long, Phys. Rev. D 9 (1974), 850. J. O'Hanlon, Phys. Rev. Lett. 29 (1972), 137. D. R. Mikkelson and M. J. Newman, Phys. Rev. D 16 (1977), 919. R. V. Wagoner, Phys. Rev. D 1 (1970), 3209. J. Z. Xu and Y. H. Chen, Gen. Relat. Gravit. J. 23 (1991), 169. K. S. Stelle, Gen. Relat. Gravit. J. 8 (1978), 631. C. Xu and G. F. R. Ellis, Class. Quant. Grav. 8 (1991), 1747. A. Eddington, The Mathematical Theory of Relativity, 2nd ed. (Cambridge University Press, Cambridge, 1924). W. Pauli, Theory of Relativity (Pergamon Press, New York, 1921). H. A. Buchdahl, Proc. Edinburgh Math. Soc. 8 (1948), 89. J. D. Barrow and A. C. Ottewill, J. of Phys. A 16 (1983), 2757. M. B. Mijic, M. S. Morris and W. M. Suen, Phys. Rev. D 34 (1986), 2934. A. L. Berkin, Phys. Rev. D 42 (1990), 1017. N. D. Birrell and P. C. W. Davies, Quantum Field in Curved Space (Cambridge University Press, 1982). E. T. Tomboulis, Quantum Theory of Gravity, ed. S. M. Christensen (Bristol: Adam Hilger 1984). H. J. Treder, Ann. der Phys. 32 (1975), 383. S. Weinberg, Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (Wiley, New York 1972). E. N. Glass and G. Szamosi

  15. A note on the fundamental unit in some types of the real quadratic number fields

    NASA Astrophysics Data System (ADS)

    Özer, Ö.

    2016-10-01

    Let k =Q (√{d }) be a real quadratic numbefield where d > 0 is a positive square-free integer. The map d →Q (√{d }) is a bijection from the set off all square-free integers d ≠ 0, 1 to the set of all quadratic fields Q (√{d })={ x +y √{d }|x ,y ∈Q } . Furthermore, integral basis element of algebraic integer's ring in real quadratic fields is determined by either wd=√{d }=[ a0;a1,a2,⋯,aℓ (d)-1,2 a0 ¯ ] in the case of d ≡ 2,3(mod 4) or wd=1/+√{d } 2 =[ a0;a1,a2,⋯,aℓ (d)-1,2 a0-1 ¯ ] in the case of d ≡ 1(mod 4) where ℓ (d ) is the period length of continued fraction expansion. The purpose of this paper is to obtain classification of some types of real quadratic fields Q (√{d }) , which include the specific form of continued fraction expansion of integral basis element wd, for which has all partial quotient elements are equal to each other and written as ξs (except the last digit of the period) for ξ positive even integer where period length is ℓ =ℓ (d ) and d ≡ 2,3(mod 4) is a square free positive integer. Moreover, the present paper deals with determining new certain parametric formula of fundamental unit ɛd=t/d+ud√{d } 2 >1 with norm N (ɛd)=(-1) ℓ (d ) for such types of real quadratic fields. Besides, Yokoi's d-invariants nd and md in the relation to continued fraction expansion of wd are calculated by using coefficients of fundamental unit. All supported results are given in numerical tables. These new results and tables are not known in the literature of real quadratic fields.

  16. Forced oscillations in quadratically damped systems

    NASA Technical Reports Server (NTRS)

    Bayliss, A.

    1978-01-01

    Bayliss (1975) has studied the question whether in the case of linear differential equations the relationship between the stability of the homogeneous equations and the existence of almost periodic solutions to the inhomogeneous equation is preserved by finite difference approximations. In the current investigation analogous properties are considered for the case in which the damping is quadratic rather than linear. The properties of the considered equation for arbitrary forcing terms are examined and the validity is proved of a theorem concerning the characteristics of the unique solution. By using the Lipschitz continuity of the mapping and the contracting mapping principle, almost periodic solutions can be found for perturbations of the considered equation. Attention is also given to the Lipschitz continuity of the solution operator and the results of numerical tests which have been conducted to test the discussed theory.

  17. Digital image restoration using quadratic programming.

    PubMed

    Abdelmalek, N N; Kasvand, T

    1980-10-01

    The problem of digital image restoration is considered by obtaining an approximate solution to the Fredholm integral equation of the first kind in two variables. The system of linear equations resulting from the discretization of the integral equation is converted to a consistent system of linear equations. The problem is then solved as a quadratic programming problem with bounded variables where the unknown solution is minimized in the L(2) norm. In this method minimum computer storage is needed, and the repeated solutions are obtained in an efficient way. Also the rank of the consistent system which gives a best or near best solution is estimated. Computer simulated examples using spatially separable pointspread functions are presented. Comments and conclusion are given.

  18. On Coupled Rate Equations with Quadratic Nonlinearities

    PubMed Central

    Montroll, Elliott W.

    1972-01-01

    Rate equations with quadratic nonlinearities appear in many fields, such as chemical kinetics, population dynamics, transport theory, hydrodynamics, etc. Such equations, which may arise from basic principles or which may be phenomenological, are generally solved by linearization and application of perturbation theory. Here, a somewhat different strategy is emphasized. Alternative nonlinear models that can be solved exactly and whose solutions have the qualitative character expected from the original equations are first searched for. Then, the original equations are treated as perturbations of those of the solvable model. Hence, the function of the perturbation theory is to improve numerical accuracy of solutions, rather than to furnish the basic qualitative behavior of the solutions of the equations. PMID:16592013

  19. Security analysis of quadratic phase based cryptography

    NASA Astrophysics Data System (ADS)

    Muniraj, Inbarasan; Guo, Changliang; Malallah, Ra'ed; Healy, John J.; Sheridan, John T.

    2016-09-01

    The linear canonical transform (LCT) is essential in modeling a coherent light field propagation through first-order optical systems. Recently, a generic optical system, known as a Quadratic Phase Encoding System (QPES), for encrypting a two-dimensional (2D) image has been reported. It has been reported together with two phase keys the individual LCT parameters serve as keys of the cryptosystem. However, it is important that such the encryption systems also satisfies some dynamic security properties. Therefore, in this work, we examine some cryptographic evaluation methods, such as Avalanche Criterion and Bit Independence, which indicates the degree of security of the cryptographic algorithms on QPES. We compare our simulation results with the conventional Fourier and the Fresnel transform based DRPE systems. The results show that the LCT based DRPE has an excellent avalanche and bit independence characteristics than that of using the conventional Fourier and Fresnel based encryption systems.

  20. Mammogram enhancement using alpha weighted quadratic filter.

    PubMed

    Zhou, Yicong; Panetta, Karen; Agaian, Sos

    2009-01-01

    Mammograms are widely used to detect breast cancer in women. The quality of the image may suffer from poor resolution or low contrast due to the limitations of the X-ray hardware systems. Image enhancement is a powerful tool to improve the visual quality of mammograms. This paper introduces a new powerful nonlinear filter called the alpha weighted quadratic filter for mammogram enhancement. The user has the flexibility to design the filter by selecting all of the parameters manually or using an existing quantitative measure to select the optimal enhancement parameters. Computer simulations show that excellent enhancement results can be obtained with no apriori knowledge of the mammogram contents. The filter can also be used for automatic segmentation.

  1. A note on quasi-generalized CR-lightlike geometry in indefinite nearly μ-Sasakian manifolds

    NASA Astrophysics Data System (ADS)

    Massamba, Fortuné; Ssekajja, Samuel

    The concept of quasi-generalized CR-lightlike was first introduced by the authors in [Quasi generalized CR-lightlike submanifolds of indefinite nearly Sasakian manifolds, Arab. J. Math. 5 (2016) 87-101]. In this paper, we focus on ascreen and co-screen quasi-generalized CR-lightlike submanifolds of indefinite nearly μ-Sasakian manifold. We prove an existence theorem for minimal ascreen quasi-generalized CR-lightlike submanifolds admitting a metric connection. Classification theorems on nearly parallel and auto-parallel distributions on a co-screen quasi-generalized CR-lightlike submanifold are also given. Several examples are also constructed, where necessary, to illustrate the main ideas.

  2. Spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity

    SciTech Connect

    Golubkov, A A; Makarov, Vladimir A

    2011-11-30

    We present a brief review of the results of fifty years of development efforts in spectroscopy of one-dimensionally inhomogeneous media with quadratic nonlinearity. The recent original results obtained by the authors show the fundamental possibility of determining, from experimental data, the coordinate dependences of complex quadratic susceptibility tensor components of a onedimensionally inhomogeneous (along the z axis) medium with an arbitrary frequency dispersion, if the linear dielectric properties of the medium also vary along the z axis and are described by a diagonal tensor of the linear dielectric constant. It is assumed that the medium in question has the form of a plane-parallel plate, whose surfaces are perpendicular to the direction of the inhomogeneity. Using the example of several components of the tensors X{sup (2)}(z, {omega}{sub 1} {+-} {omega}{sub 2}; {omega}{sub 1}, {+-} {omega}{sub 2}), we describe two methods for finding their spatial profiles, which differ in the interaction geometry of plane monochromatic fundamental waves with frequencies {omega}{sub 1} and {omega}{sub 2}. The both methods are based on assessing the intensity of the waves propagating from the plate at the sum or difference frequency and require measurements over a range of angles of incidence of the fundamental waves. Such measurements include two series of additional estimates of the intensities of the waves generated under special conditions by using the test and additional reference plates, which eliminates the need for complicated phase measurements of the complex amplitudes of the waves at the sum (difference) frequency.

  3. Potential harms outweigh benefits of indefinite monitoring of stable adnexal masses.

    PubMed

    Suh-Burgmann, Elizabeth; Kinney, Walter

    2015-12-01

    The management of women with asymptomatic adnexal masses should aim to balance potential benefit with potential harm. While masses with highly worrisome features or other signs of malignancy should be referred for surgery, the vast majority of masses have an indeterminate or benign appearance and are candidates for observation. Evidence supports the use of initial short-term serial ultrasound in distinguishing between benign and malignant masses. However, benefit from prolonged, potentially life-long monitoring of stable masses has not been demonstrated. Since the goal of monitoring an adnexal mass is to observe for worrisome growth or increasing complexity as an indicator of malignancy, if the mass remains stable, the likelihood of malignancy and therefore, the potential benefit of observation wanes with time. The recognition that Type 2 high grade serous cancers, which are responsible for the majority of deaths from ovarian cancer, arise from fallopian tube rather than ovarian precursors, further diminishes the likelihood that monitoring a stable ovarian mass will lead to early diagnosis of high grade disease. While some Type 1 cancers may develop from ovarian precursors, the available data suggest that any measurable benefit of monitoring known lesions for detection of these cancers is realized within the first year of observation. The argument in favor of indefinite, potentially life-long monitoring of stable masses also fails to adequately account for the risks of perpetual imaging, which include the risk of incidental findings, an increased likelihood of unnecessary surgery, patient anxiety and cost. It is not always better to order a test than not order a test. Given the absence of evidence of benefit, observation of stable small adnexal masses should be limited in duration in order to minimize potential harms. Copyright © 2015 Elsevier Inc. All rights reserved.

  4. Indefinite for non‐invasive neoplasia lesions in gastric intestinal metaplasia: the immunophenotype

    PubMed Central

    Mauro Cassaro; Rugge, Massimo; Tieppo, Chiara; Giacomelli, Luciano; Velo, Daniela; Nitti, Donato

    2007-01-01

    Background In the Padova International Classification, gastric precancerous lesions are labelled as “indefinite for non‐invasive neoplasia” (Indef‐NiN) cytohistological alterations mimicking non‐invasive neoplasia (NiN), but lacking all the attributes required for a definite NiN categorisation. Aim To apply a panel of immunohistochemical (IHC) markers of cell proliferation (Mib1), intestinal differentiation (Cdx2), apoptosis (pro‐caspase 3) and cell immortalisation (hTERT) to compare the IHC profiles of a series of precancerous lesions arising in gastric intestinalised (ie, IM‐positive) glands. Materials and methods By applying the histological criteria consistently provided by both the Padova Classification and the World Health Organization International Agency, 112 consecutive cases were considered: intestinal metaplasia (IM; n = 54), Indef‐NiN in IM‐positive gastric glands (n = 28) and low‐grade (LG) NiN (n = 30). In each histological category, the expression of the marker was separately scored in superficial, proliferative and coil compartments. Results In all glandular compartments, Mib1, Cdx2, hTERT and pro‐caspase 3 were consistently more expressed in LG‐NiN than in either IM or Indef‐NiN lesions (analysis of variance: p<0.001). Significant ORs (calculated by ordinal logistic regression analysis for each glandular compartment) associated IM, Indef‐NiN and LG‐NiN with the expression of the considered markers. Conclusions A consistent overexpression (unrestricted to the proliferative zone) of IHC markers of cell proliferation, intestinal differentiation, decreased apoptosis and cell immortalisation differentiates LG‐NiN from both (simple) IM and Indef‐NiN (arising in IM). An increased proliferative activity in the proliferative zone discriminates Indef‐NiN lesions (ie, hyperproliferative IM) from IM. Such divergent IHC profiles may provide a rationale for scheduling follow‐up protocols more properly tailored on

  5. Sketching the General Quadratic Equation Using Dynamic Geometry Software

    ERIC Educational Resources Information Center

    Stols, G. H.

    2005-01-01

    This paper explores a geometrical way to sketch graphs of the general quadratic in two variables with Geometer's Sketchpad. To do this, a geometric procedure as described by De Temple is used, bearing in mind that this general quadratic equation (1) represents all the possible conics (conics sections), and the fact that five points (no three of…

  6. Mixed-Integer Nonconvex Quadratic Optimization Relaxations and Performance Analysis

    DTIC Science & Technology

    2015-09-14

    problem as a cardinality constrained quadratic program and study its computational complexity. Furthermore, we develop novel semi - definite relaxation (SDR...each application scenario, we first characterize the computational complexity of the joint optimization problem, and then propose novel semi - definite ...cardinality constrained quadratic programs ( QP ) and the low rank matrix completion problems. The project addresses a fundamental question regarding the

  7. Visualising the Roots of Quadratic Equations with Complex Coefficients

    ERIC Educational Resources Information Center

    Bardell, Nicholas S.

    2014-01-01

    This paper is a natural extension of the root visualisation techniques first presented by Bardell (2012) for quadratic equations with real coefficients. Consideration is now given to the familiar quadratic equation "y = ax[superscript 2] + bx + c" in which the coefficients "a," "b," "c" are generally…

  8. Sketching the General Quadratic Equation Using Dynamic Geometry Software

    ERIC Educational Resources Information Center

    Stols, G. H.

    2005-01-01

    This paper explores a geometrical way to sketch graphs of the general quadratic in two variables with Geometer's Sketchpad. To do this, a geometric procedure as described by De Temple is used, bearing in mind that this general quadratic equation (1) represents all the possible conics (conics sections), and the fact that five points (no three of…

  9. Convexity preserving C2 rational quadratic trigonometric spline

    NASA Astrophysics Data System (ADS)

    Dube, Mridula; Tiwari, Preeti

    2012-09-01

    A C2 rational quadratic trigonometric spline interpolation has been studied using two kind of rational quadratic trigonometric splines. It is shown that under some natural conditions the solution of the problem exits and is unique. The necessary and sufficient condition that constrain the interpolation curves to be convex in the interpolating interval or subinterval are derived.

  10. Tangent Lines without Derivatives for Quadratic and Cubic Equations

    ERIC Educational Resources Information Center

    Carroll, William J.

    2009-01-01

    In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)

  11. Geometric quadratic stochastic operator on countable infinite set

    SciTech Connect

    Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar

    2015-02-03

    In this paper we construct the family of Geometric quadratic stochastic operators defined on the countable sample space of nonnegative integers and investigate their trajectory behavior. Such operators can be reinterpreted in terms of of evolutionary operator of free population. We show that Geometric quadratic stochastic operators are regular transformations.

  12. A Constructive Transition from Linear to Quadratic Functions.

    ERIC Educational Resources Information Center

    Movshovitz-Hadar, Nitsa

    1993-01-01

    Presents an approach to quadratic functions that draws upon knowledge of linear functions by looking at the product of two linear functions. Then considers the quadratic function as the sum of three monomials. Potential advantages of each approach are discussed. (Contains 17 references.) (MDH)

  13. Tangent Lines without Derivatives for Quadratic and Cubic Equations

    ERIC Educational Resources Information Center

    Carroll, William J.

    2009-01-01

    In the quadratic equation, y = ax[superscript 2] + bx + c, the equation y = bx + c is identified as the equation of the line tangent to the parabola at its y-intercept. This is extended to give a convenient method of graphing tangent lines at any point on the graph of a quadratic or a cubic equation. (Contains 5 figures.)

  14. Mixed-Integer Nonconvex Quadratic Optimization Relaxations and Performance Analysis

    DTIC Science & Technology

    2016-10-11

    constrained quadratic programs, and the matrix completion problems with non-convex regularity. The project addresses a fundamental question how to...efficiently solve these problems, such as to find a provably high quality approximate solution or to fast find a local solution with probable structure ...applications in optimal and dynamic resource management, cardinality constrained quadratic programs, and the matrix completion problems with non

  15. Some Paradoxical Results for the Quadratically Weighted Kappa

    ERIC Educational Resources Information Center

    Warrens, Matthijs J.

    2012-01-01

    The quadratically weighted kappa is the most commonly used weighted kappa statistic for summarizing interrater agreement on an ordinal scale. The paper presents several properties of the quadratically weighted kappa that are paradoxical. For agreement tables with an odd number of categories "n" it is shown that if one of the raters uses the same…

  16. Novikov algebras with associative bilinear forms

    NASA Astrophysics Data System (ADS)

    Zhu, Fuhai; Chen, Zhiqi

    2007-11-01

    Novikov algebras were introduced in connection with the Poisson brackets of hydrodynamic-type and Hamiltonian operators in formal variational calculus. The goal of this paper is to study Novikov algebras with non-degenerate associative symmetric bilinear forms, which we call quadratic Novikov algebras. Based on the classification of solvable quadratic Lie algebras of dimension not greater than 4 and Novikov algebras in dimension 3, we show that quadratic Novikov algebras up to dimension 4 are commutative. Furthermore, we obtain the classification of transitive quadratic Novikov algebras in dimension 4. But we find that not every quadratic Novikov algebra is commutative and give a non-commutative quadratic Novikov algebra in dimension 6.

  17. Local classifier weighting by quadratic programming.

    PubMed

    Cevikalp, Hakan; Polikar, Robi

    2008-10-01

    It has been widely accepted that the classification accuracy can be improved by combining outputs of multiple classifiers. However, how to combine multiple classifiers with various (potentially conflicting) decisions is still an open problem. A rich collection of classifier combination procedures -- many of which are heuristic in nature -- have been developed for this goal. In this brief, we describe a dynamic approach to combine classifiers that have expertise in different regions of the input space. To this end, we use local classifier accuracy estimates to weight classifier outputs. Specifically, we estimate local recognition accuracies of classifiers near a query sample by utilizing its nearest neighbors, and then use these estimates to find the best weights of classifiers to label the query. The problem is formulated as a convex quadratic optimization problem, which returns optimal nonnegative classifier weights with respect to the chosen objective function, and the weights ensure that locally most accurate classifiers are weighted more heavily for labeling the query sample. Experimental results on several data sets indicate that the proposed weighting scheme outperforms other popular classifier combination schemes, particularly on problems with complex decision boundaries. Hence, the results indicate that local classification-accuracy-based combination techniques are well suited for decision making when the classifiers are trained by focusing on different regions of the input space.

  18. Extremal Optimization for Quadratic Unconstrained Binary Problems

    NASA Astrophysics Data System (ADS)

    Boettcher, S.

    We present an implementation of τ-EO for quadratic unconstrained binary optimization (QUBO) problems. To this end, we transform modify QUBO from its conventional Boolean presentation into a spin glass with a random external field on each site. These fields tend to be rather large compared to the typical coupling, presenting EO with a challenging two-scale problem, exploring smaller differences in couplings effectively while sufficiently aligning with those strong external fields. However, we also find a simple solution to that problem that indicates that those external fields apparently tilt the energy landscape to a such a degree such that global minima become more easy to find than those of spin glasses without (or very small) fields. We explore the impact of the weight distribution of the QUBO formulation in the operations research literature and analyze their meaning in a spin-glass language. This is significant because QUBO problems are considered among the main contenders for NP-hard problems that could be solved efficiently on a quantum computer such as D-Wave.

  19. Linear quadratic regulator for laser beam shaping

    NASA Astrophysics Data System (ADS)

    Escárate, Pedro; Agüero, Juan C.; Zúñiga, Sebastián; Castro, Mario; Garcés, Javier

    2017-07-01

    The performance of an adaptive optics system depends on multiple factors, including the quality of the laser beam before being projected to the mesosphere. In general, cumbersome procedures are required to optimize the laser beam in terms of amplitude and phase. However, aberrations produced by the optics of the laser beam system are still detected during the operations due to, for example, uncertainty in the utilized models. In this paper we propose the use of feedback to overcome the presence of model uncertainty and disturbances. In particular we use a Linear Quadratic Regulator (LQR) for closed loop laser beam shaping using a setup of two deformable mirrors. The proposed method is studied and simulated to provide an automatic optimization of the Amplitude of the laser beam. The performance of the LQR control algorithm is evaluated via numerical simulations using the root mean square error (RMSE). The results show an effective amplitude correction of the laser system aberrations after 20 iterations of the algorithm, a RMSE less than 0.7 was obtained, with about 140 actuators per mirror and a separation of z=3 [m] among the mirrors.

  20. Approximate Graph Edit Distance in Quadratic Time.

    PubMed

    Riesen, Kaspar; Ferrer, Miquel; Bunke, Horst

    2015-09-14

    Graph edit distance is one of the most flexible and general graph matching models available. The major drawback of graph edit distance, however, is its computational complexity that restricts its applicability to graphs of rather small size. Recently the authors of the present paper introduced a general approximation framework for the graph edit distance problem. The basic idea of this specific algorithm is to first compute an optimal assignment of independent local graph structures (including substitutions, deletions, and insertions of nodes and edges). This optimal assignment is complete and consistent with respect to the involved nodes of both graphs and can thus be used to instantly derive an admissible (yet suboptimal) solution for the original graph edit distance problem in O(n3) time. For large scale graphs or graph sets, however, the cubic time complexity may still be too high. Therefore, we propose to use suboptimal algorithms with quadratic rather than cubic time for solving the basic assignment problem. In particular, the present paper introduces five different greedy assignment algorithms in the context of graph edit distance approximation. In an experimental evaluation we show that these methods have great potential for further speeding up the computation of graph edit distance while the approximated distances remain sufficiently accurate for graph based pattern classification.

  1. A Quadratic Closure for Compressible Turbulence

    SciTech Connect

    Futterman, J A

    2008-09-16

    We have investigated a one-point closure model for compressible turbulence based on third- and higher order cumulant discard for systems undergoing rapid deformation, such as might occur downstream of a shock or other discontinuity. In so doing, we find the lowest order contributions of turbulence to the mean flow, which lead to criteria for Adaptive Mesh Refinement. Rapid distortion theory (RDT) as originally applied by Herring closes the turbulence hierarchy of moment equations by discarding third order and higher cumulants. This is similar to the fourth-order cumulant discard hypothesis of Millionshchikov, except that the Millionshchikov hypothesis was taken to apply to incompressible homogeneous isotropic turbulence generally, whereas RDT is applied only to fluids undergoing a distortion that is 'rapid' in the sense that the interaction of the mean flow with the turbulence overwhelms the interaction of the turbulence with itself. It is also similar to Gaussian closure, in which both second and fourth-order cumulants are retained. Motivated by RDT, we develop a quadratic one-point closure for rapidly distorting compressible turbulence, without regard to homogeneity or isotropy, and make contact with two equation turbulence models, especially the K-{var_epsilon} and K-L models, and with linear instability growth. In the end, we arrive at criteria for Adaptive Mesh Refinement in Finite Volume simulations.

  2. On the time evolution operator for time-dependent quadratic Hamiltonians

    SciTech Connect

    Fernandez, F. M.

    1989-07-01

    The Schr/umlt o/dinger equation with a time-dependent quadratic Hamiltonian isinvestigated. The time-evolution operator is written as a product of exponentialoperators determined by the Heisenberg equations of motion. This productoperator is shown to be global in the occupation number representation when theHamiltonian is Hermitian. The success of some physical applications of theproduct-form representation is explained.

  3. Classification of constraints and degrees of freedom for quadratic discrete actions

    SciTech Connect

    Höhn, Philipp A.

    2014-11-15

    We provide a comprehensive classification of constraints and degrees of freedom for variational discrete systems governed by quadratic actions. This classification is based on the different types of null vectors of the Lagrangian two-form and employs the canonical formalism developed in Dittrich and Höhn [“Constraint analysis for variational discrete systems,” J. Math. Phys. 54, 093505 (2013); e-print http://arxiv.org/abs/arXiv:1303.4294 [math-ph

  4. Degenerate nonlinear programming with a quadratic growth condition.

    SciTech Connect

    Anitescu, M.; Mathematics and Computer Science

    2000-01-01

    We show that the quadratic growth condition and the Mangasarian-Fromovitz constraint qualification (MFCQ) imply that local minima of nonlinear programs are isolated stationary points. As a result, when started sufficiently close to such points, an L1 exact penalty sequential quadratic programming algorithm will induce at least R-linear convergence of the iterates to such a local minimum. We construct an example of a degenerate nonlinear program with a unique local minimum satisfying the quadratic growth and the MFCQ but for which no positive semidefinite augmented Lagrangian exists. We present numerical results obtained using several nonlinear programming packages on this example and discuss its implications for some algorithms.

  5. Finite-element analysis of earing using non-quadratic yield surfaces

    SciTech Connect

    Logan, R.W.

    1995-06-18

    During deep draw cupping, the phenomenon known as earing may occur as the cup wall is formed, resulting in a periodic variation of cup wall height around the perimeter of the finished cup. This is generally due to planar anisotropy of flow in rolled sheet product. It is generally observed that the anisotropy parameter R will vary in the plane of the sheet when ears are observed in cupping, with a parameter {Delta}R describing the variation of R in the plane of the sheet. For many common textures in face-centered and body-centered materials, the ears form relative to the sheet rolling direction at 0{degrees} and 90{degrees} around the perimeter if {Delta}R>0, and at -45{degrees} and +45{degrees} if {Delta}R<0. There is extensive experimental evidence that ear height shows a linear correlation with {Delta}R/R, but attempts to duplicate this using the finite-element method are highly dependent on both the methodology and yield surface used. It was shown previously that using a coarse mesh and the quadratic Hill yield surface tends to greatly under predict earing. In this study, we have used two different finite-element codes developed at LLNL to examine the predicted earing using both quadratic Hill and alternative non-quadratic yield surfaces. These results are compared to experimental data and conclusions drawn about the most desirable closed-form yield surfaces to duplicate the observed earing phenomena.

  6. Measurements of the negative refractive index of sub-diffraction waves propagating in an indefinite permittivity medium.

    PubMed

    Korobkin, Dmitriy; Neuner, Burton; Fietz, Chris; Jegenyes, Nikoletta; Ferro, Gabriel; Shvets, Gennady

    2010-10-25

    An indefinite permittivity medium (IPM) has been fabricated and optically characterized in mid-infrared spectral range (10.7 µm-11.3 µm). Phase and amplitude transmission measurements reveal two remarkable properties of IPMs: (i) transmission of sub-diffraction waves (as short as λ/4) can exceed those of diffraction-limited ones, and (ii) sub-diffraction waves can propagate with negative refractive index. We describe a novel double-detector optical technique relying on the interference between sub-diffraction and diffraction-limited waves for accurate measurement of the transmission amplitude and phase of the former.

  7. Geometric structure of pseudo-plane quadratic flows

    NASA Astrophysics Data System (ADS)

    Sun, Che

    2017-03-01

    Quadratic flows have the unique property of uniform strain and are commonly used in turbulence modeling and hydrodynamic analysis. While previous applications focused on two-dimensional homogeneous fluid, this study examines the geometric structure of three-dimensional quadratic flows in stratified fluid by solving a steady-state pseudo-plane flow model. The complete set of exact solutions reveals that steady quadratic flows have an invariant conic type in the non-rotating frame and a non-rotatory vertical structure in the rotating frame. Three baroclinic solutions with vertically non-aligned formulation disprove an earlier conjecture. All elliptic and hyperbolic solutions, except for the inertial ones, exhibit vertical concentricity. The rich geometry of quadratic flows stands in contrast to the depleted geometry of high-degree polynomial flows. A paradox in the steady solutions of shallow-water reduced-gravity models is also explained.

  8. AESOP- INTERACTIVE DESIGN OF LINEAR QUADRATIC REGULATORS AND KALMAN FILTERS

    NASA Technical Reports Server (NTRS)

    Lehtinen, B.

    1994-01-01

    AESOP was developed to solve a number of problems associated with the design of controls and state estimators for linear time-invariant systems. The systems considered are modeled in state-variable form by a set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are the linear quadratic regulator (LQR) design problem and the steady-state Kalman filter design problem. AESOP is designed to be used in an interactive manner. The user can solve design problems and analyze the solutions in a single interactive session. Both numerical and graphical information are available to the user during the session. The AESOP program is structured around a list of predefined functions. Each function performs a single computation associated with control, estimation, or system response determination. AESOP contains over sixty functions and permits the easy inclusion of user defined functions. The user accesses these functions either by inputting a list of desired functions in the order they are to be performed, or by specifying a single function to be performed. The latter case is used when the choice of function and function order depends on the results of previous functions. The available AESOP functions are divided into several general areas including: 1) program control, 2) matrix input and revision, 3) matrix formation, 4) open-loop system analysis, 5) frequency response, 6) transient response, 7) transient function zeros, 8) LQR and Kalman filter design, 9) eigenvalues and eigenvectors, 10) covariances, and 11) user-defined functions. The most important functions are those that design linear quadratic regulators and Kalman filters. The user interacts with AESOP when using these functions by inputting design weighting parameters and by viewing displays of designed system response. Support functions obtain system transient and frequency responses, transfer functions, and covariance matrices. AESOP can also provide the user

  9. Quadratic bulk viscosity and the topology of space time.

    NASA Astrophysics Data System (ADS)

    Wolf, C.

    1997-12-01

    By considering a homogeneous isotropic universe admitting quadratic bulk viscosity the author shows that if the bulk viscosity coefficient is large the effective topology of space time attains an antiintuitive interpretation in the sense that a positive curvature space time is ever-expanding. This is true for all cosmologies studied except in the case of small quadratic bulk viscosity (3γ+1-kβ ≥ 0, 3γ+1 > 0).

  10. Quadratic function approaching method for magnetotelluric soundingdata inversion

    SciTech Connect

    Liangjun, Yan; Wenbao, Hu; Zhang, Keni

    2004-04-05

    The quadratic function approaching method (QFAM) is introduced for magnetotelluric sounding (MT) data inversion. The method takes the advantage of that quadratic function has single extreme value, which avoids leading to an inversion solution for local minimum and ensures the solution for global minimization of an objective function. The method does not need calculation of sensitivity matrix and not require a strict initial earth model. Examples for synthetic data and field measurement data indicate that the proposed inversion method is effective.

  11. Chaos synchronization based on quadratic optimum regulation and control

    NASA Astrophysics Data System (ADS)

    Gong, Lihua

    2005-03-01

    Based on the method of the quadratic optimum control, a quadratic optimal regulator used for synchronizing chaotic systems is constructed to realize chaos synchronization. The synchronization method can maintain the least error with less control energy, and then realize the optimization on both sides of energy and error synthetically. In addition, the control cost can also be reduced by using this method intermittently. The simulation results of the chaotic Chua's circuit and the Rossler chaos system prove that the method is effective.

  12. AdS waves as exact solutions to quadratic gravity

    SciTech Connect

    Guellue, Ibrahim; Sisman, Tahsin Cagri; Tekin, Bayram; Guerses, Metin

    2011-04-15

    We give an exact solution of the quadratic gravity in D dimensions. The solution is a plane-fronted wave metric with a cosmological constant. This metric solves not only the full quadratic gravity field equations but also the linearized ones which include the linearized equations of the recently found critical gravity. A subset of the solutions change the asymptotic structure of the anti-de Sitter space due to their logarithmic behavior.

  13. The Quadratic Spinor Lagrangian, Axial Torsion Current and Generalizations

    NASA Astrophysics Data System (ADS)

    Da Rocha, R.; Pereira, J. G.

    We show that the Einstein-Hilbert, the Einstein-Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), when the three classes of Dirac spinor fields, under Lounesto spinor field classification, are considered. To each one of these classes, there corresponds an unique kind of action for a covariant gravity theory. In other words, it is shown to exist a one-to-one correspondence between the three classes of non-equivalent solutions of the Dirac equation, and Einstein-Hilbert, Einstein-Palatini, and Holst actions. Furthermore, it arises naturally, from Lounesto spinor field classification, that any other class of spinor field — Weyl, Majorana, flagpole, or flag-dipole spinor fields — yields a trivial (zero) QSL, up to a boundary term. To investigate this boundary term, we do not impose any constraint on the Dirac spinor field, and consequently we obtain new terms in the boundary component of the QSL. In the particular case of a teleparallel connection, an axial torsion one-form current density is obtained. New terms are also obtained in the corresponding Hamiltonian formalism. We then discuss how these new terms could shed new light on more general investigations.

  14. A quadratic regression modelling on paddy production in the area of Perlis

    NASA Astrophysics Data System (ADS)

    Goh, Aizat Hanis Annas; Ali, Zalila; Nor, Norlida Mohd; Baharum, Adam; Ahmad, Wan Muhamad Amir W.

    2017-08-01

    Polynomial regression models are useful in situations in which the relationship between a response variable and predictor variables is curvilinear. Polynomial regression fits the nonlinear relationship into a least squares linear regression model by decomposing the predictor variables into a kth order polynomial. The polynomial order determines the number of inflexions on the curvilinear fitted line. A second order polynomial forms a quadratic expression (parabolic curve) with either a single maximum or minimum, a third order polynomial forms a cubic expression with both a relative maximum and a minimum. This study used paddy data in the area of Perlis to model paddy production based on paddy cultivation characteristics and environmental characteristics. The results indicated that a quadratic regression model best fits the data and paddy production is affected by urea fertilizer application and the interaction between amount of average rainfall and percentage of area defected by pest and disease. Urea fertilizer application has a quadratic effect in the model which indicated that if the number of days of urea fertilizer application increased, paddy production is expected to decrease until it achieved a minimum value and paddy production is expected to increase at higher number of days of urea application. The decrease in paddy production with an increased in rainfall is greater, the higher the percentage of area defected by pest and disease.

  15. Exact evaluation of the quadratic longitudinal response function for an unmagnetized Maxwellian plasma

    SciTech Connect

    Layden, B.; Cairns, Iver H.; Robinson, P. A.; Percival, D. J.

    2012-07-15

    The quadratic longitudinal response function describes the second-order nonlinear response of a plasma to electrostatic wave fields. An explicit expression for this function in the weak-turbulence regime requires the evaluation of velocity-space integrals involving the velocity distribution function and various resonant denominators. Previous calculations of the quadratic longitudinal response function were performed by approximating the resonant denominators to facilitate the integration. Here, we evaluate these integrals exactly for a non-relativistic collisionless unmagnetized isotropic Maxwellian plasma in terms of generalized plasma dispersion functions, and correct certain aspects of expressions previously derived for these functions. We show that in the appropriate limits the exact expression reduces to the approximate form used for interactions between two fast waves and one slow wave, such as the electrostatic decay of Langmuir waves into Langmuir waves and ion sound waves, and the scattering of Langmuir waves off thermal ions.

  16. Numerical solution of quadratic matrix equations for free vibration analysis of structures

    NASA Technical Reports Server (NTRS)

    Gupta, K. K.

    1975-01-01

    This paper is concerned with the efficient and accurate solution of the eigenvalue problem represented by quadratic matrix equations. Such matrix forms are obtained in connection with the free vibration analysis of structures, discretized by finite 'dynamic' elements, resulting in frequency-dependent stiffness and inertia matrices. The paper presents a new numerical solution procedure of the quadratic matrix equations, based on a combined Sturm sequence and inverse iteration technique enabling economical and accurate determination of a few required eigenvalues and associated vectors. An alternative procedure based on a simultaneous iteration procedure is also described when only the first few modes are the usual requirement. The employment of finite dynamic elements in conjunction with the presently developed eigenvalue routines results in a most significant economy in the dynamic analysis of structures.

  17. On the reflection point where light reflects to a known destination on quadratic surfaces.

    PubMed

    Gonçalves, Nuno

    2010-01-15

    We address the problem of determining the reflection point on a specular surface where a light ray that travels from a source to a target is reflected. The specular surfaces considered are those expressed by a quadratic equation. So far, there is no closed form explicit equation for the general solution of this determination of the reflection point, and the usual approach is to use the Snell law or the Fermat principle whose equations are derived in multidimensional nonlinear minimizations. We prove in this Letter that one can impose a set of three restrictions to the reflection point that can impose a set of three restrictions that culminates in a very elegant formalism of searching the reflection point in a unidimensional curve in space. This curve is the intersection of two quadratic equations. Some applications of this framework are also discussed.

  18. A 3D Frictional Segment-to-Segment Contact Method for Large Deformations and Quadratic Elements

    SciTech Connect

    Puso, M; Laursen, T; Solberg, J

    2004-04-01

    Node-on-segment contact is the most common form of contact used today but has many deficiencies ranging from potential locking to non-smooth behavior with large sliding. Furthermore, node-on-segment approaches are not at all applicable to higher order discretizations (e.g. quadratic elements). In a previous work, [3, 4] we developed a segment-to-segment contact approach for eight node hexahedral elements based on the mortar method that was applicable to large deformation mechanics. The approach proved extremely robust since it eliminated the over-constraint that caused 'locking' and provided smooth force variations in large sliding. Here, we extend this previous approach to treat frictional contact problems. In addition, the method is extended to 3D quadratic tetrahedrals and hexahedrals. The proposed approach is then applied to several challenging frictional contact problems that demonstrate its effectiveness.

  19. Statistical analysis using the multiple regression research in areas of the indefinite chilled cast-iron rolls manufacturing

    NASA Astrophysics Data System (ADS)

    Kiss, I.; Alexa, V.; Cioată, V. G.

    2017-05-01

    To analyze the metallurgical processes is used, mainly, the statistical fundamental methods that permit to draw conclusions, from the observed values, about the repartition of the frequencies of various parameters, about their interaction, about verification validity of certain premises, and about the research of the dependencies among different parameters. In this sense, the realization of optimum chemical compositions of the cast-iron can constitute a technical efficient way to assure the exploitation properties, the material from which the rolling mills rolls are manufactured having an important role in this sense. This paper reviews key aspects of roll material properties and presents an analysis of the influences of chemical composition upon the mechanical properties of the indefinite cast iron rolls. Now, using the multivariate research, we present some mathematical correlations and graphical interpretations between the hardness and the chemical composition. Using the double and triple correlations variation boundaries for the chemical composition, in view the obtaining the optimal values of the hardness of indefinite cast iron rolls, are obtained. The partial results and evidence obtained by actual experiments are presented. For the multiple regression equations, correlation coefficients and graphical representations the software MATLAB was used.

  20. Moments for general quadratic densities in n dimensions

    SciTech Connect

    Furman, Miguel A.

    2002-03-20

    We present the calculation of the generating functions and the rth-order correlations for densities of the form {rho}(x) {proportional_to} where g(s) is a non-negative function of the quadratic ''action'' s(x)={summation}{sub i,j}H{sub ij}x{sub i}x{sub j}, where x = (x{sub 1},x{sub 2}...,x{sub n}) is a real n-dimensional vector and H is a real, symmetric n x n matrix whose eigenvalues are strictly positive. In particular, we find the connection between the (r+2)th-order and rth-order correlations, which constitutes a generalization of the Gaussian moment theorem, which corresponds to the particular choice g(s)=e{sup -s/2}. We present several examples for specific choices for g(s), including the explicit expression for the generating function for each case and the subspace projection of {rho}(x) in a few cases. We also provide the straightforward generalizations to: (1) the case where g=g(s(x)+a {center_dot} x), where a=(a{sub 1},a{sub 2},...,a{sub n}) is an arbitrary real n-dimensional vector, and (2) the complex case, in which the action is of the form s(z) = {summation}{sub i,j}H{sub ij}z{sup *}{sub i} z{sub j} where z=(z{sub 1},z{sub 2}...z{sub n}) is an n-dimensional complex vector and H is a Hermitian n x n matrix whose eigenvalues are strictly positive.

  1. Kinematics of the quadrate bone during feeding in mallard ducks.

    PubMed

    Dawson, Megan M; Metzger, Keith A; Baier, David B; Brainerd, Elizabeth L

    2011-06-15

    Avian cranial kinesis, in which mobility of the quadrate, pterygoid and palatine bones contribute to upper bill elevation, is believed to occur in all extant birds. The most widely accepted model for upper bill elevation is that the quadrate rotates rostrally and medially towards the pterygoid, transferring force to the mobile pterygoid-palatine complex, which pushes on the upper bill. Until now, however, it has not been possible to test this hypothesis in vivo because quadrate motions are rapid, three-dimensionally complex and not visible externally. Here we use a new in vivo X-ray motion analysis technique, X-ray reconstruction of moving morphology (XROMM), to create precise (±0.06 mm) 3-D animations of the quadrate, braincase, upper bill and mandible of three mallard ducks, Anas platyrhynchos. We defined a joint coordinate system (JCS) for the quadrato-squamosal joint with the axes aligned to the anatomical planes of the skull. In this coordinate system, the quadrate's 3-D rotations produce an elliptical path of pterygoid process motion, with medial and rostrodorsal then lateral and rostrodorsal motion as the upper bill elevates. As the upper bill depresses, the pterygoid process continues along the ellipsoidal path, with lateral and caudoventral then medial and caudoventral motion. We also found that the mandibular rami bow outwards (streptognathy) during mandibular depression, which may cause the lateral component of quadrate rotation that we observed. Relative to the JCS aligned with the anatomical planes of the skull, a second JCS aligned with quadrato-squamosal joint anatomy did not produce a simpler description of quadrate kinematics.

  2. A transient, quadratic nodal method for triangular-Z geometry

    SciTech Connect

    DeLorey, T.F.

    1993-06-01

    Many systematically-derived nodal methods have been developed for Cartesian geometry due to the extensive interest in Light Water Reactors. These methods typically model the transverse-integrated flux as either an analytic or low order polynomial function of position within the node. Recently, quadratic nodal methods have been developed for R-Z and hexagonal geometry. A static and transient quadratic nodal method is developed for triangular-Z geometry. This development is particularly challenging because the quadratic expansion in each node must be performed between the node faces and the triangular points. As a consequence, in the 2-D plane, the flux and current at the points of the triangles must be treated. Quadratic nodal equations are solved using a non-linear iteration scheme, which utilizes the corrected, mesh-centered finite difference equations, and forces these equations to match the quadratic equations by computing discontinuity factors during the solution. Transient nodal equations are solved using the improved quasi-static method, which has been shown to be a very efficient solution method for transient problems. Several static problems are used to compare the quadratic nodal method to the Coarse Mesh Finite Difference (CMFD) method. The quadratic method is shown to give more accurate node-averaged fluxes. However, it appears that the method has difficulty predicting node leakages near reactor boundaries and severe material interfaces. The consequence is that the eigenvalue may be poorly predicted for certain reactor configurations. The transient methods are tested using a simple analytic test problem, a heterogeneous heavy water reactor benchmark problem, and three thermal hydraulic test problems. Results indicate that the transient methods have been implemented correctly.

  3. Use of non-quadratic yield surfaces in design of optimal deep-draw blank geometry

    SciTech Connect

    Logan, R.W.

    1995-12-01

    Planar anisotropy in the deep-drawing of sheet can lead to the formation of ears in cylindrical cups and to undesirable metal flow in the blankholder in the general case. For design analysis purposes in non-linear finite-element codes, this anisotropy is characterized by the use of an appropriate yield surface which is then implemented into codes such as DYNA3D . The quadratic Hill yield surface offers a relatively straightforward implementation and can be formulated to be invariant to the coordinate system. Non-quadratic yield surfaces can provide more realistic strength or strain increment ratios, but they may not provide invariance and thus demand certain approximations. Forms due to Hosford and Badat et al. have been shown to more accurately address the earning phenomenon. in this work, use is made of these non-quadratic yield surfaces in order to determine the optimal blank shape for cups and other shapes using ferrous and other metal blank materials with planar anisotropy. The analyses are compared to previous experimental studies on non-uniform blank motion due to anisotropy and asymmetric geometry.

  4. New type of Weyl semimetal with quadratic double Weyl fermions

    DOE PAGES

    Huang, Shin -Ming; Xu, Su -Yang; Belopolski, Ilya; ...

    2016-01-19

    Weyl semimetals have attracted worldwide attention due to their wide range of exotic properties predicted in theories. The experimental realization had remained elusive for a long time despite much effort. Very recently, the first Weyl semimetal has been discovered in an inversion-breaking, stoichiometric solid TaAs. So far, the TaAs class remains the only Weyl semimetal available in real materials. To facilitate the transition of Weyl semimetals from the realm of purely theoretical interest to the realm of experimental studies and device applications, it is of crucial importance to identify other robust candidates that are experimentally feasible to be realized. Inmore » this paper, we propose such a Weyl semimetal candidate in an inversion-breaking, stoichiometric compound strontium silicide, SrSi2, with many new and novel properties that are distinct from TaAs. Here, we show that SrSi2 is a Weyl semimetal even without spin-orbit coupling and that, after the inclusion of spin-orbit coupling, two Weyl fermions stick together forming an exotic double Weyl fermion with quadratic dispersions and a higher chiral charge of ±2. Moreover, we find that the Weyl nodes with opposite charges are located at different energies due to the absence of mirror symmetry in SrSi2, paving the way for the realization of the chiral magnetic effect. Finally, our systematic results not only identify a much-needed robust Weyl semimetal candidate but also open the door to new topological Weyl physics that is not possible in TaAs« less

  5. New type of Weyl semimetal with quadratic double Weyl fermions

    PubMed Central

    Huang, Shin-Ming; Xu, Su-Yang; Belopolski, Ilya; Lee, Chi-Cheng; Chang, Guoqing; Chang, Tay-Rong; Wang, BaoKai; Alidoust, Nasser; Bian, Guang; Neupane, Madhab; Sanchez, Daniel; Zheng, Hao; Jeng, Horng-Tay; Bansil, Arun; Neupert, Titus; Lin, Hsin; Hasan, M. Zahid

    2016-01-01

    Weyl semimetals have attracted worldwide attention due to their wide range of exotic properties predicted in theories. The experimental realization had remained elusive for a long time despite much effort. Very recently, the first Weyl semimetal has been discovered in an inversion-breaking, stoichiometric solid TaAs. So far, the TaAs class remains the only Weyl semimetal available in real materials. To facilitate the transition of Weyl semimetals from the realm of purely theoretical interest to the realm of experimental studies and device applications, it is of crucial importance to identify other robust candidates that are experimentally feasible to be realized. In this paper, we propose such a Weyl semimetal candidate in an inversion-breaking, stoichiometric compound strontium silicide, SrSi2, with many new and novel properties that are distinct from TaAs. We show that SrSi2 is a Weyl semimetal even without spin–orbit coupling and that, after the inclusion of spin–orbit coupling, two Weyl fermions stick together forming an exotic double Weyl fermion with quadratic dispersions and a higher chiral charge of ±2. Moreover, we find that the Weyl nodes with opposite charges are located at different energies due to the absence of mirror symmetry in SrSi2, paving the way for the realization of the chiral magnetic effect. Our systematic results not only identify a much-needed robust Weyl semimetal candidate but also open the door to new topological Weyl physics that is not possible in TaAs. PMID:26787914

  6. Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation

    SciTech Connect

    Fernández, Francisco M.

    2016-06-15

    We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit. -- Highlights: •Symmetric quadratic operators are useful models for many physical applications. •Any such operator exhibits a pseudo-Hermitian matrix representation. •Its eigenvalues are the natural frequencies of the Hamiltonian operator. •The eigenvalues may be real or complex and describe a phase transition.

  7. On Volterra quadratic stochastic operators with continual state space

    SciTech Connect

    Ganikhodjaev, Nasir; Hamzah, Nur Zatul Akmar

    2015-05-15

    Let (X,F) be a measurable space, and S(X,F) be the set of all probability measures on (X,F) where X is a state space and F is σ - algebraon X. We consider a nonlinear transformation (quadratic stochastic operator) defined by (Vλ)(A) = ∫{sub X}∫{sub X}P(x,y,A)dλ(x)dλ(y), where P(x, y, A) is regarded as a function of two variables x and y with fixed A ∈ F . A quadratic stochastic operator V is called a regular, if for any initial measure the strong limit lim{sub n→∞} V{sup n }(λ) is exists. In this paper, we construct a family of quadratic stochastic operators defined on the segment X = [0,1] with Borel σ - algebra F on X , prove their regularity and show that the limit measure is a Dirac measure.

  8. A Projection Neural Network for Constrained Quadratic Minimax Optimization.

    PubMed

    Liu, Qingshan; Wang, Jun

    2015-11-01

    This paper presents a projection neural network described by a dynamic system for solving constrained quadratic minimax programming problems. Sufficient conditions based on a linear matrix inequality are provided for global convergence of the proposed neural network. Compared with some of the existing neural networks for quadratic minimax optimization, the proposed neural network in this paper is capable of solving more general constrained quadratic minimax optimization problems, and the designed neural network does not include any parameter. Moreover, the neural network has lower model complexities, the number of state variables of which is equal to that of the dimension of the optimization problems. The simulation results on numerical examples are discussed to demonstrate the effectiveness and characteristics of the proposed neural network.

  9. 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.

  10. The generalized quadratic knapsack problem. A neuronal network approach.

    PubMed

    Talaván, Pedro M; Yáñez, Javier

    2006-05-01

    The solution of an optimization problem through the continuous Hopfield network (CHN) is based on some energy or Lyapunov function, which decreases as the system evolves until a local minimum value is attained. A new energy function is proposed in this paper so that any 0-1 linear constrains programming with quadratic objective function can be solved. This problem, denoted as the generalized quadratic knapsack problem (GQKP), includes as particular cases well-known problems such as the traveling salesman problem (TSP) and the quadratic assignment problem (QAP). This new energy function generalizes those proposed by other authors. Through this energy function, any GQKP can be solved with an appropriate parameter setting procedure, which is detailed in this paper. As a particular case, and in order to test this generalized energy function, some computational experiments solving the traveling salesman problem are also included.

  11. On the So-Called Variational Consistency of Plate Models, I. Indefinite Plates: Evaluation of Dispersive Behaviour

    NASA Astrophysics Data System (ADS)

    Muller, P.; Touratier, M.

    1995-12-01

    Four groups of refined shear-deformation plate theories are examined, including the so-called variationally inconsistent theories of Schmidt-Levinson and Touratier—whose "inconsistence" is in fact weak. After a unified presentation of these two-dimensional theories, all are deduced from the three-dimensional theory of elasticity through a suitable variation procedure which disconnects the choice of the so-called virtual motions from the choice of an approximation for the small displacement field. This procedure makes obvious in a natural way the importance of the stress boundary conditions on the faces of the pate for any two-dimensional theory. As a test comparison, a wave dispersion evaluation of these theories is performed for the propagation of flexural waves in an indefinite plate. A detailed comparison leads to the conclusion that the inconsistent theories may offer some advantages in the domain of short waves.

  12. Pure double-layer bubbles in quadratic F (R ) gravity

    NASA Astrophysics Data System (ADS)

    Eiroa, Ernesto F.; Figueroa Aguirre, Griselda; Senovilla, José M. M.

    2017-06-01

    We present a class of spherically symmetric spacetimes corresponding to bubbles separating two regions with constant values of the scalar curvature, or equivalently with two different cosmological constants, in quadratic F (R ) theory. The bubbles are obtained by means of the junction formalism, and the matching hypersurface supports in general a thin shell and a gravitational double layer. In particular, we find that pure double layers are possible for appropriate values of the parameters of the model whenever the quadratic coefficient is negative. This is the first example of a pure double layer in a gravitational theory.

  13. Convergence properties of the softassign quadratic assignment algorithm.

    PubMed

    Rangarajan, A; Vuille, A; Mjolsness, E

    1999-08-15

    The softassign quadratic assignment algorithm is a discrete-time, continuous-state, synchronous updating optimizing neural network. While its effectiveness has been shown in the traveling salesman problem, graph matching, and graph partitioning in thousands of simulations, its convergence properties have not been studied. Here, we construct discrete-time Lyapunov functions for the cases of exact and approximate doubly stochastic constraint satisfaction, which show convergence to a fixed point. The combination of good convergence properties and experimental success makes the softassign algorithm an excellent choice for neural quadratic assignment optimization.

  14. A Dynamical Systems Analysis of Semidefinite Programming with Application to Quadratic Optimization with Pure Quadratic Equality Constraints

    SciTech Connect

    Orsi, R. J.; Mahony, R. E.; Moore, J. B.

    1999-09-15

    This paper considers the problem of minimizing a quadratic cost subject to purely quadratic equality constraints. This problem is tackled by first relating it to a standard semidefinite programming problem. The approach taken leads to a dynamical systems analysis of semidefinite programming and the formulation of a gradient descent flow which can be used to solve semidefinite programming problems. Though the reformulation of the initial problem as a semidefinite pro- gramming problem does not in general lead directly to a solution of the original problem, the initial problem is solved by using a modified flow incorporating a penalty function.

  15. Fiches pratiques: Domino gastronomique; Ticket de metro; Articles definis et indefinis; Texte en scenes (Practical Ideas: Gastronomic Dominos; Metro Ticket; Definite and Indefinite Articles; Text on Stage).

    ERIC Educational Resources Information Center

    Grigoriou, Marianthi; And Others

    1992-01-01

    Four language classroom activities are described, including a food game, a culture and language activity based on a Paris Metro ticket, an exercise in the use of definite and indefinite articles using a film poster, and a classroom adaptation of a fairy tale for dramatic oral presentation. (MSE)

  16. 41 CFR 301-51.203 - What must I do about my advance if my trip is canceled or postponed indefinitely?

    Code of Federal Regulations, 2010 CFR

    2010-07-01

    ... 41 Public Contracts and Property Management 4 2010-07-01 2010-07-01 false What must I do about my advance if my trip is canceled or postponed indefinitely? 301-51.203 Section 301-51.203 Public Contracts... Receiving Travel Advances § 301-51.203 What must I do about my advance if my trip is canceled or postponed...

  17. Partial quadratic eigenvalue assignment in vibrating structures using receptances and system matrices

    NASA Astrophysics Data System (ADS)

    Bai, Zheng-Jian; Wan, Qiu-Yue

    2017-05-01

    In this paper, we consider the partial quadratic eigenvalue assignment problem (PQEAP) in vibration by active feedback control. Based on the receptance measurements and system matrices, we propose a constructive method for solving PQEAP, where we only need to solve a small linear system and only a few undesired open-loop eigenvalues with associated eigenvectors are needed. Our method is designed for both single-input and multiple-input vibration controls of vibrating structures. The real form of our method is also presented. Numerical tests show that our method is effective for constructing a solution to PQEAP with both single-input and multiple-input vibration controls.

  18. Solving the transport equation with quadratic finite elements: Theory and applications

    SciTech Connect

    Ferguson, J.M.

    1997-12-31

    At the 4th Joint Conference on Computational Mathematics, the author presented a paper introducing a new quadratic finite element scheme (QFEM) for solving the transport equation. In the ensuing year the author has obtained considerable experience in the application of this method, including solution of eigenvalue problems, transmission problems, and solution of the adjoint form of the equation as well as the usual forward solution. He will present detailed results, and will also discuss other refinements of his transport codes, particularly for 3-dimensional problems on rectilinear and non-rectilinear grids.

  19. Solution of quadratic matrix equations for free vibration analysis of structures.

    NASA Technical Reports Server (NTRS)

    Gupta, K. K.

    1973-01-01

    An efficient digital computer procedure and the related numerical algorithm are presented herein for the solution of quadratic matrix equations associated with free vibration analysis of structures. Such a procedure enables accurate and economical analysis of natural frequencies and associated modes of discretized structures. The numerically stable algorithm is based on the Sturm sequence method, which fully exploits the banded form of associated stiffness and mass matrices. The related computer program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be substantially more accurate and economical than other existing procedures of such analysis. Numerical examples are presented for two structures - a cantilever beam and a semicircular arch.

  20. ORACLS - A linear-quadratic-Gaussian computer-aided design package

    NASA Technical Reports Server (NTRS)

    Armstrong, E. S.

    1982-01-01

    ORACLS, an acronym denoting Optimal Regular Algorithms for the Control of Linear Systems, is a collection of FORTRAN coded subroutines dedicated to the formulation and solution of the Linear-Quadratic-Gaussian (LQG) design problem modeled in both continuous and discrete form. The ORACLS system is under continuous development at the NASA Langley Research Center, Hampton, Virginia, and is widely used by universities and industry within the U.S.A. The current (operational) ORACLS version as well as new software under development is described.

  1. Ray-tracing simulation method using piecewise quadratic interpolant for aspheric optical systems.

    PubMed

    Morita, Shin-Ya; Nishidate, Yohei; Nagata, Takashi; Yamagata, Yutaka; Teodosiu, Cristian

    2010-06-20

    We present a new method for precise ray-tracing simulation considering form errors in the fabrication process of aspheric lenses. The Nagata patch, a quadratic interpolant for surface meshes using normal vectors, is adopted for representing the lens geometry with mid-spectral frequencies of surface profile errors. Several improvements in the ray-patch intersection calculation and its acceleration technique are also proposed. The developed algorithm is applied to ray-tracing simulation of optical disk pick-up aspheric objectives, and this technique requires 10(5) to 10(9) times fewer patches than a polygonal approximation. The simulation takes only several seconds on a standard PC.

  2. Visualising the Complex Roots of Quadratic Equations with Real Coefficients

    ERIC Educational Resources Information Center

    Bardell, Nicholas S.

    2012-01-01

    The roots of the general quadratic equation y = ax[superscript 2] + bx + c (real a, b, c) are known to occur in the following sets: (i) real and distinct; (ii) real and coincident; and (iii) a complex conjugate pair. Case (iii), which provides the focus for this investigation, can only occur when the values of the real coefficients a, b, and c are…

  3. Finding the Best Quadratic Approximation of a Function

    ERIC Educational Resources Information Center

    Yang, Yajun; Gordon, Sheldon P.

    2011-01-01

    This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x) = e[superscript x]. Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact…

  4. Analysis of Quadratic Diophantine Equations with Fibonacci Number Solutions

    ERIC Educational Resources Information Center

    Leyendekkers, J. V.; Shannon, A. G.

    2004-01-01

    An analysis is made of the role of Fibonacci numbers in some quadratic Diophantine equations. A general solution is obtained for finding factors in sums of Fibonacci numbers. Interpretation of the results is facilitated by the use of a modular ring which also permits extension of the analysis.

  5. Analysis of Quadratic Diophantine Equations with Fibonacci Number Solutions

    ERIC Educational Resources Information Center

    Leyendekkers, J. V.; Shannon, A. G.

    2004-01-01

    An analysis is made of the role of Fibonacci numbers in some quadratic Diophantine equations. A general solution is obtained for finding factors in sums of Fibonacci numbers. Interpretation of the results is facilitated by the use of a modular ring which also permits extension of the analysis.

  6. Radar Rainfall Estimation using a Quadratic Z-R equation

    NASA Astrophysics Data System (ADS)

    Hall, Will; Rico-Ramirez, Miguel Angel; Kramer, Stefan

    2016-04-01

    The aim of this work is to test a method that enables the input of event based drop size distributions to alter a quadratic reflectivity (Z) to rainfall (R) equation that is limited by fixed upper and lower points. Results will be compared to the Marshall-Palmer Z-R relation outputs and validated by a network of gauges and a single polarisation weather radar located close to Essen, Germany. The time window over which the drop size distribution measurements will be collected is varied to note any effect on the generated quadratic Z-R relation. The new quadratic algorithm shows some distinct improvement over the Marshall-Palmer relationship through multiple events. The inclusion of a minimum number of Z-R points helped to decrease the associated error by defaulting back to the Marshall-Palmer equation if the limit was not reached. More research will be done to discover why the quadratic performs poorly in some events as there appears to be little correlation between number of drops or mean rainfall amount and the associated error. In some cases it seems the spatial distribution of the disdrometers has a significant effect as a large percentage of the rain bands pass to the north of two of the three disdrometers, frequently in a slightly north-easterly direction. However during widespread precipitation events the new algorithm works very well with reductions compared to the Marshall-Palmer relation.

  7. Beam steering and routing in quadratic nonlinear media

    SciTech Connect

    Aceves, A.B.; Santos, M.C.; Torner, L.

    1997-04-01

    We show how the spatial phase modulation of weak second-harmonic signals controls the overall direction of propagation of spatial solitons in quadratic nonlinear media. We investigate numerically such a process and discuss its applications to all-optical beam routing. 5 refs., 3 figs.

  8. Confidence set interference with a prior quadratic bound. [in geophysics

    NASA Technical Reports Server (NTRS)

    Backus, George E.

    1989-01-01

    Neyman's (1937) theory of confidence sets is developed as a replacement for Bayesian interference (BI) and stochastic inversion (SI) when the prior information is a hard quadratic bound. It is recommended that BI and SI be replaced by confidence set interference (CSI) only in certain circumstances. The geomagnetic problem is used to illustrate the general theory of CSI.

  9. Solving the Quadratic Capacitated Facilities Location Problem by Computer.

    ERIC Educational Resources Information Center

    Cote, Leon C.; Smith, Wayland P.

    Several computer programs were developed to solve various versions of the quadratic capacitated facilities location problem. Matrices, which represent various business costs, are defined for the factors of sites, facilities, customers, commodities, and production units. The objective of the program is to find an optimization matrix for the lowest…

  10. A Model for Quadratic Outliers in Linear Regression.

    ERIC Educational Resources Information Center

    Elashoff, Janet Dixon; Elashoff, Robert M.

    This paper introduces a model for describing outliers (observations which are extreme in some sense or violate the apparent pattern of other observations) in linear regression which can be viewed as a mixture of a quadratic and a linear regression. The maximum likelihood estimators of the parameters in the model are derived and their asymptotic…

  11. Entanglement entropy of fermionic quadratic band touching model

    NASA Astrophysics Data System (ADS)

    Chen, Xiao; Cho, Gil Young; Fradkin, Eduardo

    2014-03-01

    The entanglement entropy has been proven to be a useful tool to diagnose and characterize strongly correlated systems such as topologically ordered phases and some critical points. Motivated by the successes, we study the entanglement entropy (EE) of a fermionic quadratic band touching model in (2 + 1) dimension. This is a fermionic ``spinor'' model with a finite DOS at k=0 and infinitesimal instabilities. The calculation on two-point correlation functions shows that a Dirac fermion model and the quadratic band touching model both have the asymptotically identical behavior in the long distance limit. This implies that EE for the quadratic band touching model also has an area law as the Dirac fermion. This is in contradiction with the expectation that dense fermi systems with a finite DOS should exhibit LlogL violations to the area law of entanglement entropy (L is the length of the boundary of the sub-region) by analogy with the Fermi surface. We performed numerical calculations of entanglement entropies on a torus of the lattice models for the quadratic band touching point and the Dirac fermion to confirm this. The numerical calculation shows that EE for both cases satisfy the area law. We further verify this result by the analytic calculation on the torus geometry. This work was supported in part by the NSF grant DMR-1064319.

  12. Visualising the Complex Roots of Quadratic Equations with Real Coefficients

    ERIC Educational Resources Information Center

    Bardell, Nicholas S.

    2012-01-01

    The roots of the general quadratic equation y = ax[superscript 2] + bx + c (real a, b, c) are known to occur in the following sets: (i) real and distinct; (ii) real and coincident; and (iii) a complex conjugate pair. Case (iii), which provides the focus for this investigation, can only occur when the values of the real coefficients a, b, and c are…

  13. Analyzing Quadratic Unconstrained Binary Optimization Problems Via Multicommodity Flows.

    PubMed

    Wang, Di; Kleinberg, Robert D

    2009-11-28

    Quadratic Unconstrained Binary Optimization (QUBO) problems concern the minimization of quadratic polynomials in n {0, 1}-valued variables. These problems are NP-complete, but prior work has identified a sequence of polynomial-time computable lower bounds on the minimum value, denoted by C(2), C(3), C(4),…. It is known that C(2) can be computed by solving a maximum-flow problem, whereas the only previously known algorithms for computing C(k) (k > 2) require solving a linear program. In this paper we prove that C(3) can be computed by solving a maximum multicommodity flow problem in a graph constructed from the quadratic function. In addition to providing a lower bound on the minimum value of the quadratic function on {0, 1}(n), this multicommodity flow problem also provides some information about the coordinates of the point where this minimum is achieved. By looking at the edges that are never saturated in any maximum multicommodity flow, we can identify relational persistencies: pairs of variables that must have the same or different values in any minimizing assignment. We furthermore show that all of these persistencies can be detected by solving single-commodity flow problems in the same network.

  14. Finding the Best Quadratic Approximation of a Function

    ERIC Educational Resources Information Center

    Yang, Yajun; Gordon, Sheldon P.

    2011-01-01

    This article examines the question of finding the best quadratic function to approximate a given function on an interval. The prototypical function considered is f(x) = e[superscript x]. Two approaches are considered, one based on Taylor polynomial approximations at various points in the interval under consideration, the other based on the fact…

  15. Confidence set interference with a prior quadratic bound. [in geophysics

    NASA Technical Reports Server (NTRS)

    Backus, George E.

    1989-01-01

    Neyman's (1937) theory of confidence sets is developed as a replacement for Bayesian interference (BI) and stochastic inversion (SI) when the prior information is a hard quadratic bound. It is recommended that BI and SI be replaced by confidence set interference (CSI) only in certain circumstances. The geomagnetic problem is used to illustrate the general theory of CSI.

  16. Solving quadratic programming problems by delayed projection neural network.

    PubMed

    Yang, Yongqing; Cao, Jinde

    2006-11-01

    In this letter, the delayed projection neural network for solving convex quadratic programming problems is proposed. The neural network is proved to be globally exponentially stable and can converge to an optimal solution of the optimization problem. Three examples show the effectiveness of the proposed network.

  17. Canonical realization of Bondi-Metzner-Sachs symmetry: Quadratic Casimir

    NASA Astrophysics Data System (ADS)

    Gomis, Joaquim; Longhi, Giorgio

    2016-01-01

    We study the canonical realization of Bondi-Metzner-Sacks symmetry for a massive scalar field introduced by Longhi and Materassi [J. Math. Phys. 40, 480 (1999)]. We construct an invariant scalar product for the generalized momenta. As a consequence we introduce a quadratic Casimir with the supertranslations.

  18. Password authentication scheme based on the quadratic residue problem

    NASA Astrophysics Data System (ADS)

    Ali, Muhammad Helmi; Ismail, Eddie Shahril

    2017-04-01

    In this paper, we propose a new password-authentication scheme based on quadratic residue problem with the following advantages: the scheme does not require a verification file, and the scheme can withstand replay attacks and resist from the guessing and impersonation attacks. We next discuss the advantages of our designated scheme over other schemes in terms of security and efficiency.

  19. Unravelling Student Challenges with Quadratics: A Cognitive Approach

    ERIC Educational Resources Information Center

    Kotsopoulos, Donna

    2007-01-01

    The author's secondary school mathematics students have often reported to her that quadratic relations are one of the most conceptually challenging aspects of the high school curriculum. From her own classroom experiences there seemed to be several aspects to the students' challenges. Many students, even in their early secondary education, have…

  20. Clustered Self Organising Migrating Algorithm for the Quadratic Assignment Problem

    NASA Astrophysics Data System (ADS)

    Davendra, Donald; Zelinka, Ivan; Senkerik, Roman

    2009-08-01

    An approach of population dynamics and clustering for permutative problems is presented in this paper. Diversity indicators are created from solution ordering and its mapping is shown as an advantage for population control in metaheuristics. Self Organising Migrating Algorithm (SOMA) is modified using this approach and vetted with the Quadratic Assignment Problem (QAP). Extensive experimentation is conducted on benchmark problems in this area.

  1. Optimization with quadratic support functions in nonconvex smooth optimization

    NASA Astrophysics Data System (ADS)

    Khamisov, O. V.

    2016-10-01

    Problem of global minimization of twice continuously differentiable function with Lipschitz second derivatives over a polytope is considered. We suggest a branch and bound method with polytopes as partition elements. Due to the Lipschitz property of the objective function we can construct a quadratic support minorant at each point of the feasible set. Global minimum of of this minorant provides a lower bound of the objective over given partition subset. The main advantage of the suggested method consists in the following. First quadratic minorants usually are nonconvex and we have to solve auxiliary global optimization problem. This problem is reduced to a mixed 0-1 linear programming problem and can be solved by an advanced 0-1 solver. Then we show that the quadratic minorants are getting convex as soon as partition elements are getting smaller in diameter. Hence, at the final steps of the branch and bound method we solve convex auxiliary quadratic problems. Therefore, the method accelerates when we are close to the global minimum of the initial problem.

  2. Robust and minimum norm partial quadratic eigenvalue assignment in vibrating systems: A new optimization approach

    NASA Astrophysics Data System (ADS)

    Bai, Zheng-Jian; Datta, Biswa Nath; Wang, Jinwei

    2010-04-01

    The partial quadratic eigenvalue assignment problem (PQEVAP) concerns reassigning a few undesired eigenvalues of a quadratic matrix pencil to suitably chosen locations and keeping the other large number of eigenvalues and eigenvectors unchanged (no spill-over). The problem naturally arises in controlling dangerous vibrations in structures by means of active feedback control design. For practical viability, the design must be robust, which requires that the norms of the feedback matrices and the condition number of the closed-loop eigenvectors are as small as possible. The problem of computing feedback matrices that satisfy the above two practical requirements is known as the Robust Partial Quadratic Eigenvalue Assignment Problem (RPQEVAP). In this paper, we formulate the RPQEVAP as an unconstrained minimization problem with the cost function involving the condition number of the closed-loop eigenvector matrix and two feedback norms. Since only a small number of eigenvalues of the open-loop quadratic pencil are computable using the state-of-the-art matrix computational techniques and/or measurable in a vibration laboratory, it is imperative that the problem is solved using these small number of eigenvalues and the corresponding eigenvectors. To this end, a class of the feedback matrices are obtained in parametric form, parameterized by a single parametric matrix, and the cost function and the required gradient formulas for the optimization problem are developed in terms of the small number of eigenvalues that are reassigned and their corresponding eigenvectors. The problem is solved directly in quadratic setting without transforming it to a standard first-order control problem and most importantly, the significant "no spill-over property" of the closed-loop eigenvalues and eigenvectors is established by means of a mathematical result. These features make the proposed method practically applicable even for very large structures. Results on numerical experiments show

  3. Electromagnetic tracking system with reduced distortion using quadratic excitation.

    PubMed

    Bien, Tomasz; Li, Mengfei; Salah, Zein; Rose, Georg

    2014-03-01

    Electromagnetic tracking systems, frequently used in minimally invasive surgery, are affected by conductive distorters. The influence of conductive distorters on electromagnetic tracking system accuracy can be reduced through magnetic field modifications. This approach was developed and tested. The voltage induced directly by the emitting coil in the sensing coil without additional influence by the conductive distorter depends on the first derivative of the voltage on the emitting coil. The voltage which is induced indirectly by the emitting coil across the conductive distorter in the sensing coil, however, depends on the second derivative of the voltage on the emitting coil. The electromagnetic tracking system takes advantage of this difference by supplying the emitting coil with a quadratic excitation voltage. The method is adaptive relative to the amount of distortion cause by the conductive distorters. This approach is evaluated with an experimental setup of the electromagnetic tracking system. In vitro testing showed that the maximal error decreased from 10.9 to 3.8 mm when the quadratic voltage was used to excite the emitting coil instead of the sinusoidal voltage. Furthermore, the root mean square error in the proximity of the aluminum disk used as a conductive distorter was reduced from 3.5 to 1.6 mm when the electromagnetic tracking system used the quadratic instead of sinusoidal excitation. Electromagnetic tracking with quadratic excitation is immune to the effects of a conductive distorter, especially compared with sinusoidal excitation of the emitting coil. Quadratic excitation of electromagnetic tracking for computer-assisted surgery is promising for clinical applications.

  4. Binary Quadratic Programing for Online Tracking of Hundreds of People in Extremely Crowded Scenes.

    PubMed

    Dehghan, Afshin; Shah, Mubarak

    2017-03-24

    Multi-object tracking has been studied for decades. However, when it comes to tracking pedestrians in extremely crowded scenes, we are limited to only few works. This is an important problem which gives rise to several challenges. Pre-trained object detectors fail to localize targets in crowded sequences. This consequently limits the use of data-association based multi-target tracking methods which rely on the outcome of an object detector. Additionally, the small apparent target size makes it challenging to extract features to discriminate targets from their surroundings. Finally, the large number of targets greatly increases computational complexity which in turn makes it hard to extend existing multi-target tracking approaches to high-density crowd scenarios. In this paper, we propose a tracker that addresses the aforementioned problems and is capable of tracking hundreds of people efficiently. We formulate online crowd tracking as Binary Quadratic Programing. Our formulation employs target's individual information in the form of appearance and motion as well as contextual cues in the form of neighborhood motion, spatial proximity and grouping, and solves detection and data association simultaneously. In order to solve the proposed quadratic optimization efficiently, where state-of art commercial quadratic programing solvers fail to find the solution in a reasonable amount of time, we propose to use the most recent version of the Modified Frank Wolfe algorithm, which takes advantage of SWAP-steps to speed up the optimization. We show that the proposed formulation can track hundreds of targets efficiently and improves state-of-art results by significant margins on eleven challenging high density crowd sequences.

  5. Ground states for irregular and indefinite superlinear Schrödinger equations

    NASA Astrophysics Data System (ADS)

    Ackermann, Nils; Chagoya, Julián

    2016-11-01

    We consider the existence of a ground state for the subcritical stationary semilinear Schrödinger equation - Δu + u = a (x) | u| p - 2 u in H1, where a ∈L∞ (RN) may change sign. Our focus is on the case where loss of compactness occurs at the ground state energy. By providing a new variant of the Splitting Lemma we do not need to assume the existence of a limit problem at infinity, be it in the form of a pointwise limit for a as | x | → ∞ or of asymptotic periodicity. That is, our problem may be irregular at infinity. In addition, we allow a to change sign near infinity, a case that has never been treated before.

  6. Topological Classification of Quadratic Polynomial Differential Systems with a Finite Semi-Elemental Triple Saddle

    NASA Astrophysics Data System (ADS)

    Artés, Joan C.; Oliveira, Regilene D. S.; Rezende, Alex C.

    The study of planar quadratic differential systems is very important not only because they appear in many areas of applied mathematics but due to their richness in structure, stability and questions concerning limit cycles, for example. Even though many papers have been written on this class of systems, a complete understanding of this family is still missing. Classical problems, and in particular Hilbert’s 16th problem [Hilbert, 1900, 1902], are still open for this family. In this article, we make a global study of the family QTS¯ of all real quadratic polynomial differential systems which have a finite semi-elemental triple saddle (triple saddle with exactly one zero eigenvalue). This family modulo the action of the affine group and time homotheties is three-dimensional and we give its bifurcation diagram with respect to a normal form, in the three-dimensional real space of the parameters of this normal form. This bifurcation diagram yields 27 phase portraits for systems in QTS¯ counting phase portraits with and without limit cycles. Algebraic invariants are used to construct the bifurcation set and we present the phase portraits on the Poincaré disk. The bifurcation set is not just algebraic due to the presence of a surface found numerically, whose points correspond to connections of separatrices.

  7. On a method for constructing the Lax pairs for integrable models via a quadratic ansatz

    NASA Astrophysics Data System (ADS)

    Habibullin, I. T.; Khakimova, A. R.

    2017-07-01

    A method for constructing the Lax pairs for nonlinear integrable models is suggested. First we look for a nonlinear invariant manifold of the linearization of the given equation. Examples show that such an invariant manifold does exist and can effectively be found. Actually, it is defined by a quadratic form. As a result we get a nonlinear Lax pair consisting of the linearized equation and the invariant manifold. Our second step consists of finding an appropriate change of the variables to linearize the found nonlinear Lax pair. The desired change of the variables is again defined by a quadratic form. The method is illustrated by the well-known KdV equation, the modified Volterra chain and a less studied coupled lattice connected to the affine Lie algebra A^11 . New Lax pairs are found. The formal asymptotic expansions for their eigenfunctions are constructed around the singular values of the spectral parameter. By applying the method of the formal diagonalization to these Lax pairs, the infinite series of the local conservation laws are obtained for the corresponding nonlinear models.

  8. Spinor condensates with a laser-induced quadratic Zeeman effect

    SciTech Connect

    Santos, L.; Fattori, M.; Stuhler, J.; Pfau, T.

    2007-05-15

    We show that an effective quadratic Zeeman effect for trapped atoms can be generated by proper laser configurations and, in particular, by the dipole trap itself. The induced quadratic Zeeman effect leads to a rich ground-state phase diagram, e.g., for a degenerate {sup 52}Cr gas, can be used to induce topological defects by controllably quenching across transitions between phases of different symmetries, allows for the observability of the Einstein-de Haas effect for relatively large magnetic fields, and may be employed to create S=1/2 systems with spinor dynamics. Similar ideas could be explored in other atomic species opening an exciting new control tool in spinor systems.

  9. QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.

    PubMed

    Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit

    2014-01-01

    We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.

  10. Quadratic grating apodized photon sieves for simultaneous multiplane microscopy

    NASA Astrophysics Data System (ADS)

    Cheng, Yiguang; Zhu, Jiangping; He, Yu; Tang, Yan; Hu, Song; Zhao, Lixin

    2017-10-01

    We present a new type of imaging device, named quadratic grating apodized photon sieve (QGPS), used as the objective for simultaneous multiplane imaging in X-rays. The proposed QGPS is structured based on the combination of two concepts: photon sieves and quadratic gratings. Its design principles are also expounded in detail. Analysis of imaging properties of QGPS in terms of point-spread function shows that QGPS can image multiple layers within an object field onto a single image plane. Simulated and experimental results in visible light both demonstrate the feasibility of QGPS for simultaneous multiplane imaging, which is extremely promising to detect dynamic specimens by X-ray microscopy in the physical and life sciences.

  11. Large Deviation Principle for Benedicks-Carleson Quadratic Maps

    NASA Astrophysics Data System (ADS)

    Chung, Yong Moo; Takahasi, Hiroki

    2012-11-01

    Since the pioneering works of Jakobson and Benedicks & Carleson and others, it has been known that a positive measure set of quadratic maps admit invariant probability measures absolutely continuous with respect to Lebesgue. These measures allow one to statistically predict the asymptotic fate of Lebesgue almost every initial condition. Estimating fluctuations of empirical distributions before they settle to equilibrium requires a fairly good control over large parts of the phase space. We use the sub-exponential slow recurrence condition of Benedicks & Carleson to build induced Markov maps of arbitrarily small scale and associated towers, to which the absolutely continuous measures can be lifted. These various lifts together enable us to obtain a control of recurrence that is sufficient to establish a level 2 large deviation principle, for the absolutely continuous measures. This result encompasses dynamics far from equilibrium, and thus significantly extends presently known local large deviations results for quadratic maps.

  12. Consistent spin-two coupling and quadratic gravitation

    SciTech Connect

    Hindawi, A.; Ovrut, B.A.; Waldram, D.

    1996-05-01

    A discussion of the field content of quadratic higher-derivative gravitation is presented, together with a new example of a massless spin-two field consistently coupled to gravity. The full quadratic gravity theory is shown to be equivalent to a canonical second-order theory of a massive scalar field, a massive spin-two symmetric tensor field, and gravity. The conditions showing that the tensor field describes only spin-two degrees of freedom are derived. A limit of the second-order theory provides a new example of a massless spin-two field consistently coupled to gravity. A restricted set of vacua of the second-order theory is also discussed. It is shown that flat space is the only stable vacuum of this type, and that the spin-two field around flat space is unfortunately always ghostlike. {copyright} {ital 1996 The American Physical Society.}

  13. Alignment of protein interaction networks by integer quadratic programming.

    PubMed

    Li, Zhenping; Wang, Yong; Zhang, Shihua; Zhang, Xiang-Sun; Chen, Luonan

    2006-01-01

    With more and more data on protein-protein interaction (PPI) network available, the discovery of conserved patterns in these networks becomes an increasingly important problem. In this paper, to find the conserved substructures, we develop an efficient algorithm for aligning PPI networks based on both the protein sequence similarity and the network architecture similarity, by using integer quadratic programming (IQP). Such an IQP can be relaxed into the corresponding quadratic programming (QP) which in the case of biological data sets almost always ensures the integer solution. Therefore, a QP algorithm can be adopted to efficiently solve this IQP with out any approximation, thereby making PPI network alignment tractable. From the viewpoint of graph theory, the proposed method can identify similar subsets between two graphs, which allow gaps for nodes and edges.

  14. Gravitomagnetic effects in quadratic gravity with a scalar field

    NASA Astrophysics Data System (ADS)

    Finch, Andrew; Said, Jackson Levi

    2016-10-01

    The two gravitomagnetic effects which influence bodies orbiting around a gravitational source are the geodetic effect and the Lense-Thirring effect. The former describes the precession angle of the axis of a spinning gyroscope while in orbit around a nonrotating gravitational source whereas the latter provides a correction for this angle in the case of a spinning source. In this paper we derive the relevant equations in quadratic gravity and relate them to their equivalents in general relativity. Starting with an investigation into Kepler's third law in quadratic gravity with a scalar field, the effects of an axisymmetric and rotating gravitational source on an orbiting body in a circular, equatorial orbit are introduced.

  15. Lifespan estimates for the semi-linear Klein-Gordon equation with a quadratic potential in dimension one

    NASA Astrophysics Data System (ADS)

    Zhang, Qidi

    2016-12-01

    We show for almost every m > 0, the solution to the semi-linear Klein-Gordon equation with a quadratic potential in dimension one, exists over a longer time interval than the one given by local existence theory, using the normal form method. By using an Lp -Lq estimate for eigenfunctions of the harmonic oscillator and by carefully analysis on the nonlinearity, we improve the result obtained by the author before.

  16. Rab11a immunohistochemical analysis does not distinguish indefinite, low-, and high-grade dysplasia in Barrett esophagus.

    PubMed

    Robert, Marie E; Washington, Mary Kay; Lee, Jeffrey R; Goldenring, James R; Bronner, Mary P; Goldblum, John R; Greenson, Joel K; Haber, Marian M; Hart, John A; Lamps, Laura W; Lauwers, Gregory Y; Lewin, David; Lazenby, Audrey J; Montgomery, Elizabeth; Crawford, James M

    2005-10-01

    Our aim was to determine whether p53 and Rab11a immunoreactivity enhance diagnostic assessment of esophageal dysplasia. Histologic sections from 68 cases of Barrett esophagus obtained as part of a 12-institution study were stained with antibodies to p53 and Rab11a, randomized, and coded. The mucosal surface layer and deeper glands were scored blindly on a semiquantitative scale. The correlations between p53 and Rab11a scoring with the consensus diagnosis of dysplasia were analyzed. The histologic scale was as follows: no dysplasia, indefinite, low-grade dysplasia, high-grade dysplasia, intramucosal carcinoma, and invasive carcinoma. Rab11a staining was most prominent in epithelia negative for dysplasia but with regenerative features. There was an inverse relationship between Rab11a staining and findings of surface dysplasia (P < .02, chi(2)). However, statistical significance largely reflected loss of Rab11a immunoreactivity in intramucosal and invasive carcinoma, which was not a diagnostic dilemma. There was a strong positive correlation of p53 immunoreactivity with an increasing degree of epithelial dysplasia and carcinoma (P < .03, chi(2)). Rab11a immunoreactivity did not enhance the diagnostic assessment of dysplasia in Barrett esophagus. The previously reported positive correlation of p53 immunoreactivity with the presence of dysplasia in Barrett esophagus was confirmed.

  17. Development of a log-quadratic model to describe microbial inactivation, illustrated by thermal inactivation of Clostridium botulinum.

    PubMed

    Stone, G; Chapman, B; Lovell, D

    2009-11-01

    In the commercial food industry, demonstration of microbiological safety and thermal process equivalence often involves a mathematical framework that assumes log-linear inactivation kinetics and invokes concepts of decimal reduction time (D(T)), z values, and accumulated lethality. However, many microbes, particularly spores, exhibit inactivation kinetics that are not log linear. This has led to alternative modeling approaches, such as the biphasic and Weibull models, that relax strong log-linear assumptions. Using a statistical framework, we developed a novel log-quadratic model, which approximates the biphasic and Weibull models and provides additional physiological interpretability. As a statistical linear model, the log-quadratic model is relatively simple to fit and straightforwardly provides confidence intervals for its fitted values. It allows a D(T)-like value to be derived, even from data that exhibit obvious "tailing." We also showed how existing models of non-log-linear microbial inactivation, such as the Weibull model, can fit into a statistical linear model framework that dramatically simplifies their solution. We applied the log-quadratic model to thermal inactivation data for the spore-forming bacterium Clostridium botulinum and evaluated its merits compared with those of popular previously described approaches. The log-quadratic model was used as the basis of a secondary model that can capture the dependence of microbial inactivation kinetics on temperature. This model, in turn, was linked to models of spore inactivation of Sapru et al. and Rodriguez et al. that posit different physiological states for spores within a population. We believe that the log-quadratic model provides a useful framework in which to test vitalistic and mechanistic hypotheses of inactivation by thermal and other processes.

  18. Secondary School Mathematics, Chapter 23, Quadratic Functions, Chapter 24, Statistics. Student's Text.

    ERIC Educational Resources Information Center

    Stanford Univ., CA. School Mathematics Study Group.

    The first chapter in the twelfth unit of this SMSG series deals with the following topics involving quadratic functions: parabolas, translations of the parabola, completing the square, solving quadratic equations, "falling body" functions, and the use of quadratics in solving other equations. The chapter on statistics discusses…

  19. Quadratic performance index generation for optimal regular design.

    NASA Technical Reports Server (NTRS)

    Bullock, T. E.; Elder, J. M.

    1971-01-01

    Application of optimal control theory to practical problems has been limited by the difficulty of prescribing a performance index which accurately reflects design requirements. The task of deriving equivalent performance indices is considered in the present paper for a plant that is a completely controllable, scalar linear system with state feedback. A quadratic index is developed which leads to an optimal design performance satisfying some of the classical performance criteria.

  20. 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.

  1. 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.

  2. A generalized quadratic flow law for sheet metals

    NASA Astrophysics Data System (ADS)

    Jones, S. E.; Gillis, P. P.

    1984-01-01

    A planar quadratic flow law is proposed for anisotropic sheet materials. This law is similar to the anisotropic strength criterion of Tsai and Wu. It has six experimentally determinable coefficients as compared to four in Hill’s flow law and, thus, allows more experimental information to be accommodated. However, the resulting strain increment vector, while unique, is not necessarily normal to the flow surface.

  3. Quantum integrals of motion for variable quadratic Hamiltonians

    SciTech Connect

    Cordero-Soto, Ricardo; Suazo, Erwin; Suslov, Sergei K.

    2010-09-15

    We construct integrals of motion for several models of the quantum damped oscillators in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic Hamiltonians. An extension of the Lewis-Riesenfeld dynamical invariant is given. The time-evolution of the expectation values of the energy-related positive operators is determined for the oscillators under consideration. A proof of uniqueness of the corresponding Cauchy initial value problem is discussed as an application.

  4. Quadratic canonical transformation theory and higher order density matrices.

    PubMed

    Neuscamman, Eric; Yanai, Takeshi; Chan, Garnet Kin-Lic

    2009-03-28

    Canonical transformation (CT) theory provides a rigorously size-extensive description of dynamic correlation in multireference systems, with an accuracy superior to and cost scaling lower than complete active space second order perturbation theory. Here we expand our previous theory by investigating (i) a commutator approximation that is applied at quadratic, as opposed to linear, order in the effective Hamiltonian, and (ii) incorporation of the three-body reduced density matrix in the operator and density matrix decompositions. The quadratic commutator approximation improves CT's accuracy when used with a single-determinant reference, repairing the previous formal disadvantage of the single-reference linear CT theory relative to singles and doubles coupled cluster theory. Calculations on the BH and HF binding curves confirm this improvement. In multireference systems, the three-body reduced density matrix increases the overall accuracy of the CT theory. Tests on the H(2)O and N(2) binding curves yield results highly competitive with expensive state-of-the-art multireference methods, such as the multireference Davidson-corrected configuration interaction (MRCI+Q), averaged coupled pair functional, and averaged quadratic coupled cluster theories.

  5. Measurement of quadratic electrogyration effect in castor oil

    NASA Astrophysics Data System (ADS)

    Izdebski, Marek; Ledzion, Rafał; Górski, Piotr

    2015-07-01

    This work presents a detailed analysis of electrogyration measurement in liquids with the usage of an optical polarimetric technique. Theoretical analysis of the optical response to an applied electric field is illustrated by experimental data for castor oil which exhibits natural optical activity, quadratic electro-optic effect and quadratic electrogyration effect. Moreover, the experimental data show that interaction of the oil with a pair of flat electrodes induces a significant dichroism and natural linear birefringence. The combination of these effects occurring at the same time complicates the procedure of measurements. It has been found that a single measurement is insufficient to separate the contribution of the electrogyration effect, but it is possible on the basis of several measurements performed with various orientations of the polarizer and the analyser. The obtained average values of the quadratic electrogyration coefficient β13 in castor oil at room temperature are from - 0.92 ×10-22 to - 1.44 ×10-22m2V-2 depending on the origin of the oil. Although this study is focused on measurements in castor oil, the presented analysis is much more general.

  6. Formability evaluation for hot-rolled HB780 steel sheet based on 3-D non-quadratic yield function

    NASA Astrophysics Data System (ADS)

    Kim, Wonjae; Koh, Youngwoo; Kim, Hyunki; Chung, Youn-Il; Lee, Myoung-Gyu; Chung, Kwansoo

    2017-05-01

    A common practice to evaluate formability in the typical sheet metal forming process is to measure hardening behavior and a forming limit diagram as separate material properties, and perform numerical forming simulations utilizing various yield functions. The measured forming limit diagram is applied as the failure criterion. However, the performance of material properties such as hardening behavior and yield functions in predicting strain localization in the simple tension and forming limit diagram tests is seldom validated before their application to forming simulation. In this study, a new numerical formability evaluation procedure was proposed, in which not only hardening behavior but also measured forming limit data were employed in characterizing the input data for the hardening behavior and the yield function. Besides, strain localization was directly monitored to determine failure without employing any forming limit criterion. The new procedure was applied for rather thick advanced high strength hot-rolled steel sheet so that 3-D continuum elements were utilized along with 3-D non-quadratic Hosford and quadratic Hill yield functions.

  7. Projection-free parallel quadratic programming for linear model predictive control

    NASA Astrophysics Data System (ADS)

    Di Cairano, S.; Brand, M.; Bortoff, S. A.

    2013-08-01

    A key component in enabling the application of model predictive control (MPC) in fields such as automotive, aerospace, and factory automation is the availability of low-complexity fast optimisation algorithms to solve the MPC finite horizon optimal control problem in architectures with reduced computational capabilities. In this paper, we introduce a projection-free iterative optimisation algorithm and discuss its application to linear MPC. The algorithm, originally developed by Brand for non-negative quadratic programs, is based on a multiplicative update rule and it is shown to converge to a fixed point which is the optimum. An acceleration technique based on a projection-free line search is also introduced, to speed-up the convergence to the optimum. The algorithm is applied to MPC through the dual of the quadratic program (QP) formulated from the MPC finite time optimal control problem. We discuss how termination conditions with guaranteed degree of suboptimality can be enforced, and how the algorithm performance can be optimised by pre-computing the matrices in a parametric form. We show computational results of the algorithm in three common case studies and we compare such results with the results obtained by other available free and commercial QP solvers.

  8. Integrability and Dynamics of Quadratic Three-Dimensional Differential Systems Having an Invariant Paraboloid

    NASA Astrophysics Data System (ADS)

    Messias, Marcelo; Reinol, Alisson C.

    Invariant algebraic surfaces are commonly observed in differential systems arising in mathematical modeling of natural phenomena. In this paper, we study the integrability and dynamics of quadratic polynomial differential systems defined in ℝ3 having an elliptic paraboloid as an invariant algebraic surface. We obtain the normal form for these kind of systems and, by using the invariant paraboloid, we prove the existence of first integrals, exponential factors, Darboux invariants and inverse Jacobi multipliers, for suitable choices of parameter values. We characterize all the possible configurations of invariant parallels and invariant meridians on the invariant paraboloid and give necessary conditions for the invariant parallel to be a limit cycle and for the invariant meridian to have two orbits heteroclinic to a point at infinity. We also study the dynamics of a particular class of the quadratic polynomial differential systems having an invariant paraboloid, giving information about localization and local stability of finite singular points and, by using the Poincaré compactification, we study their dynamics on the Poincaré sphere (at infinity). Finally, we study the well-known Rabinovich system in the case of invariant paraboloids, performing a detailed study of its dynamics restricted to these invariant algebraic surfaces.

  9. Dynamics of SU(1, 1) coherent states for the time-dependent quadratic Hamiltonian system

    NASA Astrophysics Data System (ADS)

    Choi, Jeong Ryeol

    2009-09-01

    The dynamics of SU(1, 1) coherent states introduced by Perelomov are investigated for the time-dependent quadratic Hamiltonian system. SU(1, 1) generators we employed are closely related to the invariant operator theory while those of the previous work of Gerry et al. [C.C. Gerry, P.K. Ma, E.R. Vrscay, Phys. Rev. A 39 (1989) 668] are associated to the simple harmonic oscillator. This is the main difference between the two approaches. The merit of the method used in this paper is that it admits wide sphere of analytical description for quantum features of time-dependent quadratic Hamiltonian system. Our development is applied to the Caldirola-Kanai oscillator and compared the corresponding results with those of the Gerry et al. after correcting some miscalculations of theirs. We showed that the results of our theory are in good agreement with the results of the corrected work of Gerry et al. even if the form of the SU(1, 1) generators we employed are somewhat different from those of their work. The nontrivial zero-point energy plays a dominant role in the very low energy limit (ξ→0) for the Caldirola-Kanai oscillator, leading the system to exhibit pure quantum effects as expected. On the other hand, it turn out for sufficiently high energy limit (ξ→1) that the characteristic feature of dissipating quantum energy become very much the same as that of the classical energy.

  10. Impact of quadratic non-linearity on the dynamics of periodic solutions of a wave equation

    NASA Astrophysics Data System (ADS)

    Kolesov, Andrei Yu; Rozov, Nikolai Kh

    2002-02-01

    For the non-linear telegraph equation with homogeneous Dirichlet or Neumann conditions at the end-points of a finite interval the question of the existence and the stability of time-periodic solutions bifurcating from the zero equilibrium state is considered. The dynamics of these solutions under a change of the diffusion coefficient (that is, the coefficient of the second derivative with respect to the space variable) is investigated. For the Dirichlet boundary conditions it is shown that this dynamics substantially depends on the presence - or the absence - of quadratic terms in the non-linearity. More precisely, it is shown that a quadratic non-linearity results in the occurrence, under an unbounded decrease of diffusion, of an infinite sequence of bifurcations of each periodic solution. En route, the related issue of the limits of applicability of Yu.S. Kolesov's method of quasinormal forms to the construction of self-oscillations in singularly perturbed hyperbolic boundary value problems is studied.

  11. Impact of quadratic non-linearity on the dynamics of periodic solutions of a wave equation

    SciTech Connect

    Kolesov, Andrei Yu; Rozov, Nikolai Kh

    2002-02-28

    For the non-linear telegraph equation with homogeneous Dirichlet or Neumann conditions at the end-points of a finite interval the question of the existence and the stability of time-periodic solutions bifurcating from the zero equilibrium state is considered. The dynamics of these solutions under a change of the diffusion coefficient (that is, the coefficient of the second derivative with respect to the space variable) is investigated. For the Dirichlet boundary conditions it is shown that this dynamics substantially depends on the presence - or the absence - of quadratic terms in the non-linearity. More precisely, it is shown that a quadratic non-linearity results in the occurrence, under an unbounded decrease of diffusion, of an infinite sequence of bifurcations of each periodic solution. En route, the related issue of the limits of applicability of Yu.S. Kolesov's method of quasinormal forms to the construction of self-oscillations in singularly perturbed hyperbolic boundary value problems is studied.

  12. Quadratic programming-based approach for autonomous vehicle path planning in space

    NASA Astrophysics Data System (ADS)

    Chen, Yang; Han, Jianda; Wu, Huaiyu

    2012-07-01

    Path planning for space vehicles is still a challenging problem although considerable progress has been made over the past decades. The major difficulties are that most of existing methods only adapt to static environment instead of dynamic one, and also can not solve the inherent constraints arising from the robot body and the exterior environment. To address these difficulties, this research aims to provide a feasible trajectory based on quadratic programming(QP) for path planning in three-dimensional space where an autonomous vehicle is requested to pursue a target while avoiding static or dynamic obstacles. First, the objective function is derived from the pursuit task which is defined in terms of the relative distance to the target, as well as the angle between the velocity and the position in the relative velocity coordinates(RVCs). The optimization is in quadratic polynomial form according to QP formulation. Then, the avoidance task is modeled with linear constraints in RVCs. Some other constraints, such as kinematics, dynamics, and sensor range, are included. Last, simulations with typical multiple obstacles are carried out, including in static and dynamic environments and one of human-in-the-loop. The results indicate that the optimal trajectories of the autonomous robot in three-dimensional space satisfy the required performances. Therefore, the QP model proposed in this paper not only adapts to dynamic environment with uncertainty, but also can satisfy all kinds of constraints, and it provides an efficient approach to solve the problems of path planning in three-dimensional space.

  13. Fast source optimization involving quadratic line-contour objectives for the resist image.

    PubMed

    Yu, Jue-Chin; Yu, Peichen; Chao, Hsueh-Yung

    2012-03-26

    In Abbe's formulation, source optimization (SO) is often formulated into a linear or quadratic problem, depending on the choice of objective functions. However, the conventional approach for the resist image, involving a sigmoid transformation of the aerial image, results in an objective with a functional form. The applicability of the resist-image objective to SO or simultaneous source and mask optimization (SMO) is therefore limited. In this paper, we present a linear combination of two quadratic line-contour objectives to approximate the resist image effect for fast convergence. The line-contour objectives are based on the aerial image on drawn edges using a constant threshold resist model and that of pixels associated with an intensity minimum for side-lobe suppression. A conjugate gradient method is employed to assure the convergence to the global minimum within the number of iterations less than that of source variables. We further compare the optimized illumination with the proposed line-contour objectives to that with a sigmoid resist-image using a steepest decent method. The results show a 100x speedup with comparable image fidelity and a slightly improved process window for the two cases studied.

  14. Clinical outcomes in patients with a diagnosis of "indefinite for dysplasia" in Barrett's esophagus: a multicenter cohort study.

    PubMed

    Sinh, Preetika; Anaparthy, Rajeswari; Young, Patrick E; Gaddam, Srinivas; Thota, Prashanthi; Balasubramanian, Gokulakrishnan; Singh, Mandeep; Higbee, April D; Wani, Sachin; Gupta, Neil; Rastogi, Amit; Mathur, Sharad C; Bansal, Ajay; Horwhat, John D; Cash, Brooks D; Falk, Gary W; Lieberman, David A; Vargo, John J; Sampliner, Richard E; Sharma, Prateek

    2015-08-01

    Data are limited on the natural history of patients with Barrett's esophagus with a diagnosis of "indefinite for dysplasia" (IND). The aims of this study were to: (i) determine rates of progression to high grade dysplasia (HGD) or esophageal adenocarcinoma, and compare these with rates for low grade dysplasia (LGD); and (ii) determine the proportion of patients whose histological IND diagnosis changed on follow-up endoscopy. Demographic, endoscopic, and histologic information of patients with diagnoses of IND and LGD and at least 12 months of follow-up were extracted from the database of a multicenter Barrett's esophagus study. Rates and times for progression to HGD and esophageal adenocarcinoma and regression to nondysplastic epithelium were calculated. Proportions of diagnoses upgraded to HGD/esophageal adenocarcinoma or downgraded to nondysplastic epithelium at first follow-up endoscopy were evaluated. Amongst 2264 patients, 83 with a diagnosis of IND (mean age 60 years, 95 % men, 95 % white; mean follow-up 5.6 years) and 79 with diagnosis of LGD were identified. In the IND group, annual incidences of esophageal adenocarcinoma and HGD were 0.21 % and 0.64 %, respectively, representing a combined incidence of 0.8 %. Mean time to progression was 4.72 years. Within the IND group 55 % patients showed regression to nondysplastic epithelium at first follow-up endoscopy and the overall regression rate was 80 %. Corresponding rates in LGD patients were similar. Lesions diagnosed as IND and LGD show similar biological behavior and can be treated as a single category with respect to surveillance and follow-up. © Georg Thieme Verlag KG Stuttgart · New York.

  15. Quadratic function between arterial partial oxygen pressure and mortality risk in sepsis patients: an interaction with simplified acute physiology score.

    PubMed

    Zhang, Zhongheng; Ji, Xuqing

    2016-10-13

    Oxygen therapy is widely used in emergency and critical care settings, while there is little evidence on its real therapeutic effect. The study aimed to explore the impact of arterial oxygen partial pressure (PaO2) on clinical outcomes in patients with sepsis. A large clinical database was employed for the study. Subjects meeting the diagnostic criteria of sepsis were eligible for the study. All measurements of PaO2 were extracted. The primary endpoint was death from any causes during hospital stay. Survey data analysis was performed by using individual ICU admission as the primary sampling unit. Quadratic function was assumed for PaO2 and its interaction with other covariates were explored. A total of 199,125 PaO2 samples were identified for 11,002 ICU admissions. Each ICU stay comprised 18 PaO2 samples in average. The fitted multivariable model supported our hypothesis that the effect of PaO2 on mortality risk was in quadratic form. There was significant interaction between PaO2 and SAPS-I (p = 0.007). Furthermore, the main effect of PaO2 on SOFA score was nonlinear. The study shows that the effect of PaO2 on mortality risk is in quadratic function form, and there is significant interaction between PaO2 and severity of illness.

  16. Quadratic function between arterial partial oxygen pressure and mortality risk in sepsis patients: an interaction with simplified acute physiology score

    PubMed Central

    Zhang, Zhongheng; Ji, Xuqing

    2016-01-01

    Oxygen therapy is widely used in emergency and critical care settings, while there is little evidence on its real therapeutic effect. The study aimed to explore the impact of arterial oxygen partial pressure (PaO2) on clinical outcomes in patients with sepsis. A large clinical database was employed for the study. Subjects meeting the diagnostic criteria of sepsis were eligible for the study. All measurements of PaO2 were extracted. The primary endpoint was death from any causes during hospital stay. Survey data analysis was performed by using individual ICU admission as the primary sampling unit. Quadratic function was assumed for PaO2 and its interaction with other covariates were explored. A total of 199,125 PaO2 samples were identified for 11,002 ICU admissions. Each ICU stay comprised 18 PaO2 samples in average. The fitted multivariable model supported our hypothesis that the effect of PaO2 on mortality risk was in quadratic form. There was significant interaction between PaO2 and SAPS-I (p = 0.007). Furthermore, the main effect of PaO2 on SOFA score was nonlinear. The study shows that the effect of PaO2 on mortality risk is in quadratic function form, and there is significant interaction between PaO2 and severity of illness. PMID:27734905

  17. Minimization of the root of a quadratic functional under a system of affine equality constraints with application to portfolio management

    NASA Astrophysics Data System (ADS)

    Landsman, Zinoviy

    2008-10-01

    We present an explicit closed form solution of the problem of minimizing the root of a quadratic functional subject to a system of affine constraints. The result generalizes Z. Landsman, Minimization of the root of a quadratic functional under an affine equality constraint, J. Comput. Appl. Math. 2007, to appear, see , articles in press, where the optimization problem was solved under only one linear constraint. This is of interest for solving significant problems pertaining to financial economics as well as some classes of feasibility and optimization problems which frequently occur in tomography and other fields. The results are illustrated in the problem of optimal portfolio selection and the particular case when the expected return of finance portfolio is certain is discussed.

  18. Chemotherapy for tumors: an analysis of the dynamics and a study of quadratic and linear optimal controls.

    PubMed

    de Pillis, L G; Gu, W; Fister, K R; Head, T; Maples, K; Murugan, A; Neal, T; Yoshida, K

    2007-09-01

    We investigate a mathematical model of tumor-immune interactions with chemotherapy, and strategies for optimally administering treatment. In this paper we analyze the dynamics of this model, characterize the optimal controls related to drug therapy, and discuss numerical results of the optimal strategies. The form of the model allows us to test and compare various optimal control strategies, including a quadratic control, a linear control, and a state-constraint. We establish the existence of the optimal control, and solve for the control in both the quadratic and linear case. In the linear control case, we show that we cannot rule out the possibility of a singular control. An interesting aspect of this paper is that we provide a graphical representation of regions on which the singular control is optimal.

  19. Creepers: Real quadratic orders with large class number

    NASA Astrophysics Data System (ADS)

    Patterson, Roger

    2007-03-01

    Shanks's sequence of quadratic fields Q(sqrt{S_{n}}) where S_{n}=(2^n+1)^2 + 2^{n+2} instances a class of quadratic fields for which the class number is large and, therefore, the continued fraction period is relatively short. Indeed, that period length increases linearly with n, that is: in arithmetic progression. The fields have regulator O(n^2). In the late nineties, these matters intrigued Irving Kaplansky, and led him to compute period length of the square root of sequences a^2x^{2n}+bx^{n}+c for integers a, b, c, and x. In brief, Kap found unsurprisingly that, generically, triples (a,b,c) are `leapers': they yield sequences with period length increasing at exponential rate. But there are triples yielding sequences with constant period length, Kap's `sleepers'. Finally, there are triples, as exemplified by the Shanks's sequence, for which the period lengths increase in arithmetic progression. Felicitously, Kaplansky called these `creepers'. It seems that the sleepers and creepers are precisely those for which one is able to detail the explicit continued fraction expansion for all n. Inter alia, this thesis noticeably extends the known classes of creepers and finds that not all are `kreepers' (of the shape identified by Kaplansky) and therefore not of the shape of examples studied by earlier authors looking for families of quadratic number fields with explicitly computable unit and of relatively large regulator. The work of this thesis includes the discovery of old and new families of hyperelliptic curves of increasing genus g and torsion divisor of order O(g^2). It follows that the apparent trichotomy leaper/sleeper/creeper coincides with the folk belief that the just-mentioned torsion is maximum possible.

  20. Indefinite intertwining operators

    PubMed Central

    Baldoni-Silva, M. W.; Knapp, A. W.

    1984-01-01

    For a wide class of linear connected semisimple Lie groups, one obtains formulas limiting the Langlands parameters of irreducible unitary representations obtained from maximal parabolic subgroups. The formulas relate unitarity to the number of roots satisfying certain conditions. Some evidence is presented that the formulas are sharp. The results confirm aspects of conjectures that relate unitary parameters to cohomological induction. PMID:16593424

  1. Solving the quadratic assignment problem with clues from nature.

    PubMed

    Nissen, V

    1994-01-01

    This paper describes a new evolutionary approach to solving quadratic assignment problems. The proposed technique is based loosely on a class of search and optimization algorithms known as evolution strategies (ES). These methods are inspired by the mechanics of biological evolution and have been applied successfully to a variety of difficult problems, particularly in continuous optimization. The combinatorial variant of ES presented here performs very well on the given test problems as compared with the standard 2-Opt heuristic and results with simulated annealing and tabu search. Extensions for practical applications in factory layout are described.

  2. Asymmetric Simple Exclusion Process with Open Boundaries and Quadratic Harnesses

    NASA Astrophysics Data System (ADS)

    Bryc, Włodek; Wesołowski, Jacek

    2017-04-01

    We show that the joint probability generating function of the stationary measure of a finite state asymmetric exclusion process with open boundaries can be expressed in terms of joint moments of Markov processes called quadratic harnesses. We use our representation to prove the large deviations principle for the total number of particles in the system. We use the generator of the Markov process to show how explicit formulas for the average occupancy of a site arise for special choices of parameters. We also give similar representations for limits of stationary measures as the number of sites tends to infinity.

  3. On a quadratic transformation due to Kummer and its generalizations

    NASA Astrophysics Data System (ADS)

    Shekhawat, Nidhi; Rathie, Arjun K.; Prakash, Om

    2016-05-01

    The aim of this paper is to obtain explicit expressions of (1-x ) -a2F1[a ,b 2 b +j ; -2/x 1 -x ] for j = 0, ±1,…, ±9. For j = 0, we have a well-known quadratic transformations formula of Kummer. The results are obtained by using the known hypergeometric identities available in the literature. Several known results obtained earlier by Kim, et al. follow special cases of our main findings. The results derived in this paper are simple, interesting and potentially useful in the applicable sciences.

  4. Reaction Wheel Control Design Using Linear Quadratic Controller

    NASA Astrophysics Data System (ADS)

    Nubli Muhamad, Nur; Susanto, Erwin; Syihabuddin, Budi; Prasetya Dwi Wibawa, Ig.

    2016-01-01

    This paper studies the design of active attitude control system of a nanosatellite in a single axis. In this paper, we consider dc motor based reaction wheel as an actuator, because of its pointing accuracy. However, the power consumption of the dc motor is often relatively large and needed to be optimized. Linear quadratic controller is supposed to have an ability to minimize power consumption and able to enhance the system performance. To show the advantage of this method, simulation result of attitude response, state trajectory, and trajectory of DC motor voltage are presented.

  5. Quadratic Feynman loop integrands from massless scattering equations

    NASA Astrophysics Data System (ADS)

    Gomez, Humberto

    2017-05-01

    Recently, the Cachazo-He-Yuan (CHY) approach has been extended to the loop level, but the resulting loop integrand has propagators that are linear in the loop momentum unlike Feynman's. In this paper, we present a new technique that directly produces quadratic propagators identical to Feynman's from the CHY approach. This paper focuses on the Φ3 theory, but extensions to other theories are briefly discussed. In addition, our proposal has an interesting geometric meaning; we can interpret this new formula as a unitary cut on a higher genus Riemann surface.

  6. Asymmetric Simple Exclusion Process with Open Boundaries and Quadratic Harnesses

    NASA Astrophysics Data System (ADS)

    Bryc, Włodek; Wesołowski, Jacek

    2017-02-01

    We show that the joint probability generating function of the stationary measure of a finite state asymmetric exclusion process with open boundaries can be expressed in terms of joint moments of Markov processes called quadratic harnesses. We use our representation to prove the large deviations principle for the total number of particles in the system. We use the generator of the Markov process to show how explicit formulas for the average occupancy of a site arise for special choices of parameters. We also give similar representations for limits of stationary measures as the number of sites tends to infinity.

  7. Frontogenesis driven by horizontally quadratic distributions of density

    NASA Technical Reports Server (NTRS)

    Jacqmin, David

    1991-01-01

    Attention is given to the quadratic density distribution in a channel, which has been established by Simpson and Linden to be the simplest case of the horizontally nonlinear distribution of fluid density required for the production of frontogenesis. The porous-media and Boussinesq flow models are examined, and their evolution equations are reduced to one-dimensional systems. While both the porous-media and the inviscid/nondiffusive Boussinesq systems exhibit classic frontogenesis behavior, the viscous Boussinesq system exhibits a more complex behavior: boundary-layer effects force frontogenesis away from the lower boundary, and at late times the steepest density gradients are close to mid-channel.

  8. Rigorous performance bounds for quadratic and nested dynamical decoupling

    SciTech Connect

    Xia, Yuhou; Uhrig, Goetz S.; Lidar, Daniel A.

    2011-12-15

    We present rigorous performance bounds for the quadratic dynamical decoupling pulse sequence which protects a qubit from general decoherence, and for its nested generalization to an arbitrary number of qubits. Our bounds apply under the assumptions of instantaneous pulses and of bounded perturbing environment and qubit-environment Hamiltonians such as those realized by baths of nuclear spins in quantum dots. We prove that if the total sequence time is fixed then the trace-norm distance between the unperturbed and protected system states can be made arbitrarily small by increasing the number of applied pulses.

  9. Restart-Based Genetic Algorithm for the Quadratic Assignment Problem

    NASA Astrophysics Data System (ADS)

    Misevicius, Alfonsas

    The power of genetic algorithms (GAs) has been demonstrated for various domains of the computer science, including combinatorial optimization. In this paper, we propose a new conceptual modification of the genetic algorithm entitled a "restart-based genetic algorithm" (RGA). An effective implementation of RGA for a well-known combinatorial optimization problem, the quadratic assignment problem (QAP), is discussed. The results obtained from the computational experiments on the QAP instances from the publicly available library QAPLIB show excellent performance of RGA. This is especially true for the real-life like QAPs.

  10. Compact stellar models obeying quadratic equation of state

    NASA Astrophysics Data System (ADS)

    Bhar, Piyali; Singh, Ksh. Newton; Pant, Neeraj

    2016-10-01

    In present paper we obtain a new model of compact star by considering quadratic equation of state for the matter distribution and assuming a physically reasonable choice for metric coefficient g_{rr}. The solution is singularity free and well behaved inside the stellar interior. Several features are described analytically as well as graphically. From our analysis we have shown that our model is compatible with the observational data of the compact stars. We have discussed a detail analysis of neutron star PSR J1614-2230 via different graphs after determining all the constant parameters from boundary conditions.

  11. On stability of the Kasner solution in quadratic gravity

    NASA Astrophysics Data System (ADS)

    Toporensky, A.; Müller, D.

    2017-01-01

    We consider the dynamics of a flat anisotropic Universe filled by a perfect fluid near a cosmological singularity in quadratic gravity. Two possible regimes are described—the Kasner anisotropic solution and an isotropic "vacuum radiation" solution which has three sub cases depending on whether the equation of state parameter w is bigger, smaller or equals to 1 / 3. Initial conditions for numerical integrations have been chosen near a General Relativity anisotropic solution with matter (Jacobs solution). We have found that for such initial conditions there is a range of values of the coupling constants so that the resulting cosmological singularity is isotropic.

  12. Linear-Quadratic-Gaussian Regulator Developed for a Magnetic Bearing

    NASA Technical Reports Server (NTRS)

    Choi, Benjamin B.

    2002-01-01

    Linear-Quadratic-Gaussian (LQG) control is a modern state-space technique for designing optimal dynamic regulators. It enables us to trade off regulation performance and control effort, and to take into account process and measurement noise. The Structural Mechanics and Dynamics Branch at the NASA Glenn Research Center has developed an LQG control for a fault-tolerant magnetic bearing suspension rig to optimize system performance and to reduce the sensor and processing noise. The LQG regulator consists of an optimal state-feedback gain and a Kalman state estimator. The first design step is to seek a state-feedback law that minimizes the cost function of regulation performance, which is measured by a quadratic performance criterion with user-specified weighting matrices, and to define the tradeoff between regulation performance and control effort. The next design step is to derive a state estimator using a Kalman filter because the optimal state feedback cannot be implemented without full state measurement. Since the Kalman filter is an optimal estimator when dealing with Gaussian white noise, it minimizes the asymptotic covariance of the estimation error.

  13. Confidence set inference with a prior quadratic bound

    NASA Technical Reports Server (NTRS)

    Backus, George E.

    1989-01-01

    In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z=(z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y (sup 0) = (y (sub 1) (sup 0), ..., y (sub D (sup 0)), using full or partial knowledge of the statistical distribution of the random errors in y (sup 0). The data space Y containing y(sup 0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x, Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. Confidence set inference is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface.

  14. An Instability Index Theory for Quadratic Pencils and Applications

    NASA Astrophysics Data System (ADS)

    Bronski, Jared; Johnson, Mathew A.; Kapitula, Todd

    2014-04-01

    Primarily motivated by the stability analysis of nonlinear waves in second-order in time Hamiltonian systems, in this paper we develop an instability index theory for quadratic operator pencils acting on a Hilbert space. In an extension of the known theory for linear pencils, explicit connections are made between the number of eigenvalues of a given quadratic operator pencil with positive real parts to spectral information about the individual operators comprising the coefficients of the spectral parameter in the pencil. As an application, we apply the general theory developed here to yield spectral and nonlinear stability/instability results for abstract second-order in time wave equations. More specifically, we consider the problem of the existence and stability of spatially periodic waves for the "good" Boussinesq equation. In the analysis our instability index theory provides an explicit, and somewhat surprising, connection between the stability of a given periodic traveling wave solution of the "good" Boussinesq equation and the stability of the same periodic profile, but with different wavespeed, in the nonlinear dynamics of a related generalized Korteweg-de Vries equation.

  15. Wave propagation in elastic medium with heterogeneous quadratic nonlinearity

    SciTech Connect

    Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin

    2011-06-23

    This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter {beta} when the nonlinearity distribution in the layer is a stochastic process.

  16. Hidden and Nonstandard Bifurcation Diagram of an Alternate Quadratic System

    NASA Astrophysics Data System (ADS)

    Pastor, G.; Romera, M.; Danca, M.-F.; Martin, A.; Orue, A. B.; Montoya, F.; Encinas, L. Hernández

    Alternate quadratic systems A : xn+1 = 1 - axn2,if n is even 1 - a∗xn2,if n is odd andB : xn+1 = 1 - a∗xn2,if n is even 1 - axn2, if n is odd, where a and a∗ are different parameters, seem to be interval maps in a range of the parameter values. However, after a careful graphical analysis of their bifurcation diagrams we conclude that this is true only for system B, but not for system A. In system A we find a hidden and nonstandard bifurcation diagram (“hidden” because it is not visible at normal resolution and “nonstandard” because the bifurcation diagram is empty for some ranges of the parameter values). The different behavior of the underlying critical polynomial in the range of parameter values in both alternate quadratic systems explains why the hidden and nonstandard bifurcation diagram is present in system A and not in system B. The analysis of the Lyapunov exponent also shows both the existence and the different behavior of the hidden bifurcation diagram of system A.

  17. Quadratic Reciprocity and the Group Orders of Particle States

    SciTech Connect

    DAI,YANG; BORISOV,ALEXEY B.; LONGWORTH,JAMES W.; BOYER,KEITH; RHODES,CHARLES K.

    2001-06-01

    The construction of inverse states in a finite field F{sub P{sub P{alpha}}} enables the organization of the mass scale by associating particle states with residue class designations. With the assumption of perfect flatness ({Omega}total = 1.0), this approach leads to the derivation of a cosmic seesaw congruence which unifies the concepts of space and mass. The law of quadratic reciprocity profoundly constrains the subgroup structure of the multiplicative group of units F{sub P{sub {alpha}}}* defined by the field. Four specific outcomes of this organization are (1) a reduction in the computational complexity of the mass state distribution by a factor of {approximately}10{sup 30}, (2) the extension of the genetic divisor concept to the classification of subgroup orders, (3) the derivation of a simple numerical test for any prospective mass number based on the order of the integer, and (4) the identification of direct biological analogies to taxonomy and regulatory networks characteristic of cellular metabolism, tumor suppression, immunology, and evolution. It is generally concluded that the organizing principle legislated by the alliance of quadratic reciprocity with the cosmic seesaw creates a universal optimized structure that functions in the regulation of a broad range of complex phenomena.

  18. Alignment of molecular networks by integer quadratic programming.

    PubMed

    Zhenping, Li; Zhang, Shihua; Wang, Yong; Zhang, Xiang-Sun; Chen, Luonan

    2007-07-01

    With more and more data on molecular networks (e.g. protein interaction networks, gene regulatory networks and metabolic networks) available, the discovery of conserved patterns or signaling pathways by comparing various kinds of networks among different species or within a species becomes an increasingly important problem. However, most of the conventional approaches either restrict comparative analysis to special structures, such as pathways, or adopt heuristic algorithms due to computational burden. In this article, to find the conserved substructures, we develop an efficient algorithm for aligning molecular networks based on both molecule similarity and architecture similarity, by using integer quadratic programming (IQP). Such an IQP can be relaxed into the corresponding quadratic programming (QP) which almost always ensures an integer solution, thereby making molecular network alignment tractable without any approximation. The proposed framework is very flexible and can be applied to many kinds of molecular networks including weighted and unweighted, directed and undirected networks with or without loops. Matlab code and data are available from http://zhangroup.aporc.org/bioinfo/MNAligner or http://intelligent.eic.osaka-sandai.ac.jp/chenen/software/MNAligner, or upon request from authors. Supplementary data are available at Bioinformatics online.

  19. Electric current quadratic in an applied electric field

    NASA Astrophysics Data System (ADS)

    Deyo, Eric

    The theory of the photogalvanic effect in a low frequency electric field is developed. We complete the semiclassical theory of the effect in bulk samples lacking inversion symmetry, taking into account contributions from the asymmetry of scattering, the shift current, and the effect of Berry's phase. We consider the effect in such samples both in the presence and absence of a constant magnetic field. It is found that by experimentally measuring this effect, that Berry's curvature and the average shift of the center of mass of an electron during a scattering event can be extracted. We also investigate the magnetic field dependence of the part of the electrical current which is quadratic in voltage in mesoscopic conductors. We find that the part of the current which is quadratic in bias voltage, and linear in an applied magnetic field can be related to the effective electron-electron interaction strength. We also find that in the case when the magnetic field is oriented parallel to the plane of a two dimensional sample, that the spin-orbit scattering rate can be measured.

  20. Sequential quadratic programming-based fast path planning algorithm subject to no-fly zone constraints

    NASA Astrophysics Data System (ADS)

    Liu, Wei; Ma, Shunjian; Sun, Mingwei; Yi, Haidong; Wang, Zenghui; Chen, Zengqiang

    2016-08-01

    Path planning plays an important role in aircraft guided systems. Multiple no-fly zones in the flight area make path planning a constrained nonlinear optimization problem. It is necessary to obtain a feasible optimal solution in real time. In this article, the flight path is specified to be composed of alternate line segments and circular arcs, in order to reformulate the problem into a static optimization one in terms of the waypoints. For the commonly used circular and polygonal no-fly zones, geometric conditions are established to determine whether or not the path intersects with them, and these can be readily programmed. Then, the original problem is transformed into a form that can be solved by the sequential quadratic programming method. The solution can be obtained quickly using the Sparse Nonlinear OPTimizer (SNOPT) package. Mathematical simulations are used to verify the effectiveness and rapidity of the proposed algorithm.

  1. Quadratic Forms on Complex Random Matrices and Multi-Antenna Channel Capacity

    DTIC Science & Technology

    2004-03-16

    channel capacity and capacity versus outage of multiple - input multiple - output ( MIMO ) Rayleigh-distributed wireless communication channels. Both... output ( MIMO ) wireless communication systems.jointLet us denote the number of inputs (or transmitters) and formation theory. These densities are...be represented channel capacity and capacity versus outage of multiple - by an n, ×nt complex random matrix H - CN(0, Er®Et), input multiple - output

  2. A class of stochastic optimization problems with one quadratic & several linear objective functions and extended portfolio selection model

    NASA Astrophysics Data System (ADS)

    Xu, Jiuping; Li, Jun

    2002-09-01

    In this paper a class of stochastic multiple-objective programming problems with one quadratic, several linear objective functions and linear constraints has been introduced. The former model is transformed into a deterministic multiple-objective nonlinear programming model by means of the introduction of random variables' expectation. The reference direction approach is used to deal with linear objectives and results in a linear parametric optimization formula with a single linear objective function. This objective function is combined with the quadratic function using the weighted sums. The quadratic problem is transformed into a linear (parametric) complementary problem, the basic formula for the proposed approach. The sufficient and necessary conditions for (properly, weakly) efficient solutions and some construction characteristics of (weakly) efficient solution sets are obtained. An interactive algorithm is proposed based on reference direction and weighted sums. Varying the parameter vector on the right-hand side of the model, the DM can freely search the efficient frontier with the model. An extended portfolio selection model is formed when liquidity is considered as another objective to be optimized besides expectation and risk. The interactive approach is illustrated with a practical example.

  3. Effects of quadratic and cubic nonlinearities on a perfectly tuned parametric amplifier

    NASA Astrophysics Data System (ADS)

    Neumeyer, S.; Sorokin, V. S.; Thomsen, J. J.

    2017-01-01

    We consider the performance of a parametric amplifier with perfect tuning (two-to-one ratio between the parametric and direct excitation frequencies) and quadratic and cubic nonlinearities. A forced Duffing-Mathieu equation with appended quadratic nonlinearity is considered as the model system, and approximate analytical steady-state solutions and corresponding stabilities are obtained by the method of varying amplitudes. Some general effects of pure quadratic, and mixed quadratic and cubic nonlinearities on parametric amplification are shown. In particular, the effects of mixed quadratic and cubic nonlinearities may generate additional amplitude-frequency solutions. In this case an increased response and a more phase sensitive amplitude (phase between excitation frequencies) is obtained, as compared to the case with either pure quadratic or cubic nonlinearity. Furthermore, jumps and bi-stability in the amplitude-phase characteristics are predicted, supporting previously reported experimental observations.

  4. Linear state feedback, quadratic weights, and closed loop eigenstructures. M.S. Thesis

    NASA Technical Reports Server (NTRS)

    Thompson, P. M.

    1979-01-01

    Results are given on the relationships between closed loop eigenstructures, state feedback gain matrices of the linear state feedback problem, and quadratic weights of the linear quadratic regulator. Equations are derived for the angles of general multivariable root loci and linear quadratic optimal root loci, including angles of departure and approach. The generalized eigenvalue problem is used for the first time to compute angles of approach. Equations are also derived to find the sensitivity of closed loop eigenvalues and the directional derivatives of closed loop eigenvectors (with respect to a scalar multiplying the feedback gain matrix or the quadratic control weight). An equivalence class of quadratic weights that produce the same asymptotic eigenstructure is defined, sufficient conditions to be in it are given, a canonical element is defined, and an algorithm to find it is given. The behavior of the optimal root locus in the nonasymptotic region is shown to be different for quadratic weights with the same asymptotic properties.

  5. Integrability of Quadratic Non-autonomous Quantum Linear Systems

    NASA Astrophysics Data System (ADS)

    Lopez, Raquel

    The Quantum Harmonic Oscillator is one of the most important models in Quantum Mechanics. Analogous to the classical mass vibrating back and forth on a spring, the quantum oscillator system has attracted substantial attention over the years because of its importance in many advanced and difficult quantum problems. This dissertation deals with solving generalized models of the time-dependent Schrodinger equation which are called generalized quantum harmonic oscillators, and these are characterized by an arbitrary quadratic Hamiltonian of linear momentum and position operators. The primary challenge in this work is that most quantum models with timedependence are not solvable explicitly, yet this challenge became the driving motivation for this work. In this dissertation, the methods used to solve the time-dependent Schrodinger equation are the fundamental singularity (or Green's function) and the Fourier (eigenfunction expansion) methods. Certain Riccati- and Ermakov-type systems arise, and these systems are highlighted and investigated. The overall aims of this dissertation are to show that quadratic Hamiltonian systems are completely integrable systems, and to provide explicit approaches to solving the time-dependent Schr¨odinger equation governed by an arbitrary quadratic Hamiltonian operator. The methods and results established in the dissertation are not yet well recognized in the literature, yet hold for high promise for further future research. Finally, the most recent results in the dissertation correspond to the harmonic oscillator group and its symmetries. A simple derivation of the maximum kinematical invariance groups of the free particle and quantum harmonic oscillator is constructed from the view point of the Riccati- and Ermakov-type systems, which shows an alternative to the traditional Lie Algebra approach. To conclude, a missing class of solutions of the time-dependent Schrodinger equation for the simple harmonic oscillator in one dimension is

  6. Scaling Laws for the Multidimensional Burgers Equation with Quadratic External Potential

    NASA Astrophysics Data System (ADS)

    Leonenko, N. N.; Ruiz-Medina, M. D.

    2006-07-01

    The reordering of the multidimensional exponential quadratic operator in coordinate-momentum space (see X. Wang, C.H. Oh and L.C. Kwek (1998). J. Phys. A.: Math. Gen. 31:4329-4336) is applied to derive an explicit formulation of the solution to the multidimensional heat equation with quadratic external potential and random initial conditions. The solution to the multidimensional Burgers equation with quadratic external potential under Gaussian strongly dependent scenarios is also obtained via the Hopf-Cole transformation. The limiting distributions of scaling solutions to the multidimensional heat and Burgers equations with quadratic external potential are then obtained under such scenarios.

  7. Absence of the Gribov ambiguity in a quadratic gauge

    NASA Astrophysics Data System (ADS)

    Raval, Haresh

    2016-05-01

    The Gribov ambiguity exists in various gauges. Algebraic gauges are likely to be ambiguity free. However, algebraic gauges are not Lorentz invariant, which is their fundamental flaw. In addition, they are not generally compatible with the boundary conditions on the gauge fields, which are needed to compactify the space i.e., the ambiguity continues to exist on a compact manifold. Here we discuss a quadratic gauge fixing, which is Lorentz invariant. We consider an example of a spherically symmetric gauge field configuration in which we prove that this Lorentz invariant gauge removes the ambiguity on a compact manifold {S}^3, when a proper boundary condition on the gauge configuration is taken into account. Thus, we provide one example where the ambiguity is absent on a compact manifold in the algebraic gauge. We also show that the BRST invariance is preserved in this gauge.

  8. Cosmology for quadratic gravity in generalized Weyl geometry

    SciTech Connect

    Jiménez, Jose Beltrán; Heisenberg, Lavinia; Koivisto, Tomi S.

    2016-04-26

    A class of vector-tensor theories arises naturally in the framework of quadratic gravity in spacetimes with linear vector distortion. Requiring the absence of ghosts for the vector field imposes an interesting condition on the allowed connections with vector distortion: the resulting one-parameter family of connections generalises the usual Weyl geometry with polar torsion. The cosmology of this class of theories is studied, focusing on isotropic solutions wherein the vector field is dominated by the temporal component. De Sitter attractors are found and inhomogeneous perturbations around such backgrounds are analysed. In particular, further constraints on the models are imposed by excluding pathologies in the scalar, vector and tensor fluctuations. Various exact background solutions are presented, describing a constant and an evolving dark energy, a bounce and a self-tuning de Sitter phase. However, the latter two scenarios are not viable under a closer scrutiny.

  9. Low photon count based digital holography for quadratic phase cryptography.

    PubMed

    Muniraj, Inbarasan; Guo, Changliang; Malallah, Ra'ed; Ryle, James P; Healy, John J; Lee, Byung-Geun; Sheridan, John T

    2017-07-15

    Recently, the vulnerability of the linear canonical transform-based double random phase encryption system to attack has been demonstrated. To alleviate this, we present for the first time, to the best of our knowledge, a method for securing a two-dimensional scene using a quadratic phase encoding system operating in the photon-counted imaging (PCI) regime. Position-phase-shifting digital holography is applied to record the photon-limited encrypted complex samples. The reconstruction of the complex wavefront involves four sparse (undersampled) dataset intensity measurements (interferograms) at two different positions. Computer simulations validate that the photon-limited sparse-encrypted data has adequate information to authenticate the original data set. Finally, security analysis, employing iterative phase retrieval attacks, has been performed.

  10. Repopulation Kinetics and the Linear-Quadratic Model

    NASA Astrophysics Data System (ADS)

    O'Rourke, S. F. C.; McAneney, H.; Starrett, C.; O'Sullivan, J. M.

    2009-08-01

    The standard Linear-Quadratic (LQ) survival model for radiotherapy is used to investigate different schedules of radiation treatment planning for advanced head and neck cancer. We explore how these treament protocols may be affected by different tumour repopulation kinetics between treatments. The laws for tumour cell repopulation include the logistic and Gompertz models and this extends the work of Wheldon et al. [1], which was concerned with the case of exponential repopulation between treatments. Treatment schedules investigated include standarized and accelerated fractionation. Calculations based on the present work show, that even with growth laws scaled to ensure that the repopulation kinetics for advanced head and neck cancer are comparable, considerable variation in the survival fraction to orders of magnitude emerged. Calculations show that application of the Gompertz model results in a significantly poorer prognosis for tumour eradication. Gaps in treatment also highlight the differences in the LQ model with the effect of repopulation kinetics included.

  11. Neural network for solving convex quadratic bilevel programming problems.

    PubMed

    He, Xing; Li, Chuandong; Huang, Tingwen; Li, Chaojie

    2014-03-01

    In this paper, using the idea of successive approximation, we propose a neural network to solve convex quadratic bilevel programming problems (CQBPPs), which is modeled by a nonautonomous differential inclusion. Different from the existing neural network for CQBPP, the model has the least number of state variables and simple structure. Based on the theory of nonsmooth analysis, differential inclusions and Lyapunov-like method, the limit equilibrium points sequence of the proposed neural networks can approximately converge to an optimal solution of CQBPP under certain conditions. Finally, simulation results on two numerical examples and the portfolio selection problem show the effectiveness and performance of the proposed neural network. Copyright © 2013 Elsevier Ltd. All rights reserved.

  12. Renormalisation of correlations in a barrier billiard: Quadratic irrational trajectories

    NASA Astrophysics Data System (ADS)

    Adamson, L. N. C.; Osbaldestin, A. H.

    2014-03-01

    We present an analysis of autocorrelation functions in symmetric barrier billiards using a renormalisation approach for quadratic irrational trajectories. Depending on the nature of the barrier, this leads to either self-similar or chaotic behaviour. In the self-similar case we give an analysis of the half barrier and present a detailed calculation of the locations, asymptotic heights and signs of the main peaks in the autocorrelation function. Then we consider arbitrary barriers, illustrating that typically these give rise to chaotic correlations of the autocorrelation function which we further represent by showing the invariant sets associated with these correlations. Our main ingredient here is a functional recurrence which has been previously derived and used in work on the Harper equation, strange non-chaotic attractors and a quasi-periodically forced two-level system.

  13. Schwarz and multilevel methods for quadratic spline collocation

    SciTech Connect

    Christara, C.C.; Smith, B.

    1994-12-31

    Smooth spline collocation methods offer an alternative to Galerkin finite element methods, as well as to Hermite spline collocation methods, for the solution of linear elliptic Partial Differential Equations (PDEs). Recently, optimal order of convergence spline collocation methods have been developed for certain degree splines. Convergence proofs for smooth spline collocation methods are generally more difficult than for Galerkin finite elements or Hermite spline collocation, and they require stronger assumptions and more restrictions. However, numerical tests indicate that spline collocation methods are applicable to a wider class of problems, than the analysis requires, and are very competitive to finite element methods, with respect to efficiency. The authors will discuss Schwarz and multilevel methods for the solution of elliptic PDEs using quadratic spline collocation, and compare these with domain decomposition methods using substructuring. Numerical tests on a variety of parallel machines will also be presented. In addition, preliminary convergence analysis using Schwarz and/or maximum principle techniques will be presented.

  14. Quadratic time dependent Hamiltonians and separation of variables

    NASA Astrophysics Data System (ADS)

    Anzaldo-Meneses, A.

    2017-06-01

    Time dependent quantum problems defined by quadratic Hamiltonians are solved using canonical transformations. The Green's function is obtained and a comparison with the classical Hamilton-Jacobi method leads to important geometrical insights like exterior differential systems, Monge cones and time dependent Gaussian metrics. The Wei-Norman approach is applied using unitary transformations defined in terms of generators of the associated Lie groups, here the semi-direct product of the Heisenberg group and the symplectic group. A new explicit relation for the unitary transformations is given in terms of a finite product of elementary transformations. The sequential application of adequate sets of unitary transformations leads naturally to a new separation of variables method for time dependent Hamiltonians, which is shown to be related to the Inönü-Wigner contraction of Lie groups. The new method allows also a better understanding of interacting particles or coupled modes and opens an alternative way to analyze topological phases in driven systems.

  15. Qualitative analysis of certain generalized classes of quadratic oscillator systems

    SciTech Connect

    Bagchi, Bijan Ghosh, Samiran Pal, Barnali Poria, Swarup

    2016-02-15

    We carry out a systematic qualitative analysis of the two quadratic schemes of generalized oscillators recently proposed by Quesne [J. Math. Phys. 56, 012903 (2015)]. By performing a local analysis of the governing potentials, we demonstrate that while the first potential admits a pair of equilibrium points one of which is typically a center for both signs of the coupling strength λ, the other points to a centre for λ < 0 but a saddle λ > 0. On the other hand, the second potential reveals only a center for both the signs of λ from a linear stability analysis. We carry out our study by extending Quesne’s scheme to include the effects of a linear dissipative term. An important outcome is that we run into a remarkable transition to chaos in the presence of a periodic force term fcosωt.

  16. Phonon blockade in a quadratically coupled optomechanical system

    NASA Astrophysics Data System (ADS)

    Xie, Hong; Liao, Chang-Geng; Shang, Xiao; Ye, Ming-Yong; Lin, Xiu-Min

    2017-07-01

    Phonon blockade is achieved in a quadratically coupled optomechanical system, in which the nonlinear interaction between phonons is induced by a driving field via radiation pressure. It is different from the previous standard methods, where the nonlinear interaction for observing phonon blockade is obtained by coupling the mechanical resonator to a two-level system. The effective coupling strength can be tuned by controlling the amplitudes of the driving field, which allows large nonlinearities for the optomechanical system. The second-order correlation function is discussed both analytically and numerically to characterize the phonon statistical properties and the results show that the phonon blockade is available when the effective coupling strength is larger than the mechanical decay rate. This work provides a possible way to experimentally realize phonon blockade.

  17. A combined strategy for solving quadratic assignment problem

    NASA Astrophysics Data System (ADS)

    Ahyaningsih, Faiz

    2017-08-01

    The quadratic assignment problem is a combinatorial problem of deciding the placement of facilities in specified locations in such a way as to minimize a nonconvex objective function expressed in terms of flow between facilities, and distance between location. Due to the non-convexity nature of the problem, therefore to get a `good' starting point is necessary in order to obtain a better optimal solution. In this paper we propose a combined strategy (random point strategy to get initial starting point and then use forward exchange strategy and backward exchange strategy to get `optimal' solution). As a computational experience we've solved the problem of Esc 16b, Esc 16c and Esc 16h from QAPLIB. Finally, we present a comparative study between Combined Strategy and Data -Guided Lexisearch Algorithm. The computational study shows the effectiveness of our proposed combined strategy.

  18. Application of quadratic optimization to supersonic inlet control

    NASA Technical Reports Server (NTRS)

    Lehtinen, B.; Zeller, J. R.

    1971-01-01

    The application of linear stochastic optimal control theory to the design of the control system for the air intake (inlet) of a supersonic air-breathing propulsion system is discussed. The controls must maintain a stable inlet shock position in the presence of random airflow disturbances and prevent inlet unstart. Two different linear time invariant control systems are developed. One is designed to minimize a nonquadratic index, the expected frequency of inlet unstart, and the other is designed to minimize the mean square value of inlet shock motion. The quadratic equivalence principle is used to obtain the best linear controller that minimizes the nonquadratic performance index. The two systems are compared on the basis of unstart prevention, control effort requirements, and sensitivity to parameter variations.

  19. Longitudinal force distribution using quadratically constrained linear programming

    NASA Astrophysics Data System (ADS)

    Klomp, M.

    2011-12-01

    In this paper, a new method is presented for the optimisation of force distribution for combined traction/braking and cornering. In order to provide a general, simple and flexible problem formulation, the optimisation is addressed as a quadratically constrained linear programming (QCLP) problem. Apart from fast numerical solutions, different driveline configurations can be included in the QCLP problem in a very straightforward fashion. The optimisation of the distribution of the individual wheel forces using the quasi-steady-state assumption is known to be useful for the study of the influence of particular driveline configurations on the combined lateral and longitudinal grip envelope of a particular vehicle-driveline configuration. The addition of the QCLP problem formulation makes another powerful tool available to the vehicle dynamics analyst to perform such studies.

  20. A quadratic-shaped-finger comb parametric resonator

    NASA Astrophysics Data System (ADS)

    Guo, Congzhong; Fedder, Gary K.

    2013-09-01

    A large-stroke (8 µm) parametric resonator excited by an in-plane ‘shaped-finger’ electrostatic comb drive is fabricated using a 15 µm thick silicon-on-insulator microelectromechanical systems (SOI-MEMS) process. A quadratic capacitance-engagement response is synthesized by engineering a custom-shaped comb finger profile. A folded-flexure suspension allows lateral motion while constraining rotational modes. The excitation of the nonlinear parametric resonance is realized by selecting an appropriate combination of the linear and cubic electrostatic stiffness coefficients through a specific varying-gap comb-finger design. The large-amplitude parametric resonance promotes high signal-to-noise ratio for potential use in sensitive chemical gravimetric sensors, strain gauges, and mode-matched gyroscope applications.

  1. Consultant-Guided Search Algorithms for the Quadratic Assignment Problem

    NASA Astrophysics Data System (ADS)

    Iordache, Serban

    Consultant-Guided Search (CGS) is a recent swarm intelligence metaheuristic for combinatorial optimization problems, inspired by the way real people make decisions based on advice received from consultants. Until now, CGS has been successfully applied to the Traveling Salesman Problem. Because a good metaheuristic should be able to tackle efficiently a large variety of problems, it is important to see how CGS behaves when applied to other classes of problems. In this paper, we propose an algorithm for the Quadratic Assignment Problem (QAP), which hybridizes CGS with a local search procedure. Our experimental results show that CGS is able to compete in terms of solution quality with one of the best Ant Colony Optimization algorithms, the MAX-MIN Ant System.

  2. Adiabatic theory, Liapunov exponents, and rotation number for quadratic Hamiltonians

    NASA Astrophysics Data System (ADS)

    Delyon, François; Foulon, Patrick

    1987-11-01

    We consider the adiabatic problem for general time-dependent quadratic Hamiltonians and develop a method quite different from WKB. In particular, we apply our results to the Schrödinger equation in a strip. We show that there exists a first regular step (avoiding resonance problems) providing one adiabatic invariant, bounds on the Liapunov exponents, and estimates on the rotation number at any order of the perturbation theory. The further step is shown to be equivalent to a quantum adiabatic problem, which, by the usual adiabatic techniques, provides the other possible adiabatic invariants. In the special case of the Schrödinger equation our method is simpler and more powerful than the WKB techniques.

  3. Wind turbine power tracking using an improved multimodel quadratic approach.

    PubMed

    Khezami, Nadhira; Benhadj Braiek, Naceur; Guillaud, Xavier

    2010-07-01

    In this paper, an improved multimodel optimal quadratic control structure for variable speed, pitch regulated wind turbines (operating at high wind speeds) is proposed in order to integrate high levels of wind power to actively provide a primary reserve for frequency control. On the basis of the nonlinear model of the studied plant, and taking into account the wind speed fluctuations, and the electrical power variation, a multimodel linear description is derived for the wind turbine, and is used for the synthesis of an optimal control law involving a state feedback, an integral action and an output reference model. This new control structure allows a rapid transition of the wind turbine generated power between different desired set values. This electrical power tracking is ensured with a high-performance behavior for all other state variables: turbine and generator rotational speeds and mechanical shaft torque; and smooth and adequate evolution of the control variables. 2010 ISA. Published by Elsevier Ltd. All rights reserved.

  4. Discriminative learning quadratic discriminant function for handwriting recognition.

    PubMed

    Liu, Cheng-Lin; Sako, Hiroshi; Fujisawa, Hiromichi

    2004-03-01

    In character string recognition integrating segmentation and classification, high classification accuracy and resistance to noncharacters are desired to the underlying classifier. In a previous evaluation study, the modified quadratic discriminant function (MQDF) proposed by Kimura et al. was shown to be superior in noncharacter resistance but inferior in classification accuracy to neural networks. This paper proposes a discriminative learning algorithm to optimize the parameters of MQDF with aim to improve the classification accuracy while preserving the superior noncharacter resistance. We refer to the resulting classifier as discriminative learning QDF (DLQDF). The parameters of DLQDF adhere to the structure of MQDF under the Gaussian density assumption and are optimized under the minimum classification error (MCE) criterion. The promise of DLQDF is justified in handwritten digit recognition and numeral string recognition, where the performance of DLQDF is comparable to or superior to that of neural classifiers. The results are also competitive to the best ones reported in the literature.

  5. Nonlinear equality constraints in feasible sequential quadratic programming

    SciTech Connect

    Lawrence, C.; Tits, A.

    1994-12-31

    In this talk we show that convergence of a feasible sequential quadratic programming algorithm modified to handle smooth nonlinear equality constraints. The modification of the algorithm to incorporate equality constraints is based on a scheme proposed by Mayne and Polak and is implemented in fsqp/cfsqp, an optimization package that generates feasible iterates. Nonlinear equality constraints are treated as {open_quotes}{<=}-type constraints to be satisfied by all iterates, thus precluding any positive value, and an exact penalty term is added to the objective function which penalizes negative values. For example, the problem minimize f(x) s.t. h(x) = 0, with h(x) a scalar, is replaced by minimize f(x) - ch(x) s.t. h(x) {<=} 0. The modified problem is equivalent to the original problem when c is large enough (but finite). Such a value is determined automatically via iterative adjustments.

  6. Blind deconvolution estimation of fluorescence measurements through quadratic programming

    NASA Astrophysics Data System (ADS)

    Campos-Delgado, Daniel U.; Gutierrez-Navarro, Omar; Arce-Santana, Edgar R.; Skala, Melissa C.; Walsh, Alex J.; Jo, Javier A.

    2015-07-01

    Time-deconvolution of the instrument response from fluorescence lifetime imaging microscopy (FLIM) data is usually necessary for accurate fluorescence lifetime estimation. In many applications, however, the instrument response is not available. In such cases, a blind deconvolution approach is required. An iterative methodology is proposed to address the blind deconvolution problem departing from a dataset of FLIM measurements. A linear combination of a base conformed by Laguerre functions models the fluorescence impulse response of the sample at each spatial point in our formulation. Our blind deconvolution estimation (BDE) algorithm is formulated as a quadratic approximation problem, where the decision variables are the samples of the instrument response and the scaling coefficients of the basis functions. In the approximation cost function, there is a bilinear dependence on the decision variables. Hence, due to the nonlinear nature of the estimation process, an alternating least-squares scheme iteratively solves the approximation problem. Our proposal searches for the samples of the instrument response with a global perspective, and the scaling coefficients of the basis functions locally at each spatial point. First, the iterative methodology relies on a least-squares solution for the instrument response, and quadratic programming for the scaling coefficients applied just to a subset of the measured fluorescence decays to initially estimate the instrument response to speed up the convergence. After convergence, the final stage computes the fluorescence impulse response at all spatial points. A comprehensive validation stage considers synthetic and experimental FLIM datasets of ex vivo atherosclerotic plaques and human breast cancer cell samples that highlight the advantages of the proposed BDE algorithm under different noise and initial conditions in the iterative scheme and parameters of the proposal.

  7. Confidence set inference with a prior quadratic bound

    NASA Technical Reports Server (NTRS)

    Backus, George E.

    1988-01-01

    In the uniqueness part of a geophysical inverse problem, the observer wants to predict all likely values of P unknown numerical properties z = (z sub 1,...,z sub p) of the earth from measurement of D other numerical properties y(0)=(y sub 1(0),...,y sub D(0)) knowledge of the statistical distribution of the random errors in y(0). The data space Y containing y(0) is D-dimensional, so when the model space X is infinite-dimensional the linear uniqueness problem usually is insoluble without prior information about the correct earth model x. If that information is a quadratic bound on x (e.g., energy or dissipation rate), Bayesian inference (BI) and stochastic inversion (SI) inject spurious structure into x, implied by neither the data nor the quadratic bound. Confidence set inference (CSI) provides an alternative inversion technique free of this objection. CSI is illustrated in the problem of estimating the geomagnetic field B at the core-mantle boundary (CMB) from components of B measured on or above the earth's surface. Neither the heat flow nor the energy bound is strong enough to permit estimation of B(r) at single points on the CMB, but the heat flow bound permits estimation of uniform averages of B(r) over discs on the CMB, and both bounds permit weighted disc-averages with continous weighting kernels. Both bounds also permit estimation of low-degree Gauss coefficients at the CMB. The heat flow bound resolves them up to degree 8 if the crustal field at satellite altitudes must be treated as a systematic error, but can resolve to degree 11 under the most favorable statistical treatment of the crust. These two limits produce circles of confusion on the CMB with diameters of 25 deg and 19 deg respectively.

  8. Blind deconvolution estimation of fluorescence measurements through quadratic programming.

    PubMed

    Campos-Delgado, Daniel U; Gutierrez-Navarro, Omar; Arce-Santana, Edgar R; Skala, Melissa C; Walsh, Alex J; Jo, Javier A

    2015-07-01

    Time-deconvolution of the instrument response from fluorescence lifetime imaging microscopy (FLIM) data is usually necessary for accurate fluorescence lifetime estimation. In many applications, however, the instrument response is not available. In such cases, a blind deconvolution approach is required. An iterative methodology is proposed to address the blind deconvolution problem departing from a dataset of FLIM measurements. A linear combination of a base conformed by Laguerre functions models the fluorescence impulse response of the sample at each spatial point in our formulation. Our blind deconvolution estimation (BDE) algorithm is formulated as a quadratic approximation problem, where the decision variables are the samples of the instrument response and the scaling coefficients of the basis functions. In the approximation cost function, there is a bilinear dependence on the decision variables. Hence, due to the nonlinear nature of the estimation process, an alternating least-squares scheme iteratively solves the approximation problem. Our proposal searches for the samples of the instrument response with a global perspective, and the scaling coefficients of the basis functions locally at each spatial point. First, the iterative methodology relies on a least-squares solution for the instrument response, and quadratic programming for the scaling coefficients applied just to a subset of the measured fluorescence decays to initially estimate the instrument response to speed up the convergence. After convergence, the final stage computes the fluorescence impulse response at all spatial points. A comprehensive validation stage considers synthetic and experimental FLIM datasets of ex vivo atherosclerotic plaques and human breast cancer cell samples that highlight the advantages of the proposed BDE algorithm under different noise and initial conditions in the iterative scheme and parameters of the proposal.

  9. Solutions of the Schrödinger equation with inversely quadratic Hellmann plus inversely quadratic potential using Nikiforov-Uvarov method

    NASA Astrophysics Data System (ADS)

    Ita, B. I.; Ehi-Eromosele, C. O.; Edobor-Osoh, A.; Ikeuba, A. I.

    2014-11-01

    By using the Nikiforov-Uvarov (NU) method, the Schrödinger equation has been solved for the interaction of inversely quadratic Hellmann (IQHP) and inversely quadratic potential (IQP) for any angular momentum quantum number, l. The energy eigenvalues and their corresponding eigenfunctions have been obtained in terms of Laguerre polynomials. Special cases of the sum of these potentials have been considered and their energy eigenvalues also obtained.

  10. Solutions of the Schrödinger equation with inversely quadratic Hellmann plus inversely quadratic potential using Nikiforov-Uvarov method

    SciTech Connect

    Ita, B. I.

    2014-11-12

    By using the Nikiforov-Uvarov (NU) method, the Schrödinger equation has been solved for the interaction of inversely quadratic Hellmann (IQHP) and inversely quadratic potential (IQP) for any angular momentum quantum number, l. The energy eigenvalues and their corresponding eigenfunctions have been obtained in terms of Laguerre polynomials. Special cases of the sum of these potentials have been considered and their energy eigenvalues also obtained.

  11. Bistable dark soliton solution in dispersive media with a linear and quadratic intensity-depending refraction index change

    NASA Astrophysics Data System (ADS)

    Herrmann, Joachim

    1992-08-01

    An analytical dark soliton solution of the generalized nonlinear Schrödinger equation has been found for a dispersive medium with a linear and quadratic intensity depending refraction index change of the form n= n2| A| 2+ n4| A| 4. It i s shown that for the parameter range n2n4<0, and k″ 1n2>0, two-valued (bistable) soliton states exist, which describe undistorted hol es with the same width but two different amplitudes. Under certain conditions such two-valued soliton states show an unexpected behaviour at collisions, as soliton fusion and other effects.

  12. Revealing Ozgur's Thoughts of a Quadratic Function with a Clinical Interview: Concepts and Their Underlying Reasons

    ERIC Educational Resources Information Center

    Ozaltun Celik, Aytug; Bukova Guzel, Esra

    2017-01-01

    The quadratic function is an important concept for calculus but the students at high school have many difficulties related to this concept. It is important that the teaching of the quadratic function is realized considering the students' thinking. In this context, the aim of this study conducted through a qualitative case study is to reveal the…

  13. Entire functions whose Julia sets include any finitely many copies of quadratic Julia sets

    NASA Astrophysics Data System (ADS)

    Katagata, Koh

    2017-06-01

    We prove that for any finite collection of quadratic Julia sets, a polynomial and a transcendental entire function exist whose Julia sets include copies of the given quadratic Julia sets. In order to prove the result, we construct quasiregular maps with required dynamics and employ the quasiconformal surgery to obtain the desired functions.

  14. Computing the Partial Fraction Decomposition of Rational Functions with Irreducible Quadratic Factors in the Denominators

    ERIC Educational Resources Information Center

    Man, Yiu-Kwong

    2012-01-01

    In this note, a new method for computing the partial fraction decomposition of rational functions with irreducible quadratic factors in the denominators is presented. This method involves polynomial divisions and substitutions only, without having to solve for the complex roots of the irreducible quadratic polynomial or to solve a system of linear…

  15. Computing the Partial Fraction Decomposition of Rational Functions with Irreducible Quadratic Factors in the Denominators

    ERIC Educational Resources Information Center

    Man, Yiu-Kwong

    2012-01-01

    In this note, a new method for computing the partial fraction decomposition of rational functions with irreducible quadratic factors in the denominators is presented. This method involves polynomial divisions and substitutions only, without having to solve for the complex roots of the irreducible quadratic polynomial or to solve a system of linear…

  16. Differential-geometric aspects of a nonholonomic Dirac mechanics: Lessons of a model quadratic in velocities

    NASA Astrophysics Data System (ADS)

    Pavlov, V. P.

    2014-03-01

    Faddeev and Vershik proposed the Hamiltonian and Lagrangian formulations of constrained mechanical systems that are invariant from the differential geometry standpoint. In both formulations, the description is based on a nondegenerate symplectic 2-form defined on a cotangent bundle T*Q (in the Hamiltonian formulation) or on a tangent bundle TQ (in the Lagrangian formulation), and constraints are sets of functions in involution on these manifolds. We demonstrate that this technique does not allow "invariantization" of the Dirac procedure of constraint "proliferation." We show this in an example of a typical quantum field model in which the original Lagrange function is a quadratic form in velocities with a degenerate coefficient matrix. We postulate that the initial phase space is a manifold where all arguments of the action functional including the Lagrange multipliers are defined. The Lagrange multipliers can then be naturally interpreted physically as velocities (in the Hamiltonian formulation) or momenta (in the Lagrangian formulation) related to "nonphysical" degrees of freedom. A quasisymplectic 2-form invariantly defined on such a manifold is degenerate. We propose new differential-geometric structures that allow formulating the Dirac procedure invariantly.

  17. Quadratic Optimization in the Problems of Active Control of Sound

    NASA Technical Reports Server (NTRS)

    Loncaric, J.; Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)

    2002-01-01

    We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulations of the problem. We have also obtained optimal solutions that minimize the overall absolute acoustic source strength of active control sources. These optimal solutions happen to be particular layers of monopoles on the perimeter of the protected region. Mathematically, minimization of acoustic source strength is equivalent to minimization in the sense of L(sub 1). By contrast. in the current paper we formulate and study optimization problems that involve quadratic functions of merit. Specifically, we minimize the L(sub 2) norm of the control sources, and we consider both the unconstrained and constrained minimization. The unconstrained L(sub 2) minimization is certainly the easiest problem to address numerically. On the other hand, the constrained approach allows one to analyze sophisticated geometries. In a special case, we call compare our finite-difference optimal solutions to the continuous optimal solutions obtained previously using a semi-analytic technique. We also show that the optima obtained in the sense of L(sub 2) differ drastically from those obtained in the sense of L(sub 1).

  18. GR angular momentum in the quadratic spinor Lagrangian formulation

    NASA Astrophysics Data System (ADS)

    Li, Siao-Jing

    2016-08-01

    We inquire into the question of whether the quadratic spinor Lagrangian (QSL) formulation can describe the angular momentum for a general-relativistic system. The QSL Hamiltonian has previously been shown to be able to yield an energy-momentum quasilocalization which brings a proof of the positive gravitational energy when the spinor satisfies the conformal Witten equation. After inspection, we find that, under the constraint that the spinor on the asymptotic boundary is a constant, the QSL Hamiltonian is successful in giving an angular momentum quasilocalization. We also make certain the spinor in the Hamiltonian plays the role of a gauge field, a warrant of our permission to impose constraints on the spinor. Then, by some adjustment of the QSL Hamiltonian, we gain a covariant center-of-mass moment quasilocalization only under the condition that the displacement on the asymptotic boundary is a Killing boost vector. We expect the spinor expression will bring a proof of some connection between the gravitational energy and angular momentum.

  19. Linear versus quadratic portfolio optimization model with transaction cost

    NASA Astrophysics Data System (ADS)

    Razak, Norhidayah Bt Ab; Kamil, Karmila Hanim; Elias, Siti Masitah

    2014-06-01

    Optimization model is introduced to become one of the decision making tools in investment. Hence, it is always a big challenge for investors to select the best model that could fulfill their goal in investment with respect to risk and return. In this paper we aims to discuss and compare the portfolio allocation and performance generated by quadratic and linear portfolio optimization models namely of Markowitz and Maximin model respectively. The application of these models has been proven to be significant and popular among others. However transaction cost has been debated as one of the important aspects that should be considered for portfolio reallocation as portfolio return could be significantly reduced when transaction cost is taken into consideration. Therefore, recognizing the importance to consider transaction cost value when calculating portfolio' return, we formulate this paper by using data from Shariah compliant securities listed in Bursa Malaysia. It is expected that, results from this paper will effectively justify the advantage of one model to another and shed some lights in quest to find the best decision making tools in investment for individual investors.

  20. Phase transitions in the quadratic contact process on complex networks

    NASA Astrophysics Data System (ADS)

    Varghese, Chris; Durrett, Rick

    2013-06-01

    The quadratic contact process (QCP) is a natural extension of the well-studied linear contact process where infected (1) individuals infect susceptible (0) neighbors at rate λ and infected individuals recover (10) at rate 1. In the QCP, a combination of two 1's is required to effect a 01 change. We extend the study of the QCP, which so far has been limited to lattices, to complex networks. We define two versions of the QCP: vertex-centered (VQCP) and edge-centered (EQCP) with birth events 1-0-11-1-1 and 1-1-01-1-1, respectively, where “-” represents an edge. We investigate the effects of network topology by considering the QCP on random regular, Erdős-Rényi, and power-law random graphs. We perform mean-field calculations as well as simulations to find the steady-state fraction of occupied vertices as a function of the birth rate. We find that on the random regular and Erdős-Rényi graphs, there is a discontinuous phase transition with a region of bistability, whereas on the heavy-tailed power-law graph, the transition is continuous. The critical birth rate is found to be positive in the former but zero in the latter.

  1. Phase Transitions in the Quadratic Contact Process on Complex Networks

    NASA Astrophysics Data System (ADS)

    Varghese, Chris; Durrett, Rick

    2013-03-01

    The quadratic contact process (QCP) is a natural extension of the well studied linear contact process where a single infected (1) individual can infect a susceptible (0) neighbor and infected individuals are allowed to recover (1 --> 0). In the QCP, a combination of two 1's is required to effect a 0 --> 1 change. We extend the study of the QCP, which so far has been limited to lattices, to complex networks as a model for the change in a population via sexual reproduction and death. We define two versions of the QCP - vertex centered (VQCP) and edge centered (EQCP) with birth events 1 - 0 - 1 --> 1 - 1 - 1 and 1 - 1 - 0 --> 1 - 1 - 1 respectively, where ` -' represents an edge. We investigate the effects of network topology by considering the QCP on regular, Erdős-Rényi and power law random graphs. We perform mean field calculations as well as simulations to find the steady state fraction of occupied vertices as a function of the birth rate. We find that on the homogeneous graphs (regular and Erdős-Rényi) there is a discontinuous phase transition with a region of bistability, whereas on the heavy tailed power law graph, the transition is continuous. The critical birth rate is found to be positive in the former but zero in the latter.

  2. Linear quadratic optimal controller for cable-driven parallel robots

    NASA Astrophysics Data System (ADS)

    Abdolshah, Saeed; Shojaei Barjuei, Erfan

    2015-12-01

    In recent years, various cable-driven parallel robots have been investigated for their advantages, such as low structural weight, high acceleration, and large work-space, over serial and conventional parallel systems. However, the use of cables lowers the stiffness of these robots, which in turn may decrease motion accuracy. A linear quadratic (LQ) optimal controller can provide all the states of a system for the feedback, such as position and velocity. Thus, the application of such an optimal controller in cable-driven parallel robots can result in more efficient and accurate motion compared to the performance of classical controllers such as the proportional- integral-derivative controller. This paper presents an approach to apply the LQ optimal controller on cable-driven parallel robots. To employ the optimal control theory, the static and dynamic modeling of a 3-DOF planar cable-driven parallel robot (Feriba-3) is developed. The synthesis of the LQ optimal control is described, and the significant experimental results are presented and discussed.

  3. Elastic Model Transitions Using Quadratic Inequality Constrained Least Squares

    NASA Technical Reports Server (NTRS)

    Orr, Jeb S.

    2012-01-01

    A technique is presented for initializing multiple discrete finite element model (FEM) mode sets for certain types of flight dynamics formulations that rely on superposition of orthogonal modes for modeling the elastic response. Such approaches are commonly used for modeling launch vehicle dynamics, and challenges arise due to the rapidly time-varying nature of the rigid-body and elastic characteristics. By way of an energy argument, a quadratic inequality constrained least squares (LSQI) algorithm is employed to e ect a smooth transition from one set of FEM eigenvectors to another with no requirement that the models be of similar dimension or that the eigenvectors be correlated in any particular way. The physically unrealistic and controversial method of eigenvector interpolation is completely avoided, and the discrete solution approximates that of the continuously varying system. The real-time computational burden is shown to be negligible due to convenient features of the solution method. Simulation results are presented, and applications to staging and other discontinuous mass changes are discussed

  4. Lichnerowicz modes and black hole families in Ricci quadratic gravity

    NASA Astrophysics Data System (ADS)

    Lü, Hong; Perkins, A.; Pope, C. N.; Stelle, K. S.

    2017-08-01

    A new branch of black hole solutions occurs along with the standard Schwarzschild branch in n -dimensional extensions of general relativity including terms quadratic in the Ricci tensor. The standard and new branches cross at a point determined by a static negative-eigenvalue eigenfunction of the Lichnerowicz operator, analogous to the Gross-Perry-Yaffe eigenfunction for the Schwarzschild solution in standard n =4 dimensional general relativity. This static eigenfunction has two roles: both as a perturbation away from Schwarzschild along the new black-hole branch and also as a threshold unstable mode lying at the edge of a domain of Gregory-Laflamme-type instability of the Schwarzschild solution for small-radius black holes. A thermodynamic analogy with the Gubser and Mitra conjecture on the relation between quantum thermodynamic and classical dynamical instabilities leads to a suggestion that there may be a switch of stability properties between the old and new black-hole branches for small black holes with radii below the branch crossing point.

  5. Profile-Following Entry Guidance Using Linear Quadratic Regulator Theory

    NASA Technical Reports Server (NTRS)

    Dukeman, Greg A.; Fogle, Frank (Technical Monitor)

    2002-01-01

    This paper describes one of the entry guidance concepts that is currently being tested as part of Marshall Space Flight Center's Advance Guidance and Control Project. The algorithm is of the reference profile tracking type. The reference profile consists of the reference states, range-to-go, altitude, and flight path angle, and reference controls, bank angle and angle of attack, versus energy. A linear control law using state feedback is used with energy-scheduled gains. The gains are obtained offline using Matlab's steady state linear quadratic regulator function. Lateral trajectory control is effected by performing periodic bank sign reversals based on a heading error corridor. A description and results of the AG&C test cases on which it has been tested are given. Although it is not anticipated that the algorithm will be quite as robust as algorithms with onboard trajectory re-generation capability, the results nevertheless show it to be very robust with respect to varying initial conditions and works satisfactorily even for entries from widely different orbits than that of the reference profile. Moreover, the commanded bank and angle of attack histories are very smooth, making it easier for the attitude control system to implement the guidance commands. Finally, results indicate that the guidance gains are more or less trajectory-independent which is a potentially useful property.

  6. Time-averaged quadratic functionals of a Gaussian process

    NASA Astrophysics Data System (ADS)

    Grebenkov, Denis S.

    2011-06-01

    The characterization of a stochastic process from its single random realization is a challenging problem for most single-particle tracking techniques which survey an individual trajectory of a tracer in a complex or viscoelastic medium. We consider two quadratic functionals of the trajectory: the time-averaged mean-square displacement (MSD) and the time-averaged squared root mean-square displacement (SRMS). For a large class of stochastic processes governed by the generalized Langevin equation with arbitrary frictional memory kernel and harmonic potential, the exact formulas for the mean and covariance of these functionals are derived. The formula for the mean value can be directly used for fitting experimental data, e.g., in optical tweezers microrheology. The formula for the variance (and covariance) allows one to estimate the intrinsic fluctuations of measured (or simulated) time-averaged MSD or SRMS for choosing the experimental setup appropriately. We show that the time-averaged SRMS has smaller fluctuations than the time-averaged MSD, in spite of much broader applications of the latter one. The theoretical results are successfully confirmed by Monte Carlo simulations of the Langevin dynamics. We conclude that the use of the time-averaged SRMS would result in a more accurate statistical analysis of individual trajectories and more reliable interpretation of experimental data.

  7. Quadratic Fermi node in a 3D strongly correlated semimetal

    DOE PAGES

    Kondo, Takeshi; Nakayama, M.; Chen, R.; ...

    2015-12-07

    We report that strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour ismore » predicted, for which we observe some evidence. Lastly, our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states.« less

  8. Bright nonlocal quadratic solitons induced by boundary confinement

    NASA Astrophysics Data System (ADS)

    Zheng, Yizhou; Gao, Yan; Wang, Jing; Lv, Fang; Lu, Daquan; Hu, Wei

    2017-01-01

    Under the Dirichlet boundary conditions, a family of bright quadratic solitons exists in the regime where the second harmonic can be regarded as the refractive index of the fundamental wave with an oscillatory nonlocal response. By simplifying the governing equations into the Snyder-Mitchell mode, the approximate analytical solutions are obtained. Taking them as the initial guess and using a numerical code, we found two branches of bright solitons, of which the beam width increases (branch I) and decreases (branch II) with the increase of the sample size, respectively. If the nonlocality is fixed and the sample size is varied, the soliton width varies piecewise and approximately periodically. In each period, solitons only exist in a small range of sample size. Single-hump fundamental wave solitons with the same beam width in narrower samples can be, if the second harmonics are connected smoothly, jointed to be a multihump soliton in a wider sample whose size is the sum of those for the narrower ones. The dynamical simulation shows that the found solitons are unstable.

  9. Quadratic Fermi node in a 3D strongly correlated semimetal

    SciTech Connect

    Kondo, Takeshi; Nakayama, M.; Chen, R.; Ishikawa, J. J.; Moon, E. -G.; Yamamoto, T.; Ota, Y.; Malaeb, W.; Kanai, H.; Nakashima, Y.; Ishida, Y.; Yoshida, R.; Yamamoto, H.; Matsunami, M.; Kimura, S.; Inami, N.; Ono, K.; Kumigashira, H.; Nakatsuji, S.; Balents, L.; Shin, S.

    2015-12-07

    We report that strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Lastly, our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states.

  10. Monitoring bioeroding sponges: using rubble, Quadrat, or intercept surveys?

    PubMed

    Schönberg, C H L

    2015-04-01

    Relating to recent environmental changes, bioerosion rates of calcium carbonate materials appear to be increasing worldwide, often driven by sponges that cause bioerosion and are recognized bioindicators for coral reef health. Various field methods were compared to encourage more vigorous research on bioeroding sponges and their inclusion in major monitoring projects. The rubble technique developed by Holmes et al. (2000) had drawbacks often due to small specimen sizes: it was time-costly, generated large variation, and created a biased impression about dominant species. Quadrat surveys were most rapid but overestimated cover of small specimens. Line intercepts are recommended as easiest, least spatially biased, and most accurate, especially when comparing results from different observers. Intercepts required fewer samples and provided the best statistical efficiency, evidenced by better significances and test power. Bioeroding sponge abundances and biodiversities are influenced by water depth, sediment quality, and most importantly by availability of suitable attached substrate. Any related data should thus be standardized to amount of suitable substrate to allow comparison between different environments, concentrating on dominant, easily recognized species to avoid bias due to experience of observers.

  11. Memetic algorithms for the unconstrained binary quadratic programming problem.

    PubMed

    Merz, Peter; Katayama, Kengo

    2004-12-01

    This paper presents a memetic algorithm, a highly effective evolutionary algorithm incorporating local search for solving the unconstrained binary quadratic programming problem (BQP). To justify the approach, a fitness landscape analysis is conducted experimentally for several instances of the BQP. The results of the analysis show that recombination-based variation operators are well suited for the evolutionary algorithms with local search. Therefore, the proposed approach includes--besides a highly effective randomized k-opt local search--a new variation operator that has been tailored specially for the application in the hybrid evolutionary framework. The operator is called innovative variation and is fundamentally different from traditional crossover operators, since new genetic material is included in the offspring which is not contained in one of the parents. The evolutionary heuristic is tested on 35 publicly available BQP instances, and it is shown experimentally that the algorithm is capable of finding best-known solutions to large BQPs in a short time and with a high frequency. In comparison to other approaches for the BQP, the approach appears to be much more effective, particularly for large instances of 1000 or 2500 binary variables.

  12. A Neurodynamic Optimization Approach to Bilevel Quadratic Programming.

    PubMed

    Qin, Sitian; Le, Xinyi; Wang, Jun

    2016-08-19

    This paper presents a neurodynamic optimization approach to bilevel quadratic programming (BQP). Based on the Karush-Kuhn-Tucker (KKT) theorem, the BQP problem is reduced to a one-level mathematical program subject to complementarity constraints (MPCC). It is proved that the global solution of the MPCC is the minimal one of the optimal solutions to multiple convex optimization subproblems. A recurrent neural network is developed for solving these convex optimization subproblems. From any initial state, the state of the proposed neural network is convergent to an equilibrium point of the neural network, which is just the optimal solution of the convex optimization subproblem. Compared with existing recurrent neural networks for BQP, the proposed neural network is guaranteed for delivering the exact optimal solutions to any convex BQP problems. Moreover, it is proved that the proposed neural network for bilevel linear programming is convergent to an equilibrium point in finite time. Finally, three numerical examples are elaborated to substantiate the efficacy of the proposed approach.

  13. Quadratic electro-optic Kerr effect in doped graphene

    NASA Astrophysics Data System (ADS)

    Margulis, Vl A.; Muryumin, E. E.; Gaiduk, E. A.

    2017-06-01

    We theoretically investigate one of the third-order nonlinear optical (NLO) effects, namely, the quadratic electro-optic Kerr effect (EOKE), in doped graphene. To avoid the screening of an in-plane external dc electric field by the graphene’s electrons, we propose to use ‘low-amplitude’ (≲ 10 {kV} cm-1) terahertz radiation pulses focused onto the graphene sample collinearly with a normally incident optical beam of frequency ω. Using the Dirac cone approximation for the π-electron energy bands of graphene, we calculate the real part of the effective third-order NLO susceptibility {χ }(3)(-ω ;0,0,ω ), describing the EOKE in doped graphene under the above conditions. The results obtained show that a large electro-optic modulation of the graphene’s refractive index n (up to {{Δ }}n≈ 0.1) can be achieved by proper tuning the Fermi level {E}{{F}} of charge carriers in the graphene sample via electrostatic gating. Furthemore, a change of sign of the electro-optic Kerr coefficient of doped graphene can occur in the spectral range below the photon energy threshold value of 2{E}{{F}}, corresponding to the onset of the fundamental (single-photon) interband absorption in the graphene. These theoretical findings open up new opportunities for practical exploitation of the EOKE in graphene-based NLO devices.

  14. Graph Modeling for Quadratic Assignment Problems Associated with the Hypercube

    NASA Astrophysics Data System (ADS)

    Mittelmann, Hans; Peng, Jiming; Wu, Xiaolin

    2009-07-01

    In the paper we consider the quadratic assignment problem arising from channel coding in communications where one coefficient matrix is the adjacency matrix of a hypercube in a finite dimensional space. By using the geometric structure of the hypercube, we first show that there exist at least n different optimal solutions to the underlying QAPs. Moreover, the inherent symmetries in the associated hypercube allow us to obtain partial information regarding the optimal solutions and thus shrink the search space and improve all the existing QAP solvers for the underlying QAPs. Secondly, we use graph modeling technique to derive a new integer linear program (ILP) models for the underlying QAPs. The new ILP model has n(n-1) binary variables and O(n3 log(n)) linear constraints. This yields the smallest known number of binary variables for the ILP reformulation of QAPs. Various relaxations of the new ILP model are obtained based on the graphical characterization of the hypercube, and the lower bounds provided by the LP relaxations of the new model are analyzed and compared with what provided by several classical LP relaxations of QAPs in the literature.

  15. Junction conditions in quadratic gravity: thin shells and double layers

    NASA Astrophysics Data System (ADS)

    Reina, Borja; Senovilla, José M. M.; Vera, Raül

    2016-05-01

    The junction conditions for the most general gravitational theory with a Lagrangian containing terms quadratic in the curvature are derived. We include the cases with a possible concentration of matter on the joining hypersurface—termed as thin shells, domain walls or braneworlds in the literature—as well as the proper matching conditions where only finite jumps of the energy-momentum tensor are allowed. In the latter case we prove that the matching conditions are more demanding than in general relativity. In the former case, we show that generically the shells/domain walls are of a new kind because they possess, in addition to the standard energy-momentum tensor, a double layer energy-momentum contribution which actually induces an external energy flux vector and an external scalar pressure/tension on the shell. We prove that all these contributions are necessary to make the entire energy-momentum tensor divergence-free, and we present the field equations satisfied by these energy-momentum quantities. The consequences of all these results are briefly analyzed.

  16. Mechanical cooling in single-photon optomechanics with quadratic nonlinearity

    NASA Astrophysics Data System (ADS)

    Gu, Wen-ju; Yi, Zhen; Sun, Li-hui; Xu, Da-hai

    2015-08-01

    In the paper we study the nonlinear mechanical cooling processes in an intrinsic quadratically optomechanical coupling system without linearizing the optomechanical interaction. We apply scattering theory to calculate the transition rates between different mechanical Fock states using the resolvent of the Hamiltonian, which allows for a direct identification of the underlying physical processes, where only even-phonon transitions are permitted and odd-phonon transitions are forbidden. We verify the feasibility of the approach by comparing the steady-state mean phonon number obtained from transition rates with the simulation of the full quantum master equation, and also discuss the analytical results in the weak coupling limit that coincide with two-phonon mechanical cooling processes. Furthermore, to evaluate the statistical properties of steady mechanical state, we respectively apply the Mandel Q parameter to show that the oscillator can be in nonclassical mechanical states, and the phonon number fluctuations F to display that the even-phonon transitions favor suppressing the phonon number fluctuations compared to the linear coupling optomechanical system.

  17. Quadratic Fermi node in a 3D strongly correlated semimetal

    PubMed Central

    Kondo, Takeshi; Nakayama, M.; Chen, R.; Ishikawa, J. J.; Moon, E.-G.; Yamamoto, T.; Ota, Y.; Malaeb, W.; Kanai, H.; Nakashima, Y.; Ishida, Y.; Yoshida, R.; Yamamoto, H.; Matsunami, M.; Kimura, S.; Inami, N.; Ono, K.; Kumigashira, H.; Nakatsuji, S.; Balents, L.; Shin, S.

    2015-01-01

    Strong spin–orbit coupling fosters exotic electronic states such as topological insulators and superconductors, but the combination of strong spin–orbit and strong electron–electron interactions is just beginning to be understood. Central to this emerging area are the 5d transition metal iridium oxides. Here, in the pyrochlore iridate Pr2Ir2O7, we identify a non-trivial state with a single-point Fermi node protected by cubic and time-reversal symmetries, using a combination of angle-resolved photoemission spectroscopy and first-principles calculations. Owing to its quadratic dispersion, the unique coincidence of four degenerate states at the Fermi energy, and strong Coulomb interactions, non-Fermi liquid behaviour is predicted, for which we observe some evidence. Our discovery implies that Pr2Ir2O7 is a parent state that can be manipulated to produce other strongly correlated topological phases, such as topological Mott insulator, Weyl semimetal, and quantum spin and anomalous Hall states. PMID:26640114

  18. Entanglement Entropy of Eigenstates of Quadratic Fermionic Hamiltonians

    NASA Astrophysics Data System (ADS)

    Vidmar, Lev; Hackl, Lucas; Bianchi, Eugenio; Rigol, Marcos

    2017-07-01

    In a seminal paper [D. N. Page, Phys. Rev. Lett. 71, 1291 (1993), 10.1103/PhysRevLett.71.1291], Page proved that the average entanglement entropy of subsystems of random pure states is Save≃ln DA-(1 /2 )DA2/D for 1 ≪DA≤√{D }, where DA and D are the Hilbert space dimensions of the subsystem and the system, respectively. Hence, typical pure states are (nearly) maximally entangled. We develop tools to compute the average entanglement entropy ⟨S ⟩ of all eigenstates of quadratic fermionic Hamiltonians. In particular, we derive exact bounds for the most general translationally invariant models ln DA-(ln DA)2/ln D ≤⟨S ⟩≤ln DA-[1 /(2 ln 2 )](ln DA)2/ln D . Consequently, we prove that (i) if the subsystem size is a finite fraction of the system size, then ⟨S ⟩

  19. On the structure of quadratic Gauss sums in the Talbot effect.

    PubMed

    Fernández-Pousa, Carlos R

    2017-05-01

    We report on the detailed derivation of the Gauss sums leading to the weighting phase factors in the fractional Talbot effect. In contrast to previous approaches, the derivation is directly based on the two coprime integers p and q that define the fractional Talbot effect so that, using standard techniques from the number theory, the computation is reduced, up to a global phase, to the trivial completion of the exponential of the square of a sum. In addition, it is shown that the Gauss sums can be reduced to only two cases, depending on the parity of integer q. Explicit and simpler expressions for the two forms of the Talbot weighting phases are also provided. The Gauss sums are presented as a discrete Fourier transform pair between quadratic phase sequences showing perfect periodic autocorrelation and a connection with the theory of biunimodular sequences is presented. In addition, the Talbot weighting factors of orders 1/q and 2/q are reduced to a closed form, and the equivalence to existing characterizations of Talbot weighting phases is also discussed. The relationship with one-dimensional multilevel phase structures is exemplified by the study of Talbot array illuminators. These results simplify and extend the description of the role played by Gauss sums in the fractional Talbot effect, providing a compact synthesis of previous results.

  20. Quadrate lobe: a reliable landmark for bile duct anatomy during laparoscopic cholecystectomy.

    PubMed

    Rajkomar, Kheman; Bowman, Matthew; Rodgers, Michael; Koea, Jonathan B

    2016-07-01

    This investigation was undertaken to determine whether the shape of the inferior surface quadrate lobe (segment IV) can assist in defining a safe starting point for dissection during laparoscopic cholecystectomy. Patients undergoing laparoscopic cholecystectomy were prospectively audited. Intraoperative cholangiograms and photographs of the quadrate lobe were reviewed measuring the angle between the cystic duct and common bile duct and its relationship to quadrate shape. The results of 56 patients were included. The shape of the inferior surface of the quadrate lobe was rectangular in 35, pyramidal in 13 and square in eight patients. The median cystic/bile duct angle was 43°, 37° and 26° for square, rectangular and pyramidal quadrate shapes, respectively. The angle for pyramidal-shaped lobes was narrower than that for rectangular or square lobes (P < 0.05). Regression analysis showed an inverse relationship between the shape ratio and the cystic/bile duct angle (P = 0.015). This investigation confirms a relationship between the shape of the inferior surface of the quadrate lobe and the cystic/bile duct angle and suggests that the anatomy of the inferior surface of the quadrate lobe can be used to define an optimal starting point for dissection of the biliary cystic triangle. © 2016 Royal Australasian College of Surgeons.

  1. Adjustment of design parameters for improved feedback properties in the linear quadratic regulator

    NASA Astrophysics Data System (ADS)

    McEwen, R. S.

    1982-03-01

    Classical analysis and design methods for single input-single output (SISO) systems, such as gain and phase margins, do not generalize easily to MIMO systems. Recently, the singular values of the return difference and inverse Nyquist matrices have proven useful in analyzing multiple input-multiple output (MIMO) systems. The linear quadratic formulation is useful for the design of MIMO controllers. A disadvantage of this design method is that all the design specifications must be incorporated into a quadratic cost functional. This thesis contains a systematic method for adjusting the quadratic cost to manipulate the singular value functionals and the feedback properties and thus achieve the design requirements.

  2. The fifteen theorem for universal Hermitian lattices over imaginary quadratic fields

    NASA Astrophysics Data System (ADS)

    Kim, Byeong Moon; Kim, Ji Young; Park, Poo-Sung

    2010-04-01

    We will introduce a method to get all universal Hermitian lattices over imaginary quadratic fields Q(√{-m}) for all m . For each imaginary quadratic field Q(√{-m}) , we obtain a criterion on universality of Hermitian lattices: if a Hermitian lattice L represents 1, 2, 3, 5, 6, 7, 10, 13, 14 and 15, then L is universal. We call this the fifteen theorem for universal Hermitian lattices. Note that the difference between Conway-Schneeberger's fifteen theorem and ours is the number 13. In addition, we determine the minimal rank of universal Hermitian lattices for all imaginary quadratic fields.

  3. Gravity waves from non-minimal quadratic inflation

    SciTech Connect

    Pallis, Constantinos; Shafi, Qaisar

    2015-03-12

    We discuss non-minimal quadratic inflation in supersymmetric (SUSY) and non-SUSY models which entails a linear coupling of the inflaton to gravity. Imposing a lower bound on the parameter c{sub R}, involved in the coupling between the inflaton and the Ricci scalar curvature, inflation can be attained even for subplanckian values of the inflaton while the corresponding effective theory respects the perturbative unitarity up to the Planck scale. Working in the non-SUSY context we also consider radiative corrections to the inflationary potential due to a possible coupling of the inflaton to bosons or fermions. We find ranges of the parameters, depending mildly on the renormalization scale, with adjustable values of the spectral index n{sub s}, tensor-to-scalar ratio r≃(2−4)⋅10{sup −3}, and an inflaton mass close to 3⋅10{sup 13} GeV. In the SUSY framework we employ two gauge singlet chiral superfields, a logarithmic Kähler potential including all the allowed terms up to fourth order in powers of the various fields, and determine uniquely the superpotential by applying a continuous R and a global U(1) symmetry. When the Kähler manifold exhibits a no-scale-type symmetry, the model predicts n{sub s}≃0.963 and r≃0.004. Beyond no-scale SUGRA, n{sub s} and r depend crucially on the coefficient involved in the fourth order term, which mixes the inflaton with the accompanying non-inflaton field in the Kähler potential, and the prefactor encountered in it. Increasing slightly the latter above (−3), an efficient enhancement of the resulting r can be achieved putting it in the observable range. The inflaton mass in the last case is confined in the range (5−9)⋅10{sup 13} GeV.

  4. Gravity waves from non-minimal quadratic inflation

    SciTech Connect

    Pallis, Constantinos; Shafi, Qaisar E-mail: shafi@bartol.udel.edu

    2015-03-01

    We discuss non-minimal quadratic inflation in supersymmetric (SUSY) and non-SUSY models which entails a linear coupling of the inflaton to gravity. Imposing a lower bound on the parameter c{sub R}, involved in the coupling between the inflaton and the Ricci scalar curvature, inflation can be attained even for subplanckian values of the inflaton while the corresponding effective theory respects the perturbative unitarity up to the Planck scale. Working in the non-SUSY context we also consider radiative corrections to the inflationary potential due to a possible coupling of the inflaton to bosons or fermions. We find ranges of the parameters, depending mildly on the renormalization scale, with adjustable values of the spectral index n{sub s}, tensor-to-scalar ratio r≅(2−4)⋅ 10{sup −3}, and an inflaton mass close to 3⋅ 10{sup 13} GeV. In the SUSY framework we employ two gauge singlet chiral superfields, a logarithmic Kähler potential including all the allowed terms up to fourth order in powers of the various fields, and determine uniquely the superpotential by applying a continuous R and a global U(1) symmetry. When the Kähler manifold exhibits a no-scale-type symmetry, the model predicts n{sub s} ≅ 0.963 and r≅ 0.004. Beyond no-scale SUGRA, n{sub s} and r depend crucially on the coefficient involved in the fourth order term, which mixes the inflaton with the accompanying non-inflaton field in the Kähler potential, and the prefactor encountered in it. Increasing slightly the latter above (−3), an efficient enhancement of the resulting r can be achieved putting it in the observable range. The inflaton mass in the last case is confined in the range (5−9)⋅ 10{sup 13} GeV.

  5. A decentralized linear quadratic control design method for flexible structures

    NASA Technical Reports Server (NTRS)

    Su, Tzu-Jeng; Craig, Roy R., Jr.

    1990-01-01

    A decentralized suboptimal linear quadratic control design procedure which combines substructural synthesis, model reduction, decentralized control design, subcontroller synthesis, and controller reduction is proposed for the design of reduced-order controllers for flexible structures. The procedure starts with a definition of the continuum structure to be controlled. An evaluation model of finite dimension is obtained by the finite element method. Then, the finite element model is decomposed into several substructures by using a natural decomposition called substructuring decomposition. Each substructure, at this point, still has too large a dimension and must be reduced to a size that is Riccati-solvable. Model reduction of each substructure can be performed by using any existing model reduction method, e.g., modal truncation, balanced reduction, Krylov model reduction, or mixed-mode method. Then, based on the reduced substructure model, a subcontroller is designed by an LQ optimal control method for each substructure independently. After all subcontrollers are designed, a controller synthesis method called substructural controller synthesis is employed to synthesize all subcontrollers into a global controller. The assembling scheme used is the same as that employed for the structure matrices. Finally, a controller reduction scheme, called the equivalent impulse response energy controller (EIREC) reduction algorithm, is used to reduce the global controller to a reasonable size for implementation. The EIREC reduced controller preserves the impulse response energy of the full-order controller and has the property of matching low-frequency moments and low-frequency power moments. An advantage of the substructural controller synthesis method is that it relieves the computational burden associated with dimensionality. Besides that, the SCS design scheme is also a highly adaptable controller synthesis method for structures with varying configuration, or varying mass

  6. Quadratic adaptive algorithm for solving cardiac action potential models.

    PubMed

    Chen, Min-Hung; Chen, Po-Yuan; Luo, Ching-Hsing

    2016-10-01

    An adaptive integration method is proposed for computing cardiac action potential models accurately and efficiently. Time steps are adaptively chosen by solving a quadratic formula involving the first and second derivatives of the membrane action potential. To improve the numerical accuracy, we devise an extremum-locator (el) function to predict the local extremum when approaching the peak amplitude of the action potential. In addition, the time step restriction (tsr) technique is designed to limit the increase in time steps, and thus prevent the membrane potential from changing abruptly. The performance of the proposed method is tested using the Luo-Rudy phase 1 (LR1), dynamic (LR2), and human O'Hara-Rudy dynamic (ORd) ventricular action potential models, and the Courtemanche atrial model incorporating a Markov sodium channel model. Numerical experiments demonstrate that the action potential generated using the proposed method is more accurate than that using the traditional Hybrid method, especially near the peak region. The traditional Hybrid method may choose large time steps near to the peak region, and sometimes causes the action potential to become distorted. In contrast, the proposed new method chooses very fine time steps in the peak region, but large time steps in the smooth region, and the profiles are smoother and closer to the reference solution. In the test on the stiff Markov ionic channel model, the Hybrid blows up if the allowable time step is set to be greater than 0.1ms. In contrast, our method can adjust the time step size automatically, and is stable. Overall, the proposed method is more accurate than and as efficient as the traditional Hybrid method, especially for the human ORd model. The proposed method shows improvement for action potentials with a non-smooth morphology, and it needs further investigation to determine whether the method is helpful during propagation of the action potential. Copyright © 2016 Elsevier Ltd. All rights

  7. Reduced order parameter estimation using quasilinearization and quadratic programming

    NASA Astrophysics Data System (ADS)

    Siade, Adam J.; Putti, Mario; Yeh, William W.-G.

    2012-06-01

    The ability of a particular model to accurately predict how a system responds to forcing is predicated on various model parameters that must be appropriately identified. There are many algorithms whose purpose is to solve this inverse problem, which is often computationally intensive. In this study, we propose a new algorithm that significantly reduces the computational burden associated with parameter identification. The algorithm is an extension of the quasilinearization approach where the governing system of differential equations is linearized with respect to the parameters. The resulting inverse problem therefore becomes a linear regression or quadratic programming problem (QP) for minimizing the sum of squared residuals; the solution becomes an update on the parameter set. This process of linearization and regression is repeated until convergence takes place. This algorithm has not received much attention, as the QPs can become quite large, often infeasible for real-world systems. To alleviate this drawback, proper orthogonal decomposition is applied to reduce the size of the linearized model, thereby reducing the computational burden of solving each QP. In fact, this study shows that the snapshots need only be calculated once at the very beginning of the algorithm, after which no further calculations of the reduced-model subspace are required. The proposed algorithm therefore only requires one linearized full-model run per parameter at the first iteration followed by a series of reduced-order QPs. The method is applied to a groundwater model with about 30,000 computation nodes where as many as 15 zones of hydraulic conductivity are estimated.

  8. Intermittent Antibody-based Combination Therapy Removes Allo-antibodies and Achieves Indefinite Heart Transplant Survival in Pre-sensitised Recipients

    PubMed Central

    Shariff, Hina; Tanriver, Yakup; Brown, Kathryn L.; Meader, Lucy; Greenlaw, Roseanna; Mamode, Nizam; Jurcevic, Stipo

    2010-01-01

    Background It is well established that primed/memory T cells play a critical role in heart transplant rejection. This contributes to the challenges faced in the transplant clinic since current treatments which are efficient in controlling naïve T cell alloresponses have limited efficacy on primed T cell responders. Methods Fully MHC mismatched heart transplantation was performed from BALB/c to C57BL/6 mice pre-sensitised with BALB/c splenocytes 14 days pre-transplantation. A combination therapy comprising CD70-, CD154- and CD8-specific antibodies was administered at day 0 and 4 post-transplantation with Rapamycin on days 0-4. Results The antibody combination therapy extended heart transplant survival in pre-sensitised recipients from MST 8 days (median survival time) to MST 78 days. A decrease in the number of splenic IFN-γ secreting cells measured by ELISpot assay was seen in the treated group compared to the untreated controls. However, graft-infiltrating CD8+ and CD4+ T cells persisted despite treatment and the number of intra-graft CD4+ T cells increased at day 30 post-transplantation. When an additional “rescue therapy” comprising the same antibodies was re-administered at days 30, 60 and 90 post-transplantation, T cell infiltration was reduced and indefinite graft survival was observed. Furthermore, rescue therapy resulted in gradual decrease in titre and, by day 90 post-transplantation the complete loss of the pre-existing, donor-specific antibodies. Conclusion We conclude that our antibody combination therapy extends allograft survival in pre-sensitised recipients. When combined with intermittent antibody-mediated rescue therapy, this results in indefinite allograft survival and a loss of the pre-existing, donor-specific antibodies from the circulation. PMID:20571468

  9. Using Simple Quadratic Equations to Estimate Equilibrium Concentrations of an Acid

    ERIC Educational Resources Information Center

    Brilleslyper, Michael A.

    2004-01-01

    Application of quadratic equations to standard problem in chemistry like finding equilibrium concentrations of ions in an acid solution is explained. This clearly shows that pure mathematical analysis has meaningful applications in other areas as well.

  10. Observers for a class of systems with nonlinearities satisfying an incremental quadratic inequality

    NASA Technical Reports Server (NTRS)

    Acikmese, Ahmet Behcet; Martin, Corless

    2004-01-01

    We consider the problem of state estimation from nonlinear time-varying system whose nonlinearities satisfy an incremental quadratic inequality. Observers are presented which guarantee that the state estimation error exponentially converges to zero.

  11. Observers for a class of systems with nonlinearities satisfying an incremental quadratic inequality

    NASA Technical Reports Server (NTRS)

    Acikmese, Ahmet Behcet; Martin, Corless

    2004-01-01

    We consider the problem of state estimation from nonlinear time-varying system whose nonlinearities satisfy an incremental quadratic inequality. Observers are presented which guarantee that the state estimation error exponentially converges to zero.

  12. Detection of spatial variations in temporal trends with a quadratic function.

    PubMed

    Moraga, Paula; Kulldorff, Martin

    2016-08-01

    Methods for the assessment of spatial variations in temporal trends (SVTT) are important tools for disease surveillance, which can help governments to formulate programs to prevent diseases, and measure the progress, impact, and efficacy of preventive efforts already in operation. The linear SVTT method is designed to detect areas with unusual different disease linear trends. In some situations, however, its estimation trend procedure can lead to wrong conclusions. In this article, the quadratic SVTT method is proposed as alternative of the linear SVTT method. The quadratic method provides better estimates of the real trends, and increases the power of detection in situations where the linear SVTT method fails. A performance comparison between the linear and quadratic methods is provided to help illustrate their respective properties. The quadratic method is applied to detect unusual different cervical cancer trends in white women in the United States, over the period 1969 to 1995.

  13. New trace formulae for a quadratic pencil of the Schroedinger operator

    SciTech Connect

    Yang Chuanfu

    2010-03-15

    This work deals with the eigenvalue problem for a quadratic pencil of the Schroedinger operator on a finite closed interval with the two-point boundary conditions. We will obtain new regularized trace formulas for this class of differential pencil.

  14. Using Simple Quadratic Equations to Estimate Equilibrium Concentrations of an Acid

    ERIC Educational Resources Information Center

    Brilleslyper, Michael A.

    2004-01-01

    Application of quadratic equations to standard problem in chemistry like finding equilibrium concentrations of ions in an acid solution is explained. This clearly shows that pure mathematical analysis has meaningful applications in other areas as well.

  15. On ideal structure in quadratic DDS in R{sup 2}

    SciTech Connect

    Kutnjak, Milan

    2008-11-13

    We consider the dynamics in a special case of two-dimensional quadratic homogeneous discrete dynamical systems. It is well known (c.f. [1, 2]) that homogeneous quadratic maps are in one to one correspondence with two-dimensional commutative (nonassociative) algebras. Algebraic concepts (such as the structure of algebra and existence of special elements like idempotents and nilpotents) help us to study the dynamics of the corresponding discrete homogeneous quadratic maps. It is well-known that such systems can exhibit chaotic behavior [3], In this article we consider the influence of the existence of an algebra ideal on the dynamics of the corresponding discrete homogeneous quadratic system. We also present some examples in the plane.

  16. Optimal Control Using Pontryagin's Maximum Principle in a Linear Quadratic Differential Game

    NASA Astrophysics Data System (ADS)

    Khakestari, Marzieh; Ibragimov, Gafurjan; Suleiman, Mohamed

    This paper deals with a class of two person zero-sum linear quadratic differential games, where the control functions for both players subject to integral constraints. Also the necessary conditions of the Maximum Principle are studied. Main objective in this work is to obtain optimal control by using method of Pontryagin's Maximum Principle. This method for a time-varying linear quadratic differential game is described. Finally, we discuss about an example.

  17. Sequential design of discrete linear quadratic regulators via optimal root-locus techniques

    NASA Technical Reports Server (NTRS)

    Shieh, Leang S.; Yates, Robert E.; Ganesan, Sekar

    1989-01-01

    A sequential method employing classical root-locus techniques has been developed in order to determine the quadratic weighting matrices and discrete linear quadratic regulators of multivariable control systems. At each recursive step, an intermediate unity rank state-weighting matrix that contains some invariant eigenvectors of that open-loop matrix is assigned, and an intermediate characteristic equation of the closed-loop system containing the invariant eigenvalues is created.

  18. Models of quadratic quantum algebras and their relation to classical superintegrable systems

    SciTech Connect

    Kalnins, E. G.; Miller, W.; Post, S.

    2009-05-15

    We show how to construct realizations (models) of quadratic algebras for 2D second order superintegrable systems in terms of differential or difference operators in one variable. We demonstrate how various models of the quantum algebras arise naturally from models of the Poisson algebras for the corresponding classical superintegrable system. These techniques extend to quadratic algebras related to superintegrable systems in n dimensions and are intimately related to multivariable orthogonal polynomials.

  19. Sequential design of discrete linear quadratic regulators via optimal root-locus techniques

    NASA Technical Reports Server (NTRS)

    Shieh, Leang S.; Yates, Robert E.; Ganesan, Sekar

    1989-01-01

    A sequential method employing classical root-locus techniques has been developed in order to determine the quadratic weighting matrices and discrete linear quadratic regulators of multivariable control systems. At each recursive step, an intermediate unity rank state-weighting matrix that contains some invariant eigenvectors of that open-loop matrix is assigned, and an intermediate characteristic equation of the closed-loop system containing the invariant eigenvalues is created.

  20. Bianchi type-I cosmological model with quadratic equation of state

    NASA Astrophysics Data System (ADS)

    Reddy, D. R. K.; Adhav, K. S.; Purandare, M. A.

    2015-05-01

    Bianchi type-I cosmological model containing perfect fluid with quadratic equation of state has been studied in general theory of relativity. The general solutions of the Einstein's field equations for Bianchi type-I space-time have been obtained under the assumption of quadratic equation of state (EoS) p= αρ 2- ρ, where α is constant and strictly α≠0. The physical and geometrical aspects of the model are discussed.

  1. Flight Control System Design by Quadratic Stabilization with Partial Pole Placement

    NASA Astrophysics Data System (ADS)

    Satoh, Atsushi; Sugimoto, Kenji

    The most fundamental requirements for flight control system are ensuring robust stability and improving flying quality. Quadratic stabilization is a powerful technique ensuring robust stability against parameter change of aircraft due to flight condition. Furthermore, flying quality requirements are regarded as eigenstructure assignment specifications. This paper proposes a new design method of feedback gain which simultaneously achieves quadratic stabilization and partial pole placement. This design method is reduced to a numerical optimization problem including linear matrix inequality (LMI) constraints.

  2. Controller design for nonlinear quadratic Markov jumping systems with input saturation

    NASA Astrophysics Data System (ADS)

    Chen, Fu; Xu, Shengyuan; Zou, Yun; Xu, Huiling

    2014-01-01

    This paper deals with the controller design problem of nonlinear quadratic Markov jumping systems with input saturation. Both mode-dependent and mode-independent state feedback controllers are designed. By using the concept of domain of attraction in mean square sense, sufficient conditions for stochastic stabilisation for nonlinear quadratic systems are derived in terms of linear matrix inequalities. Certain existing results are improved. Simulation examples are presented to illustrate the effectiveness of the proposed technique.

  3. Complex complete quadratic combination method for damped system with repeated eigenvalues

    NASA Astrophysics Data System (ADS)

    Yu, Ruifang; Zhou, Xiyuan; Abduwaris, Abduwahit

    2016-09-01

    A new response-spectrum mode superposition method, entirely in real value form, is developed to analyze the maximum structural response under earthquake ground motion for generally damped linear systems with repeated eigenvalues and defective eigenvectors. This algorithm has clear physical concepts and is similar to the complex complete quadratic combination (CCQC) method previously established. Since it can consider the effect of repeated eigenvalues, it is called the CCQC-R method, in which the correlation coefficients of high-order modal responses are enclosed in addition to the correlation coefficients in the normal CCQC method. As a result, the formulas for calculating the correlation coefficients of high-order modal responses are deduced in this study, including displacement, velocity and velocity-displacement correlation coefficients. Furthermore, the relationship between high-order displacement and velocity covariance is derived to make the CCQC-R algorithm only relevant to the high-order displacement response spectrum. Finally, a practical step-by-step integration procedure for calculating high-order displacement response spectrum is obtained by changing the earthquake ground motion input, which is evaluated by comparing it to the theory solution under the sine-wave input. The method derived here is suitable for generally linear systems with classical or non-classical damping.

  4. Global asymptotic stability analysis for delayed neural networks using a matrix-based quadratic convex approach.

    PubMed

    Zhang, Xian-Ming; Han, Qing-Long

    2014-06-01

    This paper is concerned with global asymptotic stability for a class of generalized neural networks with interval time-varying delays by constructing a new Lyapunov-Krasovskii functional which includes some integral terms in the form of ∫(t-h)(t)(h-t-s)(j)ẋ(T)(s)Rjẋ(s)ds(j=1,2,3). Some useful integral inequalities are established for the derivatives of those integral terms introduced in the Lyapunov-Krasovskii functional. A matrix-based quadratic convex approach is introduced to prove not only the negative definiteness of the derivative of the Lyapunov-Krasovskii functional, but also the positive definiteness of the Lyapunov-Krasovskii functional. Some novel stability criteria are formulated in two cases, respectively, where the time-varying delay is continuous uniformly bounded and where the time-varying delay is differentiable uniformly bounded with its time-derivative bounded by constant lower and upper bounds. These criteria are applicable to both static neural networks and local field neural networks. The effectiveness of the proposed method is demonstrated by two numerical examples.

  5. 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.

  6. Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method

    NASA Astrophysics Data System (ADS)

    Yang, Xiaofeng; Zhao, Jia; Wang, Qi

    2017-03-01

    The Molecular Beam Epitaxial model is derived from the variation of a free energy, that consists of either a fourth order Ginzburg-Landau double well potential or a nonlinear logarithmic potential in terms of the gradient of a height function. One challenge in solving the MBE model numerically is how to develop proper temporal discretization for the nonlinear terms in order to preserve energy stability at the time-discrete level. In this paper, we resolve this issue by developing a first and second order time-stepping scheme based on the "Invariant Energy Quadratization" (IEQ) method. The novelty is that all nonlinear terms are treated semi-explicitly, and the resulted semi-discrete equations form a linear system at each time step. Moreover, the linear operator is symmetric positive definite and thus can be solved efficiently. We then prove that all proposed schemes are unconditionally energy stable. The semi-discrete schemes are further discretized in space using finite difference methods and implemented on GPUs for high-performance computing. Various 2D and 3D numerical examples are presented to demonstrate stability and accuracy of the proposed schemes.

  7. Analysis of complete fold shape based on quadratic Bézier curves

    NASA Astrophysics Data System (ADS)

    Liu, Chun; Zhang, Yikun; Wang, Yuan

    2009-06-01

    Six segments of quadratic Bézier curve are joined together according to some geometrical rules to approximate fold shape. In a classification of folds based on this method, an ideal fold shape is determined by two parameters. The first one, u c, termed the axial lift-up ratio of the central part, generates the folds within a broad spectrum of forms ranging from box folds to chevron folds. The other one, γ, is the interlimb angle. In the quantitative description of complete folds with multiple layers, three new parameters, θ, T and E are used to describe the deflection angle of the axial plane, the thickness increment of hinge zone and the limb elongation, respectively. Based on the modeling method, the program "Bézier Fold Profiler" has been developed, with which most types of folds can be simulated by varying thirteen parameters. Two description methods, complete fold description and individual layer description, can be used for the quantitative analysis of folds. The description methods are carried out by the visual matching of the fold profile displayed on-screen from an imported digital image. The layer curves of the model are displayed on the fold image. This method has the advantage of speed and simplicity.

  8. Robust and reliable control via quadratic Lyapunov functions

    NASA Astrophysics Data System (ADS)

    Alt, Terry Robert

    In this dissertation we present a new approach to design robust and reliable controllers. Our results are used to find control laws for systems that are subject to (1) real polytopic and norm bounded uncertainties, (2) actuator and sensor variations and (3) actuator and sensor failure. In addition, we present conditions that can be added to the control design problem to constrain the controller to be stable or strictly positive real, further strengthening the robustness and reliability of the control design. The basic framework relies on the use of quadratic Lyapunov functions to accommodate potentially time varying uncertainty. Conditions are derived that, when satisfied, allow a robust control design to be obtained by performing two convex optimizations. These controllers recover the performance robustness of either state feedback or full information controllers. Sufficient conditions are presented that remove the non-convexity in terms of the control design variables. This allows a robust control design to be obtained by solving a set of linear matrix inequalities. These general robustness results are then applied to the reliability problem. Actuator and sensor variations are modeled using real polytopic uncertainties. It is shown that under some simplifying assumptions the state feedback problem reduces to a single linear matrix inequality. It also shows that the Riccati equations for standard LQR and Hsb{infty} need only a slight modification to obtain a control law that is reliable with respect to actuator variability. For the output feedback case, convex conditions are presented that yield controllers which are reliable to actuator and sensor variations. Utilizing the simultaneous Lyapunov function approach, we further extend these results to include actuator or sensor failure. Additionally, when applicable, stronger reliability guaranties may be obtained by constraining the controller to be strictly positive real. This guarantees stability for positive real

  9. Plant morphometric traits and climate gradients in northern China: a meta-analysis using quadrat and flora data.

    PubMed

    Meng, Ting-Ting; Ni, Jian; Harrison, Sandy P

    2009-11-01

    The collection of field data on plant traits is time consuming and this makes it difficult to examine changing patterns of traits along large-scale climate gradients. The present study tests whether trait information derived from regional floras can be used in conjunction with pre-existing quadrat data on species presence to derive meaningful relationships between specific morphometric traits and climate. Quadrat records were obtained for 867 species in 404 sites from northern China (38-49 degrees N, 82-132 degrees E) together with information on the presence/absence of key traits from floras. Bioclimate parameters for each site were calculated using the BIOME3 model. Principal component analysis and correlation analysis were conducted to determine the most important climate factors. The Akaike Information Criterion was used to select the best relationship between each trait and climate. Canonical correspondence analysis was used to explore the relationships between climate and trait occurrence. The changing abundance of life form, leaf type, phenology, photosynthetic pathway, leaf size and several other morphometric traits are determined by gradients in plant-available moisture (as measured by the ratio of actual to potential evapotranspiration: alpha), growing-season temperature (as measured by growing degree-days on a 0 degrees base: GDD(0)) or a combination of these. Different plant functional types (PFTs, as defined by life form, leaf type and phenology) reach maximum abundance in distinct areas of this climate space: for example, evergreen trees occur in the coldest, wettest environments (GDD(0) < 2500 degrees Cd, alpha > 0.38), and deciduous scale-leaved trees occur in drier, warmer environments than deciduous broad-leaved trees. Most leaf-level traits show similar relationships with climate independently of PFT: for example, leaf size in all PFTs increases as the environment becomes wetter and cooler. However, some traits (e.g. petiole length) display

  10. Polarity for quadratic hypersurfaces and conjugate gradient method: Relation between degenerate and nondegenerate cases

    NASA Astrophysics Data System (ADS)

    Giovanni, Fasano; Silvio, Giove; Riccardo, Gusso

    2016-10-01

    In this paper we consider a geometric viewpoint to analyze the behaviour of the Conjugate Gradient (CG) method, for the solution of a symmetric linear system, when at current step a pivot breakdown possibly occurs (degenerate case). As well known this can occur when the system matrix is indefinite or singular. In the latter case the CG gets stuck, since the steplength along the current search direction cannot be computed. We show here that a simple geometric interpretation can be provided for the degenerate case, as long as some basics on projective geometry in the Euclidean space are considered.

  11. Prediction of nucleosome DNA formation potential and nucleosome positioning using increment of diversity combined with quadratic discriminant analysis.

    PubMed

    Zhao, Xiujuan; Pei, Zhiyong; Liu, Jia; Qin, Sheng; Cai, Lu

    2010-11-01

    In this work, a novel method was developed to distinguish nucleosome DNA and linker DNA based on increment of diversity combined with quadratic discriminant analysis (IDQD), using k-mer frequency of nucleotides in genome. When used to predict DNA potential for forming nucleosomes, the model achieved a high accuracy of 94.94%, 77.60%, and 86.81%, respectively, for Saccharomyces cerevisiae, Homo sapiens, and Drosophila melanogaster. The area under the receiver operator characteristics curve of our classifier was 0.982 for S. cerevisiae. Our results indicate that DNA sequence preference is critical for nucleosome formation potential and is likely conserved across eukaryotes. The model successfully identified nucleosome-enriched or nucleosome-depleted regions in S. cerevisiae genome, suggesting nucleosome positioning depends on DNA sequence preference. Thus, IDQD classifier is useful for predicting nucleosome positioning.

  12. Preparation and laser modulation investigation of quadratic electro-optical crystal Cu:KTN with gradient refractivity effect

    NASA Astrophysics Data System (ADS)

    Wang, Xuping; Liu, Bing; Yang, Yuguo; Zhang, Yuanyuan; Lv, Xianshun; Wei, Lei; Xu, Jianhua; Ma, Ling; Wang, Jiyang

    2017-06-01

    Copper doped KTN crystals with different doping concentrations were grown by the Czochralski method. The XRD patterns show that all of the crystals are in cubic phase at room temperature. The influences of the CuO doping concentrations on dielectric properties of the crystals were measured. Cu: KTN crystals exhibited color changes depending on the doping concentrations. It was found that the inhomogeneous composition property can be used to form gradient refractivity effect in the case of ion doping. The refractive index gradient reaches 33×10-3/mm for the grown Cu: KTNN crystals. Base on the interaction between the quadratic electro-optic effect and the gradient refractivity effect, the deflection and the intensity of a Cu: KTa0.62Nb0.38O3 sample were modulated in different orientations of the crystal. The deflection efficiency and the half-wave voltage of the modulation are 45 mrad/kV and 75 V, respectively.

  13. Photon-phonon parametric oscillation induced by quadratic coupling in an optomechanical resonator

    NASA Astrophysics Data System (ADS)

    Zhang, Lin; Ji, Fengzhou; Zhang, Xu; Zhang, Weiping

    2017-07-01

    A direct photon-phonon parametric effect of quadratic coupling on the mean-field dynamics of an optomechanical resonator in the large-scale-movement regime is found and investigated. Under a weak pumping power, the mechanical resonator damps to a steady state with a nonlinear static response sensitively modified by the quadratic coupling. When the driving power increases beyond the static energy balance, the steady states lose their stabilities via Hopf bifurcations, and the resonator produces stable self-sustained oscillation (limit-circle behavior) of discrete energies with step-like amplitudes due to the parametric effect of quadratic coupling, which can be understood roughly by the power balance between gain and loss on the resonator. A further increase in the pumping power can induce a chaotic dynamic of the resonator via a typical routine of period-doubling bifurcation, but which can be stabilized by the parametric effect through an inversion-bifurcation process back to the limit-circle states. The bifurcation-to-inverse-bifurcation transitions are numerically verified by the maximal Lyapunov exponents of the dynamics, which indicate an efficient way of suppressing the chaotic behavior of the optomechanical resonator by quadratic coupling. Furthermore, the parametric effect of quadratic coupling on the dynamic transitions of an optomechanical resonator can be conveniently detected or traced by the output power spectrum of the cavity field.

  14. A wavelet bicoherence-based quadratic nonlinearity feature for translational axis condition monitoring.

    PubMed

    Li, Yong; Wang, Xiufeng; Lin, Jing; Shi, Shengyu

    2014-01-27

    The translational axis is one of the most important subsystems in modern machine tools, as its degradation may result in the loss of the product qualification and lower the control precision. Condition-based maintenance (CBM) has been considered as one of the advanced maintenance schemes to achieve effective, reliable and cost-effective operation of machine systems, however, current vibration-based maintenance schemes cannot be employed directly in the translational axis system, due to its complex structure and the inefficiency of commonly used condition monitoring features. In this paper, a wavelet bicoherence-based quadratic nonlinearity feature is proposed for translational axis condition monitoring by using the torque signature of the drive servomotor. Firstly, the quadratic nonlinearity of the servomotor torque signature is discussed, and then, a biphase randomization wavelet bicoherence is introduced for its quadratic nonlinear detection. On this basis, a quadratic nonlinearity feature is proposed for condition monitoring of the translational axis. The properties of the proposed quadratic nonlinearity feature are investigated by simulations. Subsequently, this feature is applied to the real-world servomotor torque data collected from the X-axis on a high precision vertical machining centre. All the results show that the performance of the proposed feature is much better than that of original condition monitoring features.

  15. A Wavelet Bicoherence-Based Quadratic Nonlinearity Feature for Translational Axis Condition Monitoring

    PubMed Central

    Li, Yong; Wang, Xiufeng; Lin, Jing; Shi, Shengyu

    2014-01-01

    The translational axis is one of the most important subsystems in modern machine tools, as its degradation may result in the loss of the product qualification and lower the control precision. Condition-based maintenance (CBM) has been considered as one of the advanced maintenance schemes to achieve effective, reliable and cost-effective operation of machine systems, however, current vibration-based maintenance schemes cannot be employed directly in the translational axis system, due to its complex structure and the inefficiency of commonly used condition monitoring features. In this paper, a wavelet bicoherence-based quadratic nonlinearity feature is proposed for translational axis condition monitoring by using the torque signature of the drive servomotor. Firstly, the quadratic nonlinearity of the servomotor torque signature is discussed, and then, a biphase randomization wavelet bicoherence is introduced for its quadratic nonlinear detection. On this basis, a quadratic nonlinearity feature is proposed for condition monitoring of the translational axis. The properties of the proposed quadratic nonlinearity feature are investigated by simulations. Subsequently, this feature is applied to the real-world servomotor torque data collected from the X-axis on a high precision vertical machining centre. All the results show that the performance of the proposed feature is much better than that of original condition monitoring features. PMID:24473281

  16. Outcome of "indefinite for dysplasia" in inflammatory bowel disease: correlation with DNA flow cytometry and other risk factors of colorectal cancer.

    PubMed

    Choi, Won-Tak; Rabinovitch, Peter S; Wang, Dongliang; Westerhoff, Maria

    2015-07-01

    Dysplasia that develops in the setting of inflammatory bowel disease precedes colorectal cancer (CRC). The category of "indefinite for dysplasia (IND)" is used often in equivocal cases, but its clinical significance remains unclear. Flow cytometric analysis of DNA content (aneuploidy) has shown some promise in stratifying patients into low or high risk of CRC, but there are few reports that have specifically evaluated the outcome of IND. As such, we analyzed a series of 84 IND inflammatory bowel disease patients seen at the University of Washington and Harborview Medical Centers from 2003 to 2013 to determine the outcome of IND. Hospital electronic medical records were further reviewed to correlate outcome with the type of lesion (flat versus polypoid), primary sclerosing cholangitis, active inflammation in the area of IND, and DNA flow cytometric data. The data show that 13% of IND cases were found to have low-grade dysplasia, whereas only 2% of IND cases showed advanced neoplasia (high-grade dysplasia or CRC) after a mean follow-up of 28 months. The risk of neoplasia was not significantly associated with the type of lesion (P = .94 from log-rank test), primary sclerosing cholangitis (P = .94), or active inflammation (P = .41) in this cohort. However, the finding of DNA aneuploidy at baseline IND was predictive of subsequent detection of neoplasia (P = .037). IND patients with abnormal DNA flow cytometric results may warrant more careful follow-up, but conversely, IND in the setting of normal DNA content may require less frequent surveillance colonoscopy.

  17. SERS assay of telomerase activity at single-cell level and colon cancer tissues via quadratic signal amplification.

    PubMed

    Shi, Muling; Zheng, Jing; Liu, Changhui; Tan, Guixiang; Qing, Zhihe; Yang, Sheng; Yang, Jinfeng; Tan, Yongjun; Yang, Ronghua

    2016-03-15

    As an important biomarker and therapeutic target, telomerase has attracted extensive attention concerning its detection and monitoring. Recently, enzyme-assisted amplification approaches have provided useful platforms for the telomerase activity detection, however, further improvement in sensitivity is still hindered by the single-step signal amplification. Herein, we develop a quadratic signal amplification strategy for ultrasensitive surface-enhanced Raman scattering (SERS) detection of telomerase activity. The central idea of our design is using telomerase-induced silver nanoparticles (AgNPs) assembly and silver ions (Ag(+))-mediated cascade amplification. In our approach, each telomerase-aided DNA sequence extension could trigger the formation of a long double-stranded DNA (dsDNA), making numerous AgNPs assembling along with this long strand through specific Ag-S bond, to form a primary amplification element. For secondary amplification, each conjugated AgNP was dissolved into Ag(+), which can effectively induce the 4-aminobenzenethiol (4-ABT) modified gold nanoparticles (AuNPs@4-ABT) to undergo aggregation to form numerous "hot-spots". Through quadratic amplifications, a limit of detection down to single HeLa cell was achieved. More importantly, this method demonstrated good performance when applied to tissues from colon cancer patients, which exhibits great potential in the practical application of telomerase-based cancer diagnosis in early stages. To demonstrate the potential in screening the telomerase inhibitors and telomerase-targeted drugs, the proposed design is successfully employed to measure the inhibition of telomerase activity by 3'-azido-3'-deoxythymidine. Copyright © 2015 Elsevier B.V. All rights reserved.

  18. Optimal Linear Quadratic Regulators for Control of Nonlinear Mechanical Systems with Redundant Degrees-of-Freedom

    NASA Astrophysics Data System (ADS)

    Arimoto, Suguru

    An optimal regulator problem for endpoint position control of a robot arm with (or without) redundancy in its total degrees-of-freedom (DOF) is solved by combining Riemannian geometry with nonlinear control theory. Given a target point, within the task-space, that the arm endpoint should reach, a task-space position feedback with joint damping is shown to asymptotically stabilize reaching movements even if the number of DOF of the arm is greater than the dimension of the task space and thereby the inverse kinematics is ill-posed. Usually the speed of convergence of the endpoint trajectory is unsatisfactory, depending on the choice of feedback gains for joint damping. Hence, to speed up the convergence without incurring further energy consumption, an optimal control design for minimizing a performance index composed of an integral of joint dissipation energy plus a linear quadratic form of the task-space control input and output is introduced. It is then shown that the Hamilton-Jacobi-Bellman equation derived from the principle of optimality is solvable in control variables and the Hamilton-Jacobi equation itself has an explicit solution. Although the state of the original dynamics (the Euler-Lagrange equation) with DOF-redundancy contains uncontrollable and unobservable manifolds, the dynamics satisfies a nonlinear version of the Kalman-Yakubovich-Popov lemma and the task-space input-output passivity. An inverse problem of optimal regulator design for robotic arms under the effect of gravity is also tackled by combining Riemannian geometry with passivity-based control theory.

  19. Sequential Quadratic Programming (SQP) for optimal control in direct numerical simulation of turbulent flow

    NASA Astrophysics Data System (ADS)

    Badreddine, Hassan; Vandewalle, Stefan; Meyers, Johan

    2014-01-01

    The current work focuses on the development and application of an efficient algorithm for optimization of three-dimensional turbulent flows, simulated using Direct Numerical Simulation (DNS) or Large-Eddy Simulations, and further characterized by large-dimensional optimization-parameter spaces. The optimization algorithm is based on Sequential Quadratic Programming (SQP) in combination with a damped formulation of the limited-memory BFGS method. The latter is suitable for solving large-scale constrained optimization problems whose Hessian matrices cannot be computed and stored at a reasonable cost. We combine the algorithm with a line-search merit function based on an L1-norm to enforce the convergence from any remote point. It is first shown that the proposed form of the damped L-BFGS algorithm is suitable for solving equality constrained Rosenbrock type functions. Then, we apply the algorithm to an optimal-control test problem that consists of finding the optimal initial perturbations to a turbulent temporal mixing layer such that mixing is improved at the end of a simulation time horizon T. The controls are further subject to a non-linear equality constraint on the total control energy. DNSs are used to resolve all turbulent scales of motion, and a continuous adjoint formulation is employed to calculate the gradient of the cost functionals. We compare the convergence speed of the SQP L-BFGS algorithm to a conventional non-linear conjugate-gradient method (i.e. the current standard in DNS-based optimal control), and find that the SQP algorithm is more than an order of magnitude faster than the conjugate-gradient method.

  20. Estimating nonlinear selection gradients using quadratic regression coefficients: double or nothing?

    PubMed

    Stinchcombe, John R; Agrawal, Aneil F; Hohenlohe, Paul A; Arnold, Stevan J; Blows, Mark W

    2008-09-01

    The use of regression analysis has been instrumental in allowing evolutionary biologists to estimate the strength and mode of natural selection. Although directional and correlational selection gradients are equal to their corresponding regression coefficients, quadratic regression coefficients must be doubled to estimate stabilizing/disruptive selection gradients. Based on a sample of 33 papers published in Evolution between 2002 and 2007, at least 78% of papers have not doubled quadratic regression coefficients, leading to an appreciable underestimate of the strength of stabilizing and disruptive selection. Proper treatment of quadratic regression coefficients is necessary for estimation of fitness surfaces and contour plots, canonical analysis of the gamma matrix, and modeling the evolution of populations on an adaptive landscape.

  1. Resurrecting quadratic inflation in no-scale supergravity in light of BICEP2

    SciTech Connect

    Ellis, John; García, Marcos A.G.; Olive, Keith A.; Nanopoulos, Dimitri V. E-mail: garciagarcia@physics.umn.edu E-mail: olive@physics.umn.edu

    2014-05-01

    The magnitude of primordial tensor perturbations reported by the BICEP2 experiment is consistent with simple models of chaotic inflation driven by a single scalar field with a power-law potential ∝ φ{sup n} : n ≅ 2, in contrast to the WMAP and Planck results, which favored models resembling the Starobinsky R+R{sup 2} model if running of the scalar spectral index could be neglected. While models of inflation with a quadratic potential may be constructed in simple N = 1 supergravity, these constructions are more challenging in no-scale supergravity. We discuss here how quadratic inflation can be accommodated within supergravity, focusing primarily on the no-scale case. We also argue that the quadratic inflaton may be identified with the supersymmetric partner of a singlet (right-handed) neutrino, whose subsequent decay could have generated the baryon asymmetry via leptogenesis.

  2. Fast parallel DNA-based algorithms for molecular computation: quadratic congruence and factoring integers.

    PubMed

    Chang, Weng-Long

    2012-03-01

    Assume that n is a positive integer. If there is an integer such that M (2) ≡ C (mod n), i.e., the congruence has a solution, then C is said to be a quadratic congruence (mod n). If the congruence does not have a solution, then C is said to be a quadratic noncongruence (mod n). The task of solving the problem is central to many important applications, the most obvious being cryptography. In this article, we describe a DNA-based algorithm for solving quadratic congruence and factoring integers. In additional to this novel contribution, we also show the utility of our encoding scheme, and of the algorithm's submodules. We demonstrate how a variety of arithmetic, shifted and comparative operations, namely bitwise and full addition, subtraction, left shifter and comparison perhaps are performed using strands of DNA.

  3. Detection of code spread OFDM based on 0-1 integer quadratic programming

    NASA Astrophysics Data System (ADS)

    Elghariani, Ali; Zoltowski, Michael D.

    2012-05-01

    In this paper we introduce Integer Quadratic Programming (MIQP) approach to optimally detect QPSK Code Spread OFDM (CS-OFDM) by formulating the problem as a combinatorial optimization problem. The Branch and Bound (BB) algorithm is utilized to solve this integer quadratic programming problem. Furthermore, we propose combined preprocessing steps that can be applied prior to BB so that the computational complexity of the optimum receiver is reduced. The first step in this combination is to detect as much as possible symbols using procedures presented in [9], which is basically based on the gradient of quadratic function. The second step detects the undetected symbols from the first step using MMSE estimator. The result of the latter step will be used to predict the initial upper bound of the BB algorithm. Simulation results show that the proposed preprocessing combination when applied prior to BB provides optimal performance with a significantly reduced computational complexity.

  4. Comparing performance of instrumental drift correction by linear and quadratic adjusting in inductive electromagnetic data

    NASA Astrophysics Data System (ADS)

    dos Santos, Vinícius Rafael Neris; Porsani, Jorge Luís

    2011-01-01

    Electromagnetic induction (EMI) method results are shown for vertical magnetic dipole (VMD) configuration by using the EM38 equipment. Performance in the location of metallic pipes and electrical cables is compared as a function of instrumental drift correction by linear and quadratic adjusting under controlled conditions. Metallic pipes and electrical cables are buried at the IAG/USP shallow geophysical test site in São Paulo City, Brazil. Results show that apparent electrical conductivity and magnetic susceptibility data were affected by ambient temperature variation. In order to obtain better contrast between background and metallic targets it was necessary to correct the drift. This correction was accomplished by using linear and quadratic relation between conductivity/susceptibility and temperature intending comparative studies. The correction of temperature drift by using a quadratic relation was effective, showing that all metallic targets were located as well deeper targets were also improved.

  5. Propagator for the time-dependent charged oscillator via linear and quadratic invariants

    SciTech Connect

    Abdalla, M. Sebawe Choi, Jeong-Ryeol

    2007-12-15

    The problem of a charged particle in the presence of a variable magnetic field is considered. Using the linear and the quadratic invariants as a tool, the wave functions in Fock state as well as in coherent state are obtained. The corresponding propagators which propagate the wave functions in the space-time are derived. Using numerical computations we have managed to draw some plots for the real, imaginary, and absolute values of the propagators. This has been used to analyze the properties of the propagators associated with both of the linear and the quadratic invariants. It has been shown that there is no essential difference between the behavior of the absolute value of the propagators in both of the linear and the quadratic invariants.

  6. The non-avian theropod quadrate I: standardized terminology with an overview of the anatomy and function

    PubMed Central

    Araújo, Ricardo; Mateus, Octávio

    2015-01-01

    The quadrate of reptiles and most other tetrapods plays an important morphofunctional role by allowing the articulation of the mandible with the cranium. In Theropoda, the morphology of the quadrate is particularly complex and varies importantly among different clades of non-avian theropods, therefore conferring a strong taxonomic potential. Inconsistencies in the notation and terminology used in discussions of the theropod quadrate anatomy have been noticed, including at least one instance when no less than eight different terms were given to the same structure. A standardized list of terms and notations for each quadrate anatomical entity is proposed here, with the goal of facilitating future descriptions of this important cranial bone. In addition, an overview of the literature on quadrate function and pneumaticity in non-avian theropods is presented, along with a discussion of the inferences that could be made from this research. Specifically, the quadrate of the large majority of non-avian theropods is akinetic but the diagonally oriented intercondylar sulcus of the mandibular articulation allowed both rami of the mandible to move laterally when opening the mouth in many of theropods. Pneumaticity of the quadrate is also present in most averostran clades and the pneumatic chamber—invaded by the quadrate diverticulum of the mandibular arch pneumatic system—was connected to one or several pneumatic foramina on the medial, lateral, posterior, anterior or ventral sides of the quadrate. PMID:26401455

  7. Finite Element Simulation of Articular Contact Mechanics with Quadratic Tetrahedral Elements

    PubMed Central

    Maas, Steve A.; Ellis, Benjamin J.; Rawlins, David S.; Weiss, Jeffrey A.

    2016-01-01

    Although it is easier to generate finite element discretizations with tetrahedral elements, trilinear hexahedral (HEX8) elements are more often used in simulations of articular contact mechanics. This is due to numerical shortcomings of linear tetrahedral (TET4) elements, limited availability of quadratic tetrahedron elements in combination with effective contact algorithms, and the perceived increased computational expense of quadratic finite elements. In this study we implemented both ten-node (TET10) and fifteen-node (TET15) quadratic tetrahedral elements in FEBio (www.febio.org) and compared their accuracy, robustness in terms of convergence behavior and computational cost for simulations relevant to articular contact mechanics. Suitable volume integration and surface integration rules were determined by comparing the results of several benchmark contact problems. The results demonstrated that the surface integration rule used to evaluate the contact integrals for quadratic elements affected both convergence behavior and accuracy of predicted stresses. The computational expense and robustness of both quadratic tetrahedral formulations compared favorably to the HEX8 models. Of note, the TET15 element demonstrated superior convergence behavior and lower computational cost than both the TET10 and HEX8 elements for meshes with similar numbers of degrees of freedom in the contact problems that we examined. Finally, the excellent accuracy and relative efficiency of these quadratic tetrahedral elements was illustrated by comparing their predictions with those for a HEX8 mesh for simulation of articular contact in a fully validated model of the hip. These results demonstrate that TET10 and TET15 elements provide viable alternatives to HEX8 elements for simulation of articular contact mechanics. PMID:26900037

  8. Finite element simulation of articular contact mechanics with quadratic tetrahedral elements.

    PubMed

    Maas, Steve A; Ellis, Benjamin J; Rawlins, David S; Weiss, Jeffrey A

    2016-03-21

    Although it is easier to generate finite element discretizations with tetrahedral elements, trilinear hexahedral (HEX8) elements are more often used in simulations of articular contact mechanics. This is due to numerical shortcomings of linear tetrahedral (TET4) elements, limited availability of quadratic tetrahedron elements in combination with effective contact algorithms, and the perceived increased computational expense of quadratic finite elements. In this study we implemented both ten-node (TET10) and fifteen-node (TET15) quadratic tetrahedral elements in FEBio (www.febio.org) and compared their accuracy, robustness in terms of convergence behavior and computational cost for simulations relevant to articular contact mechanics. Suitable volume integration and surface integration rules were determined by comparing the results of several benchmark contact problems. The results demonstrated that the surface integration rule used to evaluate the contact integrals for quadratic elements affected both convergence behavior and accuracy of predicted stresses. The computational expense and robustness of both quadratic tetrahedral formulations compared favorably to the HEX8 models. Of note, the TET15 element demonstrated superior convergence behavior and lower computational cost than both the TET10 and HEX8 elements for meshes with similar numbers of degrees of freedom in the contact problems that we examined. Finally, the excellent accuracy and relative efficiency of these quadratic tetrahedral elements was illustrated by comparing their predictions with those for a HEX8 mesh for simulation of articular contact in a fully validated model of the hip. These results demonstrate that TET10 and TET15 elements provide viable alternatives to HEX8 elements for simulation of articular contact mechanics. Copyright © 2016 Elsevier Ltd. All rights reserved.

  9. New Combined Serum Creatinine and Cystatin C Quadratic Formula for GFR Assessment in Children

    PubMed Central

    Cachat, Francois; Jannot, Anne-Sophie; Meyrat, Blaise-Julien; Mosig, Dolores; Bardy, Daniel; Parvex, Paloma; Girardin, Eric

    2014-01-01

    Summary Background and objectives The estimated GFR (eGFR) is important in clinical practice. To find the best formula for eGFR, this study assessed the best model of correlation between sinistrin clearance (iGFR) and the solely or combined cystatin C (CysC)– and serum creatinine (SCreat)–derived models. It also evaluated the accuracy of the combined Schwartz formula across all GFR levels. Design, setting, participants, & measurements Two hundred thirty-eight iGFRs performed between January 2012 and April 2013 for 238 children were analyzed. Regression techniques were used to fit the different equations used for eGFR (i.e., logarithmic, inverse, linear, and quadratic). The performance of each model was evaluated using the Cohen κ correlation coefficient and the percentage reaching 30% accuracy was calculated. Results The best model of correlation between iGFRs and CysC is linear; however, it presents a low κ coefficient (0.24) and is far below the Kidney Disease Outcomes Quality Initiative targets to be validated, with only 84% of eGFRs reaching accuracy of 30%. SCreat and iGFRs showed the best correlation in a fitted quadratic model with a κ coefficient of 0.53 and 93% accuracy. Adding CysC significantly (P<0.001) increased the κ coefficient to 0.56 and the quadratic model accuracy to 97%. Therefore, a combined SCreat and CysC quadratic formula was derived and internally validated using the cross-validation technique. This quadratic formula significantly outperformed the combined Schwartz formula, which was biased for an iGFR≥91 ml/min per 1.73 m2. Conclusions This study allowed deriving a new combined SCreat and CysC quadratic formula that could replace the combined Schwartz formula, which is accurate only for children with moderate chronic kidney disease. PMID:24202134

  10. Analysis of quadratic nonlinearities in hydrodynamic transport systems employing numerical simulations

    NASA Astrophysics Data System (ADS)

    Bicken, Gurcan

    This dissertation deals with the analysis and identification of quadratic non-linearities in hydrodynamic transport problems arising in engineering and science. As representative application areas, homogenous oscillations of electron and ion plasmas in a 1-D periodic domain and the forced voltage-current dynamics of a semiconductor device are considered. The time series data obtained from numerical solutions of the associated hydrodynamic equations are used for the spectral analysis of the quadratic nonlinearities in these respective systems. More specifically, electron plasma oscillations are analyzed using power spectra and cross-bicoherency spectra to gain insight into the quadratic interactions predicted by a simple model of the energy transfer that cascades from lower modes to higher modes within a small amplitude range of oscillations. The efficiency of the bicoherency function in detecting the quadratic wave interactions from the complex time series of the mode amplitudes is observed. The difference in the modal interactions for isentropic and isothermal plasma models are investigated based on numerical 'experiments' simulating the modal dynamics in each case. Furthermore, the concentration oscillations of cold ion plasmas in a Lagrangian frame are analyzed for different Debye lengths. The detailed effects of linear and nonlinear mechanisms in the hydrodynamic model on the power spectra of the oscillations are investigated. Second-order Volterra models are considered for approximating the dynamics of input-output systems with quadratic nonlinear terms. The linear and quadratic kernels of the Volterra model are estimated using multi- tone inputs and least-squares minimization. The implications of the non-orthogonality of the model are investigated in detail. To circumvent the negative effects of non-orthogonality on the accuracy of the kernel estimation, an 'odd-even' separation technique is utilized in the kernel estimation. This approach for estimating an

  11. Scalable Effective Approaches for Quadratic Assignment Problems Based on Conic Optimization and Applications

    DTIC Science & Technology

    2012-02-09

    For this, we consider the splitting B=B1-B2, where both B1 and B2 are positive semi - definite . We then introduced a new notion called non-redundant...Volume 20(6), pp. 3408-3426, 2010. [3] J. Peng, T. Zhu, H.Zh. Luo and K.Ch. Toh. Semi - definite Relaxation of Quadratic Assignment Problems based on...Government position , policy or decision, unless so designated by other documentation. 14. ABSTRACT This project deals with quadratic assignment problems

  12. Parameter estimation of optical fringes with quadratic phase using the fractional Fourier transform

    NASA Astrophysics Data System (ADS)

    Lu, Ming-Feng; Zhang, Feng; Tao, Ran; Ni, Guo-Qiang; Bai, Ting-Zhu; Yang, Wen-Ming

    2015-11-01

    Optical fringes with a quadratic phase are often encountered in optical metrology. Parameter estimation of such fringes plays an important role in interferometric measurements. A novel method is proposed for accurate and direct parameter estimation using the fractional Fourier transform (FRFT), even in the presence of noise and obstacles. We take Newton's rings fringe patterns and electronic speckle pattern interferometry (ESPI) interferograms as classic examples of optical fringes that have a quadratic phase and present simulation and experimental results demonstrating the performance of the proposed method.

  13. OPTIMAL SHRINKAGE ESTIMATION OF MEAN PARAMETERS IN FAMILY OF DISTRIBUTIONS WITH QUADRATIC VARIANCE

    PubMed Central

    Xie, Xianchao; Kou, S. C.; Brown, Lawrence

    2015-01-01

    This paper discusses the simultaneous inference of mean parameters in a family of distributions with quadratic variance function. We first introduce a class of semi-parametric/parametric shrinkage estimators and establish their asymptotic optimality properties. Two specific cases, the location-scale family and the natural exponential family with quadratic variance function, are then studied in detail. We conduct a comprehensive simulation study to compare the performance of the proposed methods with existing shrinkage estimators. We also apply the method to real data and obtain encouraging results. PMID:27041778

  14. Nonadiabatic effects in ultracold molecules via anomalous linear and quadratic Zeeman shifts.

    PubMed

    McGuyer, B H; Osborn, C B; McDonald, M; Reinaudi, G; Skomorowski, W; Moszynski, R; Zelevinsky, T

    2013-12-13

    Anomalously large linear and quadratic Zeeman shifts are measured for weakly bound ultracold 88Sr2 molecules near the intercombination-line asymptote. Nonadiabatic Coriolis coupling and the nature of long-range molecular potentials explain how this effect arises and scales roughly cubically with the size of the molecule. The linear shifts yield nonadiabatic mixing angles of the molecular states. The quadratic shifts are sensitive to nearby opposite f-parity states and exhibit fourth-order corrections, providing a stringent test of a state-of-the-art ab initio model.

  15. Design of linear quadratic regulators with eigenvalue placement in a specified region

    NASA Technical Reports Server (NTRS)

    Shieh, Leang-San; Zhen, Liu; Coleman, Norman P.

    1990-01-01

    Two linear quadratic regulators are developed for placing the closed-loop poles of linear multivariable continuous-time systems within the common region of an open sector, bounded by lines inclined at +/- pi/2k (for a specified integer k not less than 1) from the negative real axis, and the left-hand side of a line parallel to the imaginary axis in the complex s-plane, and simultaneously minimizing a quadratic performance index. The design procedure mainly involves the solution of either Liapunov equations or Riccati equations. The general expression for finding the lower bound of a constant gain gamma is also developed.

  16. Neutron Distribution in the Nuclear Fuel Cell using Collision Probability Method with Quadratic Flux Approach

    NASA Astrophysics Data System (ADS)

    Shafii, M. A.; Fitriyani, D.; Tongkukut, S. H. J.; Abdullah, A. G.

    2017-03-01

    To solve the integral neutron transport equation using collision probability (CP) method usually requires flat flux (FF) approach. In this research, it has been carried out in the cylindrical nuclear fuel cell with the spatial of mesh with quadratic flux approach. This means that the neutron flux at any region of the nuclear fuel cell is forced to follow the pattern of a quadratic function. The mechanism may be referred to as the process of non-flat flux (NFF) approach. The parameters that calculated in this study are the k-eff and the distribution of neutron flux. The result shows that all parameters are in accordance with the result of SRAC.

  17. An application of nonlinear programming to the design of regulators of a linear-quadratic formulation

    NASA Technical Reports Server (NTRS)

    Fleming, P.

    1983-01-01

    A design technique is proposed for linear regulators in which a feedback controller of fixed structure is chosen to minimize an integral quadratic objective function subject to the satisfaction of integral quadratic constraint functions. Application of a nonlinear programming algorithm to this mathematically tractable formulation results in an efficient and useful computer aided design tool. Particular attention is paid to computational efficiency and various recommendations are made. Two design examples illustrate the flexibility of the approach and highlight the special insight afforded to the designer. One concerns helicopter longitudinal dynamics and the other the flight dynamics of an aerodynamically unstable aircraft.

  18. Sequential design of linear quadratic state regulators via the optimal root-locus techniques

    NASA Technical Reports Server (NTRS)

    Shieh, L. S.; Dib, H. M.; Yates, R. E.

    1988-01-01

    The use of well-known root-locus techniques for sequentially finding the weighting matrices and the linear quadratic state regulators of multivariable control systems in the frequency domain is considered. This sequential design method permits the retention of some stable open-loop poles and the associated eigenvectors in the closed-loop system; it also allows some optimal closed-loop poles to be placed in a specific region of the complex plane. In addition, it provides a design procedure for determining the weighting matrices and linear quadratic state regulators for the optimal control of multivariable systems in the frequency domain.

  19. A Branch and Bound Based Heuristic for Solving the Quadratic Assignment Problem,

    DTIC Science & Technology

    1981-10-01

    the Quadratic Assignment Problem M. S. Bazaraa and 0. Kirca FDRC-81-13 V Contract N~o. N00014-8O-k-0709 A Branch and Bound Based Heuristic for...Solving the Quadratic Assignment Problem M. S. Bazaraa and 0. Kirca Abstract I\\ .... In this paper a branch and bound algorithm is proposed for solving the...concept of branch and bound or im- plicit enumeration, as in the works of Gilmore (1962), Lawler (1963), Craves and Whinston (1970), Bazaraa and Elshafei

  20. Extension of the coherence function to quadratic models. [applied to plasma density and potential fluctuations

    NASA Technical Reports Server (NTRS)

    Kim, Y. C.; Wong, W. F.; Powers, E. J.; Roth, J. R.

    1979-01-01

    It is shown how the use of higher coherence functions can recover some of the lost coherence due to nonlinear relationship between two fluctuating quantities whose degree of mutual coherence is being measured. The relationship between the two processes is modeled with the aid of a linear term and a quadratic term. As a specific example, the relationship between plasma density and potential fluctuations in a plasma is considered. The fraction of power in the auto-power spectrum of the potential fluctuations due to a linear relationship and to a quadratic relationship between the density and potential fluctuations is estimated.