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Sample records for algebraic modeling system

  1. 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.

  2. Lie algebraic similarity transformed Hamiltonians for lattice model systems

    NASA Astrophysics Data System (ADS)

    Wahlen-Strothman, Jacob M.; Jiménez-Hoyos, Carlos A.; Henderson, Thomas M.; Scuseria, Gustavo E.

    2015-01-01

    We present a class of Lie algebraic similarity transformations generated by exponentials of two-body on-site Hermitian operators whose Hausdorff series can be summed exactly without truncation. The correlators are defined over the entire lattice and include the Gutzwiller factor ni ↑ni ↓ , and two-site products of density (ni ↑+ni ↓) and spin (ni ↑-ni ↓) operators. The resulting non-Hermitian many-body Hamiltonian can be solved in a biorthogonal mean-field approach with polynomial computational cost. The proposed similarity transformation generates locally weighted orbital transformations of the reference determinant. Although the energy of the model is unbound, projective equations in the spirit of coupled cluster theory lead to well-defined solutions. The theory is tested on the one- and two-dimensional repulsive Hubbard model where it yields accurate results for small and medium sized interaction strengths.

  3. Intelligently deciphering unintelligible designs: algorithmic algebraic model checking in systems biology

    PubMed Central

    Mishra, Bud

    2009-01-01

    Systems biology, as a subject, has captured the imagination of both biologists and systems scientists alike. But what is it? This review provides one researcher's somewhat idiosyncratic view of the subject, but also aims to persuade young scientists to examine the possible evolution of this subject in a rich historical context. In particular, one may wish to read this review to envision a subject built out of a consilience of many interesting concepts from systems sciences, logic and model theory, and algebra, culminating in novel tools, techniques and theories that can reveal deep principles in biology—seen beyond mere observations. A particular focus in this review is on approaches embedded in an embryonic program, dubbed ‘algorithmic algebraic model checking’, and its powers and limitations. PMID:19364723

  4. New directions in algebraic dynamical systems

    NASA Astrophysics Data System (ADS)

    Schmidt, Klaus; Verbitskiy, Evgeny

    2011-02-01

    The logarithmic Mahler measure of certain multivariate polynomials occurs frequently as the entropy or the free energy of solvable lattice models (especially dimer models). It is also known that the entropy of an algebraic dynamical system is the logarithmic Mahler measure of the defining polynomial. The connection between the lattice models and the algebraic dynamical systems is still rather mysterious.

  5. ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra

    PubMed Central

    2011-01-01

    Background Many biological systems are modeled qualitatively with discrete models, such as probabilistic Boolean networks, logical models, Petri nets, and agent-based models, to gain a better understanding of them. The computational complexity to analyze the complete dynamics of these models grows exponentially in the number of variables, which impedes working with complex models. There exist software tools to analyze discrete models, but they either lack the algorithmic functionality to analyze complex models deterministically or they are inaccessible to many users as they require understanding the underlying algorithm and implementation, do not have a graphical user interface, or are hard to install. Efficient analysis methods that are accessible to modelers and easy to use are needed. Results We propose a method for efficiently identifying attractors and introduce the web-based tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other analysis methods for discrete models. ADAM converts several discrete model types automatically into polynomial dynamical systems and analyzes their dynamics using tools from computer algebra. Specifically, we propose a method to identify attractors of a discrete model that is equivalent to solving a system of polynomial equations, a long-studied problem in computer algebra. Based on extensive experimentation with both discrete models arising in systems biology and randomly generated networks, we found that the algebraic algorithms presented in this manuscript are fast for systems with the structure maintained by most biological systems, namely sparseness and robustness. For a large set of published complex discrete models, ADAM identified the attractors in less than one second. Conclusions Discrete modeling techniques are a useful tool for analyzing complex biological systems and there is a need in the biological community for accessible efficient analysis tools. ADAM provides analysis methods based on

  6. Sensitivity analysis and model reduction of nonlinear differential-algebraic systems. Final progress report

    SciTech Connect

    Petzold, L.R.; Rosen, J.B.

    1997-12-30

    Differential-algebraic equations arise in a wide variety of engineering and scientific problems. Relatively little work has been done regarding sensitivity analysis and model reduction for this class of problems. Efficient methods for sensitivity analysis are required in model development and as an intermediate step in design optimization of engineering processes. Reduced order models are needed for modelling complex physical phenomena like turbulent reacting flows, where it is not feasible to use a fully-detailed model. The objective of this work has been to develop numerical methods and software for sensitivity analysis and model reduction of nonlinear differential-algebraic systems, including large-scale systems. In collaboration with Peter Brown and Alan Hindmarsh of LLNL, the authors developed an algorithm for finding consistent initial conditions for several widely occurring classes of differential-algebraic equations (DAEs). The new algorithm is much more robust than the previous algorithm. It is also very easy to use, having been designed to require almost no information about the differential equation, Jacobian matrix, etc. in addition to what is already needed to take the subsequent time steps. The new algorithm has been implemented in a version of the software for solution of large-scale DAEs, DASPK, which has been made available on the internet. The new methods and software have been used to solve a Tokamak edge plasma problem at LLNL which could not be solved with the previous methods and software because of difficulties in finding consistent initial conditions. The capability of finding consistent initial values is also needed for the sensitivity and optimization efforts described in this paper.

  7. Theory of equivalence systems for describing algebraic closures of a generalized estimation model. II

    NASA Astrophysics Data System (ADS)

    D'Yakonov, A. G.

    2011-03-01

    Characteristic matrices and metrics of equivalence systems are studied that help give an efficient description of conjunctions of equivalence systems. Using these results, families of correct polynomials in the algebraic approach to classification are described.

  8. Fast and accurate computation of system matrix for area integral model-based algebraic reconstruction technique

    NASA Astrophysics Data System (ADS)

    Zhang, Shunli; Zhang, Dinghua; Gong, Hao; Ghasemalizadeh, Omid; Wang, Ge; Cao, Guohua

    2014-11-01

    Iterative algorithms, such as the algebraic reconstruction technique (ART), are popular for image reconstruction. For iterative reconstruction, the area integral model (AIM) is more accurate for better reconstruction quality than the line integral model (LIM). However, the computation of the system matrix for AIM is more complex and time-consuming than that for LIM. Here, we propose a fast and accurate method to compute the system matrix for AIM. First, we calculate the intersection of each boundary line of a narrow fan-beam with pixels in a recursive and efficient manner. Then, by grouping the beam-pixel intersection area into six types according to the slopes of the two boundary lines, we analytically compute the intersection area of the narrow fan-beam with the pixels in a simple algebraic fashion. Overall, experimental results show that our method is about three times faster than the Siddon algorithm and about two times faster than the distance-driven model (DDM) in computation of the system matrix. The reconstruction speed of our AIM-based ART is also faster than the LIM-based ART that uses the Siddon algorithm and DDM-based ART, for one iteration. The fast reconstruction speed of our method was accomplished without compromising the image quality.

  9. Modelling and temporal performances evaluation of networked control systems using (max, +) algebra

    NASA Astrophysics Data System (ADS)

    Ammour, R.; Amari, S.

    2015-01-01

    In this paper, we address the problem of temporal performances evaluation of producer/consumer networked control systems. The aim is to develop a formal method for evaluating the response time of this type of control systems. Our approach consists on modelling, using Petri nets classes, the behaviour of the whole architecture including the switches that support multicast communications used by this protocol. (max, +) algebra formalism is then exploited to obtain analytical formulas of the response time and the maximal and minimal bounds. The main novelty is that our approach takes into account all delays experienced at the different stages of networked automation systems. Finally, we show how to apply the obtained results through an example of networked control system.

  10. MODEL IDENTIFICATION AND COMPUTER ALGEBRA

    PubMed Central

    Bollen, Kenneth A.; Bauldry, Shawn

    2011-01-01

    Multiequation models that contain observed or latent variables are common in the social sciences. To determine whether unique parameter values exist for such models, one needs to assess model identification. In practice analysts rely on empirical checks that evaluate the singularity of the information matrix evaluated at sample estimates of parameters. The discrepancy between estimates and population values, the limitations of numerical assessments of ranks, and the difference between local and global identification make this practice less than perfect. In this paper we outline how to use computer algebra systems (CAS) to determine the local and global identification of multiequation models with or without latent variables. We demonstrate a symbolic CAS approach to local identification and develop a CAS approach to obtain explicit algebraic solutions for each of the model parameters. We illustrate the procedures with several examples, including a new proof of the identification of a model for handling missing data using auxiliary variables. We present an identification procedure for Structural Equation Models that makes use of CAS and that is a useful complement to current methods. PMID:21769158

  11. MODEL IDENTIFICATION AND COMPUTER ALGEBRA.

    PubMed

    Bollen, Kenneth A; Bauldry, Shawn

    2010-10-01

    Multiequation models that contain observed or latent variables are common in the social sciences. To determine whether unique parameter values exist for such models, one needs to assess model identification. In practice analysts rely on empirical checks that evaluate the singularity of the information matrix evaluated at sample estimates of parameters. The discrepancy between estimates and population values, the limitations of numerical assessments of ranks, and the difference between local and global identification make this practice less than perfect. In this paper we outline how to use computer algebra systems (CAS) to determine the local and global identification of multiequation models with or without latent variables. We demonstrate a symbolic CAS approach to local identification and develop a CAS approach to obtain explicit algebraic solutions for each of the model parameters. We illustrate the procedures with several examples, including a new proof of the identification of a model for handling missing data using auxiliary variables. We present an identification procedure for Structural Equation Models that makes use of CAS and that is a useful complement to current methods.

  12. Flipping an Algebra Classroom: Analyzing, Modeling, and Solving Systems of Linear Equations

    ERIC Educational Resources Information Center

    Kirvan, Rebecca; Rakes, Christopher R.; Zamora, Regie

    2015-01-01

    The present study investigated whether flipping an algebra classroom led to a stronger focus on conceptual understanding and improved learning of systems of linear equations for 54 seventh- and eighth-grade students using teacher journal data and district-mandated unit exam items. Multivariate analysis of covariance was used to compare scores on…

  13. Algebraic Systems and Pushdown Automata

    NASA Astrophysics Data System (ADS)

    Petre, Ion; Salomaa, Arto

    We concentrate in this chapter on the core aspects of algebraic series, pushdown automata, and their relation to formal languages. We choose to follow here a presentation of their theory based on the concept of properness. We introduce in Sect. 2 some auxiliary notions and results needed throughout the chapter, in particular the notions of discrete convergence in semirings and C-cycle free infinite matrices. In Sect. 3 we introduce the algebraic power series in terms of algebraic systems of equations. We focus on interconnections with context-free grammars and on normal forms. We then conclude the section with a presentation of the theorems of Shamir and Chomsky-Schützenberger. We discuss in Sect. 4 the algebraic and the regulated rational transductions, as well as some representation results related to them. Section 5 is dedicated to pushdown automata and focuses on the interconnections with classical (non-weighted) pushdown automata and on the interconnections with algebraic systems. We then conclude the chapter with a brief discussion of some of the other topics related to algebraic systems and pushdown automata.

  14. Computational algebraic geometry of epidemic models

    NASA Astrophysics Data System (ADS)

    Rodríguez Vega, Martín.

    2014-06-01

    Computational Algebraic Geometry is applied to the analysis of various epidemic models for Schistosomiasis and Dengue, both, for the case without control measures and for the case where control measures are applied. The models were analyzed using the mathematical software Maple. Explicitly the analysis is performed using Groebner basis, Hilbert dimension and Hilbert polynomials. These computational tools are included automatically in Maple. Each of these models is represented by a system of ordinary differential equations, and for each model the basic reproductive number (R0) is calculated. The effects of the control measures are observed by the changes in the algebraic structure of R0, the changes in Groebner basis, the changes in Hilbert dimension, and the changes in Hilbert polynomials. It is hoped that the results obtained in this paper become of importance for designing control measures against the epidemic diseases described. For future researches it is proposed the use of algebraic epidemiology to analyze models for airborne and waterborne diseases.

  15. Handheld Computer Algebra Systems in the Pre-Algebra Classroom

    ERIC Educational Resources Information Center

    Gantz, Linda Ann Galofaro

    2010-01-01

    This mixed method analysis sought to investigate several aspects of student learning in pre-algebra through the use of computer algebra systems (CAS) as opposed to non-CAS learning. This research was broken into two main parts, one which compared results from both the experimental group (instruction using CAS, N = 18) and the control group…

  16. Symmetric linear systems - An application of algebraic systems theory

    NASA Technical Reports Server (NTRS)

    Hazewinkel, M.; Martin, C.

    1983-01-01

    Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.

  17. Solving stochastic epidemiological models using computer algebra

    NASA Astrophysics Data System (ADS)

    Hincapie, Doracelly; Ospina, Juan

    2011-06-01

    Mathematical modeling in Epidemiology is an important tool to understand the ways under which the diseases are transmitted and controlled. The mathematical modeling can be implemented via deterministic or stochastic models. Deterministic models are based on short systems of non-linear ordinary differential equations and the stochastic models are based on very large systems of linear differential equations. Deterministic models admit complete, rigorous and automatic analysis of stability both local and global from which is possible to derive the algebraic expressions for the basic reproductive number and the corresponding epidemic thresholds using computer algebra software. Stochastic models are more difficult to treat and the analysis of their properties requires complicated considerations in statistical mathematics. In this work we propose to use computer algebra software with the aim to solve epidemic stochastic models such as the SIR model and the carrier-borne model. Specifically we use Maple to solve these stochastic models in the case of small groups and we obtain results that do not appear in standard textbooks or in the books updated on stochastic models in epidemiology. From our results we derive expressions which coincide with those obtained in the classical texts using advanced procedures in mathematical statistics. Our algorithms can be extended for other stochastic models in epidemiology and this shows the power of computer algebra software not only for analysis of deterministic models but also for the analysis of stochastic models. We also perform numerical simulations with our algebraic results and we made estimations for the basic parameters as the basic reproductive rate and the stochastic threshold theorem. We claim that our algorithms and results are important tools to control the diseases in a globalized world.

  18. Shapes and stability of algebraic nuclear models

    NASA Technical Reports Server (NTRS)

    Lopez-Moreno, Enrique; Castanos, Octavio

    1995-01-01

    A generalization of the procedure to study shapes and stability of algebraic nuclear models introduced by Gilmore is presented. One calculates the expectation value of the Hamiltonian with respect to the coherent states of the algebraic structure of the system. Then equilibrium configurations of the resulting energy surface, which depends in general on state variables and a set of parameters, are classified through the Catastrophe theory. For one- and two-body interactions in the Hamiltonian of the interacting Boson model-1, the critical points are organized through the Cusp catastrophe. As an example, we apply this Separatrix to describe the energy surfaces associated to the Rutenium and Samarium isotopes.

  19. Algebraic methods in system theory

    NASA Technical Reports Server (NTRS)

    Brockett, R. W.; Willems, J. C.; Willsky, A. S.

    1975-01-01

    Investigations on problems of the type which arise in the control of switched electrical networks are reported. The main results concern the algebraic structure and stochastic aspects of these systems. Future reports will contain more detailed applications of these results to engineering studies.

  20. Multiobjective algebraic synthesis of neural control systems by implicit model following.

    PubMed

    Ferrari, Silvia

    2009-03-01

    The advantages brought about by using classical linear control theory in conjunction with neural approximators have long been recognized in the literature. In particular, using linear controllers to obtain the starting neural control design has been shown to be a key step for the successful development and implementation of adaptive-critic neural controllers. Despite their adaptive capabilities, neural controllers are often criticized for not providing the same performance and stability guarantees as classical linear designs. Therefore, this paper develops an algebraic synthesis procedure for designing dynamic output-feedback neural controllers that are closed-loop stable and meet the same performance objectives as any classical linear design. The performance synthesis problem is addressed by deriving implicit model-following algebraic relationships between model matrices, obtained from the classical design, and the neural control parameters. Additional linear matrix inequalities (LMIs) conditions for closed-loop exponential stability of the neural controller are derived using existing integral quadratic constraints (IQCs) for operators with repeated slope-restricted nonlinearities. The approach is demonstrated by designing a recurrent neural network controller for a highly maneuverable tailfin-controlled missile that meets multiple design objectives, including pole placement for transient tuning, H(infinity) and H(2) performance in the presence of parameter uncertainty, and command-input tracking. PMID:19203887

  1. Computer Algebra Systems, Pedagogy, and Epistemology

    ERIC Educational Resources Information Center

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

    2004-01-01

    The advent of powerful Computer Algebra Systems (CAS) continues to dramatically affect curricula, pedagogy, and epistemology in secondary and college algebra classrooms. However, epistemological and pedagogical research regarding the role and effectiveness of CAS in the learning of algebra lags behind. This paper investigates concerns regarding…

  2. Computer Algebra System

    SciTech Connect

    1992-05-04

    DOE-MACSYMA (Project MAC''s SYmbolic MAnipulation system) is a large computer programming system written in LISP. With DOE-MACSYMA the user can differentiate, integrate, take limits, solve systems of linear or polynomial equations, factor polynomials, expand functions in Laurent or Taylor series, solve differential equations (using direct or transform methods), compute Poisson series, plot curves, and manipulate matrices and tensors. A language similar to ALGOL-60 permits users to write their own programs for transforming symbolic expressions. Franz Lisp OPUS 38 provides the environment for the Encore, Celerity, and DEC VAX11 UNIX,SUN(OPUS) versions under UNIX and the Alliant version under Concentrix. Kyoto Common Lisp (KCL) provides the environment for the SUN(KCL),Convex, and IBM PC under UNIX and Data General under AOS/VS.

  3. Computer Algebra System

    1992-05-04

    DOE-MACSYMA (Project MAC''s SYmbolic MAnipulation system) is a large computer programming system written in LISP. With DOE-MACSYMA the user can differentiate, integrate, take limits, solve systems of linear or polynomial equations, factor polynomials, expand functions in Laurent or Taylor series, solve differential equations (using direct or transform methods), compute Poisson series, plot curves, and manipulate matrices and tensors. A language similar to ALGOL-60 permits users to write their own programs for transforming symbolic expressions. Franzmore » Lisp OPUS 38 provides the environment for the Encore, Celerity, and DEC VAX11 UNIX,SUN(OPUS) versions under UNIX and the Alliant version under Concentrix. Kyoto Common Lisp (KCL) provides the environment for the SUN(KCL),Convex, and IBM PC under UNIX and Data General under AOS/VS.« less

  4. Bohr model as an algebraic collective model

    SciTech Connect

    Rowe, D. J.; Welsh, T. A.; Caprio, M. A.

    2009-05-15

    Developments and applications are presented of an algebraic version of Bohr's collective model. Illustrative examples show that fully converged calculations can be performed quickly and easily for a large range of Hamiltonians. As a result, the Bohr model becomes an effective tool in the analysis of experimental data. The examples are chosen both to confirm the reliability of the algebraic collective model and to show the diversity of results that can be obtained by its use. The focus of the paper is to facilitate identification of the limitations of the Bohr model with a view to developing more realistic, computationally tractable models.

  5. Some Applications of Algebraic System Solving

    ERIC Educational Resources Information Center

    Roanes-Lozano, Eugenio

    2011-01-01

    Technology and, in particular, computer algebra systems, allows us to change both the way we teach mathematics and the mathematical curriculum. Curiously enough, unlike what happens with linear system solving, algebraic system solving is not widely known. The aim of this paper is to show that, although the theory lying behind the "exact solve"…

  6. Entanglement and algebraic independence in fermion systems

    NASA Astrophysics Data System (ADS)

    Benatti, Fabio; Floreanini, Roberto

    2014-04-01

    In the case of systems composed of identical particles, a typical instance in quantum statistical mechanics, the standard approach to separability and entanglement ought to be reformulated and rephrased in terms of correlations between operators from subalgebras localized in spatially disjoint regions. While this algebraic approach is straightforward for bosons, in the case of fermions it is subtler since one has to distinguish between micro-causality, that is the anti-commutativity of the basic creation and annihilation operators, and algebraic independence that is the commutativity of local observables. We argue that a consistent algebraic formulation of separability and entanglement should be compatible with micro-causality rather than with algebraic independence.

  7. Using Students' Interests as Algebraic Models

    ERIC Educational Resources Information Center

    Whaley, Kenneth A.

    2012-01-01

    Fostering algebraic thinking is an important goal for middle-grades mathematics teachers. Developing mathematical reasoning requires that teachers cultivate students' habits of mind. Teachers develop students' understanding of algebra by engaging them in tasks that involve modeling and representation. This study was designed to investigate how…

  8. Teaching Modeling and Axiomatization with Boolean Algebra.

    ERIC Educational Resources Information Center

    De Villiers, Michael D.

    1987-01-01

    Presented is an alternative approach to the traditional teaching of Boolean algebra for secondary school mathematics. The main aim of the approach is to use Boolean algebra to teach pupils such mathematical processes as modeling and axiomatization. A course using the approach is described. (RH)

  9. Algebraic operator approach to gas kinetic models

    NASA Astrophysics Data System (ADS)

    Il'ichov, L. V.

    1997-02-01

    Some general properties of the linear Boltzmann kinetic equation are used to present it in the form ∂ tϕ = - †Âϕ with the operators Âand† possessing some nontrivial algebraic properties. When applied to the Keilson-Storer kinetic model, this method gives an example of quantum ( q-deformed) Lie algebra. This approach provides also a natural generalization of the “kangaroo model”.

  10. An algebraic cluster model based on the harmonic oscillator basis

    NASA Technical Reports Server (NTRS)

    Levai, Geza; Cseh, J.

    1995-01-01

    We discuss the semimicroscopic algebraic cluster model introduced recently, in which the internal structure of the nuclear clusters is described by the harmonic oscillator shell model, while their relative motion is accounted for by the Vibron model. The algebraic formulation of the model makes extensive use of techniques associated with harmonic oscillators and their symmetry group, SU(3). The model is applied to some cluster systems and is found to reproduce important characteristics of nuclei in the sd-shell region. An approximate SU(3) dynamical symmetry is also found to hold for the C-12 + C-12 system.

  11. A spatial operator algebra for manipulator modeling and control

    NASA Technical Reports Server (NTRS)

    Rodriguez, G.; Kreutz, K.; Milman, M.

    1988-01-01

    A powerful new spatial operator algebra for modeling, control, and trajectory design of manipulators is discussed along with its implementation in the Ada programming language. Applications of this algebra to robotics include an operator representation of the manipulator Jacobian matrix; the robot dynamical equations formulated in terms of the spatial algebra, showing the complete equivalence between the recursive Newton-Euler formulations to robot dynamics; the operator factorization and inversion of the manipulator mass matrix which immediately results in O(N) recursive forward dynamics algorithms; the joint accelerations of a manipulator due to a tip contact force; the recursive computation of the equivalent mass matrix as seen at the tip of a manipulator; and recursive forward dynamics of a closed chain system. Finally, additional applications and current research involving the use of the spatial operator algebra are discussed in general terms.

  12. Prospective Teachers' Views on the Use of Calculators with Computer Algebra System in Algebra Instruction

    ERIC Educational Resources Information Center

    Ozgun-Koca, S. Ash

    2010-01-01

    Although growing numbers of secondary school mathematics teachers and students use calculators to study graphs, they mainly rely on paper-and-pencil when manipulating algebraic symbols. However, the Computer Algebra Systems (CAS) on computers or handheld calculators create new possibilities for teaching and learning algebraic manipulation. This…

  13. Constraint algebra for interacting quantum systems

    NASA Astrophysics Data System (ADS)

    Fubini, S.; Roncadelli, M.

    1988-04-01

    We consider relativistic constrained systems interacting with external fields. We provide physical arguments to support the idea that the quantum constraint algebra should be the same as in the free quantum case. For systems with ordering ambiguities this principle is essential to obtain a unique quantization. This is shown explicitly in the case of a relativistic spinning particle, where our assumption about the constraint algebra plus invariance under general coordinate transformations leads to a unique S-matrix. On leave from Dipartimento di Fisica Nucleare e Teorica, Università di Pavia and INFN, I-27100 Pavia, Italy.

  14. Algebraic Systems Biology: A Case Study for the Wnt Pathway.

    PubMed

    Gross, Elizabeth; Harrington, Heather A; Rosen, Zvi; Sturmfels, Bernd

    2016-01-01

    Steady-state analysis of dynamical systems for biological networks gives rise to algebraic varieties in high-dimensional spaces whose study is of interest in their own right. We demonstrate this for the shuttle model of the Wnt signaling pathway. Here, the variety is described by a polynomial system in 19 unknowns and 36 parameters. It has degree 9 over the parameter space. This case study explores multistationarity, model comparison, dynamics within regions of the state space, identifiability, and parameter estimation, from a geometric point of view. We employ current methods from computational algebraic geometry, polyhedral geometry, and combinatorics.

  15. Algebraic Systems Biology: A Case Study for the Wnt Pathway.

    PubMed

    Gross, Elizabeth; Harrington, Heather A; Rosen, Zvi; Sturmfels, Bernd

    2016-01-01

    Steady-state analysis of dynamical systems for biological networks gives rise to algebraic varieties in high-dimensional spaces whose study is of interest in their own right. We demonstrate this for the shuttle model of the Wnt signaling pathway. Here, the variety is described by a polynomial system in 19 unknowns and 36 parameters. It has degree 9 over the parameter space. This case study explores multistationarity, model comparison, dynamics within regions of the state space, identifiability, and parameter estimation, from a geometric point of view. We employ current methods from computational algebraic geometry, polyhedral geometry, and combinatorics. PMID:26645985

  16. Optical linear algebra processors: noise and error-source modeling.

    PubMed

    Casasent, D; Ghosh, A

    1985-06-01

    The modeling of system and component noise and error sources in optical linear algebra processors (OLAP's) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.

  17. Optical linear algebra processors - Noise and error-source modeling

    NASA Technical Reports Server (NTRS)

    Casasent, D.; Ghosh, A.

    1985-01-01

    The modeling of system and component noise and error sources in optical linear algebra processors (OLAPs) are considered, with attention to the frequency-multiplexed OLAP. General expressions are obtained for the output produced as a function of various component errors and noise. A digital simulator for this model is discussed.

  18. A process algebra model of QED

    NASA Astrophysics Data System (ADS)

    Sulis, William

    2016-03-01

    The process algebra approach to quantum mechanics posits a finite, discrete, determinate ontology of primitive events which are generated by processes (in the sense of Whitehead). In this ontology, primitive events serve as elements of an emergent space-time and of emergent fundamental particles and fields. Each process generates a set of primitive elements, using only local information, causally propagated as a discrete wave, forming a causal space termed a causal tapestry. Each causal tapestry forms a discrete and finite sampling of an emergent causal manifold (space-time) M and emergent wave function. Interactions between processes are described by a process algebra which possesses 8 commutative operations (sums and products) together with a non-commutative concatenation operator (transitions). The process algebra possesses a representation via nondeterministic combinatorial games. The process algebra connects to quantum mechanics through the set valued process and configuration space covering maps, which associate each causal tapestry with sets of wave functions over M. Probabilities emerge from interactions between processes. The process algebra model has been shown to reproduce many features of the theory of non-relativistic scalar particles to a high degree of accuracy, without paradox or divergences. This paper extends the approach to a semi-classical form of quantum electrodynamics.

  19. A modular approach to modeling an isolated power system on a finite voltage bus using a differential algebraic equation solving routine

    NASA Astrophysics Data System (ADS)

    Kipps, Mark R.

    1994-03-01

    The modeling of power systems has been primarily driven by the commercial power utility industry. These models usually involve the assumption that system bus voltage and frequency are constant. However, in applications such as shipboard power systems this infinite bus assumption is not valid. This thesis investigates the modeling of a synchronous generator and various loads in a modular fashion on a finite bus. The simulation presented allows the interconnection of multiple state-space models via a bus voltage model. The major difficulty encountered in building a model which computes bus voltage at each time step is that bus voltage is a function of current and current derivative terms. Bus voltage is also an input to the state equations which produce the current and current derivatives. This creates an algebraic loop which is a form of implicit differential equation. A routine has been developed by Linda Petzold of Lawrence Livermore Laboratory for solving these types of equations. The routine, called Differential Algebraic System Solver (DASSL), has been implemented in a pre-release version of the software Advanced Continuous Simulation Language (ACSL) and has been made available to the Naval Postgraduate School on a trial basis. An isolated power system is modeled using this software and the DASSL routine. The system response to several dynamic situations is studied and the results are presented.

  20. Some Unexpected Results Using Computer Algebra Systems.

    ERIC Educational Resources Information Center

    Alonso, Felix; Garcia, Alfonsa; Garcia, Francisco; Hoya, Sara; Rodriguez, Gerardo; de la Villa, Agustin

    2001-01-01

    Shows how teachers can often use unexpected outputs from Computer Algebra Systems (CAS) to reinforce concepts and to show students the importance of thinking about how they use the software and reflecting on their results. Presents different examples where DERIVE, MAPLE, or Mathematica does not work as expected and suggests how to use them as a…

  1. Static friction, differential algebraic systems and numerical stability

    NASA Astrophysics Data System (ADS)

    Chen, Jian; Schinner, Alexander; Matuttis, Hans-Georg

    We show how Differential Algebraic Systems (Ordinary Differential Equations with algebraic constraints) in mechanics are affected by stability issues and we implement Lubich's projection method to reduce the error to practically zero. Then, we explain how the "numerically exact" implementation for static friction by Differential Algebraic Systems can be stabilized. We conclude by comparing the corresponding steps in the "Contact mechanics" introduced by Moreau.

  2. Spatial Operator Algebra for multibody system dynamics

    NASA Technical Reports Server (NTRS)

    Rodriguez, G.; Jain, A.; Kreutz-Delgado, K.

    1992-01-01

    The Spatial Operator Algebra framework for the dynamics of general multibody systems is described. The use of a spatial operator-based methodology permits the formulation of the dynamical equations of motion of multibody systems in a concise and systematic way. The dynamical equations of progressively more complex grid multibody systems are developed in an evolutionary manner beginning with a serial chain system, followed by a tree topology system and finally, systems with arbitrary closed loops. Operator factorizations and identities are used to develop novel recursive algorithms for the forward dynamics of systems with closed loops. Extensions required to deal with flexible elements are also discussed.

  3. Generalization of Richardson-Gaudin models to rank-2 algebras

    SciTech Connect

    Errea, B; Lerma, S; Dukelsky, J; Dimitrova, S S; Pittel, S; Van Isacker, P; Gueorguiev, V G

    2006-07-20

    A generalization of Richardson-Gaudin models to the rank-2 SO(5) and SO(3,2) algebras is used to describe systems of two kinds of fermions or bosons interacting through a pairing force. They are applied to the proton-neutron neutron isovector pairing model and to the Interacting Boson Model 2, in the transition from vibration to gamma-soft nuclei, respectively. In both cases, the integrals of motion and their eigenvalues are obtained.

  4. A New Reynolds Stress Algebraic Equation Model

    NASA Technical Reports Server (NTRS)

    Shih, Tsan-Hsing; Zhu, Jiang; Lumley, John L.

    1994-01-01

    A general turbulent constitutive relation is directly applied to propose a new Reynolds stress algebraic equation model. In the development of this model, the constraints based on rapid distortion theory and realizability (i.e. the positivity of the normal Reynolds stresses and the Schwarz' inequality between turbulent velocity correlations) are imposed. Model coefficients are calibrated using well-studied basic flows such as homogeneous shear flow and the surface flow in the inertial sublayer. The performance of this model is then tested in complex turbulent flows including the separated flow over a backward-facing step and the flow in a confined jet. The calculation results are encouraging and point to the success of the present model in modeling turbulent flows with complex geometries.

  5. Algebraic Reasoning in the Middle Grades: A View of Student Strategies in Pictorial and Algebraic System of Equations

    ERIC Educational Resources Information Center

    Falcon, Raymond

    2009-01-01

    Teachers use action research in order to improve their teaching and student learning. This action research will analyze students' algebraic reasoning in finding values of variables in systems of equations pictorially and algebraically. This research will look at students solving linear systems of equations without knowing the algebraic algorithms.…

  6. A spatial operator algebra for manipulator modeling and control

    NASA Technical Reports Server (NTRS)

    Rodriguez, G.; Jain, A.; Kreutz-Delgado, K.

    1991-01-01

    A recently developed spatial operator algebra for manipulator modeling, control, and trajectory design is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be efficiently obtained via techniques of recursive filtering and smoothing. The operator algebra provides a high-level framework for describing the dynamic and kinematic behavior of a manipulator and for control and trajectory design algorithms. The interpretation of expressions within the algebraic framework leads to enhanced conceptual and physical understanding of manipulator dynamics and kinematics.

  7. A Simple Iterative Solution of Nonlinear Algebraic Systems

    NASA Astrophysics Data System (ADS)

    Gousidou, Maria; Koutitas, Christopher

    2009-09-01

    A simple, robust, easily programmable and efficient method for the iterative solution of nonlinear algebraic systems, commonly appearing in nonlinear mechanics, based on Newton-Raphson method (without repeatedly solving linear algebraic systems), is proposed, synoptically described and experimentally investigated. Fast convergence and easy programming are its main qualifications.

  8. Preparing Secondary Mathematics Teachers: A Focus on Modeling in Algebra

    ERIC Educational Resources Information Center

    Jung, Hyunyi; Mintos, Alexia; Newton, Jill

    2015-01-01

    This study addressed the opportunities to learn (OTL) modeling in algebra provided to secondary mathematics pre-service teachers (PSTs). To investigate these OTL, we interviewed five instructors of required mathematics and mathematics education courses that had the potential to include opportunities for PSTs to learn algebra at three universities.…

  9. On explicit algebraic stress models for complex turbulent flows

    NASA Technical Reports Server (NTRS)

    Gatski, T. B.; Speziale, C. G.

    1992-01-01

    Explicit algebraic stress models that are valid for three-dimensional turbulent flows in noninertial frames are systematically derived from a hierarchy of second-order closure models. This represents a generalization of the model derived by Pope who based his analysis on the Launder, Reece, and Rodi model restricted to two-dimensional turbulent flows in an inertial frame. The relationship between the new models and traditional algebraic stress models -- as well as anistropic eddy visosity models -- is theoretically established. The need for regularization is demonstrated in an effort to explain why traditional algebraic stress models have failed in complex flows. It is also shown that these explicit algebraic stress models can shed new light on what second-order closure models predict for the equilibrium states of homogeneous turbulent flows and can serve as a useful alternative in practical computations.

  10. Algebraic Systems: Applications in the Behavioral and Social Sciences.

    ERIC Educational Resources Information Center

    Hirshfeld, Stephen F.; Bart, William M.

    A variety of uses of algebra in the behavioral and social sciences is provided along with descriptions of several algebraic systems. This volume is intended to be a sourcebook for theoretical conceptualizations for professionals in the behavioral and social sciences. This publication with its emphasis on description, application, and utility…

  11. Quadratic algebra for superintegrable monopole system in a Taub-NUT space

    NASA Astrophysics Data System (ADS)

    Hoque, Md Fazlul; Marquette, Ian; Zhang, Yao-Zhong

    2016-09-01

    We introduce a Hartmann system in the generalized Taub-NUT space with Abelian monopole interaction. This quantum system includes well known Kaluza-Klein monopole and MIC-Zwanziger monopole as special cases. It is shown that the corresponding Schrödinger equation of the Hamiltonian is separable in both spherical and parabolic coordinates. We obtain the integrals of motion of this superintegrable model and construct the quadratic algebra and Casimir operator. This algebra can be realized in terms of a deformed oscillator algebra and has finite dimensional unitary representations (unirreps) which provide energy spectra of the system. This result coincides with the physical spectra obtained from the separation of variables.

  12. L∞-algebra models and higher Chern-Simons theories

    NASA Astrophysics Data System (ADS)

    Ritter, Patricia; Sämann, Christian

    2016-10-01

    We continue our study of zero-dimensional field theories in which the fields take values in a strong homotopy Lie algebra. In the first part, we review in detail how higher Chern-Simons theories arise in the AKSZ-formalism. These theories form a universal starting point for the construction of L∞-algebra models. We then show how to describe superconformal field theories and how to perform dimensional reductions in this context. In the second part, we demonstrate that Nambu-Poisson and multisymplectic manifolds are closely related via their Heisenberg algebras. As a byproduct of our discussion, we find central Lie p-algebra extensions of 𝔰𝔬(p + 2). Finally, we study a number of L∞-algebra models which are physically interesting and which exhibit quantized multisymplectic manifolds as vacuum solutions.

  13. Action Algebras and Model Algebras in Denotational Semantics

    NASA Astrophysics Data System (ADS)

    Guedes, Luiz Carlos Castro; Haeusler, Edward Hermann

    This article describes some results concerning the conceptual separation of model dependent and language inherent aspects in a denotational semantics of a programming language. Before going into the technical explanation, the authors wish to relate a story that illustrates how correctly and precisely posed questions can influence the direction of research. By means of his questions, Professor Mosses aided the PhD research of one of the authors of this article and taught the other, who at the time was a novice supervisor, the real meaning of careful PhD supervision. The student’s research had been partially developed towards the implementation of programming languages through denotational semantics specification, and the student had developed a prototype [12] that compared relatively well to some industrial compilers of the PASCAL language. During a visit to the BRICS lab in Aarhus, the student’s supervisor gave Professor Mosses a draft of an article describing the prototype and its implementation experiments. The next day, Professor Mosses asked the supervisor, “Why is the generated code so efficient when compared to that generated by an industrial compiler?” and “You claim that the efficiency is simply a consequence of the Object- Orientation mechanisms used by the prototype programming language (C++); this should be better investigated. Pay more attention to the class of programs that might have this good comparison profile.” As a result of these aptly chosen questions and comments, the student and supervisor made great strides in the subsequent research; the advice provided by Professor Mosses made them perceive that the code generated for certain semantic domains was efficient because it mapped to the “right aspect” of the language semantics. (Certain functional types, used to represent mappings such as Stores and Environments, were pushed to the level of the object language (as in gcc). This had the side-effect of generating

  14. Applied Algebra: The Modeling Technique of Least Squares

    ERIC Educational Resources Information Center

    Zelkowski, Jeremy; Mayes, Robert

    2008-01-01

    The article focuses on engaging students in algebra through modeling real-world problems. The technique of least squares is explored, encouraging students to develop a deeper understanding of the method. (Contains 2 figures and a bibliography.)

  15. Robust algebraic image enhancement for intelligent control systems

    NASA Technical Reports Server (NTRS)

    Lerner, Bao-Ting; Morrelli, Michael

    1993-01-01

    Robust vision capability for intelligent control systems has been an elusive goal in image processing. The computationally intensive techniques a necessary for conventional image processing make real-time applications, such as object tracking and collision avoidance difficult. In order to endow an intelligent control system with the needed vision robustness, an adequate image enhancement subsystem capable of compensating for the wide variety of real-world degradations, must exist between the image capturing and the object recognition subsystems. This enhancement stage must be adaptive and must operate with consistency in the presence of both statistical and shape-based noise. To deal with this problem, we have developed an innovative algebraic approach which provides a sound mathematical framework for image representation and manipulation. Our image model provides a natural platform from which to pursue dynamic scene analysis, and its incorporation into a vision system would serve as the front-end to an intelligent control system. We have developed a unique polynomial representation of gray level imagery and applied this representation to develop polynomial operators on complex gray level scenes. This approach is highly advantageous since polynomials can be manipulated very easily, and are readily understood, thus providing a very convenient environment for image processing. Our model presents a highly structured and compact algebraic representation of grey-level images which can be viewed as fuzzy sets.

  16. Algebraic Modeling of Information Retrieval in XML Documents

    NASA Astrophysics Data System (ADS)

    Georgiev, Bozhidar; Georgieva, Adriana

    2009-11-01

    This paper presents an information retrieval approach in XML documents using tools, based on the linear algebra. The well-known transformation languages as XSLT (XPath) are grounded on the features of higher-order logic for manipulating hierarchical trees. The presented conception is compared to existing higher-order logic formalisms, where the queries are realized by both languages XSLT and XPath. The possibilities of the proposed linear algebraic model combined with hierarchy data models permit more efficient solutions for searching, extracting and manipulating semi-structured data with hierarchical structures avoiding the global navigation over the XML tree components. The main purpose of this algebraic model representation, applied to the hierarchical relationships in the XML data structures, is to make the implementation of linear algebra tools possible for XML data manipulations and to eliminate existing problems, related to regular grammars theory and also to avoid the difficulties, connected with higher -order logic (first-order logic, monadic second- order logic etc.).

  17. Tikhonov solutions of approximately given systems of linear algebraic equations under finite perturbations of their matrices

    NASA Astrophysics Data System (ADS)

    Volkov, V. V.; Erokhin, V. I.

    2010-04-01

    The properties of a mathematical programming problem that arises in finding a stable (in the sense of Tikhonov) solution to a system of linear algebraic equations with an approximately given augmented coefficient matrix are examined. Conditions are obtained that determine whether this problem can be reduced to the minimization of a smoothing functional or to the minimal matrix correction of the underlying system of linear algebraic equations. A method for constructing (exact or approximately given) model systems of linear algebraic equations with known Tikhonov solutions is described. Sharp lower bounds are derived for the maximal error in the solution of an approximately given system of linear algebraic equations under finite perturbations of its coefficient matrix. Numerical examples are given.

  18. Multidimensional integrable systems and deformations of Lie algebra homomorphisms

    SciTech Connect

    Dunajski, Maciej; Grant, James D. E.; Strachan, Ian A. B.

    2007-09-15

    We use deformations of Lie algebra homomorphisms to construct deformations of dispersionless integrable systems arising as symmetry reductions of anti-self-dual Yang-Mills equations with a gauge group Diff(S{sup 1})

  19. The algebraic criteria for the stability of control systems

    NASA Technical Reports Server (NTRS)

    Cremer, H.; Effertz, F. H.

    1986-01-01

    This paper critically examines the standard algebraic criteria for the stability of linear control systems and their proofs, reveals important previously unnoticed connections, and presents new representations. Algebraic stability criteria have also acquired significance for stability studies of non-linear differential equation systems by the Krylov-Bogoljubov-Magnus Method, and allow realization conditions to be determined for classes of broken rational functions as frequency characteristics of electrical network.

  20. A Frame Manipulation Algebra for ER Logical Stage Modelling

    NASA Astrophysics Data System (ADS)

    Furtado, Antonio L.; Casanova, Marco A.; Breitman, Karin K.; Barbosa, Simone D. J.

    The ER model is arguably today's most widely accepted basis for the conceptual specification of information systems. A further common practice is to use the Relational Model at an intermediate logical stage, in order to adequately prepare for physical implementation. Although the Relational Model still works well in contexts relying on standard databases, it imposes certain restrictions, not inherent in ER specifications, which make it less suitable in Web environments. This paper proposes frames as an alternative to move from ER specifications to logical stage modelling, and treats frames as an abstract data type equipped with a Frame Manipulation Algebra (FMA). It is argued that frames, with a long tradition in AI applications, are able to accommodate the irregularities of semi-structured data, and that frame-sets generalize relational tables, allowing to drop the strict homogeneity requirement. A prototype logic-programming tool has been developed to experiment with FMA. Examples are included to help describe the use of the operators.

  1. Improving model-based diagnosis through algebraic analysis: The Petri net challenge

    SciTech Connect

    Portinale, L.

    1996-12-31

    The present paper describes the empirical evaluation of a linear algebra approach to model-based diagnosis, in case the behavioral model of the device under examination is described through a Petri net model. In particular, we show that algebraic analysis based on P-invariants of the net model, can significantly improve the performance of a model-based diagnostic system, while keeping the integrity of a general framework defined from a formal logical theory. A system called INVADS is described and experimental results, performed on a car fault domain and involving the comparison of different implementations of P-invariant based diagnosis, are then discussed.

  2. The BCS-Bogoliubov and the su(2)-Algebraic Approach to the Pairing Model in Many-Fermion System --- The Quasiparticle in the Conservation of the Fermion Number ---

    NASA Astrophysics Data System (ADS)

    Tsue, Y.; Providência, C.; Providência, J. d.; Yamamura, M.

    2012-10-01

    The relation between two approaches to the su(2)-algebraic many-fermion model is discussed: (1) the BCS-Bogoliubov approach in terms of the use of the quasiparticles representing all the degrees of freedom except those related to the Cooper-pairs and (2) the conventional algebraic approach in terms of the use of the minimum weight states, from which the Cooper-pairs are excluded. In order to arrive at the goal, the idea of the quasiparticles is brought up in the conservation of the fermion number. Under the c-number replacement for the three su(2)-generators, the quasiparticles suggested in this paper are reduced to those in the BCS-Bogoliubov approach. It is also shown that the two approaches are equivalent through the c-number replacement. Further, a certain modification of the BCS-Bogoliubov approach is discussed.

  3. SD-CAS: Spin Dynamics by Computer Algebra System.

    PubMed

    Filip, Xenia; Filip, Claudiu

    2010-11-01

    A computer algebra tool for describing the Liouville-space quantum evolution of nuclear 1/2-spins is introduced and implemented within a computational framework named Spin Dynamics by Computer Algebra System (SD-CAS). A distinctive feature compared with numerical and previous computer algebra approaches to solving spin dynamics problems results from the fact that no matrix representation for spin operators is used in SD-CAS, which determines a full symbolic character to the performed computations. Spin correlations are stored in SD-CAS as four-entry nested lists of which size increases linearly with the number of spins into the system and are easily mapped into analytical expressions in terms of spin operator products. For the so defined SD-CAS spin correlations a set of specialized functions and procedures is introduced that are essential for implementing basic spin algebra operations, such as the spin operator products, commutators, and scalar products. They provide results in an abstract algebraic form: specific procedures to quantitatively evaluate such symbolic expressions with respect to the involved spin interaction parameters and experimental conditions are also discussed. Although the main focus in the present work is on laying the foundation for spin dynamics symbolic computation in NMR based on a non-matrix formalism, practical aspects are also considered throughout the theoretical development process. In particular, specific SD-CAS routines have been implemented using the YACAS computer algebra package (http://yacas.sourceforge.net), and their functionality was demonstrated on a few illustrative examples.

  4. SD-CAS: Spin Dynamics by Computer Algebra System

    NASA Astrophysics Data System (ADS)

    Filip, Xenia; Filip, Claudiu

    2010-11-01

    A computer algebra tool for describing the Liouville-space quantum evolution of nuclear 1/2-spins is introduced and implemented within a computational framework named Spin Dynamics by Computer Algebra System (SD-CAS). A distinctive feature compared with numerical and previous computer algebra approaches to solving spin dynamics problems results from the fact that no matrix representation for spin operators is used in SD-CAS, which determines a full symbolic character to the performed computations. Spin correlations are stored in SD-CAS as four-entry nested lists of which size increases linearly with the number of spins into the system and are easily mapped into analytical expressions in terms of spin operator products. For the so defined SD-CAS spin correlations a set of specialized functions and procedures is introduced that are essential for implementing basic spin algebra operations, such as the spin operator products, commutators, and scalar products. They provide results in an abstract algebraic form: specific procedures to quantitatively evaluate such symbolic expressions with respect to the involved spin interaction parameters and experimental conditions are also discussed. Although the main focus in the present work is on laying the foundation for spin dynamics symbolic computation in NMR based on a non-matrix formalism, practical aspects are also considered throughout the theoretical development process. In particular, specific SD-CAS routines have been implemented using the YACAS computer algebra package (http://yacas.sourceforge.net), and their functionality was demonstrated on a few illustrative examples.

  5. A Process Algebraic Framework for Modeling Resource Demand and Supply

    NASA Astrophysics Data System (ADS)

    Philippou, Anna; Lee, Insup; Sokolsky, Oleg; Choi, Jin-Young

    As real-time embedded systems become more complex, resource partitioning is increasingly used to guarantee real-time performance. Recently, several compositional frameworks of resource partitioning have been proposed using real-time scheduling theory with various notions of real-time tasks running under restricted resource supply environments. However, these real-time scheduling-based approaches are limited in their expressiveness in that, although capable of describing resource-demand tasks, they are unable to model resource supply. This paper describes a process algebraic framework for reasoning about resource demand and supply inspired by the timed process algebra ACSR. In ACSR, real-time tasks are specified by enunciating their consumption needs for resources. To also accommodate resource-supply processes we define PADS where, given a resource CPU, the complimented resource overline{CPU} denotes for availability of CPU for the corresponding demand process. Using PADS, we define a supply-demand relation where a pair (S, T) belongs to the relation if the demand process T can be scheduled under supply S. We develop a theory of compositional schedulability analysis as well as a technique for synthesizing an optimal supply process for a set of tasks. We illustrate our technique via a number of examples.

  6. Gup-Based and Snyder Noncommutative Algebras, Relativistic Particle Models, Deformed Symmetries and Interaction: a Unified Approach

    NASA Astrophysics Data System (ADS)

    Pramanik, Souvik; Ghosh, Subir

    2013-08-01

    We have developed a unified scheme for studying noncommutative algebras based on generalized uncertainty principle (GUP) and Snyder form in a relativistically covariant point particle Lagrangian (or symplectic) framework. Even though the GUP-based algebra and Snyder algebra are very distinct, the more involved latter algebra emerges from an approximation of the Lagrangian model of the former algebra. Deformed Poincaré generators for the systems that keep space-time symmetries of the relativistic particle models have been studied thoroughly. From a purely constrained dynamical analysis perspective the models studied here are very rich and provide insights on how to consistently construct approximate models from the exact ones when nonlinear constraints are present in the system. We also study dynamics of the GUP particle in presence of external electromagnetic field.

  7. Gup-Based and Snyder Noncommutative Algebras, Relativistic Particle Models, Deformed Symmetries and Interaction: a Unified Approach

    NASA Astrophysics Data System (ADS)

    Pramanik, Souvik; Ghosh, Subir

    2013-10-01

    We have developed a unified scheme for studying noncommutative algebras based on generalized uncertainty principle (GUP) and Snyder form in a relativistically covariant point particle Lagrangian (or symplectic) framework. Even though the GUP-based algebra and Snyder algebra are very distinct, the more involved latter algebra emerges from an approximation of the Lagrangian model of the former algebra. Deformed Poincaré generators for the systems that keep space-time symmetries of the relativistic particle models have been studied thoroughly. From a purely constrained dynamical analysis perspective the models studied here are very rich and provide insights on how to consistently construct approximate models from the exact ones when nonlinear constraints are present in the system. We also study dynamics of the GUP particle in presence of external electromagnetic field.

  8. Description of DASSL: a differential/algebraic system solver

    SciTech Connect

    Petzold, L.R.

    1982-09-01

    This paper describes a new code DASSL, for the numerical solution of implicit systems of differential/algebraic equations. These equations are written in the form F(t,y,y') = 0, and they can include systems which are substantially more complex than standard form ODE systems y' = f(t,y). Differential/algebraic equations occur in several diverse applications in the physical world. We outline the algorithms and strategies used in DASSL, and explain some of the features of the code. In addition, we outline briefly what needs to be done to solve a problem using DASSL.

  9. A Cognitive Model of Experts' Algebraic Solving Methods

    ERIC Educational Resources Information Center

    Cortes, Anibal

    2003-01-01

    We studied experts' solving methods and analyzed the nature of mathematical knowledge as well as their efficiency in algebraic calculations. We constructed a model of the experts cognitive functioning (notably teachers) in which the observed automatisms were modeled in terms of schemes and instruments. Mathematical justification of transformation…

  10. Inverse Modelling Problems in Linear Algebra Undergraduate Courses

    ERIC Educational Resources Information Center

    Martinez-Luaces, Victor E.

    2013-01-01

    This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different…

  11. Entanglement in algebraic quantum mechanics: Majorana fermion systems

    NASA Astrophysics Data System (ADS)

    Benatti, F.; Floreanini, R.

    2016-07-01

    Many-body entanglement is studied within the algebraic approach to quantum physics in systems made of Majorana fermions. In this framework, the notion of separability stems from partitions of the algebra of observables and properties of the associated correlation functions, rather than on particle tensor products. This allows a complete characterization of non-separable Majorana fermion states to be obtained. These results may have direct application in quantum metrology: using Majorana systems, sub-shot-noise accuracy in parameter estimations can be achieved without preliminary resource-consuming, state entanglement operations.

  12. Motivating Constraints of a Pedagogy-Embedded Computer Algebra System

    ERIC Educational Resources Information Center

    Dana-Picard, Thierry

    2007-01-01

    The constraints of a computer algebra system (CAS) generally induce limitations on its usage. Via the pedagogical features implemented in such a system, "motivating constraints" can appear, encouraging advanced theoretical learning, providing a broader mathematical knowledge and more profound mathematical understanding. We discuss this issue,…

  13. A spatial operator algebra for manipulator modeling and control

    NASA Technical Reports Server (NTRS)

    Rodriguez, G.; Kreutz, Kenneth; Jain, Abhinandan

    1989-01-01

    A recently developed spatial operator algebra, useful for modeling, control, and trajectory design of manipulators is discussed. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of a manipulator. Inversion of operators can be efficiently obtained via techniques of recursive filtering and smoothing. The operator algebra provides a high level framework for describing the dynamic and kinematic behavior of a manipulator and control and trajectory design algorithms. The interpretation of expressions within the algebraic framework leads to enhanced conceptual and physical understanding of manipulator dynamics and kinematics. Furthermore, implementable recursive algorithms can be immediately derived from the abstract operator expressions by inspection. Thus, the transition from an abstract problem formulation and solution to the detailed mechanizaton of specific algorithms is greatly simplified. The analytical formulation of the operator algebra, as well as its implementation in the Ada programming language are discussed.

  14. Algebraic approach to small-world network models

    NASA Astrophysics Data System (ADS)

    Rudolph-Lilith, Michelle; Muller, Lyle E.

    2014-01-01

    We introduce an analytic model for directed Watts-Strogatz small-world graphs and deduce an algebraic expression of its defining adjacency matrix. The latter is then used to calculate the small-world digraph's asymmetry index and clustering coefficient in an analytically exact fashion, valid nonasymptotically for all graph sizes. The proposed approach is general and can be applied to all algebraically well-defined graph-theoretical measures, thus allowing for an analytical investigation of finite-size small-world graphs.

  15. Seeking Simplicity: Algebraic and Topological Modelling in Educational Research.

    ERIC Educational Resources Information Center

    Preece, Peter F. W.

    2001-01-01

    Quantitative algebraic and qualitative topological models can be used in the quest for simple explanations in the field of teaching and learning. The examples described cover such diverse topics as teacher anxiety and classroom control, process-product studies, aptitude-treatment interactions, the pace of instruction, the size of classes, and…

  16. Phase transitions for rotational states within an algebraic cluster model

    NASA Astrophysics Data System (ADS)

    López Moreno, E.; Morales Hernández, G. E.; Hess, P. O.; Yépez Martínez, H.

    2016-07-01

    The ground state and excited, rotational phase transitions are investigated within the Semimicroscopic Algebraic Cluster Model (SACM). The catastrophe theory is used to describe these phase transitions. Short introductions to the SACM and the catastrophe theory are given. We apply the formalism to the case of 16O+α→20Ne.

  17. 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.

  18. An application of computer algebra system Cadabra to scientific problems of physics

    NASA Astrophysics Data System (ADS)

    Sevastianov, L. A.; Kulyabov, D. S.; Kokotchikova, M. G.

    2009-12-01

    In this article we present two examples solved in a new problem-oriented computer algebra system Cadabra. Solution of the same examples in widespread universal computer algebra system Maple turn out to be more difficult.

  19. Analysis of Computer Algebra System Tutorials Using Cognitive Load Theory

    ERIC Educational Resources Information Center

    May, Patricia

    2004-01-01

    Most research in the area of Computer Algebra Systems (CAS) has been designed to compare the effectiveness of instructional technology to traditional lecture-based formats. While results are promising, research also indicates evidence of the steep learning curve imposed by the technology. Yet no studies have been conducted to investigate this…

  20. Construction of coherent states for physical algebraic systems

    SciTech Connect

    Hassouni, Y.; Curado, E.M.F.; Rego-Monteiro, M.A.

    2005-02-01

    We construct a general state which is an eigenvector of the annihilation operator of the generalized Heisenberg algebra. We show, for several systems characterized by different energy spectra, that this general state satisfies the minimal set of conditions required to obtain Klauder's minimal coherent states.

  1. Computer Algebra Systems and Theorems on Real Roots of Polynomials

    ERIC Educational Resources Information Center

    Aidoo, Anthony Y.; Manthey, Joseph L.; Ward, Kim Y.

    2010-01-01

    A computer algebra system is used to derive a theorem on the existence of roots of a quadratic equation on any bounded real interval. This is extended to a cubic polynomial. We discuss how students could be led to derive and prove these theorems. (Contains 1 figure.)

  2. Numerical solution to systems of delay integrodifferential algebraic equations

    NASA Astrophysics Data System (ADS)

    Dmitriev, S. S.; Kuznetsov, E. B.

    2008-03-01

    The numerical solution of the initial value problem for a system of delay integrodifferential algebraic equations is examined in the framework of the parametric continuation method. Necessary and sufficient conditions are obtained for transforming this problem to the best argument, which is the arc length along the integral curve of the problem. The efficiency of the transformation is demonstrated using test examples.

  3. Computer Algebra Systems: Permitted but Are They Used?

    ERIC Educational Resources Information Center

    Pierce, Robyn; Bardini, Caroline

    2015-01-01

    Since the 1990s, computer algebra systems (CAS) have been available in Australia as hand-held devices designed for students with the expectation that they will be used in the mathematics classroom. The data discussed in this paper was collected as part of a pilot study that investigated first year university mathematics and statistics students'…

  4. Analysis of DIRAC's behavior using model checking with process algebra

    NASA Astrophysics Data System (ADS)

    Remenska, Daniela; Templon, Jeff; Willemse, Tim; Bal, Henri; Verstoep, Kees; Fokkink, Wan; Charpentier, Philippe; Graciani Diaz, Ricardo; Lanciotti, Elisa; Roiser, Stefan; Ciba, Krzysztof

    2012-12-01

    DIRAC is the grid solution developed to support LHCb production activities as well as user data analysis. It consists of distributed services and agents delivering the workload to the grid resources. Services maintain database back-ends to store dynamic state information of entities such as jobs, queues, staging requests, etc. Agents use polling to check and possibly react to changes in the system state. Each agent's logic is relatively simple; the main complexity lies in their cooperation. Agents run concurrently, and collaborate using the databases as shared memory. The databases can be accessed directly by the agents if running locally or through a DIRAC service interface if necessary. This shared-memory model causes entities to occasionally get into inconsistent states. Tracing and fixing such problems becomes formidable due to the inherent parallelism present. We propose more rigorous methods to cope with this. Model checking is one such technique for analysis of an abstract model of a system. Unlike conventional testing, it allows full control over the parallel processes execution, and supports exhaustive state-space exploration. We used the mCRL2 language and toolset to model the behavior of two related DIRAC subsystems: the workload and storage management system. Based on process algebra, mCRL2 allows defining custom data types as well as functions over these. This makes it suitable for modeling the data manipulations made by DIRAC's agents. By visualizing the state space and replaying scenarios with the toolkit's simulator, we have detected race-conditions and deadlocks in these systems, which, in several cases, were confirmed to occur in the reality. Several properties of interest were formulated and verified with the tool. Our future direction is automating the translation from DIRAC to a formal model.

  5. Rosen’s (M,R) system in process algebra

    PubMed Central

    2013-01-01

    Background Robert Rosen’s Metabolism-Replacement, or (M,R), system can be represented as a compact network structure with a single source and three products derived from that source in three consecutive reactions. (M,R) has been claimed to be non-reducible to its components and algorithmically non-computable, in the sense of not being evaluable as a function by a Turing machine. If (M,R)-like structures are present in real biological networks, this suggests that many biological networks will be non-computable, with implications for those branches of systems biology that rely on in silico modelling for predictive purposes. Results We instantiate (M,R) using the process algebra Bio-PEPA, and discuss the extent to which our model represents a true realization of (M,R). We observe that under some starting conditions and parameter values, stable states can be achieved. Although formal demonstration of algorithmic computability remains elusive for (M,R), we discuss the extent to which our Bio-PEPA representation of (M,R) allows us to sidestep Rosen’s fundamental objections to computational systems biology. Conclusions We argue that the behaviour of (M,R) in Bio-PEPA shows life-like properties. PMID:24237684

  6. Inverse modelling problems in linear algebra undergraduate courses

    NASA Astrophysics Data System (ADS)

    Martinez-Luaces, Victor E.

    2013-10-01

    This paper will offer an analysis from a theoretical point of view of mathematical modelling, applications and inverse problems of both causation and specification types. Inverse modelling problems give the opportunity to establish connections between theory and practice and to show this fact, a simple linear algebra example in two different presentations will be discussed. Finally, several results will be presented and some conclusions proposed.

  7. On Generating Discrete Integrable Systems via Lie Algebras and Commutator Equations

    NASA Astrophysics Data System (ADS)

    Zhang, Yu-Feng; Tam, Honwah

    2016-03-01

    In the paper, we introduce the Lie algebras and the commutator equations to rewrite the Tu-d scheme for generating discrete integrable systems regularly. By the approach the various loop algebras of the Lie algebra A1 are defined so that the well-known Toda hierarchy and a novel discrete integrable system are obtained, respectively. A reduction of the later hierarchy is just right the famous Ablowitz–Ladik hierarchy. Finally, via two different enlarging Lie algebras of the Lie algebra A1, we derive two resulting differential-difference integrable couplings of the Toda hierarchy, of course, they are all various discrete expanding integrable models of the Toda hierarchy. When the introduced spectral matrices are higher degrees, the way presented in the paper is more convenient to generate discrete integrable equations than the Tu-d scheme by using the software Maple. Supported by the National Natural Science Foundation of China under Grant No. 11371361, the Innovation Team of Jiangsu Province hosted by China University of Mining and Technology (2014), and Hong Kong Research Grant Council under Grant No. HKBU202512, as well as the Natural Science Foundation of Shandong Province under Grant No. ZR2013AL016

  8. On Generating Discrete Integrable Systems via Lie Algebras and Commutator Equations

    NASA Astrophysics Data System (ADS)

    Zhang, Yu-Feng; Tam, Honwah

    2016-03-01

    In the paper, we introduce the Lie algebras and the commutator equations to rewrite the Tu-d scheme for generating discrete integrable systems regularly. By the approach the various loop algebras of the Lie algebra A1 are defined so that the well-known Toda hierarchy and a novel discrete integrable system are obtained, respectively. A reduction of the later hierarchy is just right the famous Ablowitz-Ladik hierarchy. Finally, via two different enlarging Lie algebras of the Lie algebra A1, we derive two resulting differential-difference integrable couplings of the Toda hierarchy, of course, they are all various discrete expanding integrable models of the Toda hierarchy. When the introduced spectral matrices are higher degrees, the way presented in the paper is more convenient to generate discrete integrable equations than the Tu-d scheme by using the software Maple. Supported by the National Natural Science Foundation of China under Grant No. 11371361, the Innovation Team of Jiangsu Province hosted by China University of Mining and Technology (2014), and Hong Kong Research Grant Council under Grant No. HKBU202512, as well as the Natural Science Foundation of Shandong Province under Grant No. ZR2013AL016

  9. The algebra of Grassmann canonical anticommutation relations and its applications to fermionic systems

    SciTech Connect

    Keyl, Michael; Schlingemann, Dirk-M.

    2010-02-15

    We present an approach to a noncommutativelike phase space which allows to analyze quasifree states on the algebra of canonical anti-commutation relations (CAR) in analogy to quasifree states on the algebra of canonical commutation relations (CCR). The used mathematical tools are based on a new algebraic structure the 'Grassmann algebra of canonical anticommutation relations' (GAR algebra) which is given by the twisted tensor product of a Grassmann and a CAR algebra. As a new application, the corresponding theory provides an elegant tool for calculating the fidelity of two quasifree fermionic states which is needed for the study of entanglement distillation within fermionic systems.

  10. Computer Algebra.

    ERIC Educational Resources Information Center

    Pavelle, Richard; And Others

    1981-01-01

    Describes the nature and use of computer algebra and its applications to various physical sciences. Includes diagrams illustrating, among others, a computer algebra system and flow chart of operation of the Euclidean algorithm. (SK)

  11. Spatial operator algebra framework for multibody system dynamics

    NASA Technical Reports Server (NTRS)

    Rodriguez, G.; Jain, Abhinandan; Kreutz, K.

    1989-01-01

    The Spatial Operator Algebra framework for the dynamics of general multibody systems is described. The use of a spatial operator-based methodology permits the formulation of the dynamical equations of motion of multibody systems in a concise and systematic way. The dynamical equations of progressively more complex grid multibody systems are developed in an evolutionary manner beginning with a serial chain system, followed by a tree topology system and finally, systems with arbitrary closed loops. Operator factorizations and identities are used to develop novel recursive algorithms for the forward dynamics of systems with closed loops. Extensions required to deal with flexible elements are also discussed.

  12. Generalized Lotka—Volterra systems connected with simple Lie algebras

    NASA Astrophysics Data System (ADS)

    Charalambides, Stelios A.; Damianou, Pantelis A.; Evripidou, Charalambos A.

    2015-06-01

    We devise a new method for producing Hamiltonian systems by constructing the corresponding Lax pairs. This is achieved by considering a larger subset of the positive roots than the simple roots of the root system of a simple Lie algebra. We classify all subsets of the positive roots of the root system of type An for which the corresponding Hamiltonian systems are transformed, via a simple change of variables, to Lotka-Volterra systems. For some special cases of subsets of the positive roots of the root system of type An, we produce new integrable Hamiltonian systems.

  13. Assessment of an Explicit Algebraic Reynolds Stress Model

    NASA Technical Reports Server (NTRS)

    Carlson, Jan-Renee

    2005-01-01

    This study assesses an explicit algebraic Reynolds stress turbulence model in the in the three-dimensional Reynolds averaged Navier-Stokes (RANS) solver, ISAAC (Integrated Solution Algorithm for Arbitrary Con gurations). Additionally, it compares solutions for two select configurations between ISAAC and the RANS solver PAB3D. This study compares with either direct numerical simulation data, experimental data, or empirical models for several different geometries with compressible, separated, and high Reynolds number flows. In general, the turbulence model matched data or followed experimental trends well, and for the selected configurations, the computational results of ISAAC closely matched those of PAB3D using the same turbulence model.

  14. Linking Computer Algebra Systems and Paper-and-Pencil Techniques To Support the Teaching of Mathematics.

    ERIC Educational Resources Information Center

    van Herwaarden, Onno A.; Gielen, Joseph L. W.

    2002-01-01

    Focuses on students showing a lack of conceptual insight while using computer algebra systems (CAS) in the setting of an elementary calculus and linear algebra course for first year university students in social sciences. The use of a computer algebra environment has been incorporated into a more traditional course but with special attention on…

  15. A spatial operator algebra for manipulator modeling and control

    NASA Technical Reports Server (NTRS)

    Rodriguez, G.; Kreutz, K.; Jain, A.

    1989-01-01

    A spatial operator algebra for modeling the control and trajectory design of manipulation is discussed, with emphasis on its analytical formulation and implementation in the Ada programming language. The elements of this algebra are linear operators whose domain and range spaces consist of forces, moments, velocities, and accelerations. The effect of these operators is equivalent to a spatial recursion along the span of the manipulator. Inversion is obtained using techniques of recursive filtering and smoothing. The operator alegbra provides a high-level framework for describing the dynamic and kinematic behavior of a manipulator and control and trajectory design algorithms. Implementable recursive algorithms can be immediately derived from the abstract operator expressions by inspection, thus greatly simplifying the transition from an abstract problem formulation and solution to the detailed mechanization of a specific algorithm.

  16. A Realizable Reynolds Stress Algebraic Equation Model

    NASA Technical Reports Server (NTRS)

    Shih, Tsan-Hsing; Zhu, Jiang; Lumley, John L.

    1993-01-01

    The invariance theory in continuum mechanics is applied to analyze Reynolds stresses in high Reynolds number turbulent flows. The analysis leads to a turbulent constitutive relation that relates the Reynolds stresses to the mean velocity gradients in a more general form in which the classical isotropic eddy viscosity model is just the linear approximation of the general form. On the basis of realizability analysis, a set of model coefficients are obtained which are functions of the time scale ratios of the turbulence to the mean strain rate and the mean rotation rate. The coefficients will ensure the positivity of each component of the mean rotation rate. These coefficients will ensure the positivity of each component of the turbulent kinetic energy - realizability that most existing turbulence models fail to satisfy. Separated flows over backward-facing step configurations are taken as applications. The calculations are performed with a conservative finite-volume method. Grid-independent and numerical diffusion-free solutions are obtained by using differencing schemes of second-order accuracy on sufficiently fine grids. The calculated results are compared in detail with the experimental data for both mean and turbulent quantities. The comparison shows that the present proposal significantly improves the predictive capability of K-epsilon based two equation models. In addition, the proposed model is able to simulate rotational homogeneous shear flows with large rotation rates which all conventional eddy viscosity models fail to simulate.

  17. DOE-MACSYMA. Computer Algebra System

    SciTech Connect

    Harten, L.

    1989-08-01

    DOE-MACSYMA (Project MAC`s SYmbolic MAnipulation system) is a large computer programming system written in LISP. With DOE-MACSYMA the user can differentiate, integrate, take limits, solve systems of linear or polynomial equations, factor polynomials, expand functions in Laurent or Taylor series, solve differential equations (using direct or transform methods), compute Poisson series, plot curves, and manipulate matrices and tensors. A language similar to ALGOL-60 permits users to write their own programs for transforming symbolic expressions.

  18. DOE-MACSYMA. Computer Algebra System

    SciTech Connect

    Cook, G.

    1987-10-01

    DOE-MACSYMA (Project MAC`s SYmbolic MAnipulation system) is a large computer programming system written in LISP. With DOE-MACSYMA the user can differentiate, integrate, take limits, solve systems of linear or polynomial equations, factor polynomials, expand functions in Laurent or Taylor series, solve differential equations (using direct or transform methods), compute Poisson series, plot curves, and manipulate matrices and tensors. A language similar to ALGOL-60 permits users to write their own programs for transforming symbolic expressions.

  19. DOE-MACSYMA. Computer Algebra System

    SciTech Connect

    Cook, G.

    1985-03-01

    DOE-MACSYMA (Project MAC`s SYmbolic MAnipulation system) is a large computer programming system written in LISP. With DOE-MACSYMA the user can differentiate, integrate, take limits, solve systems of linear or polynomial equations, factor polynomials, expand functions in Laurent or Taylor series, solve differential equations (using direct or transform methods), compute Poisson series, plot curves, and manipulate matrices and tensors. A language similar to ALGOL-60 permits users to write their own programs for transforming symbolic expressions.

  20. Using computer algebra and SMT-solvers to analyze a mathematical model of cholera propagation

    NASA Astrophysics Data System (ADS)

    Trujillo Arredondo, Mariana

    2014-06-01

    We analyze a mathematical model for the transmission of cholera. The model is already defined and involves variables such as the pathogen agent, which in this case is the bacterium Vibrio cholera, and the human population. The human population is divided into three classes: susceptible, infectious and removed. Using Computer Algebra, specifically Maple we obtain two equilibrium states: the disease free state and the endemic state. Using Maple it is possible to prove that the disease free state is locally asymptotically stable if and only if R0 < 1. Using Maple it is possible to prove that the endemic equilibrium state is locally stable when it exists, it is to say when R0 > 1. Using the package Red-Log of the Computer algebra system Reduce and the SMT-Solver Z3Py it is possible to obtain numerical conditions for the model. The formula for the basic reproductive number makes a synthesis with all epidemic parameters in the model. Also it is possible to make numerical simulations which are very illustrative about the epidemic patters that are expected to be observed in real situations. We claim that these kinds of software are very useful in the analysis of epidemic models given that the symbolic computation provides algebraic formulas for the basic reproductive number and such algebraic formulas are very useful to derive control measures. For other side, computer algebra software is a powerful tool to make the stability analysis for epidemic models given that the all steps in the stability analysis can be made automatically: finding the equilibrium points, computing the jacobian, computing the characteristic polynomial for the jacobian, and applying the Routh-Hurwitz theorem to the characteristic polynomial. Finally, using SMT-Solvers is possible to make automatically checks of satisfiability, validity and quantifiers elimination being these computations very useful to analyse complicated epidemic models.

  1. Algebraic Turbulence-Chemistry Interaction Model

    NASA Technical Reports Server (NTRS)

    Norris, Andrew T.

    2012-01-01

    The results of a series of Perfectly Stirred Reactor (PSR) and Partially Stirred Reactor (PaSR) simulations are compared to each other over a wide range of operating conditions. It is found that the PaSR results can be simulated by a PSR solution with just an adjusted chemical reaction rate. A simple expression has been developed that gives the required change in reaction rate for a PSR solution to simulate the PaSR results. This expression is the basis of a simple turbulence-chemistry interaction model. The interaction model that has been developed is intended for use with simple one-step global reaction mechanisms and for steady-state flow simulations. Due to the simplicity of the model there is very little additional computational cost in adding it to existing CFD codes.

  2. Developing ontological model of computational linear algebra - preliminary considerations

    NASA Astrophysics Data System (ADS)

    Wasielewska, K.; Ganzha, M.; Paprzycki, M.; Lirkov, I.

    2013-10-01

    The aim of this paper is to propose a method for application of ontologically represented domain knowledge to support Grid users. The work is presented in the context provided by the Agents in Grid system, which aims at development of an agent-semantic infrastructure for efficient resource management in the Grid. Decision support within the system should provide functionality beyond the existing Grid middleware, specifically, help the user to choose optimal algorithm and/or resource to solve a problem from a given domain. The system assists the user in at least two situations. First, for users without in-depth knowledge about the domain, it should help them to select the method and the resource that (together) would best fit the problem to be solved (and match the available resources). Second, if the user explicitly indicates the method and the resource configuration, it should "verify" if her choice is consistent with the expert recommendations (encapsulated in the knowledge base). Furthermore, one of the goals is to simplify the use of the selected resource to execute the job; i.e., provide a user-friendly method of submitting jobs, without required technical knowledge about the Grid middleware. To achieve the mentioned goals, an adaptable method of expert knowledge representation for the decision support system has to be implemented. The selected approach is to utilize ontologies and semantic data processing, supported by multicriterial decision making. As a starting point, an area of computational linear algebra was selected to be modeled, however, the paper presents a general approach that shall be easily extendable to other domains.

  3. Petri nets modeling and analysis using extended bag-theoretic relational algebra.

    PubMed

    Kim, Y C; Kim, T G

    1996-01-01

    Petri nets are a powerful modeling tool for studying reactive, concurrent systems. Analysis of the nets can reveal important information concerning the behavior of a modeled system. While various means for the analysis of the nets has been developed, a major limitation in the analysis, is explosion of large states space in simulation. An efficient method to manage large states space would overcome such a limitation. This paper proposes a framework for the modeling and analysis of Petri nets using relational database technologies. Formalism of the framework is based on a bag-theoretic relational algebra extended from the conventional, Within the framework, Petri nets are formalized by bag relations, and analysis algorithms are developed based on such formal relations. Properties associated with the nets are formalized by queries described in terms of the bag-theoretic relational algebra. The framework has been realized in a commercial relational database system using a standard SQL.

  4. Modelling Simply, Without Algebra: Beyond the Spreadsheet

    ERIC Educational Resources Information Center

    Lawrence, Ian

    2004-01-01

    Using computers to provide dynamic modelling of physical situations is a valuable teaching tool. This is the first of two articles which look in detail at the use of two tools: this article considers the use of VnR whilst the second considers Modellus. This article provides useful approaches using VnR to teach physics. It also considers the…

  5. DOE-MACSYMA. Computer Algebra System

    SciTech Connect

    Schelter, W.F.

    1990-02-01

    DOE-MACSYMA (Project MAC`s SYmbolic MAnipulation system) is a large computer programming system written in LISP. With DOE-MACSYMA the user can differentiate, integrate, take limits, solve systems of linear or polynomial equations, factor polynomials, expand functions in Laurent or Taylor series, solve differential equations (using direct or transform methods), compute Poisson series, plot curves, and manipulate matrices and tensors. A language similar to ALGOL-60 permits users to write their own programs for transforming symbolic expressions.Kyoto Common Lisp (KCL) provides the environment for the SUN(KCL),Convex, and IBM PC under UNIX and Data General under AOS/VS.

  6. DOE-MACSYMA. Computer Algebra System

    SciTech Connect

    Cook, G.

    1987-08-01

    DOE-MACSYMA (Project MAC`s SYmbolic MAnipulation system) is a large computer programming system written in LISP. With DOE-MACSYMA the user can differentiate, integrate, take limits, solve systems of linear or polynomial equations, factor polynomials, expand functions in Laurent or Taylor series, solve differential equations (using direct or transform methods), compute Poisson series, plot curves, and manipulate matrices and tensors. A language similar to ALGOL-60 permits users to write their own programs for transforming symbolic expressions. NIL (a New Implementation of Lisp) provides the environment for MACSYMA`s development and use on the DEC VAX11 under VMS.

  7. DOE-MACSYMA. Computer Algebra System

    SciTech Connect

    O`Dell, J.E.

    1987-07-01

    DOE-MACSYMA (Project MAC`s SYmbolic MAnipulation system) is a large computer programming system written in LISP. With DOE-MACSYMA the user can differentiate, integrate, take limits, solve systems of linear or polynomial equations, factor polynomials, expand functions in Laurent or Taylor series, solve differential equations (using direct or transform methods), compute Poisson series, plot curves, and manipulate matrices and tensors. A language similar to ALGOL-60 permits users to write their own programs for transforming symbolic expressions. Franz Lisp OPUS 38 provides the environment for the Encore, Celerity, and DEC VAX11 UNIX, SUN(OPUS) versions under UNIX and the Alliant version under Concentrix.

  8. DOE-MACSYMA. Computer Algebra System

    SciTech Connect

    Harten, L.

    1988-01-01

    DOE-MACSYMA (Project MAC`s SYmbolic MAnipulation system) is a large computer programming system written in LISP. With DOE-MACSYMA the user can differentiate, integrate, take limits, solve systems of linear or polynomial equations, factor polynomials, expand functions in Laurent or Taylor series, solve differential equations (using direct or transform methods), compute Poisson series, plot curves, and manipulate matrices and tensors. A language similar to ALGOL-60 permits users to write their own programs for transforming symbolic expressions. Franz Lisp OPUS 38 provides the environment for the Encore, Celerity, and DEC VAX11 UNIX, SUN(OPUS) versions under UNIX and the Alliant version under Concentrix.

  9. DOE-MACSYMA. Computer Algebra System

    SciTech Connect

    Palka, D.M.

    1987-11-01

    DOE-MACSYMA (Project MAC`s SYmbolic MAnipulation system) is a large computer programming system written in LISP. With DOE-MACSYMA the user can differentiate, integrate, take limits, solve systems of linear or polynomial equations, factor polynomials, expand functions in Laurent or Taylor series, solve differential equations (using direct or transform methods), compute Poisson series, plot curves, and manipulate matrices and tensors. A language similar to ALGOL-60 permits users to write their own programs for transforming symbolic expressions. Franz Lisp OPUS 38 provides the environment for the Encore, Celerity, and DEC VAX11 UNIX, SUN(OPUS) versions under UNIX and the Alliant version under Concentrix.

  10. DOE-MACSYMA. Computer Algebra System

    SciTech Connect

    Lancaster, D.; Golan, D.

    1990-11-01

    DOE-MACSYMA (Project MAC`s SYmbolic MAnipulation system) is a large computer programming system written in LISP. With DOE-MACSYMA the user can differentiate, integrate, take limits, solve systems of linear or polynomial equations, factor polynomials, expand functions in Laurent or Taylor series, solve differential equations (using direct or transform methods), compute Poisson series, plot curves, and manipulate matrices and tensors. A language similar to ALGOL-60 permits users to write their own programs for transforming symbolic expressions. Kyoto Common Lisp (KCL) provides the environment for the SUN(KCL), Convex, and IBM PC under UNIX and Data General under AOS/VS.

  11. VAXIMA. Computer Algebra System Under UNIX

    SciTech Connect

    Fateman, R.

    1992-03-16

    VAXIMA, derived from Project MAC`s SYmbolic MAnipulation system MACSYMA, is a large computer programming system written in LISP, used for performing symbolic as well as numerical mathematical manipulations. With VAXIMA, the user can differentiate, integrate, take limits, solve systems of linear or polynomial equations, factor polynomials, expand functions in Laurent or Taylor series, solve differential equations with direct or transform methods, compute Poisson series, plot curves, and manipulate matrices and tensors. A language similar to ALGOL-60 permits users to write their own program for transforming symbolic expressions. Franz Lisp OPUS 38 provides the environment for VAXIMA`s development and use on the DEC VAX11 executing under the Berkeley UNIX Release 4.2 operating system. An executable version of Lisp (the Lisp interpreter) and Liszt (the Lisp compiler) as well as the complete documentation files are included.

  12. Discrete interference modeling via boolean algebra.

    PubMed

    Beckhoff, Gerhard

    2011-01-01

    Two types of boolean functions are considered, the locus function of n variables, and the interval function of ν = n - 1 variables. A 1-1 mapping is given that takes elements (cells) of the interval function to antidual pairs of elements in the locus function, and vice versa. A set of ν binary codewords representing the intervals are defined and used to generate the codewords of all genomic regions. Next a diallelic three-point system is reviewed in the light of boolean functions, which leads to redefining complete interference by a logic function. Together with the upper bound of noninterference already defined by a boolean function, it confines the region of interference. Extensions of these two functions to any finite number of ν are straightforward, but have been also made in terms of variables taken from the inclusion-exclusion principle (expressing "at least" and "exactly equal to" a decimal integer). Two coefficients of coincidence for systems with more than three loci are defined and discussed, one using the average of several individual coefficients and the other taking as coefficient a real number between zero and one. Finally, by way of a malfunction of the mod-2 addition, it is shown that a four-point system may produce two different functions, one of which exhibiting loss of a class of odd recombinants.

  13. DOE-MACSYMA. Computer Algebra System

    SciTech Connect

    O`dell, J.E.

    1987-09-01

    DOE-MACSYMA (Project MAC`s SYmbolic MAnipulation system) is a large computer programming system written in LISP. With DOE-MACSYMA the user can differentiate, integrate, take limits, solve systems of linear or polynomial equations, factor polynomials, expand functions in Laurent or Taylor series, solve differential equations (using direct or transform methods), compute Poisson series, plot curves, and manipulate matrices and tensors. A language similar to ALGOL-60 permits users to write their own programs for transforming symbolic expressions. Franz Lisp OPUS 38 provides the environment for the Encore, Celerity, and DEC VAX11 UNIX,SUN(OPUS) versions under UNIX and the Alliant version under Concentrix. Kyoto Common Lisp (KCL) provides the environment for the SUN(KCL),Convex, and IBM PC under UNIX and Data General under AOS/VS.

  14. Deformed oscillator algebra approach of some quantum superintegrable Lissajous systems on the sphere and of their rational extensions

    SciTech Connect

    Marquette, Ian; Quesne, Christiane

    2015-06-15

    We extend the construction of 2D superintegrable Hamiltonians with separation of variables in spherical coordinates using combinations of shift, ladder, and supercharge operators to models involving rational extensions of the two-parameter Lissajous systems on the sphere. These new families of superintegrable systems with integrals of arbitrary order are connected with Jacobi exceptional orthogonal polynomials of type I (or II) and supersymmetric quantum mechanics. Moreover, we present an algebraic derivation of the degenerate energy spectrum for the one- and two-parameter Lissajous systems and the rationally extended models. These results are based on finitely generated polynomial algebras, Casimir operators, realizations as deformed oscillator algebras, and finite-dimensional unitary representations. Such results have only been established so far for 2D superintegrable systems separable in Cartesian coordinates, which are related to a class of polynomial algebras that display a simpler structure. We also point out how the structure function of these deformed oscillator algebras is directly related with the generalized Heisenberg algebras spanned by the nonpolynomial integrals.

  15. Numerical integration of systems of delay differential-algebraic equations

    NASA Astrophysics Data System (ADS)

    Kuznetsov, E. B.; Mikryukov, V. N.

    2007-01-01

    The numerical solution of the initial value problem for a system of delay differential-algebraic equations is examined in the framework of the parametric continuation method. Necessary and sufficient conditions are obtained for transforming this problem to the best argument, which ensures the best condition for the corresponding system of continuation equations. The best argument is the arc length along the integral curve of the problem. Algorithms and programs based on the continuous and discrete continuation methods are developed for the numerical integration of this problem. The efficiency of the suggested transformation is demonstrated using test examples.

  16. Numerical investigation of algebraic oceanic turbulent mixing-layer models

    NASA Astrophysics Data System (ADS)

    Chacón-Rebollo, T.; Gómez-Mármol, M.; Rubino, S.

    2013-11-01

    In this paper we investigate the finite-time and asymptotic behaviour of algebraic turbulent mixing-layer models by numerical simulation. We compare the performances given by three different settings of the eddy viscosity. We consider Richardson number-based vertical eddy viscosity models. Two of these are classical algebraic turbulence models usually used in numerical simulations of global oceanic circulation, i.e. the Pacanowski-Philander and the Gent models, while the other one is a more recent model (Bennis et al., 2010) proposed to prevent numerical instabilities generated by physically unstable configurations. The numerical schemes are based on the standard finite element method. We perform some numerical tests for relatively large deviations of realistic initial conditions provided by the Tropical Atmosphere Ocean (TAO) array. These initial conditions correspond to states close to mixing-layer profiles, measured on the Equatorial Pacific region called the West-Pacific Warm Pool. We conclude that mixing-layer profiles could be considered as kinds of "absorbing configurations" in finite time that asymptotically evolve to steady states under the application of negative surface energy fluxes.

  17. Phased-mission system analysis using Boolean algebraic methods

    NASA Technical Reports Server (NTRS)

    Somani, Arun K.; Trivedi, Kishor S.

    1993-01-01

    Most reliability analysis techniques and tools assume that a system is used for a mission consisting of a single phase. However, multiple phases are natural in many missions. The failure rates of components, system configuration, and success criteria may vary from phase to phase. In addition, the duration of a phase may be deterministic or random. Recently, several researchers have addressed the problem of reliability analysis of such systems using a variety of methods. A new technique for phased-mission system reliability analysis based on Boolean algebraic methods is described. Our technique is computationally efficient and is applicable to a large class of systems for which the failure criterion in each phase can be expressed as a fault tree (or an equivalent representation). Our technique avoids state space explosion that commonly plague Markov chain-based analysis. A phase algebra to account for the effects of variable configurations and success criteria from phase to phase was developed. Our technique yields exact (as opposed to approximate) results. The use of our technique was demonstrated by means of an example and present numerical results to show the effects of mission phases on the system reliability.

  18. AN ADA LINEAR ALGEBRA PACKAGE MODELED AFTER HAL/S

    NASA Technical Reports Server (NTRS)

    Klumpp, A. R.

    1994-01-01

    This package extends the Ada programming language to include linear algebra capabilities similar to those of the HAL/S programming language. The package is designed for avionics applications such as Space Station flight software. In addition to the HAL/S built-in functions, the package incorporates the quaternion functions used in the Shuttle and Galileo projects, and routines from LINPAK that solve systems of equations involving general square matrices. Language conventions in this package follow those of HAL/S to the maximum extent practical and minimize the effort required for writing new avionics software and translating existent software into Ada. Valid numeric types in this package include scalar, vector, matrix, and quaternion declarations. (Quaternions are fourcomponent vectors used in representing motion between two coordinate frames). Single precision and double precision floating point arithmetic is available in addition to the standard double precision integer manipulation. Infix operators are used instead of function calls to define dot products, cross products, quaternion products, and mixed scalar-vector, scalar-matrix, and vector-matrix products. The package contains two generic programs: one for floating point, and one for integer. The actual component type is passed as a formal parameter to the generic linear algebra package. The procedures for solving systems of linear equations defined by general matrices include GEFA, GECO, GESL, and GIDI. The HAL/S functions include ABVAL, UNIT, TRACE, DET, INVERSE, TRANSPOSE, GET, PUT, FETCH, PLACE, and IDENTITY. This package is written in Ada (Version 1.2) for batch execution and is machine independent. The linear algebra software depends on nothing outside the Ada language except for a call to a square root function for floating point scalars (such as SQRT in the DEC VAX MATHLIB library). This program was developed in 1989, and is a copyrighted work with all copyright vested in NASA.

  19. Geometric and algebraic properties of minimal bases of singular systems

    NASA Astrophysics Data System (ADS)

    Karcanias, Nicos

    2013-11-01

    For a general singular system ? with an associated pencil T(S), a complete classification of the right polynomial vector pairs ?, connected with the ? rational vector space, is given according to the proper-nonproper property, characterising the relationship of the degrees of those two vectors. An integral part of the classification of right pairs is the development of the notions of canonical and normal minimal bases for ? and ? rational vector spaces, where R(s) is the state restriction pencil of ?. It is shown that the notions of canonical and normal minimal bases are equivalent; the first notion characterises the pure algebraic aspect of the classification, whereas the second is intimately connected to the real geometry properties and the underlying generation mechanism of the proper and nonproper state vectors ?. The results describe the algebraic and geometric dimensions of the invariant partitioning of the set of reachability indices of singular systems. The classification of all proper and nonproper polynomial vectors ? induces a corresponding classification for the reachability spaces to proper-nonproper and results related to the possible dimensions feedback-spectra assignment properties of them are also given. The classification of minimal bases introduces new feedback invariants for singular systems, based on the real geometry of polynomial minimal bases, and provides an extension of the standard theory for proper systems (Warren, M.E., & Eckenberg, A.E. (1975).

  20. Astronomy Education using the Web and a Computer Algebra System

    NASA Astrophysics Data System (ADS)

    Flurchick, K. M.; Culver, Roger B.; Griego, Ben

    2013-04-01

    The combination of a web server and a Computer Algebra System to provide students the ability to explore and investigate astronomical concepts presented in a class can help student understanding. This combination of technologies provides a framework to extend the classroom experience with independent student exploration. In this presentation we report on the developmen of this web based material and some initial results of students making use of the computational tools using webMathematica^TM. The material developed allow the student toanalyze and investigate a variety of astronomical phenomena, including topics such as the Runge-Lenz vector, descriptions of the orbits of some of the exo-planets, Bode' law and other topics related to celestial mechanics. The server based Computer Algebra System system allows for computations without installing software on the student's computer but provides a powerful environment to explore the various concepts. The current system is installed at North Carolina A&T State University and has been used in several undergraduate classes.

  1. Topological basis realization for BMW algebra and Heisenberg XXZ spin chain model

    NASA Astrophysics Data System (ADS)

    Liu, Bo; Xue, Kang; Wang, Gangcheng; Liu, Ying; Sun, Chunfang

    2015-04-01

    In this paper, we study three-dimensional (3D) reduced Birman-Murakami-Wenzl (BMW) algebra based on topological basis theory. Several examples of BMW algebra representations are reviewed. We also discuss a special solution of BMW algebra, which can be used to construct Heisenberg XXZ model. The theory of topological basis provides a useful method to solve quantum spin chain models. It is also shown that the ground state of XXZ spin chain is superposition state of topological basis.

  2. Max-plus Algebraic Tools for Discrete Event Systems, Static Analysis, and Zero-Sum Games

    NASA Astrophysics Data System (ADS)

    Gaubert, Stéphane

    The max-plus algebraic approach of timed discrete event systems emerged in the eighties, after the discovery that synchronization phenomena can be modeled in a linear way in the max-plus setting. This led to a number of results, like the determination of long term characteristics (throughput, stationary regime) by spectral theory methods or the representation of the input-output behavior by rational series.

  3. A rigorous approach to investigating common assumptions about disease transmission: Process algebra as an emerging modelling methodology for epidemiology.

    PubMed

    McCaig, Chris; Begon, Mike; Norman, Rachel; Shankland, Carron

    2011-03-01

    Changing scale, for example, the ability to move seamlessly from an individual-based model to a population-based model, is an important problem in many fields. In this paper, we introduce process algebra as a novel solution to this problem in the context of models of infectious disease spread. Process algebra allows us to describe a system in terms of the stochastic behaviour of individuals, and is a technique from computer science. We review the use of process algebra in biological systems, and the variety of quantitative and qualitative analysis techniques available. The analysis illustrated here solves the changing scale problem: from the individual behaviour we can rigorously derive equations to describe the mean behaviour of the system at the level of the population. The biological problem investigated is the transmission of infection, and how this relates to individual interactions.

  4. Entanglement in a model for Hawking radiation: An application of quadratic algebras

    SciTech Connect

    Bambah, Bindu A.; Mukku, C.; Shreecharan, T.; Siva Prasad, K.

    2013-03-15

    Quadratic polynomially deformed su(1,1) and su(2) algebras are utilized in model Hamiltonians to show how the gravitational system consisting of a black hole, infalling radiation and outgoing (Hawking) radiation can be solved exactly. The models allow us to study the long-time behaviour of the black hole and its outgoing modes. In particular, we calculate the bipartite entanglement entropies of subsystems consisting of (a) infalling plus outgoing modes and (b) black hole modes plus the infalling modes, using the Janus-faced nature of the model. The long-time behaviour also gives us glimpses of modifications in the character of Hawking radiation. Finally, we study the phenomenon of superradiance in our model in analogy with atomic Dicke superradiance. - Highlights: Black-Right-Pointing-Pointer We examine a toy model for Hawking radiation with quantized black hole modes. Black-Right-Pointing-Pointer We use quadratic polynomially deformed su(1,1) algebras to study its entanglement properties. Black-Right-Pointing-Pointer We study the 'Dicke Superradiance' in black hole radiation using quadratically deformed su(2) algebras. Black-Right-Pointing-Pointer We study the modification of the thermal character of Hawking radiation due to quantized black hole modes.

  5. Classical-quantum correspondence in bosonic two-mode conversion systems: Polynomial algebras and Kummer shapes

    NASA Astrophysics Data System (ADS)

    Graefe, Eva-Maria; Korsch, Hans Jürgen; Rush, Alexander

    2016-04-01

    Bosonic quantum conversion systems can be modeled by many-particle single-mode Hamiltonians describing a conversion of m molecules of type A into n molecules of type B and vice versa. These Hamiltonians are analyzed in terms of generators of a polynomially deformed su(2) algebra. In the mean-field limit of large particle numbers, these systems become classical and their Hamiltonian dynamics can again be described by polynomial deformations of a Lie algebra, where quantum commutators are replaced by Poisson brackets. The Casimir operator restricts the motion to Kummer shapes, deformed Bloch spheres with cusp singularities depending on m and n . It is demonstrated that the many-particle eigenvalues can be recovered from the mean-field dynamics using a WKB-type quantization condition. The many-particle state densities can be semiclassically approximated by the time periods of periodic orbits, which show characteristic steps and singularities related to the fixed points, whose bifurcation properties are analyzed.

  6. The Use of a Computer Algebra System in Capstone Mathematics Courses for Undergraduate Mathematics Majors.

    ERIC Educational Resources Information Center

    Harris, Gary A.

    2000-01-01

    Discusses the use of a computer algebra system in a capstone mathematics course for undergraduate mathematics majors preparing to teach secondary school mathematics. Provides sample exercises intended to demonstrate how the power of a computer algebra system such as MAPLE can contribute to desired outcomes including reinforcing and strengthening…

  7. An algebraic turbulence model for three-dimensional viscous flows

    NASA Technical Reports Server (NTRS)

    Chima, R. V.; Giel, P. W.; Boyle, R. J.

    1993-01-01

    An algebraic turbulence model is proposed for use with three-dimensional Navier-Stokes analyses. It incorporates features of both the Baldwin-Lomax and Cebeci-Smith models. The Baldwin-Lomax model uses the maximum of a function f(y) to determine length and velocity scales. An analysis of the Baldwin-Lomax model shows that f(y) can have a spurious maximum close to the wall, causing numerical problems and non-physical results. The proposed model uses integral relations to determine delta(*) u(sub e) and delta used in the Cebeci-Smith mode. It eliminates a constant in the Baldwin-Lomax model and determines the two remaining constants by comparison to the Cebeci-Smith formulation. Pressure gradient effects, a new wake model, and the implementation of these features in a three-dimensional Navier-Stokes code are also described. Results are shown for a flat plate boundary layer, an annular turbine cascade, and endwall heat transfer in a linear turbine cascade. The heat transfer results agree well with experimental data which shows large variations in endwall Stanton number contours with Reynolds number.

  8. Integrable and superintegrable Hamiltonian systems with four dimensional real Lie algebras as symmetry of the systems

    SciTech Connect

    Abedi-Fardad, J.; Rezaei-Aghdam, A.; Haghighatdoost, Gh.

    2014-05-15

    We construct integrable and superintegrable Hamiltonian systems using the realizations of four dimensional real Lie algebras as a symmetry of the system with the phase space R{sup 4} and R{sup 6}. Furthermore, we construct some integrable and superintegrable Hamiltonian systems for which the symmetry Lie group is also the phase space of the system.

  9. PREFACE: Infinite Dimensional Algebras and their Applications to Quantum Integrable Systems

    NASA Astrophysics Data System (ADS)

    Fring, Andreas; Kulish, Petr P.; Manojlović, Nenad; Nagy, Zoltán; Nunes da Costa, Joana; Samtleben, Henning

    2008-05-01

    This special issue is centred around the workshop Infinite Dimensional Algebras and Quantum Integrable Systems II—IDAQUIS 2007, held at the University of Algarve, Faro, Portugal in July 2007. It was the second workshop in the IDAQUIS series following a previous meeting at the same location in 2003. The latest workshop gathered around forty experts in the field reviewing recent developments in the theory and applications of integrable systems in the form of invited lectures and in a number of contributions from the participants. All contributions contain significant new results or provide a survey of the state of the art of the subject or a critical assessment of the present understanding of the topic and a discussion of open problems. Original contributions from non-participants are also included. The origins of the topic of this issue can be traced back a long way to the early investigations of completely integrable systems of classical mechanics in the fundamental papers by Euler, Lagrange, Jacobi, Liouville, Kowalevski and others. By the end of the nineteenth century all interesting examples seemed to have been exhausted. A revival in the study of integrable systems began with the development of the classical inverse scattering method, or the theory of solitons. Later developments led to the basic geometrical ideas of the theory, of which infinite dimensional algebras are a key ingredient. In a loose sense one may think that all integrable systems possess some hidden symmetry. In the quantum version of these systems the representation theory of these algebras may be exploited in the description of the structure of the Hilbert space of states. Modern examples of field theoretical systems such as conformal field theories, with the Liouville model being a prominent example, affine Toda field theories and the AdS/CFT correspondence are based on algebraic structures like quantum groups, modular doubles, global conformal invariance, Hecke algebras, Kac

  10. Re"modeling" College Algebra: An Active Learning Approach

    ERIC Educational Resources Information Center

    Pinzon, D.; Pinzon, K.; Stackpole, M.

    2016-01-01

    In this paper, we discuss active learning in College Algebra at Georgia Gwinnett College. This approach has been used in more than 20 sections of College Algebra taught by the authors in the past four semesters. Students work in small, structured groups on guided inquiry activities after watching 15-20 minutes of videos before class. We discuss a…

  11. Combining Automated Theorem Provers with Symbolic Algebraic Systems: Position Paper

    NASA Technical Reports Server (NTRS)

    Schumann, Johann; Koga, Dennis (Technical Monitor)

    1999-01-01

    In contrast to pure mathematical applications where automated theorem provers (ATPs) are quite capable, proof tasks arising form real-world applications from the area of Software Engineering show quite different characteristics: they usually do not only contain much arithmetic (albeit often quite simple one), but they also often contain reasoning about specific structures (e.g. graphics, sets). Thus, an ATP must be capable of performing reasoning together with a fair amount of simplification, calculation and solving. Therefore, powerful simplifiers and other (symbolic and semi-symbolic) algorithms seem to be ideally suited to augment ATPs. In the following we shortly describe two major points of interest in combining SASs (symbolic algebraic systems) with top-down automated theorem provers (here: SETHEO [Let92, GLMS94]).

  12. A Modeling-Based College Algebra Course and Its Effect on Student Achievement

    ERIC Educational Resources Information Center

    Ellington, Aimee J.

    2005-01-01

    In Fall 2004, Virginia Commonwealth University (VCU) piloted a modeling-based approach to college algebra. This paper describes the course and an assessment that was conducted to determine the effect of this approach on student achievement in comparison to a traditional approach to college algebra. The results show that compared with their…

  13. Excited states of the Calogero-Sutherland model and singular vectors of the WN algebra

    NASA Astrophysics Data System (ADS)

    Awata, Hidetoshi; Matsuo, Yutaka; Odake, Satoru; Shiraishi, Jun'ichi

    1995-02-01

    Using the collective field method, we find a relation between the Jack symmetric polynomials, which describe the excited states of the Calogero-Sutherland model, and the singular vectors of the WN algebra. Based on this relation, we obtain their integral representations. We also give a direct algebraic method which leads to the same result, and integral representations of the skew-Jack polynomials.

  14. Second-Order Algebraic Theories

    NASA Astrophysics Data System (ADS)

    Fiore, Marcelo; Mahmoud, Ola

    Fiore and Hur [10] recently introduced a conservative extension of universal algebra and equational logic from first to second order. Second-order universal algebra and second-order equational logic respectively provide a model theory and a formal deductive system for languages with variable binding and parameterised metavariables. This work completes the foundations of the subject from the viewpoint of categorical algebra. Specifically, the paper introduces the notion of second-order algebraic theory and develops its basic theory. Two categorical equivalences are established: at the syntactic level, that of second-order equational presentations and second-order algebraic theories; at the semantic level, that of second-order algebras and second-order functorial models. Our development includes a mathematical definition of syntactic translation between second-order equational presentations. This gives the first formalisation of notions such as encodings and transforms in the context of languages with variable binding.

  15. The Design of a System to Support Exploratory Learning of Algebraic Generalisation

    ERIC Educational Resources Information Center

    Noss, Richard; Poulovassilis, Alexandra; Geraniou, Eirini; Gutierrez-Santos, Sergio; Hoyles, Celia; Kahn, Ken; Magoulas, George D.; Mavrikis, Manolis

    2012-01-01

    This paper charts the design and application of a system to support 11-14 year old students' learning of algebraic generalisation, presenting students with the means to develop their understanding of the meaning of generality, see its power for mathematics and develop algebraic ways of thinking. We focus squarely on design, while taking account of…

  16. The Effect of an Intelligent Tutoring System (ITS) on Student Achievement in Algebraic Expression

    ERIC Educational Resources Information Center

    Chien, Tsai Chen; Md. Yunus, Aida Suraya; Ali, Wan Zah Wan; Bakar, Ab. Rahim

    2008-01-01

    In this experimental study, use of Computer Assisted Instruction (CAI) followed by use of an Intelligent Tutoring System (CAI+ITS) was compared to the use of CAI (CAI only) in tutoring students on the topic of Algebraic Expression. Two groups of students participated in the study. One group of 32 students studied algebraic expression in a CAI…

  17. Maple (Computer Algebra System) in Teaching Pre-Calculus: Example of Absolute Value Function

    ERIC Educational Resources Information Center

    Tuluk, Güler

    2014-01-01

    Modules in Computer Algebra Systems (CAS) make Mathematics interesting and easy to understand. The present study focused on the implementation of the algebraic, tabular (numerical), and graphical approaches used for the construction of the concept of absolute value function in teaching mathematical content knowledge along with Maple 9. The study…

  18. Applications of computer algebra to distributed parameter systems

    NASA Technical Reports Server (NTRS)

    Storch, Joel A.

    1993-01-01

    In the analysis of vibrations of continuous elastic systems, one often encounters complicated transcendental equations with roots directly related to the system's natural frequencies. Typically, these equations contain system parameters whose values must be specified before a numerical solution can be obtained. The present paper presents a method whereby the fundamental frequency can be obtained in analytical form to any desired degree of accuracy. The method is based upon truncation of rapidly converging series involving inverse powers of the system natural frequencies. A straightforward method to developing these series and summing them in closed form is presented. It is demonstrated how Computer Algebra can be exploited to perform the intricate analytical procedures which otherwise would render the technique difficult to apply in practice. We illustrate the method by developing two analytical approximations to the fundamental frequency of a vibrating cantilever carrying a rigid tip body. The results are compared to the numerical solution of the exact (transcendental) frequency equation over a range of system parameters.

  19. Kiddie Algebra

    ERIC Educational Resources Information Center

    Cavanagh, Sean

    2009-01-01

    As educators and policymakers search for ways to prepare students for the rigors of algebra, teachers in the Helena, Montana, school system are starting early by attempting to nurture students' algebraic-reasoning ability, as well as their basic number skills, in early elementary school, rather than waiting until middle or early high school.…

  20. Using process algebra to develop predator-prey models of within-host parasite dynamics.

    PubMed

    McCaig, Chris; Fenton, Andy; Graham, Andrea; Shankland, Carron; Norman, Rachel

    2013-07-21

    As a first approximation of immune-mediated within-host parasite dynamics we can consider the immune response as a predator, with the parasite as its prey. In the ecological literature of predator-prey interactions there are a number of different functional responses used to describe how a predator reproduces in response to consuming prey. Until recently most of the models of the immune system that have taken a predator-prey approach have used simple mass action dynamics to capture the interaction between the immune response and the parasite. More recently Fenton and Perkins (2010) employed three of the most commonly used prey-dependent functional response terms from the ecological literature. In this paper we make use of a technique from computing science, process algebra, to develop mathematical models. The novelty of the process algebra approach is to allow stochastic models of the population (parasite and immune cells) to be developed from rules of individual cell behaviour. By using this approach in which individual cellular behaviour is captured we have derived a ratio-dependent response similar to that seen in the previous models of immune-mediated parasite dynamics, confirming that, whilst this type of term is controversial in ecological predator-prey models, it is appropriate for models of the immune system.

  1. Unified algebraic approach to few- and many-body correlated systems

    NASA Astrophysics Data System (ADS)

    Gurappa, N.; Panigrahi, Prasanta K.

    2003-04-01

    The present paper is an extended version of another paper [Phys. Rev. B 59, R2490 (1999)], where we have established the equivalence of the Calogero-Sutherland model to decoupled oscillators. Here, we first employ the same approach for finding the eigenstates of a large class of Hamiltonians, dealing with correlated systems. A number of few- and many-body interacting models are studied and the relationship between their respective Hilbert spaces, with that of oscillators, is found. This connection is then used to obtain the spectrum generating algebras for these systems and make an algebraic statement about correlated systems. The procedure to generate solvable interacting models is outlined. We then point out the inadequacies of the present technique and make use of a method for solving linear differential equations to diagonalize the Sutherland model and establish a precise connection between this correlated system’s wave functions, with those of the free particles on a circle. In the process, we obtain an expression for the Jack polynomials. In two dimensions, we analyze the Hamiltonian having Laughlin wave function as the ground state and point out the natural emergence of the underlying linear W1+∞ symmetry in this approach.

  2. Dynamical analysis of a differential algebraic bio-economic model with stage-structured and stochastic fluctuations

    NASA Astrophysics Data System (ADS)

    Zhang, Yue; Zheng, Yan; Liu, Xi; Zhang, Qingling; Li, Aihua

    2016-11-01

    This study considers a class of differential algebraic stage-structured bio-economic models with stochastic fluctuations. The stochastic bio-economic model is simplified to an Itô equation using the stochastic averaging method. The stochastic stability, Hopf bifurcation, and P-bifurcation are discussed based on the singular boundary theory of the diffusion process for the system and the invariant measure theory of dynamic systems. Numerical simulations are presented to illustrate our main results.

  3. Lectures on algebraic system theory: Linear systems over rings

    NASA Technical Reports Server (NTRS)

    Kamen, E. W.

    1978-01-01

    The presentation centers on four classes of systems that can be treated as linear systems over a ring. These are: (1) discrete-time systems over a ring of scalars such as the integers; (2) continuous-time systems containing time delays; (3) large-scale discrete-time systems; and (4) time-varying discrete-time systems.

  4. Differential algebraic methods for space charge modeling and applications to the University of Maryland Electron Ring

    NASA Astrophysics Data System (ADS)

    Nissen, Edward W.

    2011-12-01

    The future of particle accelerators is moving towards the intensity frontier; the need to place more particles into a smaller space is a common requirement of nearly all applications of particle accelerators. Putting large numbers of particles in a small space means that the mutual repulsion of these charged particles becomes a significant factor, this effect is called space charge. In this work we develop a series of differential algebra based methods to simulate the effects of space charge in particle accelerators. These methods were used to model the University of Maryland Electron Ring, a small 3.8 meter diameter 10 KeV electron storage ring designed to observe the effects of space charge in a safe, cost effective manner. The methods developed here are designed to not only simulate the effects of space charge on the motions of the test particles in the system but to add their effects to the transfer map of the system. Once they have been added useful information about the beam, such as tune shifts and chromaticities, can be extracted directly from the map. In order to make the simulation self consistent, the statistical moments of the distribution are used to create a self consistent Taylor series representing the distribution function, which is combined with pre-stored integrals solved using a Duffy transformation to find the potential. This method can not only find the map of the system, but also advance the particles under most conditions. For conditions where it cannot be used to accurately advance the particles a differential algebra based fast multipole method is implemented. By using differential algebras to create local expansions, noticeable time savings are found.

  5. Non-Hermitian systems of Euclidean Lie algebraic type with real energy spectra

    SciTech Connect

    Dey, Sanjib Fring, Andreas Mathanaranjan, Thilagarajah

    2014-07-15

    We study several classes of non-Hermitian Hamiltonian systems, which can be expressed in terms of bilinear combinations of Euclidean–Lie algebraic generators. The classes are distinguished by different versions of antilinear (PT)-symmetries exhibiting various types of qualitative behaviour. On the basis of explicitly computed non-perturbative Dyson maps we construct metric operators, isospectral Hermitian counterparts for which we solve the corresponding time-independent Schrödinger equation for specific choices of the coupling constants. In these cases general analytical expressions for the solutions are obtained in the form of Mathieu functions, which we analyze numerically to obtain the corresponding energy spectra. We identify regions in the parameter space for which the corresponding spectra are entirely real and also domains where the PT symmetry is spontaneously broken and sometimes also regained at exceptional points. In some cases it is shown explicitly how the threshold region from real to complex spectra is characterized by the breakdown of the Dyson maps or the metric operator. We establish the explicit relationship to models currently under investigation in the context of beam dynamics in optical lattices. -- Highlights: •Different PT-symmetries lead to qualitatively different systems. •Construction of non-perturbative Dyson maps and isospectral Hermitian counterparts. •Numerical discussion of the eigenvalue spectra for one of the E(2)-systems. •Established link to systems studied in the context of optical lattices. •Setup for the E(3)-algebra is provided.

  6. Realization theory and quadratic optimal controllers for systems defined over Banach and Frechet algebras

    NASA Technical Reports Server (NTRS)

    Byrnes, C. I.

    1980-01-01

    It is noted that recent work by Kamen (1979) on the stability of half-plane digital filters shows that the problem of the existence of a feedback law also arises for other Banach algebras in applications. This situation calls for a realization theory and stabilizability criteria for systems defined over Banach for Frechet algebra A. Such a theory is developed here, with special emphasis placed on the construction of finitely generated realizations, the existence of coprime factorizations for T(s) defined over A, and the solvability of the quadratic optimal control problem and the associated algebraic Riccati equation over A.

  7. ηc elastic and transition form factors: Contact interaction and algebraic model

    NASA Astrophysics Data System (ADS)

    Bedolla, Marco A.; Raya, Khépani; Cobos-Martínez, J. J.; Bashir, Adnan

    2016-05-01

    For the flavor-singlet heavy-quark system of charmonia in the pseudoscalar [ηc(1 S ) ] channel, we calculate the elastic (EFF) and transition form factors (TFFs) [ηc(1 S )→γ γ* ] for a wide range of photon momentum transfer squared (Q2). The framework for this analysis is provided by a symmetry-preserving Schwinger-Dyson equation and Bethe-Salpeter equation treatment of a vector×vector contact interaction. We also employ an algebraic model, developed earlier to describe the light-quark systems. It correctly correlates infrared and ultraviolet dynamics of quantum chromodynamics (QCD). The contact interaction results agree with the lattice data for low Q2. For Q2≥Q02 , the results start deviating from the lattice results by more than 20%. Q02≈2.5 GeV2 for the EFF, and ≈25 GeV2 for the TFF. We also present the results for the EFF, TFF, and ηc(1 S ) parton distribution amplitude for the algebraic model. Wherever the comparison is possible, these results are in excellent agreement with the lattice, perturbative QCD, results obtained through a Schwinger-Dyson equation-Bethe-Salpeter equation study, employing refined truncations, and the experimental findings of the BABAR experiment.

  8. Linear-algebraic bath transformation for simulating complex open quantum systems

    NASA Astrophysics Data System (ADS)

    Huh, Joonsuk; Mostame, Sarah; Fujita, Takatoshi; Yung, Man-Hong; Aspuru-Guzik, Alán

    2014-12-01

    In studying open quantum systems, the environment is often approximated as a collection of non-interacting harmonic oscillators, a configuration also known as the star-bath model. It is also well known that the star-bath can be transformed into a nearest-neighbor interacting chain of oscillators. The chain-bath model has been widely used in renormalization group approaches. The transformation can be obtained by recursion relations or orthogonal polynomials. Based on a simple linear algebraic approach, we propose a bath partition strategy to reduce the system-bath coupling strength. As a result, the non-interacting star-bath is transformed into a set of weakly coupled multiple parallel chains. The transformed bath model allows complex problems to be practically implemented on quantum simulators, and it can also be employed in various numerical simulations of open quantum dynamics.

  9. Computer algebra methods in the study of nonlinear differential systems

    NASA Astrophysics Data System (ADS)

    Irtegov, V. D.; Titorenko, T. N.

    2013-06-01

    Some issues concerning computer algebra methods as applied to the qualitative analysis of differential equations with first integrals are discussed. The problems of finding stationary sets and analyzing their stability and bifurcations are considered. Special attention is given to algorithms for finding and analyzing peculiar stationary sets. It is shown that computer algebra tools, combined with qualitative analysis methods for differential equations, make it possible not only to enhance the computational efficiency of classical algorithms, but also to implement new approaches to the solution of well-known problems and, in this way, to obtain new results.

  10. Steady state analysis of Boolean molecular network models via model reduction and computational algebra

    PubMed Central

    2014-01-01

    Background A key problem in the analysis of mathematical models of molecular networks is the determination of their steady states. The present paper addresses this problem for Boolean network models, an increasingly popular modeling paradigm for networks lacking detailed kinetic information. For small models, the problem can be solved by exhaustive enumeration of all state transitions. But for larger models this is not feasible, since the size of the phase space grows exponentially with the dimension of the network. The dimension of published models is growing to over 100, so that efficient methods for steady state determination are essential. Several methods have been proposed for large networks, some of them heuristic. While these methods represent a substantial improvement in scalability over exhaustive enumeration, the problem for large networks is still unsolved in general. Results This paper presents an algorithm that consists of two main parts. The first is a graph theoretic reduction of the wiring diagram of the network, while preserving all information about steady states. The second part formulates the determination of all steady states of a Boolean network as a problem of finding all solutions to a system of polynomial equations over the finite number system with two elements. This problem can be solved with existing computer algebra software. This algorithm compares favorably with several existing algorithms for steady state determination. One advantage is that it is not heuristic or reliant on sampling, but rather determines algorithmically and exactly all steady states of a Boolean network. The code for the algorithm, as well as the test suite of benchmark networks, is available upon request from the corresponding author. Conclusions The algorithm presented in this paper reliably determines all steady states of sparse Boolean networks with up to 1000 nodes. The algorithm is effective at analyzing virtually all published models even those of moderate

  11. Excel Spreadsheets for Algebra: Improving Mental Modeling for Problem Solving

    ERIC Educational Resources Information Center

    Engerman, Jason; Rusek, Matthew; Clariana, Roy

    2014-01-01

    This experiment investigates the effectiveness of Excel spreadsheets in a high school algebra class. Students in the experiment group convincingly outperformed the control group on a post lesson assessment. The student responses, teacher observations involving Excel spreadsheet revealed that it operated as a mindtool, which formed the users'…

  12. Evaluation of algebraic iterative image reconstruction methods for tetrahedron beam computed tomography systems.

    PubMed

    Kim, Joshua; Guan, Huaiqun; Gersten, David; Zhang, Tiezhi

    2013-01-01

    Tetrahedron beam computed tomography (TBCT) performs volumetric imaging using a stack of fan beams generated by a multiple pixel X-ray source. While the TBCT system was designed to overcome the scatter and detector issues faced by cone beam computed tomography (CBCT), it still suffers the same large cone angle artifacts as CBCT due to the use of approximate reconstruction algorithms. It has been shown that iterative reconstruction algorithms are better able to model irregular system geometries and that algebraic iterative algorithms in particular have been able to reduce cone artifacts appearing at large cone angles. In this paper, the SART algorithm is modified for the use with the different TBCT geometries and is tested using both simulated projection data and data acquired using the TBCT benchtop system. The modified SART reconstruction algorithms were able to mitigate the effects of using data generated at large cone angles and were also able to reconstruct CT images without the introduction of artifacts due to either the longitudinal or transverse truncation in the data sets. Algebraic iterative reconstruction can be especially useful for dual-source dual-detector TBCT, wherein the cone angle is the largest in the center of the field of view.

  13. From matrix models' topological expansion to topological string theories: counting surfaces with algebraic geometry

    NASA Astrophysics Data System (ADS)

    Orantin, N.

    2007-09-01

    The 2-matrix model has been introduced to study Ising model on random surfaces. Since then, the link between matrix models and combinatorics of discrete surfaces has strongly tightened. This manuscript aims to investigate these deep links and extend them beyond the matrix models, following my work's evolution. First, I take care to define properly the hermitian 2 matrix model which gives rise to generating functions of discrete surfaces equipped with a spin structure. Then, I show how to compute all the terms in the topological expansion of any observable by using algebraic geometry tools. They are obtained as differential forms on an algebraic curve associated to the model: the spectral curve. In a second part, I show how to define such differentials on any algebraic curve even if it does not come from a matrix model. I then study their numerous symmetry properties under deformations of the algebraic curve. In particular, I show that these objects coincide with the topological expansion of the observable of a matrix model if the algebraic curve is the spectral curve of this model. Finally, I show that fine tuning the parameters ensure that these objects can be promoted to modular invariants and satisfy the holomorphic anomaly equation of the Kodaira-Spencer theory. This gives a new hint that the Dijkgraaf-Vafa conjecture is correct.

  14. Algebraic coarsening methods for linear and nonlinear PDE and systems

    SciTech Connect

    McWilliams, J C

    2000-11-06

    -grid variables. Once a coarse grid is chosen for which compatible relaxation converges fast, it follows that the dependence of the coarse-grid variables on each other decays exponentially or faster with the distance between them, measured in mesh-sizes. This implies that highly accurate coarse-grid equations can be constructed locally. A method for doing this by solving local constrained minimization problems is described in [1]. It is also shown how this approach can be applied to devise prolongation operators, which can be used for Galerkin coarsening in the usual way. In the present research we studied and developed methods based, in part, on these ideas. We developed and implemented an AMG approach which employs compatible relaxation to define the prolongation operator (hut is otherwise similar in its structure to classical AMG); we introduced a novel method for direct (i.e., non-Galerkin) algebraic coarsening, which is in the spirit of the approach originally proposed by Brandt in [1], hut is more efficient and well-defined; we investigated an approach for treating systems of equations and other problems where there is no unambiguous correspondence between equations and unknowns.

  15. An algebraic criterion for the onset of chaos in nonlinear dynamic systems

    NASA Technical Reports Server (NTRS)

    Unal, A.; Tobak, M.

    1987-01-01

    The correspondence between iterated integrals and a noncommutative algebra is used to recast the given dynamical system from the time domain to the Laplace-Borel transform domain. It is then shown that the following algebraic criterion has to be satisfied for the outset of chaos: the limit (as tau approaches infinity and x sub 0 approaches infinity) of ((sigma(k=0) (tau sup k) / (k* x sub 0 sup k)) G II G = 0, where G is the generating power series of the trajectories, the symbol II is the shuffle product (le melange) of the noncommutative algebra, x sub 0 is a noncommutative variable, and tau is the correlation parameter. In the given equation, symbolic forms for both G and II can be obtained by use of one of the currently available symbolic languages such as PLI, REDUCE, and MACSYMA. Hence, the criterion is a computer-algebraic one.

  16. Lie algebraic structures of (1+1)-dimensional Lax integrable systems

    SciTech Connect

    Chen, D.; Zhang, D.

    1996-11-01

    An approach of constructing isospectral flows {ital K}{sub {ital l}}, nonisospectral flows {sigma}{sub {ital k}} and their implicit representations of a general Lax integrable system is proposed. By introducing product function matrices, it is shown that the two sets of flows and of related symmetries both constitute infinite-dimensional Lie algebras with respect to the commutator [{center_dot},{center_dot}] given in this paper. Algebraic properties for some well-known integrable systems such as the AKNS system, the generalized Harry Dym system, and the {ital n}-wave interaction system are obtained as particular examples. {copyright} {ital 1996 American Institute of Physics.}

  17. Quantization of Algebraic Reduction

    SciTech Connect

    Sniatycki, Jeodrzej

    2007-11-14

    For a Poisson algebra obtained by algebraic reduction of symmetries of a quantizable system we develop an analogue of geometric quantization based on the quantization structure of the original system.

  18. The case of bruce: A teacher's model of his students' algebraic thinking about equivalent expressions

    NASA Astrophysics Data System (ADS)

    Hallagan, Jean E.

    2006-05-01

    The purpose of this article is to describe a middle school mathematics teacher's model of his students' responses to algebraic tasks involving equivalent expressions and the distributive property. The teacher engaged in two model-eliciting activities designed for teachers by creating a library of his students' work and an accompanying "Ways of Thinking"[WOT] sheet (Doerr & Lesh, 2003). These activities were designed to help reveal the teachers' models of students' algebraic thinking and to promote the development of that model. Results of the analysis showed that the teacher developed a clearer understanding of the role of a variable in algebraic instruction. The teacher employed visual strategies for the first time and began to perceive their usefulness in helping students understand the equivalence of two expressions.

  19. Algebraic turbulence models for the computation of two-dimensional high speed flows using unstructured grids

    NASA Technical Reports Server (NTRS)

    Rostand, Philippe

    1988-01-01

    The incorporation of algebraic turbulence models in a solver for the 2-D compressible Navier-Stokes equations using triangular grids is described. A practical way to use the Cebeci Smith model, and to modify it in separated regions is proposed. The ability of the model to predict high speed, perfect gas boundary layers is investigated from a numerical point of view.

  20. Designing Tasks for Math Modeling in College Algebra: A Critical Review

    ERIC Educational Resources Information Center

    Staats, Susan; Robertson, Douglas

    2014-01-01

    Over the last decade, the pedagogical approach known as mathematical modeling has received increased interest in college algebra classes in the United States. Math modeling assignments ask students to develop their own problem-solving tools to address non-routine, realistic scenarios. The open-ended quality of modeling activities creates dilemmas…

  1. Supersymmetry and the discrete light-cone quantization limit of the Lie 3-algebra model of M theory

    NASA Astrophysics Data System (ADS)

    Sato, Matsuo

    2012-02-01

    In M. Sato, J. High Energy Phys.JHEPFG1029-8479 07 (2010) 02610.1007/JHEP07(2010)026, we proposed two models of M theory, the Hermitian 3-algebra model and Lie 3-algebra model. In this paper, we study the Lie 3-algebra model with a Lorentzian Lie 3-algebra. This model is ghost-free despite the Lorentzian 3-algebra. We show that our model satisfies two criteria as a model of M theory. First, we show that the model possesses N=1 supersymmetry in 11 dimensions. Second, we show the model reduces to Banks-Fischler-Shenker-Susskind matrix theory with finite size matrices in a discrete light-cone quantization limit.

  2. Mathematical modelling in engineering: an alternative way to teach Linear Algebra

    NASA Astrophysics Data System (ADS)

    Domínguez-García, S.; García-Planas, M. I.; Taberna, J.

    2016-10-01

    Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic classroom approach in which students modelled real-world problems and turn gain a deeper knowledge of the Linear Algebra subject. Considering that most students are digital natives, we use the e-portfolio as a tool of communication between students and teachers, besides being a good place making the work visible. In this article, we present an overview of the design and implementation of a project-based learning for a Linear Algebra course taught during the 2014-2015 at the 'ETSEIB'of Universitat Politècnica de Catalunya (UPC).

  3. G/G gauged WZW-matter model, Bethe Ansatz for q-boson model and Commutative Frobenius algebra

    NASA Astrophysics Data System (ADS)

    Okuda, Satoshi; Yoshida, Yutaka

    2014-03-01

    We investigate the correspondence between two dimensional topological gauge theories and quantum integrable systems discovered by Moore, Nekrasov, Shatashvili. This correspondence means that the hidden quantum integrable structure exists in the topological gauge theories. We showed the correspondence between the G/G gauged WZW model and the phase model in JHEP 11 (2012) 146 (arXiv:1209.3800). In this paper, we study a one-parameter deformation for this correspondence and show that the G/G gauged WZW model coupled to additional matters corresponds to the q-boson model. Furthermore, we investigate this correspondence from the viewpoint of the commutative Frobenius algebra, the axiom of the two dimensional topological quantum field theory.

  4. A note on probabilistic models over strings: the linear algebra approach.

    PubMed

    Bouchard-Côté, Alexandre

    2013-12-01

    Probabilistic models over strings have played a key role in developing methods that take into consideration indels as phylogenetically informative events. There is an extensive literature on using automata and transducers on phylogenies to do inference on these probabilistic models, in which an important theoretical question is the complexity of computing the normalization of a class of string-valued graphical models. This question has been investigated using tools from combinatorics, dynamic programming, and graph theory, and has practical applications in Bayesian phylogenetics. In this work, we revisit this theoretical question from a different point of view, based on linear algebra. The main contribution is a set of results based on this linear algebra view that facilitate the analysis and design of inference algorithms on string-valued graphical models. As an illustration, we use this method to give a new elementary proof of a known result on the complexity of inference on the "TKF91" model, a well-known probabilistic model over strings. Compared to previous work, our proving method is easier to extend to other models, since it relies on a novel weak condition, triangular transducers, which is easy to establish in practice. The linear algebra view provides a concise way of describing transducer algorithms and their compositions, opens the possibility of transferring fast linear algebra libraries (for example, based on GPUs), as well as low rank matrix approximation methods, to string-valued inference problems. PMID:24135792

  5. A note on probabilistic models over strings: the linear algebra approach.

    PubMed

    Bouchard-Côté, Alexandre

    2013-12-01

    Probabilistic models over strings have played a key role in developing methods that take into consideration indels as phylogenetically informative events. There is an extensive literature on using automata and transducers on phylogenies to do inference on these probabilistic models, in which an important theoretical question is the complexity of computing the normalization of a class of string-valued graphical models. This question has been investigated using tools from combinatorics, dynamic programming, and graph theory, and has practical applications in Bayesian phylogenetics. In this work, we revisit this theoretical question from a different point of view, based on linear algebra. The main contribution is a set of results based on this linear algebra view that facilitate the analysis and design of inference algorithms on string-valued graphical models. As an illustration, we use this method to give a new elementary proof of a known result on the complexity of inference on the "TKF91" model, a well-known probabilistic model over strings. Compared to previous work, our proving method is easier to extend to other models, since it relies on a novel weak condition, triangular transducers, which is easy to establish in practice. The linear algebra view provides a concise way of describing transducer algorithms and their compositions, opens the possibility of transferring fast linear algebra libraries (for example, based on GPUs), as well as low rank matrix approximation methods, to string-valued inference problems.

  6. On Development of a Problem Based Learning System for Linear Algebra with Simple Input Method

    NASA Astrophysics Data System (ADS)

    Yokota, Hisashi

    2011-08-01

    Learning how to express a matrix using a keyboard inputs requires a lot of time for most of college students. Therefore, for a problem based learning system for linear algebra to be accessible for college students, it is inevitable to develop a simple method for expressing matrices. Studying the two most widely used input methods for expressing matrices, a simpler input method for expressing matrices is obtained. Furthermore, using this input method and educator's knowledge structure as a concept map, a problem based learning system for linear algebra which is capable of assessing students' knowledge structure and skill is developed.

  7. Mixing Microworld and CAS Features in Building Computer Systems that Help Students Learn Algebra

    ERIC Educational Resources Information Center

    Nicaud, Jean-Francois; Bouhineau, Denis; Chaachoua, Hamid

    2004-01-01

    We present the design principles for a new kind of computer system that helps students learn algebra. The fundamental idea is to have a system based on the microworld paradigm that allows students to make their own calculations, as they do with paper and pencil, without being obliged to use commands, and to verify the correctness of these…

  8. Exploring Interactive and Dynamic Simulations Using a Computer Algebra System in an Advanced Placement Chemistry Course

    ERIC Educational Resources Information Center

    Matsumoto, Paul S.

    2014-01-01

    The article describes the use of Mathematica, a computer algebra system (CAS), in a high school chemistry course. Mathematica was used to generate a graph, where a slider controls the value of parameter(s) in the equation; thus, students can visualize the effect of the parameter(s) on the behavior of the system. Also, Mathematica can show the…

  9. Computing the Moore-Penrose Inverse of a Matrix with a Computer Algebra System

    ERIC Educational Resources Information Center

    Schmidt, Karsten

    2008-01-01

    In this paper "Derive" functions are provided for the computation of the Moore-Penrose inverse of a matrix, as well as for solving systems of linear equations by means of the Moore-Penrose inverse. Making it possible to compute the Moore-Penrose inverse easily with one of the most commonly used Computer Algebra Systems--and to have the blueprint…

  10. Introduction to Number Systems, Boolean Algebra, Logic Circuits. Navy Electricity and Electronics Training Series. Module 13.

    ERIC Educational Resources Information Center

    Naval Education and Training Program Development Center, Pensacola, FL.

    This textbook is one of a series of publications designed to provide information needed by Navy personnel whose duties require an elementary and general knowledge of the fundamental concepts of number systems, logic circuits, and Boolean algebra. Topic 1, Number Systems, describes the radix; the positional notation; the decimal, binary, octal, and…

  11. Developing a TI-92 Manual Generator Based on Computer Algebra Systems

    ERIC Educational Resources Information Center

    Jun, Youngcook

    2004-01-01

    The electronic medium suitable for mathematics learning and teaching is often designed with a notebook interface provided in a computer algebra system. Such a notebook interface facilitates a workspace for mathematical activities along with an online help system. In this paper, the proposed feature is implemented in the Mathematica's notebook…

  12. Fully-Explicit and Self-Consistent Algebraic Reynolds Stress Models

    NASA Technical Reports Server (NTRS)

    Girimaji, Sharath S.

    1995-01-01

    A fully-explicit, self-consistent algebraic expression for the Reynolds stress, which is the exact solution to the Reynolds stress transport equation in the 'weak equilibrium' limit for two-dimensional mean flows for all linear and some quasi-linear pressure-strain models, is derived. Current explicit algebraic Reynolds stress models derived by employing the 'weak equilibrium' assumption treat the production-to-dissipation (P/epsilon) ratio implicitly, resulting in an effective viscosity that can be singular away from the equilibrium limit. In the present paper, the set of simultaneous algebraic Reynolds stress equations are solved in the full non-linear form and the eddy viscosity is found to be non-singular. Preliminary tests indicate that the model performs adequately, even for three dimensional mean flow cases. Due to the explicit and non-singular nature of the effective viscosity, this model should mitigate many of the difficulties encountered in computing complex turbulent flows with the algebraic Reynolds stress models.

  13. Graded Poisson-sigma models and dilaton-deformed 2D supergravity algebra

    NASA Astrophysics Data System (ADS)

    Bergamin, Luzi; Kummer, Wolfgang

    2003-05-01

    Supergravity extensions of generic 2d gravity theories obtained from the graded Poisson-Sigma model (gPSM) approach show a large degree of ambiguity. On the other hand, obstructions may reduce the allowed range of fields as given by the bosonic theory, or even prohibit any extension in certain cases. In our present work we relate the finite W-algebras inherent in the gPSM algebra of constraints to supergravity algebras (Neuveu-Schwarz or Ramond algebras resp.), deformed by the presence of the dilaton field. With very straightforward and natural assumptions on them - like the one linking the anti-commutator of certain fermionic charges to the Hamiltonian constraint without deformation - we are able not only to remove the ambiguities but, at the same time, the singularities referred to above. Thus all especially interesting bosonic models (spherically reduced gravity, the Jackiw-Teitelboim model etc.) under these conditions possess a unique fermionic extension and are free from new singularities. The superspace supergravity model of Howe is found as a special case of this supergravity action. For this class of models the relation between bosonic potential and prepotential does not introduce obstructions as well.

  14. A stochastic extension of the explicit algebraic subgrid-scale models

    SciTech Connect

    Rasam, A. Brethouwer, G.; Johansson, A. V.

    2014-05-15

    The explicit algebraic subgrid-scale (SGS) stress model (EASM) of Marstorp et al. [“Explicit algebraic subgrid stress models with application to rotating channel flow,” J. Fluid Mech. 639, 403–432 (2009)] and explicit algebraic SGS scalar flux model (EASFM) of Rasam et al. [“An explicit algebraic model for the subgrid-scale passive scalar flux,” J. Fluid Mech. 721, 541–577 (2013)] are extended with stochastic terms based on the Langevin equation formalism for the subgrid-scales by Marstorp et al. [“A stochastic subgrid model with application to turbulent flow and scalar mixing,” Phys. Fluids 19, 035107 (2007)]. The EASM and EASFM are nonlinear mixed and tensor eddy-diffusivity models, which improve large eddy simulation (LES) predictions of the mean flow, Reynolds stresses, and scalar fluxes of wall-bounded flows compared to isotropic eddy-viscosity and eddy-diffusivity SGS models, especially at coarse resolutions. The purpose of the stochastic extension of the explicit algebraic SGS models is to further improve the characteristics of the kinetic energy and scalar variance SGS dissipation, which are key quantities that govern the small-scale mixing and dispersion dynamics. LES of turbulent channel flow with passive scalar transport shows that the stochastic terms enhance SGS dissipation statistics such as length scale, variance, and probability density functions and introduce a significant amount of backscatter of energy from the subgrid to the resolved scales without causing numerical stability problems. The improvements in the SGS dissipation predictions in turn enhances the predicted resolved statistics such as the mean scalar, scalar fluxes, Reynolds stresses, and correlation lengths. Moreover, the nonalignment between the SGS stress and resolved strain-rate tensors predicted by the EASM with stochastic extension is in much closer agreement with direct numerical simulation data.

  15. Conservation laws for multidimensional systems and related linear algebra problems

    NASA Astrophysics Data System (ADS)

    Igonin, Sergei

    2002-12-01

    We consider multidimensional systems of PDEs of generalized evolution form with t-derivatives of arbitrary order on the left-hand side and with the right-hand side dependent on lower order t-derivatives and arbitrary space derivatives. For such systems we find an explicit necessary condition for the existence of higher conservation laws in terms of the system's symbol. For systems that violate this condition we give an effective upper bound on the order of conservation laws. Using this result, we completely describe conservation laws for viscous transonic equations, for the Brusselator model and the Belousov-Zhabotinskii system. To achieve this, we solve over an arbitrary field the matrix equations SA = AtS and SA = -AtS for a quadratic matrix A and its transpose At, which may be of independent interest.

  16. A system of nonlinear algebraic equations connected with the multisoliton solution of the Benjamin-Ono equation

    NASA Astrophysics Data System (ADS)

    Matsuno, Yoshimasa

    2004-02-01

    The multisoliton solution of the Benjamin-Ono equation is derived from the system of nonlinear algebraic equations. This finding is unexpected from the scheme of the inverse scattering transform method, which constructs the multisoliton solution through the system of linear algebraic equations. The anlaysis developed here is also applied to the rational multisoliton solution of the Kadomtsev-Petviashvili equation.

  17. Solving multi-customer FPR model with quality assurance and discontinuous deliveries using a two-phase algebraic approach.

    PubMed

    Chiu, Yuan-Shyi Peter; Chou, Chung-Li; Chang, Huei-Hsin; Chiu, Singa Wang

    2016-01-01

    A multi-customer finite production rate (FPR) model with quality assurance and discontinuous delivery policy was investigated in a recent paper (Chiu et al. in J Appl Res Technol 12(1):5-13, 2014) using differential calculus approach. This study employs mathematical modeling along with a two-phase algebraic method to resolve such a specific multi-customer FPR model. As a result, the optimal replenishment lot size and number of shipments can be derived without using the differential calculus. Such a straightforward method may assist practitioners who with insufficient knowledge of calculus in learning and managing the real multi-customer FPR systems more effectively. PMID:27186457

  18. The algebra of the general Markov model on phylogenetic trees and networks.

    PubMed

    Sumner, J G; Holland, B R; Jarvis, P D

    2012-04-01

    It is known that the Kimura 3ST model of sequence evolution on phylogenetic trees can be extended quite naturally to arbitrary split systems. However, this extension relies heavily on mathematical peculiarities of the associated Hadamard transformation, and providing an analogous augmentation of the general Markov model has thus far been elusive. In this paper, we rectify this shortcoming by showing how to extend the general Markov model on trees to include incompatible edges; and even further to more general network models. This is achieved by exploring the algebra of the generators of the continuous-time Markov chain together with the “splitting” operator that generates the branching process on phylogenetic trees. For simplicity, we proceed by discussing the two state case and then show that our results are easily extended to more states with little complication. Intriguingly, upon restriction of the two state general Markov model to the parameter space of the binary symmetric model, our extension is indistinguishable from the Hadamard approach only on trees; as soon as any incompatible splits are introduced the two approaches give rise to differing probability distributions with disparate structure. Through exploration of a simple example, we give an argument that our extension to more general networks has desirable properties that the previous approaches do not share. In particular, our construction allows for convergent evolution of previously divergent lineages; a property that is of significant interest for biological applications.

  19. Fock space, symbolic algebra, and analytical solutions for small stochastic systems.

    PubMed

    Santos, Fernando A N; Gadêlha, Hermes; Gaffney, Eamonn A

    2015-12-01

    Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity. Nevertheless, classical studies remained limited to the abstract level, demonstrating a more general applicability and equivalence between systems in physics and biology rather than exploiting the physics tools to study biological systems. Here the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the chemical master equations describing small, well-mixed, biochemical, or biological systems. This is illustrated with an exact solution for a Michaelis-Menten single enzyme interacting with limited substrate, including a consideration of very short time scales, which emphasizes when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for Michaelis-Menten kinetics with an arbitrary number of enzymes and substrates that, following diagonalization, leads to the solution of this ubiquitous, nonlinear enzyme kinetics problem. For this, a flexible symbolic maple code is provided, demonstrating the prospective advantages of this framework compared to stochastic simulation algorithms. This further highlights the possibilities for analytically based studies of stochastic systems in biology and chemistry using tools from theoretical quantum physics.

  20. Fock space, symbolic algebra, and analytical solutions for small stochastic systems

    NASA Astrophysics Data System (ADS)

    Santos, Fernando A. N.; Gadêlha, Hermes; Gaffney, Eamonn A.

    2015-12-01

    Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity. Nevertheless, classical studies remained limited to the abstract level, demonstrating a more general applicability and equivalence between systems in physics and biology rather than exploiting the physics tools to study biological systems. Here the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the chemical master equations describing small, well-mixed, biochemical, or biological systems. This is illustrated with an exact solution for a Michaelis-Menten single enzyme interacting with limited substrate, including a consideration of very short time scales, which emphasizes when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for Michaelis-Menten kinetics with an arbitrary number of enzymes and substrates that, following diagonalization, leads to the solution of this ubiquitous, nonlinear enzyme kinetics problem. For this, a flexible symbolic maple code is provided, demonstrating the prospective advantages of this framework compared to stochastic simulation algorithms. This further highlights the possibilities for analytically based studies of stochastic systems in biology and chemistry using tools from theoretical quantum physics.

  1. Fock space, symbolic algebra, and analytical solutions for small stochastic systems.

    PubMed

    Santos, Fernando A N; Gadêlha, Hermes; Gaffney, Eamonn A

    2015-12-01

    Randomness is ubiquitous in nature. From single-molecule biochemical reactions to macroscale biological systems, stochasticity permeates individual interactions and often regulates emergent properties of the system. While such systems are regularly studied from a modeling viewpoint using stochastic simulation algorithms, numerous potential analytical tools can be inherited from statistical and quantum physics, replacing randomness due to quantum fluctuations with low-copy-number stochasticity. Nevertheless, classical studies remained limited to the abstract level, demonstrating a more general applicability and equivalence between systems in physics and biology rather than exploiting the physics tools to study biological systems. Here the Fock space representation, used in quantum mechanics, is combined with the symbolic algebra of creation and annihilation operators to consider explicit solutions for the chemical master equations describing small, well-mixed, biochemical, or biological systems. This is illustrated with an exact solution for a Michaelis-Menten single enzyme interacting with limited substrate, including a consideration of very short time scales, which emphasizes when stiffness is present even for small copy numbers. Furthermore, we present a general matrix representation for Michaelis-Menten kinetics with an arbitrary number of enzymes and substrates that, following diagonalization, leads to the solution of this ubiquitous, nonlinear enzyme kinetics problem. For this, a flexible symbolic maple code is provided, demonstrating the prospective advantages of this framework compared to stochastic simulation algorithms. This further highlights the possibilities for analytically based studies of stochastic systems in biology and chemistry using tools from theoretical quantum physics. PMID:26764734

  2. Existence of standard models of conic fibrations over non-algebraically-closed fields

    SciTech Connect

    Avilov, A A

    2014-12-31

    We prove an analogue of Sarkisov's theorem on the existence of a standard model of a conic fibration over an algebraically closed field of characteristic different from two for three-dimensional conic fibrations over an arbitrary field of characteristic zero with an action of a finite group. Bibliography: 16 titles.

  3. Mathematical Modelling in Engineering: An Alternative Way to Teach Linear Algebra

    ERIC Educational Resources Information Center

    Domínguez-García, S.; García-Planas, M. I.; Taberna, J.

    2016-01-01

    Technological advances require that basic science courses for engineering, including Linear Algebra, emphasize the development of mathematical strengths associated with modelling and interpretation of results, which are not limited only to calculus abilities. Based on this consideration, we have proposed a project-based learning, giving a dynamic…

  4. CSOS models descending from chiral Potts models: degeneracy of the eigenspace and loop algebra

    NASA Astrophysics Data System (ADS)

    Au-Yang, Helen; Perk, Jacques H. H.

    2016-04-01

    Monodromy matrices of the {{\\boldsymbol{τ }}}2\\phantom{^{\\prime }} model are known to satisfy a Yang-Baxter equation with a six-vertex R-matrix as the intertwiner. The commutation relations of the elements of the monodromy matrices are completely determined by this R-matrix. We show the reason why in the superintegrable case the eigenspace is degenerate, but not in the general case. We then show that the eigenspaces of special CSOS models descending from the chiral Potts model are also degenerate. The existence of an L({{sl}}2) quantum loop algebra (or subalgebra) in these models is established by showing that the Serre relations hold for the generators. The highest weight polynomial (or the Drinfeld polynomial) of the representation is obtained by using the method of Baxter for the superintegrable case. As a byproduct, the eigenvalues of all such CSOS models are given explicitly.

  5. Algebraic grid adaptation method using non-uniform rational B-spline surface modeling

    NASA Technical Reports Server (NTRS)

    Yang, Jiann-Cherng; Soni, B. K.

    1992-01-01

    An algebraic adaptive grid system based on equidistribution law and utilized by the Non-Uniform Rational B-Spline (NURBS) surface for redistribution is presented. A weight function, utilizing a properly weighted boolean sum of various flow field characteristics is developed. Computational examples are presented to demonstrate the success of this technique.

  6. Some Algebraic Symmetries of (2, 2)-Supersymmetric Systems

    NASA Astrophysics Data System (ADS)

    Hübsch, Tristan

    The Hilbert spaces of supersymmetric systems admit symmetries which are often related to the topology and geometry of the (target) field-space. Here, we study certain (2, 2)-supersymmetric systems in two-dimensional space-time which are closely related to superstring models. They all turn out to possess some hitherto unexploited and geometrically and topologically unobstructed symmetries, providing new tools for studying the topology and geometry of superstring target space-times, and so the dynamics of the effective field theory in these. There ain't no such thing as a free lunch. - Supposedly

  7. On a modification of minimal iteration methods for solving systems of linear algebraic equations

    NASA Astrophysics Data System (ADS)

    Yukhno, L. F.

    2010-04-01

    Modifications of certain minimal iteration methods for solving systems of linear algebraic equations are proposed and examined. The modified methods are shown to be superior to the original versions with respect to the round-off error accumulation, which makes them applicable to solving ill-conditioned problems. Numerical results demonstrating the efficiency of the proposed modifications are given.

  8. CENTER CONDITIONS AND CYCLICITY FOR A FAMILY OF CUBIC SYSTEMS: COMPUTER ALGEBRA APPROACH

    PubMed Central

    Ferčec, Brigita; Mahdi, Adam

    2013-01-01

    Using methods of computational algebra we obtain an upper bound for the cyclicity of a family of cubic systems. We overcame the problem of nonradicality of the associated Bautin ideal by moving from the ring of polynomials to a coordinate ring. Finally, we determine the number of limit cycles bifurcating from each component of the center variety. PMID:24223469

  9. Numerical solutions of linear differential-algebraic equation systems via Hartley series

    NASA Astrophysics Data System (ADS)

    Ünal, Emrah; Yalçın, Numan; ćelik, Ercan

    2014-08-01

    In this paper, Hartley series are presented first. Then, the operational matrix of integration together with the product and coefficient matrices are presented. They are used to transform linear differential equation systems to a set of linear algebraic equations. Finally, numerical examples are given.

  10. Teaching of Real Numbers by Using the Archimedes-Cantor Approach and Computer Algebra Systems

    ERIC Educational Resources Information Center

    Vorob'ev, Evgenii M.

    2015-01-01

    Computer technologies and especially computer algebra systems (CAS) allow students to overcome some of the difficulties they encounter in the study of real numbers. The teaching of calculus can be considerably more effective with the use of CAS provided the didactics of the discipline makes it possible to reveal the full computational potential of…

  11. Integrating Computer Algebra Systems in Post-Secondary Mathematics Education: Preliminary Results of a Literature Review

    ERIC Educational Resources Information Center

    Buteau, Chantal; Marshall, Neil; Jarvis, Daniel; Lavicza, Zsolt

    2010-01-01

    We present results of a literature review pilot study (326 papers) regarding the use of Computer Algebra Systems (CAS) in tertiary mathematics education. Several themes that have emerged from the review are discussed: diverse uses of CAS, benefits to student learning, issues of integration and mathematics learning, common and innovative usage of…

  12. How Do Traditional Examination Questions Fare in the Presence of a Computer Algebra System (CAS)?

    ERIC Educational Resources Information Center

    Malabar, Ian; Pountney, Dave

    2001-01-01

    Describes the outcomes and discusses possible implications for the development of assessment with a Computer Algebra System (CAS) when a group of undergraduate mathematics students, familiar with using a CAS in examinations, tackled an assortment of traditional (i.e., non-CAS type) questions. (Author/MM)

  13. CENTER CONDITIONS AND CYCLICITY FOR A FAMILY OF CUBIC SYSTEMS: COMPUTER ALGEBRA APPROACH.

    PubMed

    Ferčec, Brigita; Mahdi, Adam

    2013-01-01

    Using methods of computational algebra we obtain an upper bound for the cyclicity of a family of cubic systems. We overcame the problem of nonradicality of the associated Bautin ideal by moving from the ring of polynomials to a coordinate ring. Finally, we determine the number of limit cycles bifurcating from each component of the center variety.

  14. A Study of the Use of a Handheld Computer Algebra System in Discrete Mathematics

    ERIC Educational Resources Information Center

    Powers, Robert A.; Allison, Dean E.; Grassl, Richard M.

    2005-01-01

    This study investigated the impact of the TI-92 handheld Computer Algebra System (CAS) on student achievement in a discrete mathematics course. Specifically, the researchers examined the differences between a CAS section and a control section of discrete mathematics on students' in-class examinations. Additionally, they analysed student approaches…

  15. Examining the Use of Computer Algebra Systems in University-Level Mathematics Teaching

    ERIC Educational Resources Information Center

    Lavicza, Zsolt

    2009-01-01

    The use of Computer Algebra Systems (CAS) is becoming increasingly important and widespread in mathematics research and teaching. In this paper, I will report on a questionnaire study enquiring about mathematicians' use of CAS in mathematics teaching in three countries; the United States, the United Kingdom, and Hungary. Based on the responses…

  16. Introducing a Computer Algebra System in Mathematics Education--Empirical Evidence from Germany

    ERIC Educational Resources Information Center

    Schmidt, Karsten; Kohler, Anke; Moldenhauer, Wolfgang

    2009-01-01

    This paper reports on the effects the use of a pocket calculator-based computer algebra system (CAS) has on the performance in mathematics of grade 11 students in Germany. A project started at 8 of about one hundred upper secondary schools in the federal state of Thuringia in 1999; 3 years later the former restrictions on the use of technology in…

  17. Students' Relationship to Technology and Conceptions of Mathematics while Learning in a Computer Algebra System Environment

    ERIC Educational Resources Information Center

    Meagher, Michael

    2012-01-01

    The research presented here is a group case study of students learning calculus in a Computer Algebra System (CAS) environment which examines the following research questions: What are students' perceptions of the role of technology in their learning? What is the students' relationship to CAS? What is the effect of learning in a CAS environment on…

  18. On the Integration of Computer Algebra Systems (CAS) by Canadian Mathematicians: Results of a National Survey

    ERIC Educational Resources Information Center

    Buteau, Chantal; Jarvis, Daniel H.; Lavicza, Zsolt

    2014-01-01

    In this article, we outline the findings of a Canadian survey study (N = 302) that focused on the extent of computer algebra systems (CAS)-based technology use in postsecondary mathematics instruction. Results suggest that a considerable number of Canadian mathematicians use CAS in research and teaching. CAS use in research was found to be the…

  19. Differences between Expected Answers and the Answers Given by Computer Algebra Systems to School Equations

    ERIC Educational Resources Information Center

    Tonisson, Eno

    2015-01-01

    Sometimes Computer Algebra Systems (CAS) offer an answer that is somewhat different from the answer that is probably expected by the student or teacher. These (somewhat unexpected) answers could serve as a catalyst for rich mathematical discussion. In this study, over 120 equations from school mathematics were solved using 8 different CAS. Many…

  20. Instrumenting Mathematical Activity: Reflections on Key Studies of the Educational Use of Computer Algebra Systems.

    ERIC Educational Resources Information Center

    Ruthven, Kenneth

    2002-01-01

    Examines the process through which students learn to make functional use of computer algebra systems (CAS) and the interaction between that process and the wider mathematical development of students. Highlights important challenges that arise in instrumenting classroom mathematical activity and instrumentalizing CAS correspondingly. Reveals…

  1. Step-by-Step Solution Possibilities in Different Computer Algebra Systems.

    ERIC Educational Resources Information Center

    Tonisson, Eno

    This paper compares a number of different Computer Algebra Systems (CAS) in their solution of one-step and multi-step problems. The CAS programs considered include DERIVE, Maple, Mathematica, and MuPAD while the problems are taken from the final examinations of grades 9 and 12 in Estonian schools. The different outputs to one-step problems with…

  2. Exploring Students' Understanding of Ordinary Differential Equations Using Computer Algebraic System (CAS)

    ERIC Educational Resources Information Center

    Maat, Siti Mistima; Zakaria, Effandi

    2011-01-01

    Ordinary differential equations (ODEs) are one of the important topics in engineering mathematics that lead to the understanding of technical concepts among students. This study was conducted to explore the students' understanding of ODEs when they solve ODE questions using a traditional method as well as a computer algebraic system, particularly…

  3. Teaching Algebra without Algebra

    ERIC Educational Resources Information Center

    Kalman, Richard S.

    2008-01-01

    Algebra is, among other things, a shorthand way to express quantitative reasoning. This article illustrates ways for the classroom teacher to convert algebraic solutions to verbal problems into conversational solutions that can be understood by students in the lower grades. Three reasonably typical verbal problems that either appeared as or…

  4. A Coursewriter II Function (FCALC) For the Manipulation of Numerical and Algebraic Expressions. Systems Memo Number One.

    ERIC Educational Resources Information Center

    Smith, Authella; And Others

    Documentation of the Coursewriter II Function FCALC is provided. The function is designed for use on the IBM 1500 instructional system and has three major applications: 1) comparison of a numeric expression in buffer 5 with a numeric expression in buffer 0; 2) comparison of an algebraic expression in buffer 5 with an algebraic expression in buffer…

  5. Predicting NonInertial Effects with Algebraic Stress Models which Account for Dissipation Rate Anisotropies

    NASA Technical Reports Server (NTRS)

    Jongen, T.; Machiels, L.; Gatski, T. B.

    1997-01-01

    Three types of turbulence models which account for rotational effects in noninertial frames of reference are evaluated for the case of incompressible, fully developed rotating turbulent channel flow. The different types of models are a Coriolis-modified eddy-viscosity model, a realizable algebraic stress model, and an algebraic stress model which accounts for dissipation rate anisotropies. A direct numerical simulation of a rotating channel flow is used for the turbulent model validation. This simulation differs from previous studies in that significantly higher rotation numbers are investigated. Flows at these higher rotation numbers are characterized by a relaminarization on the cyclonic or suction side of the channel, and a linear velocity profile on the anticyclonic or pressure side of the channel. The predictive performance of the three types of models are examined in detail, and formulation deficiencies are identified which cause poor predictive performance for some of the models. Criteria are identified which allow for accurate prediction of such flows by algebraic stress models and their corresponding Reynolds stress formulations.

  6. A stopping criterion for the iterative solution of an overdetermined system of linear algebraic equations

    NASA Astrophysics Data System (ADS)

    Yukhno, L. F.

    2008-12-01

    For an overdetermined system of linear algebraic equations, systems obtained by introducing independent random errors into the original right-hand side are examined. Under certain assumptions on how these random variables are distributed, a practical stopping criterion is proposed for an iterative process that minimizes the sum of the squares of the residuals for the above systems. Numerical results demonstrating the efficiency of this criterion for some ill-conditioned problems are presented.

  7. Mathematical Model for Dengue Epidemics with Differential Susceptibility and Asymptomatic Patients Using Computer Algebra

    NASA Astrophysics Data System (ADS)

    Saldarriaga Vargas, Clarita

    When there are diseases affecting large populations where the social, economic and cultural diversity is significant within the same region, the biological parameters that determine the behavior of the dispersion disease analysis are affected by the selection of different individuals. Therefore and because of the variety and magnitude of the communities at risk of contracting dengue disease around all over the world, suggest defining differentiated populations with individual contributions in the results of the dispersion dengue disease analysis. In this paper those conditions were taken in account when several epidemiologic models were analyzed. Initially a stability analysis was done for a SEIR mathematical model of Dengue disease without differential susceptibility. Both free disease and endemic equilibrium states were found in terms of the basic reproduction number and were defined in the Theorem (3.1). Then a DSEIR model was solved when a new susceptible group was introduced to consider the effects of important biological parameters of non-homogeneous populations in the spreading analysis. The results were compiled in the Theorem (3.2). Finally Theorems (3.3) and (3.4) resumed the basic reproduction numbers for three and n different susceptible groups respectively, giving an idea of how differential susceptibility affects the equilibrium states. The computations were done using an algorithmic method implemented in Maple 11, a general-purpose computer algebra system.

  8. Numerical algebraic geometry and algebraic kinematics

    NASA Astrophysics Data System (ADS)

    Wampler, Charles W.; Sommese, Andrew J.

    In this article, the basic constructs of algebraic kinematics (links, joints, and mechanism spaces) are introduced. This provides a common schema for many kinds of problems that are of interest in kinematic studies. Once the problems are cast in this algebraic framework, they can be attacked by tools from algebraic geometry. In particular, we review the techniques of numerical algebraic geometry, which are primarily based on homotopy methods. We include a review of the main developments of recent years and outline some of the frontiers where further research is occurring. While numerical algebraic geometry applies broadly to any system of polynomial equations, algebraic kinematics provides a body of interesting examples for testing algorithms and for inspiring new avenues of work.

  9. Priority in Process Algebras

    NASA Technical Reports Server (NTRS)

    Cleaveland, Rance; Luettgen, Gerald; Natarajan, V.

    1999-01-01

    This paper surveys the semantic ramifications of extending traditional process algebras with notions of priority that allow for some transitions to be given precedence over others. These enriched formalisms allow one to model system features such as interrupts, prioritized choice, or real-time behavior. Approaches to priority in process algebras can be classified according to whether the induced notion of preemption on transitions is global or local and whether priorities are static or dynamic. Early work in the area concentrated on global pre-emption and static priorities and led to formalisms for modeling interrupts and aspects of real-time, such as maximal progress, in centralized computing environments. More recent research has investigated localized notions of pre-emption in which the distribution of systems is taken into account, as well as dynamic priority approaches, i.e., those where priority values may change as systems evolve. The latter allows one to model behavioral phenomena such as scheduling algorithms and also enables the efficient encoding of real-time semantics. Technically, this paper studies the different models of priorities by presenting extensions of Milner's Calculus of Communicating Systems (CCS) with static and dynamic priority as well as with notions of global and local pre- emption. In each case the operational semantics of CCS is modified appropriately, behavioral theories based on strong and weak bisimulation are given, and related approaches for different process-algebraic settings are discussed.

  10. Integrating programming features with an algebraic modeling language for optimization

    SciTech Connect

    Fourer, R.; Gay, D.

    1994-12-31

    In describing optimization models to a computer, programming is best avoided. In using models as part of a larger scheme, however, programs must be written to specify how information is passed between models. We describe a programming environment for this purpose that has been integrated with the AMPL modeling language.

  11. Construction of linear models: A framework based on commutative Jordan algebras

    NASA Astrophysics Data System (ADS)

    Covas, R.; Carvalho, F.

    2016-06-01

    We show how to obtain the necessary structures for statistical analysis of the folllowing orthogonal models Y˜(1 μ +∑i Xiβi ,∑j σj2Mj+σ2I ) . These structures rely on the existence of Jordan algebras, in the sequence of [24], [8], [12], [9], [5] and [10].

  12. On the Gaudin model associated to Lie algebras of classical types

    NASA Astrophysics Data System (ADS)

    Lu, Kang; Mukhin, E.; Varchenko, A.

    2016-10-01

    We derive explicit formulas for solutions of the Bethe ansatz equations of the Gaudin model associated to the tensor product of one arbitrary finite-dimensional irreducible module and one vector representation for all simple Lie algebras of classical type. We use this result to show that the Bethe ansatz is complete in any tensor product where all but one factor are vector representations and the evaluation parameters are generic.

  13. Generating Invariants for Non-linear Hybrid Systems by Linear Algebraic Methods

    NASA Astrophysics Data System (ADS)

    Matringe, Nadir; Moura, Arnaldo Vieira; Rebiha, Rachid

    We describe powerful computational methods, relying on linear algebraic methods, for generating ideals for non-linear invariants of algebraic hybrid systems. We show that the preconditions for discrete transitions and the Lie-derivatives for continuous evolution can be viewed as morphisms and so can be suitably represented by matrices. We reduce the non-trivial invariant generation problem to the computation of the associated eigenspaces by encoding the new consecution requirements as specific morphisms represented by matrices. More specifically, we establish very general sufficient conditions that show the existence and allow the computation of invariant ideals. Our methods also embody a strategy to estimate degree bounds, leading to the discovery of rich classes of inductive, i.e. provable, invariants. Our approach avoids first-order quantifier elimination, Grobner basis computation or direct system resolution, thereby circumventing difficulties met by other recent techniques.

  14. Closure of the algebra of constraints for a nonprojectable Horava model

    SciTech Connect

    Bellorin, Jorge; Restuccia, Alvaro

    2011-02-15

    We perform the Hamiltonian analysis for a nonprojectable Horava model whose potential is composed of R and R{sup 2} terms. We show that Dirac's algorithm for the preservation of the constraints can be done in a closed way, hence the algebra of constraints for this model is consistent. The model has an extra, odd, scalar mode whose decoupling limit can be seen in a linear-order perturbative analysis on weakly varying backgrounds. Although our results for this model point in favor of the consistency of the Horava theory, the validity of the full nonprojectable theory still remains unanswered.

  15. Procedural Knowledge in the Presence of a Computer Algebra System (CAS): Rating the Drawbacks Using a Multi-Factorial Evaluation Approach

    ERIC Educational Resources Information Center

    Abdullah, Lazim M.

    2007-01-01

    Computer algebra systems (CASs) have been used by thousands of teachers and students for teaching and learning algebra. They have the ability to perform efficiently almost all of the algebraic expansions and simplifications. Nevertheless, the traditional approach of using paper and pencil in acquiring procedural knowledge is still widely…

  16. Simultaneously stabilising controllers for time-varying linear systems within the framework of nest algebras

    NASA Astrophysics Data System (ADS)

    Wang, Hongzhu; Yu, Tianqiu; Xiao, Jinmei

    2016-08-01

    From the perspective of strong transitivity, a controller design method is provided to simultaneously stabilise a collection of time-varying linear systems within the framework of nest algebras. In particular, all simultaneously stabilising controllers for a class of linear plants are characterised based on the doubly coprime factorisations. These results hold as well in the time-invariant case. An illustrative example is given to demonstrate the validity of the method.

  17. Analytical-Algebraic Approach to Solving Chaotic System

    NASA Astrophysics Data System (ADS)

    Beran, Zdeněk; Čelikovský, Sergej

    The aim of this paper is to present the application of the analytical series technique to study properties of the nonlinear chaotic dynamical systems. More specifically, Laplace-Adomian decomposition method is applied to Rössler system and the so-called generalized Lorenz system. Some advantages and possible applications of this approach are discussed. Results are illustrated by numerical computations.

  18. A deformation of quantum affine algebra in squashed Wess-Zumino-Novikov-Witten models

    SciTech Connect

    Kawaguchi, Io; Yoshida, Kentaroh

    2014-06-01

    We proceed to study infinite-dimensional symmetries in two-dimensional squashed Wess-Zumino-Novikov-Witten models at the classical level. The target space is given by squashed S³ and the isometry is SU(2){sub L}×U(1){sub R}. It is known that SU(2){sub L} is enhanced to a couple of Yangians. We reveal here that an infinite-dimensional extension of U(1){sub R} is a deformation of quantum affine algebra, where a new deformation parameter is provided with the coefficient of the Wess-Zumino term. Then we consider the relation between the deformed quantum affine algebra and the pair of Yangians from the viewpoint of the left-right duality of monodromy matrices. The integrable structure is also discussed by computing the r/s-matrices that satisfy the extended classical Yang-Baxter equation. Finally, two degenerate limits are discussed.

  19. FAST TRACK COMMUNICATION: Kac Moody algebras and controlled chaos

    NASA Astrophysics Data System (ADS)

    Wesley, Daniel H.

    2007-02-01

    Compactification can control chaotic Mixmaster behaviour in gravitational systems with p-form matter: we consider this in light of the connection between supergravity models and Kac Moody algebras. We show that different compactifications define 'mutations' of the algebras associated with the noncompact theories. We list the algebras obtained in this way, and find novel examples of wall systems determined by Lorentzian (but not hyperbolic) algebras. Cosmological models with a smooth pre-big bang phase require that chaos is absent: we show that compactification alone cannot eliminate chaos in the simplest compactifications of the heterotic string on a Calabi Yau, or M theory on a manifold of G2 holonomy.

  20. Non-Hermitian systems of Euclidean Lie algebraic type with real energy spectra

    NASA Astrophysics Data System (ADS)

    Dey, Sanjib; Fring, Andreas; Mathanaranjan, Thilagarajah

    2014-07-01

    We study several classes of non-Hermitian Hamiltonian systems, which can be expressed in terms of bilinear combinations of Euclidean-Lie algebraic generators. The classes are distinguished by different versions of antilinear (PT)-symmetries exhibiting various types of qualitative behaviour. On the basis of explicitly computed non-perturbative Dyson maps we construct metric operators, isospectral Hermitian counterparts for which we solve the corresponding time-independent Schrödinger equation for specific choices of the coupling constants. In these cases general analytical expressions for the solutions are obtained in the form of Mathieu functions, which we analyze numerically to obtain the corresponding energy spectra. We identify regions in the parameter space for which the corresponding spectra are entirely real and also domains where the PT symmetry is spontaneously broken and sometimes also regained at exceptional points. In some cases it is shown explicitly how the threshold region from real to complex spectra is characterized by the breakdown of the Dyson maps or the metric operator. We establish the explicit relationship to models currently under investigation in the context of beam dynamics in optical lattices.

  1. A realizable explicit algebraic Reynolds stress model for compressible turbulent flow with significant mean dilatation

    NASA Astrophysics Data System (ADS)

    Grigoriev, I. A.; Wallin, S.; Brethouwer, G.; Johansson, A. V.

    2013-10-01

    The explicit algebraic Reynolds stress model of Wallin and Johansson [J. Fluid Mech. 403, 89 (2000)] is extended to compressible and variable-density turbulent flows. This is achieved by correctly taking into account the influence of the mean dilatation on the rapid pressure-strain correlation. The resulting model is formally identical to the original model in the limit of constant density. For two-dimensional mean flows the model is analyzed and the physical root of the resulting quartic equation is identified. Using a fixed-point analysis of homogeneously sheared and strained compressible flows, we show that the new model is realizable, unlike the previous model. Application of the model together with a K - ω model to quasi one-dimensional plane nozzle flow, transcending from subsonic to supersonic regime, also demonstrates realizability. Negative "dilatational" production of turbulence kinetic energy competes with positive "incompressible" production, eventually making the total production negative during the spatial evolution of the nozzle flow. Finally, an approach to include the baroclinic effect into the dissipation equation is proposed and an algebraic model for density-velocity correlations is outlined to estimate the corrections associated with density fluctuations. All in all, the new model can become a significant tool for CFD (computational fluid dynamics) of compressible flows.

  2. On the effect of linear algebra implementations in real-time multibody system dynamics

    NASA Astrophysics Data System (ADS)

    González, Manuel; González, Francisco; Dopico, Daniel; Luaces, Alberto

    2008-03-01

    This paper compares the efficiency of multibody system (MBS) dynamic simulation codes that rely on different implementations of linear algebra operations. The dynamics of an N-loop four-bar mechanism has been solved with an index-3 augmented Lagrangian formulation combined with the trapezoidal rule as numerical integrator. Different implementations for this method, both dense and sparse, have been developed, using a number of linear algebra software libraries (including sparse linear equation solvers) and optimized sparse matrix computation strategies. Numerical experiments have been performed in order to measure their performance, as a function of problem size and matrix filling. Results show that optimal implementations can increase the simulation efficiency in a factor of 2 3, compared with our starting classical implementations, and in some topics they disagree with widespread beliefs in MBS dynamics. Finally, advices are provided to select the implementation which delivers the best performance for a certain MBS dynamic simulation.

  3. Teaching Algebra and Geometry Concepts by Modeling Telescope Optics

    ERIC Educational Resources Information Center

    Siegel, Lauren M.; Dickinson, Gail; Hooper, Eric J.; Daniels, Mark

    2008-01-01

    This article describes preparation and delivery of high school mathematics lessons that integrate mathematics and astronomy through The Geometer's Sketchpad models, traditional proof, and inquiry-based activities. The lessons were created by a University of Texas UTeach preservice teacher as part of a project-based field experience in which high…

  4. The addition of algebraic turbulence modeling to program LAURA

    NASA Astrophysics Data System (ADS)

    Cheatwood, F. Mcneil; Thompson, R. A.

    1993-04-01

    The Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA) is modified to allow the calculation of turbulent flows. This is accomplished using the Cebeci-Smith and Baldwin-Lomax eddy-viscosity models in conjunction with the thin-layer Navier-Stokes options of the program. Turbulent calculations can be performed for both perfect-gas and equilibrium flows. However, a requirement of the models is that the flow be attached. It is seen that for slender bodies, adequate resolution of the boundary-layer gradients may require more cells in the normal direction than a laminar solution, even when grid stretching is employed. Results for axisymmetric and three-dimensional flows are presented. Comparison with experimental data and other numerical results reveal generally good agreement, except in the regions of detached flow.

  5. Algebraic Mean Field Theory

    NASA Astrophysics Data System (ADS)

    Dankova, T. S.; Rosensteel, G.

    1998-10-01

    Mean field theory has an unexpected group theoretic mathematical foundation. Instead of representation theory which applies to most group theoretic quantum models, Hartree-Fock and Hartree-Fock-Bogoliubov have been formulated in terms of coadjoint orbits for the groups U(n) and O(2n). The general theory of mean fields is formulated for an arbitrary Lie algebra L of fermion operators. The moment map provides the correspondence between the Hilbert space of microscopic wave functions and the dual space L^* of densities. The coadjoint orbits of the group in the dual space are phase spaces on which time-dependent mean field theory is equivalent to a classical Hamiltonian dynamical system. Indeed it forms a finite-dimensional Lax system. The mean field theories for the Elliott SU(3) and symplectic Sp(3,R) algebras are constructed explicitly in the coadjoint orbit framework.

  6. A Metric Conceptual Space Algebra

    NASA Astrophysics Data System (ADS)

    Adams, Benjamin; Raubal, Martin

    The modeling of concepts from a cognitive perspective is important for designing spatial information systems that interoperate with human users. Concept representations that are built using geometric and topological conceptual space structures are well suited for semantic similarity and concept combination operations. In addition, concepts that are more closely grounded in the physical world, such as many spatial concepts, have a natural fit with the geometric structure of conceptual spaces. Despite these apparent advantages, conceptual spaces are underutilized because existing formalizations of conceptual space theory have focused on individual aspects of the theory rather than the creation of a comprehensive algebra. In this paper we present a metric conceptual space algebra that is designed to facilitate the creation of conceptual space knowledge bases and inferencing systems. Conceptual regions are represented as convex polytopes and context is built in as a fundamental element. We demonstrate the applicability of the algebra to spatial information systems with a proof-of-concept application.

  7. Algebraic approach to the projected deformed oscillator model

    NASA Astrophysics Data System (ADS)

    Asherova, R. M.; Smirnov, Yu. F.; Tolstoy, V. N.; Shustov, A. P.

    1981-03-01

    A new method of calculation in terms of the projected deformed oscillator model is proposed. The method involves expansion of its wave functions in terms of the wave functions of an isotropic oscillator potential. Only overlap integrals between projected wave functions and reduced probabilities B(E2) of E2 transitions are examined. B(E2) values are expressed as a series containing the corresponding values of the Elliott SU(3) scheme. The convergence of these expansions is shown to be fairly good. The expectation values of operators ( QQ) and ( QQQ), which characterize the effective internal non-sphericity and non-axiality of the nucleus, are also calculated and discussed.

  8. Numerical solution of two-dimensional integral-algebraic systems using Legendre functions

    NASA Astrophysics Data System (ADS)

    Nemati, S.; Lima, P.; Ordokhani, Y.

    2012-09-01

    We consider a method for computing approximate solutions to systems of two-dimensional Volterra integral equations. The approximate solution is sought in the form of a linear combination of two-variable shifted Legendre functions. The operational matrices technique is used to reduce the problem to a system of linear algebraic equations. Some numerical tests have been carried out and the results show that this method has a good performance, even in the case when the system matrix is singular in the whole considered domain.

  9. Generalized model of double random phase encoding based on linear algebra

    NASA Astrophysics Data System (ADS)

    Nakano, Kazuya; Takeda, Masafumi; Suzuki, Hiroyuki; Yamaguchi, Masahiro

    2013-01-01

    We propose a generalized model for double random phase encoding (DRPE) based on linear algebra. We defined the DRPE procedure in six steps. The first three steps form an encryption procedure, while the later three steps make up a decryption procedure. We noted that the first (mapping) and second (transform) steps can be generalized. As an example of this generalization, we used 3D mapping and a transform matrix, which is a combination of a discrete cosine transform and two permutation matrices. Finally, we investigated the sensitivity of the proposed model to errors in the decryption key.

  10. Analyzing the nonlinear vibrational wave differential equation for the simplified model of Tower Cranes by Algebraic Method

    NASA Astrophysics Data System (ADS)

    Akbari, M. R.; Ganji, D. D.; Ahmadi, A. R.; Kachapi, Sayyid H. Hashemi

    2014-03-01

    In the current paper, a simplified model of Tower Cranes has been presented in order to investigate and analyze the nonlinear differential equation governing on the presented system in three different cases by Algebraic Method (AGM). Comparisons have been made between AGM and Numerical Solution, and these results have been indicated that this approach is very efficient and easy so it can be applied for other nonlinear equations. It is citable that there are some valuable advantages in this way of solving differential equations and also the answer of various sets of complicated differential equations can be achieved in this manner which in the other methods, so far, they have not had acceptable solutions. The simplification of the solution procedure in Algebraic Method and its application for solving a wide variety of differential equations not only in Vibrations but also in different fields of study such as fluid mechanics, chemical engineering, etc. make AGM be a powerful and useful role model for researchers in order to solve complicated nonlinear differential equations.

  11. Duality in spin systems via the SU(4) algebra

    NASA Astrophysics Data System (ADS)

    Schaller, Gernot; Schützhold, Ralf

    2016-05-01

    We provide several examples and an intuitive diagrammatic representation demonstrating the use of two-qubit unitary transformations for mapping coupled spin Hamiltonians to simpler ones and vice versa. The corresponding dualities may be exploited to identify phase transition points or to aid the diagonalization of such Hamiltonians. For example, our method shows that a suitable one-parameter family of coupled Hamiltonians whose ground states transform from an initially factorizing state to a final cluster state on a lattice of arbitrary dimension is dual to a family of trivial decoupled Hamiltonians containing local on-site terms only. As a consequence, the minimum energy gap (which determines the adiabatic run-time) does not scale with system size, which facilitates an efficient and simple adiabatic preparation of e.g. the two-dimensional cluster state used for measurement-based quantum computation.

  12. Algebraic varieties in the Birkhoff strata of the Grassmannian Gr(2): Harrison cohomology and integrable systems

    NASA Astrophysics Data System (ADS)

    Konopelchenko, B. G.; Ortenzi, G.

    2011-11-01

    The local properties of the families of algebraic subsets Wg in the Birkhoff strata Σ2g of Gr(2) containing the hyperelliptic curves of genus g are studied. It is shown that the tangent spaces Tg for Wg are isomorphic to the linear spaces of 2-coboundaries. Particular subsets in Wg are described by the integrable dispersionless coupled KdV systems of hydrodynamical type defining a special class of 2-cocycles and 2-coboundaries in Tg. It is demonstrated that the blows-ups of such 2-cocycles and 2-coboundaries and gradient catastrophes for associated integrable systems are interrelated.

  13. Accuracy requirements of optical linear algebra processors in adaptive optics imaging systems

    NASA Technical Reports Server (NTRS)

    Downie, John D.; Goodman, Joseph W.

    1989-01-01

    The accuracy requirements of optical processors in adaptive optics systems are determined by estimating the required accuracy in a general optical linear algebra processor (OLAP) that results in a smaller average residual aberration than that achieved with a conventional electronic digital processor with some specific computation speed. Special attention is given to an error analysis of a general OLAP with regard to the residual aberration that is created in an adaptive mirror system by the inaccuracies of the processor, and to the effect of computational speed of an electronic processor on the correction. Results are presented on the ability of an OLAP to compete with a digital processor in various situations.

  14. Static Analysis of Large-Scale Multibody System Using Joint Coordinates and Spatial Algebra Operator

    PubMed Central

    Omar, Mohamed A.

    2014-01-01

    Initial transient oscillations inhibited in the dynamic simulations responses of multibody systems can lead to inaccurate results, unrealistic load prediction, or simulation failure. These transients could result from incompatible initial conditions, initial constraints violation, and inadequate kinematic assembly. Performing static equilibrium analysis before the dynamic simulation can eliminate these transients and lead to stable simulation. Most exiting multibody formulations determine the static equilibrium position by minimizing the system potential energy. This paper presents a new general purpose approach for solving the static equilibrium in large-scale articulated multibody. The proposed approach introduces an energy drainage mechanism based on Baumgarte constraint stabilization approach to determine the static equilibrium position. The spatial algebra operator is used to express the kinematic and dynamic equations of the closed-loop multibody system. The proposed multibody system formulation utilizes the joint coordinates and modal elastic coordinates as the system generalized coordinates. The recursive nonlinear equations of motion are formulated using the Cartesian coordinates and the joint coordinates to form an augmented set of differential algebraic equations. Then system connectivity matrix is derived from the system topological relations and used to project the Cartesian quantities into the joint subspace leading to minimum set of differential equations. PMID:25045732

  15. Static analysis of large-scale multibody system using joint coordinates and spatial algebra operator.

    PubMed

    Omar, Mohamed A

    2014-01-01

    Initial transient oscillations inhibited in the dynamic simulations responses of multibody systems can lead to inaccurate results, unrealistic load prediction, or simulation failure. These transients could result from incompatible initial conditions, initial constraints violation, and inadequate kinematic assembly. Performing static equilibrium analysis before the dynamic simulation can eliminate these transients and lead to stable simulation. Most exiting multibody formulations determine the static equilibrium position by minimizing the system potential energy. This paper presents a new general purpose approach for solving the static equilibrium in large-scale articulated multibody. The proposed approach introduces an energy drainage mechanism based on Baumgarte constraint stabilization approach to determine the static equilibrium position. The spatial algebra operator is used to express the kinematic and dynamic equations of the closed-loop multibody system. The proposed multibody system formulation utilizes the joint coordinates and modal elastic coordinates as the system generalized coordinates. The recursive nonlinear equations of motion are formulated using the Cartesian coordinates and the joint coordinates to form an augmented set of differential algebraic equations. Then system connectivity matrix is derived from the system topological relations and used to project the Cartesian quantities into the joint subspace leading to minimum set of differential equations.

  16. A computer code for calculations in the algebraic collective model of the atomic nucleus

    NASA Astrophysics Data System (ADS)

    Welsh, T. A.; Rowe, D. J.

    2016-03-01

    A Maple code is presented for algebraic collective model (ACM) calculations. The ACM is an algebraic version of the Bohr model of the atomic nucleus, in which all required matrix elements are derived by exploiting the model's SU(1 , 1) × SO(5) dynamical group. This paper reviews the mathematical formulation of the ACM, and serves as a manual for the code. The code enables a wide range of model Hamiltonians to be analysed. This range includes essentially all Hamiltonians that are rational functions of the model's quadrupole moments qˆM and are at most quadratic in the corresponding conjugate momenta πˆN (- 2 ≤ M , N ≤ 2). The code makes use of expressions for matrix elements derived elsewhere and newly derived matrix elements of the operators [ π ˆ ⊗ q ˆ ⊗ π ˆ ] 0 and [ π ˆ ⊗ π ˆ ] LM. The code is made efficient by use of an analytical expression for the needed SO(5)-reduced matrix elements, and use of SO(5) ⊃ SO(3)  Clebsch-Gordan coefficients obtained from precomputed data files provided with the code.

  17. Explicit algebraic reynolds stress models for anisotropic wall-bounded flows

    NASA Astrophysics Data System (ADS)

    Menter, F. R.; Garbaruk, A. V.; Egorov, Y.

    2012-01-01

    In the present paper, two variants of Explicit Algebraic Reynolds Stress Model (EARSM) are presented and applied to a number of test cases. Both formulations start from the Wallin Johansson (WJ) EARSM stress-strain relationship. The goal of the first step was to combine the EARSM with the ω-equation-based Baseline (BSL) model, to avoid freestream sensitivities and ambiguities in comparison with the Shear Stress Transport (SST) model. This could be achieved by a slight change in the A1 constant. In addition, the standard eddy-viscosity formulation is used in the diffusion terms of the k- and the ω-equations. Secondly, a simplified version of the stress-strain relationship was developed. It is based on a linear form of the implicit algebraic model. It is not clear at the time if this formulation possess significant advantages against the WJ stress-strain model. For the current cases, both variants produced essentially identical results. Several test cases have been computed. The main interest in the simulations was on corner flow separation.

  18. A computer code for calculations in the algebraic collective model of the atomic nucleus

    NASA Astrophysics Data System (ADS)

    Welsh, T. A.; Rowe, D. J.

    2016-03-01

    A Maple code is presented for algebraic collective model (ACM) calculations. The ACM is an algebraic version of the Bohr model of the atomic nucleus, in which all required matrix elements are derived by exploiting the model's SU(1 , 1) × SO(5) dynamical group. This paper reviews the mathematical formulation of the ACM, and serves as a manual for the code. The code enables a wide range of model Hamiltonians to be analysed. This range includes essentially all Hamiltonians that are rational functions of the model's quadrupole moments qˆM and are at most quadratic in the corresponding conjugate momenta πˆN (- 2 ≤ M , N ≤ 2). The code makes use of expressions for matrix elements derived elsewhere and newly derived matrix elements of the operators [ π ˆ ⊗ q ˆ ⊗ π ˆ ] 0 and [ π ˆ ⊗ π ˆ ] LM. The code is made efficient by use of an analytical expression for the needed SO(5)-reduced matrix elements, and use of SO(5) ⊃ SO(3) Clebsch-Gordan coefficients obtained from precomputed data files provided with the code.

  19. Using geometric algebra to understand pattern rotations in multiple mirror optical systems

    SciTech Connect

    Hanlon, J.; Ziock, H.

    1997-05-01

    Geometric Algebra (GA) is a new formulation of Clifford Algebra that includes vector analysis without notation changes. Most applications of Ga have been in theoretical physics, but GA is also a very good analysis tool for engineering. As an example, the authors use GA to study pattern rotation in optical systems with multiple mirror reflections. The common ways to analyze pattern rotations are to use rotation matrices or optical ray trace codes, but these are often inconvenient. The authors use GA to develop a simple expression for pattern rotation that is useful for designing or tolerancing pattern rotations in a multiple mirror optical system by inspection. Pattern rotation is used in many optical engineering systems, but it is not normally covered in optical system engineering texts. Pattern rotation is important in optical systems such as: (1) the 192 beam National ignition Facility (NIF), which uses square laser beams in close packed arrays to cut costs; (2) visual optical systems, which use pattern rotation to present the image to the observer in the appropriate orientation, and (3) the UR90 unstable ring resonator, which uses pattern rotation to fill a rectangular laser gain region and provide a filled-in laser output beam.

  20. Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model

    NASA Astrophysics Data System (ADS)

    Cirilo António, N.; Manojlović, N.; Salom, I.

    2014-12-01

    We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression for the off shell action of the transfer matrix, deriving the spectrum and the relevant Bethe equations. We explore further these results by obtaining the off shell action of the generating function of the Gaudin Hamiltonians on the corresponding Bethe vectors through the so-called quasi-classical limit. Moreover, this action is as simple as it could possibly be, yielding the spectrum and the Bethe equations of the Gaudin model.

  1. Assessing Elementary Algebra with STACK

    ERIC Educational Resources Information Center

    Sangwin, Christopher J.

    2007-01-01

    This paper concerns computer aided assessment (CAA) of mathematics in which a computer algebra system (CAS) is used to help assess students' responses to elementary algebra questions. Using a methodology of documentary analysis, we examine what is taught in elementary algebra. The STACK CAA system, http://www.stack.bham.ac.uk/, which uses the CAS…

  2. An Ada Linear-Algebra Software Package Modeled After HAL/S

    NASA Technical Reports Server (NTRS)

    Klumpp, Allan R.; Lawson, Charles L.

    1990-01-01

    New avionics software written more easily. Software package extends Ada programming language to include linear-algebra capabilities similar to those of HAL/S programming language. Designed for such avionics applications as Space Station flight software. In addition to built-in functions of HAL/S, package incorporates quaternion functions used in Space Shuttle and Galileo projects and routines from LINPAK solving systems of equations involving general square matrices. Contains two generic programs: one for floating-point computations and one for integer computations. Written on IBM/AT personal computer running under PC DOS, v.3.1.

  3. μ -symmetry breaking: An algebraic approach to finding mean fields of quantum many-body systems

    NASA Astrophysics Data System (ADS)

    Higashikawa, Sho; Ueda, Masahito

    2016-07-01

    One of the most fundamental problems in quantum many-body systems is the identification of a mean field in spontaneous symmetry breaking which is usually made in a heuristic manner. We propose a systematic method of finding a mean field based on the Lie algebra and the dynamical symmetry by introducing a class of symmetry-broken phases which we call μ -symmetry breaking. We show that for μ -symmetry breaking the quadratic part of an effective Lagrangian of Nambu-Goldstone modes can be block-diagonalized and that homotopy groups of topological excitations can be calculated systematically.

  4. The development of an algebraic multigrid algorithm for symmetric positive definite linear systems

    SciTech Connect

    Vanek, P.; Mandel, J.; Brezina, M.

    1996-12-31

    An algebraic multigrid algorithm for symmetric, positive definite linear systems is developed based on the concept of prolongation by smoothed aggregation. Coarse levels are generated automatically. We present a set of requirements motivated heuristically by a convergence theory. The algorithm then attempts to satisfy the requirements. Input to the method are the coefficient matrix and zero energy modes, which are determined from nodal coordinates and knowledge of the differential equation. Efficiency of the resulting algorithm is demonstrated by computational results on real world problems from solid elasticity, plate blending, and shells.

  5. Algebraic turbulence models for the computation of two-dimensional high-speed flows using unstructured grids

    NASA Technical Reports Server (NTRS)

    Rostand, Philippe

    1989-01-01

    The incorporation of algebraic turbulence models in a solver for the 2-D compressible Navier-Stokes equations using triangular grids is described. A practial way to use the Cebeci Smith model, and to modify it in separated regions is proposed. The ability of the model to predict high speed, perfect gas boundary layers is investigated from a numerical point of view.

  6. Ready, Set, Algebra?

    ERIC Educational Resources Information Center

    Levy, Alissa Beth

    2012-01-01

    The California Department of Education (CDE) has long asserted that success Algebra I by Grade 8 is the goal for all California public school students. In fact, the state's accountability system penalizes schools that do not require all of their students to take the Algebra I end-of-course examination by Grade 8 (CDE, 2009). In this…

  7. Development of an algebraic stress/two-layer model for calculating thrust chamber flow fields

    NASA Astrophysics Data System (ADS)

    Chen, C. P.; Shang, H. M.; Huang, J.

    1993-07-01

    Following the consensus of a workshop in Turbulence Modeling for Liquid Rocket Thrust Chambers, the current effort was undertaken to study the effects of second-order closure on the predictions of thermochemical flow fields. To reduce the instability and computational intensity of the full second-order Reynolds Stress Model, an Algebraic Stress Model (ASM) coupled with a two-layer near wall treatment was developed. Various test problems, including the compressible boundary layer with adiabatic and cooled walls, recirculating flows, swirling flows and the entire SSME nozzle flow were studied to assess the performance of the current model. Detailed calculations for the SSME exit wall flow around the nozzle manifold were executed. As to the overall flow predictions, the ASM removes another assumption for appropriate comparison with experimental data, to account for the non-isotropic turbulence effects.

  8. Development of an algebraic stress/two-layer model for calculating thrust chamber flow fields

    NASA Technical Reports Server (NTRS)

    Chen, C. P.; Shang, H. M.; Huang, J.

    1993-01-01

    Following the consensus of a workshop in Turbulence Modeling for Liquid Rocket Thrust Chambers, the current effort was undertaken to study the effects of second-order closure on the predictions of thermochemical flow fields. To reduce the instability and computational intensity of the full second-order Reynolds Stress Model, an Algebraic Stress Model (ASM) coupled with a two-layer near wall treatment was developed. Various test problems, including the compressible boundary layer with adiabatic and cooled walls, recirculating flows, swirling flows and the entire SSME nozzle flow were studied to assess the performance of the current model. Detailed calculations for the SSME exit wall flow around the nozzle manifold were executed. As to the overall flow predictions, the ASM removes another assumption for appropriate comparison with experimental data, to account for the non-isotropic turbulence effects.

  9. Algebraic Reynolds stress modeling of turbulence subject to rapid homogeneous and non-homogeneous compression or expansion

    NASA Astrophysics Data System (ADS)

    Grigoriev, I. A.; Wallin, S.; Brethouwer, G.; Grundestam, O.; Johansson, A. V.

    2016-02-01

    A recently developed explicit algebraic Reynolds stress model (EARSM) by Grigoriev et al. ["A realizable explicit algebraic Reynolds stress model for compressible turbulent flow with significant mean dilatation," Phys. Fluids 25(10), 105112 (2013)] and the related differential Reynolds stress model (DRSM) are used to investigate the influence of homogeneous shear and compression on the evolution of turbulence in the limit of rapid distortion theory (RDT). The DRSM predictions of the turbulence kinetic energy evolution are in reasonable agreement with RDT while the evolution of diagonal components of anisotropy correctly captures the essential features, which is not the case for standard compressible extensions of DRSMs. The EARSM is shown to give a realizable anisotropy tensor and a correct trend of the growth of turbulence kinetic energy K, which saturates at a power law growth versus compression ratio, as well as retaining a normalized strain in the RDT regime. In contrast, an eddy-viscosity model results in a rapid exponential growth of K and excludes both realizability and high magnitude of the strain rate. We illustrate the importance of using a proper algebraic treatment of EARSM in systems with high values of dilatation and vorticity but low shear. A homogeneously compressed and rotating gas cloud with cylindrical symmetry, related to astrophysical flows and swirling supercritical flows, was investigated too. We also outline the extension of DRSM and EARSM to include the effect of non-homogeneous density coupled with "local mean acceleration" which can be important for, e.g., stratified flows or flows with heat release. A fixed-point analysis of direct numerical simulation data of combustion in a wall-jet flow demonstrates that our model gives quantitatively correct predictions of both streamwise and cross-stream components of turbulent density flux as well as their influence on the anisotropies. In summary, we believe that our approach, based on a proper

  10. MAMA: an algebraic map for the secular dynamics of planetesimals in tight binary systems

    NASA Astrophysics Data System (ADS)

    Leiva, A. M.; Correa-Otto, J. A.; Beaugé, C.

    2013-12-01

    We present an algebraic map (MAMA) for the dynamical and collisional evolution of a planetesimal swarm orbiting the main star of a tight binary system. The orbital evolution of each planetesimal is dictated by the secular perturbations of the secondary star and gas drag due to interactions with a protoplanetary disc. The gas disc is assumed eccentric with a constant precession rate. Gravitational interactions between the planetesimals are ignored. All bodies are assumed coplanar. A comparison with full N-body simulations shows that the map is of the order of 102 times faster, while preserving all the main characteristics of the full system. In a second part of the work, we apply multiparticle algebraic map for accretion (MAMA) to the γ-Cephei, searching for friendly scenarios that may explain the formation of the giant planet detected in this system. For low-mass protoplanetary discs, we find that a low-eccentricity static disc aligned with the binary yields impact velocities between planetesimals below the disruption threshold. All other scenarios appear hostile to planetary formation.

  11. Algebraic solutions for two-level pairing model in IBM-2 and IVBM

    NASA Astrophysics Data System (ADS)

    Jalili-Majarshin, A.; Jafarizadeh, M. A.; Fouladi, N.

    2016-09-01

    In this paper the affine SU(1,1) approach is applied to numerically solve two pairing problems. A dynamical symmetry limit of the two-fluid interacting boson model-2 (IBM-2) and of the interacting vector boson model (IVBM) defined through the chains U_{π}(6) ⊗ U_{ν}(6) supset SO_{π}(5)⊗ SO_{ν}(5) supset SO_{π}(3) ⊗ SO_{ν}(3) supset SO(3) and U(6) supset U_{π}(3) ⊗ U_{ν}(3) supset SO_{π}(3) ⊗ SO_{ν}(3) supset SO(3) are introduced, respectively. The quantum phase transition between spherical and γ-soft shapes in medium-mass nuclei is analyzed using U(5) leftrightarrow SO(6) transitional nuclei in IBM-2 and one case U_{π}(3) ⊗ U_{ν}(3) leftrightarrow SO(6) transitional nuclei in IVBM found by using an infinite dimensional algebraic method based on affine SU(1,1) Lie algebra. The calculated energy spectra, energy ratio and energy staggering of Mo isotopes are compared with experimental results. The interplay between phase transitions and configuration mixing of intruder excitations between spherical vibrations and the γ-soft shapes in Mo isotopes is succinctly addressed and displays fingerprints of the transitional dynamical symmetry E(5).

  12. A possible framework of the Lipkin model obeying the SU(n) algebra in arbitrary fermion number. I: The SU(2) algebras extended from the conventional fermion pair and determination of the minimum weight states

    NASA Astrophysics Data System (ADS)

    Tsue, Yasuhiko; Providência, Constança; Providência, João da; Yamamura, Masatoshi

    2016-08-01

    The minimum weight states of the Lipkin model consisting of n single-particle levels and obeying the SU(n) algebra are investigated systematically. The basic idea is to use the SU(2) algebra, which is independent of the SU(n) algebra. This idea has already been presented by the present authors in the case of the conventional Lipkin model consisting of two single-particle levels and obeying the SU(2) algebra. If this idea is followed, the minimum weight states are determined for any fermion number appropriately occupying n single-particle levels. Naturally, the conventional minimum weight state is included: all fermions occupy energetically the lowest single-particle level in the absence of interaction. The cases n=2, 3, 4, and 5 are discussed in some detail.

  13. A two-dimensional algebraic quantum liquid produced by an atomic simulator of the quantum Lifshitz model

    PubMed Central

    Po, Hoi Chun; Zhou, Qi

    2015-01-01

    Bosons have a natural instinct to condense at zero temperature. It is a long-standing challenge to create a high-dimensional quantum liquid that does not exhibit long-range order at the ground state, as either extreme experimental parameters or sophisticated designs of microscopic Hamiltonians are required for suppressing the condensation. Here we show that synthetic gauge fields for ultracold atoms, using either the Raman scheme or shaken lattices, provide physicists a simple and practical scheme to produce a two-dimensional algebraic quantum liquid at the ground state. This quantum liquid arises at a critical Lifshitz point, where a two-dimensional quartic dispersion emerges in the momentum space, and many fundamental properties of two-dimensional bosons are changed in its proximity. Such an ideal simulator of the quantum Lifshitz model allows experimentalists to directly visualize and explore the deconfinement transition of topological excitations, an intriguing phenomenon that is difficult to access in other systems. PMID:26268154

  14. A two-dimensional algebraic quantum liquid produced by an atomic simulator of the quantum Lifshitz model.

    PubMed

    Po, Hoi Chun; Zhou, Qi

    2015-08-13

    Bosons have a natural instinct to condense at zero temperature. It is a long-standing challenge to create a high-dimensional quantum liquid that does not exhibit long-range order at the ground state, as either extreme experimental parameters or sophisticated designs of microscopic Hamiltonians are required for suppressing the condensation. Here we show that synthetic gauge fields for ultracold atoms, using either the Raman scheme or shaken lattices, provide physicists a simple and practical scheme to produce a two-dimensional algebraic quantum liquid at the ground state. This quantum liquid arises at a critical Lifshitz point, where a two-dimensional quartic dispersion emerges in the momentum space, and many fundamental properties of two-dimensional bosons are changed in its proximity. Such an ideal simulator of the quantum Lifshitz model allows experimentalists to directly visualize and explore the deconfinement transition of topological excitations, an intriguing phenomenon that is difficult to access in other systems.

  15. A two-dimensional algebraic quantum liquid produced by an atomic simulator of the quantum Lifshitz model

    NASA Astrophysics Data System (ADS)

    Po, Hoi Chun; Zhou, Qi

    2015-08-01

    Bosons have a natural instinct to condense at zero temperature. It is a long-standing challenge to create a high-dimensional quantum liquid that does not exhibit long-range order at the ground state, as either extreme experimental parameters or sophisticated designs of microscopic Hamiltonians are required for suppressing the condensation. Here we show that synthetic gauge fields for ultracold atoms, using either the Raman scheme or shaken lattices, provide physicists a simple and practical scheme to produce a two-dimensional algebraic quantum liquid at the ground state. This quantum liquid arises at a critical Lifshitz point, where a two-dimensional quartic dispersion emerges in the momentum space, and many fundamental properties of two-dimensional bosons are changed in its proximity. Such an ideal simulator of the quantum Lifshitz model allows experimentalists to directly visualize and explore the deconfinement transition of topological excitations, an intriguing phenomenon that is difficult to access in other systems.

  16. "We Want a Statement That Is Always True": Criteria for Good Algebraic Representations and the Development of Modeling Knowledge.

    ERIC Educational Resources Information Center

    Izsak, Andrew

    2003-01-01

    Presents a case study in which two 8th grade students developed knowledge for modeling a physical device called a winch. Demonstrates that students have and can use criteria for evaluating algebraic representations. Explains how students can develop modeling knowledge by coordinating criteria with knowledge for generating and using algebraic…

  17. Comparing Cognitive Models of Domain Mastery and Task Performance in Algebra: Validity Evidence for a State Assessment

    ERIC Educational Resources Information Center

    Warner, Zachary B.

    2013-01-01

    This study compared an expert-based cognitive model of domain mastery with student-based cognitive models of task performance for Integrated Algebra. Interpretations of student test results are limited by experts' hypotheses of how students interact with the items. In reality, the cognitive processes that students use to solve each item may be…

  18. Teaching of real numbers by using the Archimedes-Cantor approach and computer algebra systems

    NASA Astrophysics Data System (ADS)

    Vorob'ev, Evgenii M.

    2015-11-01

    Computer technologies and especially computer algebra systems (CAS) allow students to overcome some of the difficulties they encounter in the study of real numbers. The teaching of calculus can be considerably more effective with the use of CAS provided the didactics of the discipline makes it possible to reveal the full computational potential of CAS. In the case of real numbers, the Archimedes-Cantor approach satisfies this requirement. The name of Archimedes brings back the exhaustion method. Cantor's name reminds us of the use of Cauchy rational sequences to represent real numbers. The usage of CAS with the Archimedes-Cantor approach enables the discussion of various representations of real numbers such as graphical, decimal, approximate decimal with precision estimates, and representation as points on a straight line. Exercises with numbers such as e, π, the golden ratio ϕ, and algebraic irrational numbers can help students better understand the real numbers. The Archimedes-Cantor approach also reveals a deep and close relationship between real numbers and continuity, in particular the continuity of functions.

  19. Constructing a coherent problem model to facilitate algebra problem solving in a chemistry context

    NASA Astrophysics Data System (ADS)

    Hiong Ngu, Bing; Seeshing Yeung, Alexander; Phan, Huy P.

    2015-04-01

    An experiment using a sample of 11th graders compared text editing and worked examples approaches in learning to solve dilution and molarity algebra word problems in a chemistry context. Text editing requires students to assess the structure of a word problem by specifying whether the problem text contains sufficient, missing, or irrelevant information for reaching a solution. Worked examples direct students to follow steps toward the solution, and its emphasis is on computation instead of the formation of a coherent problem model. Text editing yielded higher scores in a transfer test (which shared the same solution procedure as in the acquisition problems but differed in contexts), but not a similar test (which resembled acquisition problems in terms of both solution procedure and context). Results provide some theoretical support and practical implications for using text editing to develop a coherent problem model to facilitate problem-solving skills in chemistry.

  20. Conceptual explanation for the algebra in the noncommutative approach to the standard model.

    PubMed

    Chamseddine, Ali H; Connes, Alain

    2007-11-01

    The purpose of this Letter is to remove the arbitrariness of the ad hoc choice of the algebra and its representation in the noncommutative approach to the standard model, which was begging for a conceptual explanation. We assume as before that space-time is the product of a four-dimensional manifold by a finite noncommmutative space F. The spectral action is the pure gravitational action for the product space. To remove the above arbitrariness, we classify the irreducible geometries F consistent with imposing reality and chiral conditions on spinors, to avoid the fermion doubling problem, which amounts to have total dimension 10 (in the K-theoretic sense). It gives, almost uniquely, the standard model with all its details, predicting the number of fermions per generation to be 16, their representations and the Higgs breaking mechanism, with very little input.

  1. Structure of 23Al from a multi-channel algebraic scattering model based on mirror symmetry

    NASA Astrophysics Data System (ADS)

    Fraser, P. R.; Kadyrov, A. S.; Massen-Hane, K.; Amos, K.; Canton, L.; Karataglidis, S.; van der Knijff, D.; Bray, I.

    2016-09-01

    The proton-rich nucleus 23Al has a ground state just 123 keV below the one-proton emission threshold, and as a result comparatively little is known experimentally about its properties, as with many such nuclei. Theoretical investigations have tended to model exclusively the ground and first one to three excited states known. In this paper, we theoretically model most of the known spectrum, and predict what states may as yet be unobserved. We use the multichannel algebraic scattering method to describe states as resonances of a valence proton coupled to a 22Mg rotor core. Six states with low-excitation energies and defined {J}π are matched, and we make the first prediction of the properties of four others and propound the possible existence of several more.

  2. Using Linear Algebra to Introduce Computer Algebra, Numerical Analysis, Data Structures and Algorithms (and To Teach Linear Algebra, Too).

    ERIC Educational Resources Information Center

    Gonzalez-Vega, Laureano

    1999-01-01

    Using a Computer Algebra System (CAS) to help with the teaching of an elementary course in linear algebra can be one way to introduce computer algebra, numerical analysis, data structures, and algorithms. Highlights the advantages and disadvantages of this approach to the teaching of linear algebra. (Author/MM)

  3. Model of adaptive temporal development of structured finite systems

    NASA Astrophysics Data System (ADS)

    Patera, Jiri; Shaw, Gordon L.; Slansky, Richard; Leng, Xiaodan

    1989-07-01

    The weight systems of level-zero representations of affine Kac-Moody algebras provide an appropriate kinematical framework for studying structured finite systems with adaptive temporal development. Much of the structure is determined by Lie algebra theory, so it is possible to restrict greatly the connection space and analytic results are possible. The time development of these systems often evolves to cyclic temporal-spatial patterns, depending on the definition of the dynamics. The purpose of this paper is to set up the mathematical formalism for this ``memory in Lie algebras'' class of models. An illustration is used to show the kinds of complex behavior that occur in simple cases.

  4. The Heisenberg-Weyl algebra on the circle and a related quantum mechanical model for hindered rotation.

    PubMed

    Kouri, Donald J; Markovich, Thomas; Maxwell, Nicholas; Bodmann, Bernhard G

    2009-07-01

    We discuss a periodic variant of the Heisenberg-Weyl algebra, associated with the group of translations and modulations on the circle. Our study of uncertainty minimizers leads to a periodic version of canonical coherent states. Unlike the canonical, Cartesian case, there are states for which the uncertainty product associated with the generators of the algebra vanishes. Next, we explore the supersymmetric (SUSY) quantum mechanical setting for the uncertainty-minimizing states and interpret them as leading to a family of "hindered rotors". Finally, we present a standard quantum mechanical treatment of one of these hindered rotor systems, including numerically generated eigenstates and energies.

  5. Unifying Algebraic and Large-Scale Shell-Model Approaches in Nuclear Structure Calculations

    NASA Astrophysics Data System (ADS)

    Draayer, Jerry P.

    1997-04-01

    The shell model is the most robust theory for addressing nuclear structure questions. Unfortunately, it is only as good as the input hamiltonian and the appropriateness of the selected model space, and both of these elements usually prove to be a significant challenge. There are three basic theories: 1) algebraic models, boson and fermion, which focus on symmetries, exact and approximate, of a hamiltonian and usually use model spaces that are severely truncated; 2) numerically oriented schemes that accommodate larger spaces but rely on special techniques and algorithms for producing convergent results; and 3) models that employ statistical concepts, like statistical spectroscopy of the 70s and 80s and Monte Carlo methods of the 90s, schemes that are not limited by the usual dimensionality considerations. These three approaches and their various realizations and extensions, with their pluses and minuses, will be considered. In addition, opportunities that exist for defining a scheme that employs the best of all three approaches to yield a symmetry adapted theory that is not limited to simplified spaces and hamiltonians and yet remains tractable even for large-scale calculations of the type that are required for testing a theory against experimental data and for predicting new physical phenomena will be explored. Special attention will be focused on unifying themes linking the shell-model with the simpler and yet highly successful mean-field and collective-model theories. As a example of the latter, some recent results using the symplectic shell model will be presented.

  6. Extension of the algebraic transition model for the wall roughness effect

    NASA Astrophysics Data System (ADS)

    Straka, Petr; Příhoda, Jaromír

    2016-03-01

    The contribution deals with the simulation of the laminar/turbulent transition taking into account the effect of wall roughness. The correlation for the transition onset proposed by Straka and Příhoda [1] was modified for the effect of the wall roughness using the correlation according to Boyle and Stripf [2]. This correlation derived for the wall roughness formed by regularly distributed truncated cones was modified for flows over the distributed wall roughness. The algebraic transition model proposed by Straka and Příhoda [1] with the modified relation for the transition onset was verified by means of the incompressible flat-plate boundary-layer and the compressible flow through the turbine blade cascade with rough blades.

  7. Algebraic geometry methods associated to the one-dimensional Hubbard model

    NASA Astrophysics Data System (ADS)

    Martins, M. J.

    2016-06-01

    In this paper we study the covering vertex model of the one-dimensional Hubbard Hamiltonian constructed by Shastry in the realm of algebraic geometry. We show that the Lax operator sits in a genus one curve which is not isomorphic but only isogenous to the curve suitable for the AdS/CFT context. We provide an uniformization of the Lax operator in terms of ratios of theta functions allowing us to establish relativistic like properties such as crossing and unitarity. We show that the respective R-matrix weights lie on an Abelian surface being birational to the product of two elliptic curves with distinct J-invariants. One of the curves is isomorphic to that of the Lax operator but the other is solely fourfold isogenous. These results clarify the reason the R-matrix can not be written using only difference of spectral parameters of the Lax operator.

  8. Validating Cognitive Models of Task Performance in Algebra on the SAT®. Research Report No. 2009-3

    ERIC Educational Resources Information Center

    Gierl, Mark J.; Leighton, Jacqueline P.; Wang, Changjiang; Zhou, Jiawen; Gokiert, Rebecca; Tan, Adele

    2009-01-01

    The purpose of the study is to present research focused on validating the four algebra cognitive models in Gierl, Wang, et al., using student response data collected with protocol analysis methods to evaluate the knowledge structures and processing skills used by a sample of SAT test takers.

  9. Study of Transitions in the Atmospheric Boundary Layer Using Explicit Algebraic Turbulence Models

    NASA Astrophysics Data System (ADS)

    Lazeroms, W. M. J.; Svensson, G.; Bazile, E.; Brethouwer, G.; Wallin, S.; Johansson, A. V.

    2016-10-01

    We test a recently developed engineering turbulence model, a so-called explicit algebraic Reynolds-stress (EARS) model, in the context of the atmospheric boundary layer. First of all, we consider a stable boundary layer used as the well-known first test case from the Global Energy and Water Cycle Experiment Atmospheric Boundary Layer Study (GABLS1). The model is shown to agree well with data from large-eddy simulations (LES), and this agreement is significantly better than for a standard operational scheme with a prognostic equation for turbulent kinetic energy. Furthermore, we apply the model to a case with a (idealized) diurnal cycle and make a qualitative comparison with a simpler first-order model. Some interesting features of the model are highlighted, pertaining to its stronger foundation on physical principles. In particular, the use of more prognostic equations in the model is shown to give a more realistic dynamical behaviour. This qualitative study is the first step towards a more detailed comparison, for which additional LES data are needed.

  10. Study of Transitions in the Atmospheric Boundary Layer Using Explicit Algebraic Turbulence Models

    NASA Astrophysics Data System (ADS)

    Lazeroms, W. M. J.; Svensson, G.; Bazile, E.; Brethouwer, G.; Wallin, S.; Johansson, A. V.

    2016-08-01

    We test a recently developed engineering turbulence model, a so-called explicit algebraic Reynolds-stress (EARS) model, in the context of the atmospheric boundary layer. First of all, we consider a stable boundary layer used as the well-known first test case from the Global Energy and Water Cycle Experiment Atmospheric Boundary Layer Study (GABLS1). The model is shown to agree well with data from large-eddy simulations (LES), and this agreement is significantly better than for a standard operational scheme with a prognostic equation for turbulent kinetic energy. Furthermore, we apply the model to a case with a (idealized) diurnal cycle and make a qualitative comparison with a simpler first-order model. Some interesting features of the model are highlighted, pertaining to its stronger foundation on physical principles. In particular, the use of more prognostic equations in the model is shown to give a more realistic dynamical behaviour. This qualitative study is the first step towards a more detailed comparison, for which additional LES data are needed.

  11. Students' Comparison of Their Trigonometric Answers with the Answers of a Computer Algebra System in Terms of Equivalence and Correctness

    ERIC Educational Resources Information Center

    Tonisson, Eno; Lepp, Marina

    2015-01-01

    The answers offered by computer algebra systems (CAS) can sometimes differ from those expected by the students or teachers. The comparison of the students' answers and CAS answers could provide ground for discussion about equivalence and correctness. Investigating the students' comparison of the answers gives the possibility to study different…

  12. Do Mathematicians Integrate Computer Algebra Systems in University Teaching? Comparing a Literature Review to an International Survey Study

    ERIC Educational Resources Information Center

    Marshall, Neil; Buteau, Chantal; Jarvis, Daniel H.; Lavicza, Zsolt

    2012-01-01

    We present a comparative study of a literature review of 326 selected contributions (Buteau, Marshall, Jarvis & Lavicza, 2010) to an international (US, UK, Hungary) survey of mathematicians (Lavicza, 2008) regarding the use of Computer Algebra Systems (CAS) in post-secondary mathematics education. The comparison results are organized with respect…

  13. Effects of Using a Computer Algebra System (CAS) on Junior College Students' Attitudes towards CAS and Achievement in Mathematics

    ERIC Educational Resources Information Center

    Leng, Ng Wee; Choo, Kwee Tiow; Soon, Lau Hock; Yi-Huak, Koh; Sun, Yap Yew

    2005-01-01

    This study examines the effects of using Texas Instruments' Voyage 200 calculator (V200), a graphing calculator with a built-in computer algebra system (CAS), on attitudes towards CAS and achievement in mathematics of junior college students (17 year olds). Students' attitudes towards CAS were examined using a 40-item Likert-type instrument…

  14. Aprepro - Algebraic Preprocessor

    2005-08-01

    Aprepro is an algebraic preprocessor that reads a file containing both general text and algebraic, string, or conditional expressions. It interprets the expressions and outputs them to the output file along witht the general text. Aprepro contains several mathematical functions, string functions, and flow control constructs. In addition, functions are included that, with some additional files, implement a units conversion system and a material database lookup system.

  15. Modelling for Feedback Control of Skin Friction Drag in Algebraic Growth

    NASA Astrophysics Data System (ADS)

    Jones, Bryn; Kerrigan, Eric; Naguib, Ahmed; Morrison, Jonathan

    2008-11-01

    We address the following problem: given spanwise arrays of wall- mounted shear-stress sensors at upstream and downstream locations, obtain accurate estimates of the flow field above an array of actuators located between the sensors. The accuracy of these estimates is of crucial importance in the design of any closed-loop drag reduction controller. To achieve satisfactory estimates we employ feedback from the sensors in conjunction with a dynamic model, based on that of Luchini (2000), describing perturbation evolution within a laminar boundary layer. The novelty of this work lies in the derivation of a state-space model of sufficiently low order to enable Kalman filter synthesis. Rather than obtaining a reduced- order model via numerical methods such as balanced truncation (Zhou, Doyle, Glover; 1996), we employ a series of approximations based on the results of Andersson, Berggren et al. (1999), to derive a low-order model analytically. A Kalman filter is synthesised and tested on the algebraic growth region of the DNS of Zaki (2005). Despite the use of a low-order model and significant free-stream turbulence, the results demonstrate good performance of the filter.

  16. Algebraic integrability: a survey.

    PubMed

    Vanhaecke, Pol

    2008-03-28

    We give a concise introduction to the notion of algebraic integrability. Our exposition is based on examples and phenomena, rather than on detailed proofs of abstract theorems. We mainly focus on algebraic integrability in the sense of Adler-van Moerbeke, where the fibres of the momentum map are affine parts of Abelian varieties; as it turns out, most examples from classical mechanics are of this form. Two criteria are given for such systems (Kowalevski-Painlevé and Lyapunov) and each is illustrated in one example. We show in the case of a relatively simple example how one proves algebraic integrability, starting from the differential equations for the integrable vector field. For Hamiltonian systems that are algebraically integrable in the generalized sense, two examples are given, which illustrate the non-compact analogues of Abelian varieties which typically appear in such systems. PMID:17588863

  17. Earth Algebra.

    ERIC Educational Resources Information Center

    Schaufele, Christopher; Zumoff, Nancy

    Earth Algebra is an entry level college algebra course that incorporates the spirit of the National Council of Teachers of Mathematics (NCTM) Curriculum and Evaluation Standards for School Mathematics at the college level. The context of the course places mathematics at the center of one of the major current concerns of the world. Through…

  18. Critical RSOS and minimal models: fermionic paths, Virasoro algebra and fields

    NASA Astrophysics Data System (ADS)

    Feverati, Giovanni; Pearce, Paul A.

    2003-07-01

    A framework is presented to extend the finitized characters and recursion methods of (off-critical) corner transfer matrices (CTMs), in a self-consistent fashion, to the calculation of CFT characters and conformal partition functions. More specifically, in this paper we consider sℓ(2) minimal conformal field theories on a cylinder from a lattice perspective. We argue that a general energy-preserving bijection exists between the one-dimensional configuration paths of the AL restricted solid-on-solid (RSOS) lattice models and the eigenstates of their double row transfer matrices and exhibit this bijection for the critical and tricritical Ising models in the vacuum sector. To each allowed one-dimensional configuration path we associate a physical state and a monomial in a finite fermionic algebra. The orthonormal states produced by the action of these monomials on the primary states | h> generate finite Virasoro modules with dimensions given by the finitized Virasoro characters χ( N) h( q). These finitized characters are the generating functions for the double row transfer matrix spectra of the critical RSOS models. We also propose a general level-by-level algorithm to build matrix representations of the Virasoro generators and chiral vertex operators (CVOs). The algorithm employs a distinguished basis which we call the L1-basis. Our results extend to ZL-1 parafermion models by duality.

  19. A computational neural model of orientation detection based on multiple guesses: comparison of geometrical and algebraic models.

    PubMed

    Wei, Hui; Ren, Yuan; Wang, Zi Yan

    2013-10-01

    The implementation of Hubel-Wiesel hypothesis that orientation selectivity of a simple cell is based on ordered arrangement of its afferent cells has some difficulties. It requires the receptive fields (RFs) of those ganglion cells (GCs) and LGN cells to be similar in size and sub-structure and highly arranged in a perfect order. It also requires an adequate number of regularly distributed simple cells to match ubiquitous edges. However, the anatomical and electrophysiological evidence is not strong enough to support this geometry-based model. These strict regularities also make the model very uneconomical in both evolution and neural computation. We propose a new neural model based on an algebraic method to estimate orientations. This approach synthesizes the guesses made by multiple GCs or LGN cells and calculates local orientation information subject to a group of constraints. This algebraic model need not obey the constraints of Hubel-Wiesel hypothesis, and is easily implemented with a neural network. By using the idea of a satisfiability problem with constraints, we also prove that the precision and efficiency of this model are mathematically practicable. The proposed model makes clear several major questions which Hubel-Wiesel model does not account for. Image-rebuilding experiments are conducted to check whether this model misses any important boundary in the visual field because of the estimation strategy. This study is significant in terms of explaining the neural mechanism of orientation detection, and finding the circuit structure and computational route in neural networks. For engineering applications, our model can be used in orientation detection and as a simulation platform for cell-to-cell communications to develop bio-inspired eye chips. PMID:24427212

  20. Acceleration of multiple solution of a boundary value problem involving a linear algebraic system

    NASA Astrophysics Data System (ADS)

    Gazizov, Talgat R.; Kuksenko, Sergey P.; Surovtsev, Roman S.

    2016-06-01

    Multiple solution of a boundary value problem that involves a linear algebraic system is considered. New approach to acceleration of the solution is proposed. The approach uses the structure of the linear system matrix. Particularly, location of entries in the right columns and low rows of the matrix, which undergo variation due to the computing in the range of parameters, is used to apply block LU decomposition. Application of the approach is considered on the example of multiple computing of the capacitance matrix by method of moments used in numerical electromagnetics. Expressions for analytic estimation of the acceleration are presented. Results of the numerical experiments for solution of 100 linear systems with matrix orders of 1000, 2000, 3000 and different relations of variated and constant entries of the matrix show that block LU decomposition can be effective for multiple solution of linear systems. The speed up compared to pointwise LU factorization increases (up to 15) for larger number and order of considered systems with lower number of variated entries.

  1. Modeling formalisms in Systems Biology

    PubMed Central

    2011-01-01

    Systems Biology has taken advantage of computational tools and high-throughput experimental data to model several biological processes. These include signaling, gene regulatory, and metabolic networks. However, most of these models are specific to each kind of network. Their interconnection demands a whole-cell modeling framework for a complete understanding of cellular systems. We describe the features required by an integrated framework for modeling, analyzing and simulating biological processes, and review several modeling formalisms that have been used in Systems Biology including Boolean networks, Bayesian networks, Petri nets, process algebras, constraint-based models, differential equations, rule-based models, interacting state machines, cellular automata, and agent-based models. We compare the features provided by different formalisms, and discuss recent approaches in the integration of these formalisms, as well as possible directions for the future. PMID:22141422

  2. Modeling formalisms in Systems Biology.

    PubMed

    Machado, Daniel; Costa, Rafael S; Rocha, Miguel; Ferreira, Eugénio C; Tidor, Bruce; Rocha, Isabel

    2011-01-01

    Systems Biology has taken advantage of computational tools and high-throughput experimental data to model several biological processes. These include signaling, gene regulatory, and metabolic networks. However, most of these models are specific to each kind of network. Their interconnection demands a whole-cell modeling framework for a complete understanding of cellular systems. We describe the features required by an integrated framework for modeling, analyzing and simulating biological processes, and review several modeling formalisms that have been used in Systems Biology including Boolean networks, Bayesian networks, Petri nets, process algebras, constraint-based models, differential equations, rule-based models, interacting state machines, cellular automata, and agent-based models. We compare the features provided by different formalisms, and discuss recent approaches in the integration of these formalisms, as well as possible directions for the future. PMID:22141422

  3. An Example of Competence-Based Learning: Use of Maxima in Linear Algebra for Engineers

    ERIC Educational Resources Information Center

    Diaz, Ana; Garcia, Alfonsa; de la Villa, Agustin

    2011-01-01

    This paper analyses the role of Computer Algebra Systems (CAS) in a model of learning based on competences. The proposal is an e-learning model Linear Algebra course for Engineering, which includes the use of a CAS (Maxima) and focuses on problem solving. A reference model has been taken from the Spanish Open University. The proper use of CAS is…

  4. Reduction of quantum analogs of Hamiltonian systems described by Lie algebras to orbits in a coadjoint representation

    NASA Astrophysics Data System (ADS)

    Lisitsyn, Ya. V.; Shapovalov, A. V.

    1998-05-01

    A study is made of the possibility of reducing quantum analogs of Hamiltonian systems to Lie algebras. The procedure of reducing classical systems to orbits in a coadjoint representation based on Lie algebra is well-known. An analog of this procedure for quantum systems described by linear differential equations (LDEs) in partial derivatives is proposed here on the basis of the method of noncommutative integration of LDEs. As an example illustrating the procedure, an examination is made of nontrivial systems that cannot be integrated by separation of variables: the Gryachev-Chaplygin hydrostat and the Kovalevskii gyroscope. In both cases, the problem is reduced to a system with a smaller number of variables.

  5. Calculus domains modelled using an original bool algebra based on polygons

    NASA Astrophysics Data System (ADS)

    Oanta, E.; Panait, C.; Raicu, A.; Barhalescu, M.; Axinte, T.

    2016-08-01

    Analytical and numerical computer based models require analytical definitions of the calculus domains. The paper presents a method to model a calculus domain based on a bool algebra which uses solid and hollow polygons. The general calculus relations of the geometrical characteristics that are widely used in mechanical engineering are tested using several shapes of the calculus domain in order to draw conclusions regarding the most effective methods to discretize the domain. The paper also tests the results of several CAD commercial software applications which are able to compute the geometrical characteristics, being drawn interesting conclusions. The tests were also targeting the accuracy of the results vs. the number of nodes on the curved boundary of the cross section. The study required the development of an original software consisting of more than 1700 computer code lines. In comparison with other calculus methods, the discretization using convex polygons is a simpler approach. Moreover, this method doesn't lead to large numbers as the spline approximation did, in that case being required special software packages in order to offer multiple, arbitrary precision. The knowledge resulted from this study may be used to develop complex computer based models in engineering.

  6. Computation of turbulent boundary layer flows with an algebraic stress turbulence model

    NASA Technical Reports Server (NTRS)

    Kim, Sang-Wook; Chen, Yen-Sen

    1986-01-01

    An algebraic stress turbulence model is presented, characterized by the following: (1) the eddy viscosity expression is derived from the Reynolds stress turbulence model; (2) the turbulent kinetic energy dissipation rate equation is improved by including a production range time scale; and (3) the diffusion coefficients for turbulence equations are adjusted so that the kinetic energy profile extends further into the free stream region found in most experimental data. The turbulent flow equations were solved using a finite element method. Examples include: fully developed channel flow, fully developed pipe flow, flat plate boundary layer flow, plane jet exhausting into a moving stream, circular jet exhausting into a moving stream, and wall jet flow. Computational results compare favorably with experimental data for most of the examples considered. Significantly improved results were obtained for the plane jet flow, the circular jet flow, and the wall jet flow; whereas the remainder are comparable to those obtained by finite difference methods using the standard kappa-epsilon turbulence model. The latter seems to be promising with further improvement of the expression for the eddy viscosity coefficient.

  7. Matrix Algebra for GPU and Multicore Architectures (MAGMA) for Large Petascale Systems

    SciTech Connect

    Dongarra, Jack J.; Tomov, Stanimire

    2014-03-24

    The goal of the MAGMA project is to create a new generation of linear algebra libraries that achieve the fastest possible time to an accurate solution on hybrid Multicore+GPU-based systems, using all the processing power that future high-end systems can make available within given energy constraints. Our efforts at the University of Tennessee achieved the goals set in all of the five areas identified in the proposal: 1. Communication optimal algorithms; 2. Autotuning for GPU and hybrid processors; 3. Scheduling and memory management techniques for heterogeneity and scale; 4. Fault tolerance and robustness for large scale systems; 5. Building energy efficiency into software foundations. The University of Tennessee’s main contributions, as proposed, were the research and software development of new algorithms for hybrid multi/many-core CPUs and GPUs, as related to two-sided factorizations and complete eigenproblem solvers, hybrid BLAS, and energy efficiency for dense, as well as sparse, operations. Furthermore, as proposed, we investigated and experimented with various techniques targeting the five main areas outlined.

  8. Modifications of the law of the wall and algebraic turbulence modelling for separated boundary layers

    NASA Technical Reports Server (NTRS)

    Baldwin, B. S.; Maccormack, R. W.

    1976-01-01

    Various modifications of the conventional algebraic eddy viscosity turbulence model are investigated for application to separated flows. Friction velocity is defined in a way that avoids singular behavior at separation and reattachment but reverts to the conventional definition for flows with small pressure gradients. This leads to a modified law of the wall for separated flows. The effect on the calculated flow field of changes in the model that affect the eddy viscosity at various distances from the wall are determined by (1) switching from Prandtl's form to an inner layer formula due to Clauser at various distances from the wall, (2) varying the constant in the Van Driest damping factor, (3) using Clauser's inner layer formula all the way to the wall, and (4) applying a relaxation procedure in the evaluation of the constant in Clauser's inner layer formula. Numerical solutions of the compressible Navier-Stokes equations are used to determine the effects of the modifications. Experimental results from shock-induced separated flows at Mach numbers 2.93 and 8.45 are used for comparison. For these cases improved predictions of wall pressure distribution and positions of separation and reattachment are obtained from the relaxation version of the Clauser inner layer eddy viscosity formula.

  9. Phase shift of interacting algebraic solitary waves in a two-layer fluid system

    SciTech Connect

    Matsuno, Y. )

    1994-09-05

    The interaction of interfacial solitary waves of algebraic type is investigated on the basis of a higher-order Benjamin-Ono equation. By developing a multisoliton perturbation theory, we show analytically that the overtaking collision between two solitary waves exhibits the phase shift but the amplitudes are not altered after interaction. The prediction of the phase shift that takes place between algebraic solitary waves is the first example reported in the literature.

  10. Super-Lie n-algebra extensions, higher WZW models and super-p-branes with tensor multiplet fields

    NASA Astrophysics Data System (ADS)

    Fiorenza, Domenico; Sati, Hisham; Schreiber, Urs

    2015-12-01

    We formalize higher-dimensional and higher gauge WZW-type sigma-model local prequantum field theory, and discuss its rationalized/perturbative description in (super-)Lie n-algebra homotopy theory (the true home of the "FDA"-language used in the supergravity literature). We show generally how the intersection laws for such higher WZW-type σ-model branes (open brane ending on background brane) are encoded precisely in (super-)L∞-extension theory and how the resulting "extended (super-)space-times" formalize spacetimes containing σ-model brane condensates. As an application we prove in Lie n-algebra homotopy theory that the complete super-p-brane spectrum of superstring/M-theory is realized this way, including the pure σ-model branes (the "old brane scan") but also the branes with tensor multiplet worldvolume fields, notably the D-branes and the M5-brane. For instance the degree-0 piece of the higher symmetry algebra of 11-dimensional (11D) spacetime with an M2-brane condensate turns out to be the "M-theory super-Lie algebra". We also observe that in this formulation there is a simple formal proof of the fact that type IIA spacetime with a D0-brane condensate is the 11D sugra/M-theory spacetime, and of (prequantum) S-duality for type IIB string theory. Finally we give the non-perturbative description of all this by higher WZW-type σ-models on higher super-orbispaces with higher WZW terms in stacky differential cohomology.

  11. A Genetically Optimized Predictive System for Success in General Chemistry Using a Diagnostic Algebra Test

    NASA Astrophysics Data System (ADS)

    Cooper, Cameron I.; Pearson, Paul T.

    2012-02-01

    In higher education, many high-enrollment introductory courses have evolved into "gatekeeper" courses due to their high failure rates. These courses prevent many students from attaining their educational goals and often become graduation roadblocks. At the authors' home institution, general chemistry has become a gatekeeper course in which approximately 25% of students do not pass. This failure rate in chemistry is common, and often higher, at many other institutions of higher education, and mathematical deficiencies are perceived to be a large contributing factor. This paper details the development of a highly accurate predictive system that identifies students at the beginning of the semester who are "at-risk" for earning a grade of C- or below in chemistry. The predictive accuracy of this system is maximized by using a genetically optimized neural network to analyze the results of a diagnostic algebra test designed for a specific population. Once at-risk students have been identified, they can be helped to improve their chances of success using techniques such as concurrent support courses, online tutorials, "just-in-time" instructional aides, study skills, motivational interviewing, and/or peer mentoring.

  12. Geometry of Higgs bundles over elliptic curves related to automorphisms of simple Lie algebras, Calogero-Moser systems, and KZB equations

    NASA Astrophysics Data System (ADS)

    Levin, A. M.; Olshanetsky, M. A.; Zotov, A. V.

    2016-08-01

    We construct twisted Calogero-Moser systems with spins as Hitchin systems derived from the Higgs bundles over elliptic curves, where the transition operators are defined by arbitrary finite-order automorphisms of the underlying Lie algebras. We thus obtain a spin generalization of the twisted D'Hoker-Phong and Bordner-Corrigan-Sasaki-Takasaki systems. In addition, we construct the corresponding twisted classical dynamical r-matrices and the Knizhnik-Zamolodchikov-Bernard equations related to the automorphisms of Lie algebras.

  13. On some spurious mode issues in shallow-water models using a linear algebra approach

    NASA Astrophysics Data System (ADS)

    Le Roux, D. Y.; Sène, A.; Rostand, V.; Hanert, E.

    Numerical methods that are usually employed in ocean modelling are typically finite-difference, finite and spectral-element techniques. For most of these methods the coupling between the momentum and continuity equations is a delicate problem and it usually leads to spurious solutions in the representation of inertia-gravity waves. The spurious modes have a wide range of characteristics and may take the form of pressure (surface-elevation), velocity and/or Coriolis modes. The modes usually cause aliasing and an accumulation of energy in the smallest-resolvable scale, leading to noisy solutions. The Fourier analysis has proven practical and beneficial to describe the spurious solutions of several classical schemes. However it is restricted to uniform meshes on which the variables are regularly distributed. In this paper, a linear algebra approach is proposed to study the existence and the behaviour of stationary spurious modes associated with zero frequency, for some popular finite-difference and finite-element grids. The present approach is performed on uniform meshes but it applies equally well to regular as well as unstructured meshes with irregular geometry for the finite-element schemes.

  14. Topological phase entanglements of membrane solitons in division algebra sigma models with a Hopf term

    NASA Astrophysics Data System (ADS)

    Tze, Chia-Hsiung; Nam, Soonkeon

    1989-08-01

    Exploiting the unique connection between the division algebras of the complex numbers ( C), quaternions ( H), octonions ( Ω) and the essential Hopf maps S2 n - 1 → Sn with n = 2, 4, 8, we study Sn - 2 -membrane solitons in three D-dimensional KP(1) σ-models with a Hopf term, (D, K) = (3, C), (7, H), and (15, Ω). We present a comprehensive analysis of their topological phase entanglements. Extending Polyakov's approach to Fermi-Bose transmutations to higher dimensions, we detail a geometric regularization of Gauss' linking coefficient, its connections to the self-linking, twisting, writhing numbers of the Feynman paths of the solitons in their thin membrane limit. Alternative forms of the Hopf invariant show the latter as an Aharonov-Bohm-Berry phase of topologically massive, rank ( n - 1) antisymmetric tensor U(1) gauge fields coupled to the Sn - 2 -membranes. Via a K-bundle formulation of the dynamics of electrically and magnetically charged extended objects these phases are shown to induce a dyon-like structure on these membranes. We briefly discuss the connections to harmonic mappings, higher dimensional monopoles and instantons. We point out the relevance of the Gauss-Bonnet-Chern theorem on the connection between spin and statistics. By way of the topology of the infinite groups of sphere mappings Sn → Sn, n = 2, 4, 8, we also analyze the implications of the Hopf phases on the fractional spin and statistics of the membranes.

  15. Comparison of an algebraic multigrid algorithm to two iterative solvers used for modeling ground water flow and transport

    USGS Publications Warehouse

    Detwiler, R.L.; Mehl, S.; Rajaram, H.; Cheung, W.W.

    2002-01-01

    Numerical solution of large-scale ground water flow and transport problems is often constrained by the convergence behavior of the iterative solvers used to solve the resulting systems of equations. We demonstrate the ability of an algebraic multigrid algorithm (AMG) to efficiently solve the large, sparse systems of equations that result from computational models of ground water flow and transport in large and complex domains. Unlike geometric multigrid methods, this algorithm is applicable to problems in complex flow geometries, such as those encountered in pore-scale modeling of two-phase flow and transport. We integrated AMG into MODFLOW 2000 to compare two- and three-dimensional flow simulations using AMG to simulations using PCG2, a preconditioned conjugate gradient solver that uses the modified incomplete Cholesky preconditioner and is included with MODFLOW 2000. CPU times required for convergence with AMG were up to 140 times faster than those for PCG2. The cost of this increased speed was up to a nine-fold increase in required random access memory (RAM) for the three-dimensional problems and up to a four-fold increase in required RAM for the two-dimensional problems. We also compared two-dimensional numerical simulations of steady-state transport using AMG and the generalized minimum residual method with an incomplete LU-decomposition preconditioner. For these transport simulations, AMG yielded increased speeds of up to 17 times with only a 20% increase in required RAM. The ability of AMG to solve flow and transport problems in large, complex flow systems and its ready availability make it an ideal solver for use in both field-scale and pore-scale modeling.

  16. Adaptive control based on fast online algebraic identification and GPI control for magnetic levitation systems with time-varying input gain

    NASA Astrophysics Data System (ADS)

    Morales, R.; Sira-Ramírez, H.; Feliu, V.

    2014-08-01

    This paper considers the position tracking problem of a voltage-controlled magnetic levitation system (MLS) in the presence of modelling errors caused by uncertainties in the system's physical parameters. An adaptive control based on fast online algebraic parameter estimation and generalised proportional integral (GPI) output feedback control is considered as a control scheme candidate. The GPI controller guarantees an asymptotically exponentially stable behaviour of the controlled ball position and the possibilities of carrying out rest-to-rest trajectory tracking tasks. The nature of the control input gain in an MLS is that of a state-dependent time-varying gain, reflecting the nonlinear character of the magnetic force with regard to the distance and the properties of the metallic ball. The system gain has therefore been locally approximated using a periodically updated time polynomial function (of second degree), where the coefficients of the polynomial are estimated during a very short period of time. This estimation is achieved using the recently introduced algebraic online parameter estimation approach. The stability of the closed-loop system is demonstrated under the assumption that no external factors cause changes in the parameter during the time interval in which the stability is analysed. Finally, experimental results are presented for the controlled MLS demonstrating the excellent stabilisation and position tracking performance of the control system designed in the presence of significant nonlinearities and uncertainties of the underlying system.

  17. The explanation of the twin paradox using Poincare transformation and computer algebra system REDUCE

    NASA Astrophysics Data System (ADS)

    Hermanto, Arief

    2012-06-01

    We explain the twin (A and B) paradox using Poincare transformation (as the generalization of Lorentz transformation) in Special Relativity. We want to emphasize the fact that the paradox can really be explained in the context of Special Relativity. The twin A stays at home whereas B makes a round trip. We can still stay in Special Relativity if the non-inertial reference frame of B is in the form of a set of two inertial frames (K1 and K2) moving with different velocities with respect to a fixed inertial reference frame (K0) of A. K1 and K2 are each connected to K0 with Poincare Transformation. We use the CAS (computer algebra system) REDUCE to assist the computation. To make the discussion realistic and simpler we use rational numbers (so that we will get exact computational results) instead of symbols. The important point is that we will show how the fact can be understood by both parties (A and B) by simulating numerically the trip from the points of view of each A and B. A will accept the fact that B is younger and B will also accept the fact that A is older at the reunion. We hope the paradox will thus be explained away satisfactorily.

  18. Modelling and performance analysis of clinical pathways using the stochastic process algebra PEPA

    PubMed Central

    2012-01-01

    Background Hospitals nowadays have to serve numerous patients with limited medical staff and equipment while maintaining healthcare quality. Clinical pathway informatics is regarded as an efficient way to solve a series of hospital challenges. To date, conventional research lacks a mathematical model to describe clinical pathways. Existing vague descriptions cannot fully capture the complexities accurately in clinical pathways and hinders the effective management and further optimization of clinical pathways. Method Given this motivation, this paper presents a clinical pathway management platform, the Imperial Clinical Pathway Analyzer (ICPA). By extending the stochastic model performance evaluation process algebra (PEPA), ICPA introduces a clinical-pathway-specific model: clinical pathway PEPA (CPP). ICPA can simulate stochastic behaviours of a clinical pathway by extracting information from public clinical databases and other related documents using CPP. Thus, the performance of this clinical pathway, including its throughput, resource utilisation and passage time can be quantitatively analysed. Results A typical clinical pathway on stroke extracted from a UK hospital is used to illustrate the effectiveness of ICPA. Three application scenarios are tested using ICPA: 1) redundant resources are identified and removed, thus the number of patients being served is maintained with less cost; 2) the patient passage time is estimated, providing the likelihood that patients can leave hospital within a specific period; 3) the maximum number of input patients are found, helping hospitals to decide whether they can serve more patients with the existing resource allocation. Conclusions ICPA is an effective platform for clinical pathway management: 1) ICPA can describe a variety of components (state, activity, resource and constraints) in a clinical pathway, thus facilitating the proper understanding of complexities involved in it; 2) ICPA supports the performance analysis of

  19. On modification of certain methods of the conjugate direction type for solving rectangular systems of linear algebraic equations

    NASA Astrophysics Data System (ADS)

    Yukhno, L. F.

    2007-12-01

    The use of modifications of certain well-known methods of the conjugate direction type for solving systems of linear algebraic equations with rectangular matrices is examined. The modified methods are shown to be superior to the original versions with respect to the round-off accumulation; the advantage is especially large for ill-conditioned matrices. Examples are given of the efficient use of the modified methods for solving certain fairly large ill-conditioned problems.

  20. On modification of certain methods of the conjugate direction type for solving systems of linear algebraic equations

    NASA Astrophysics Data System (ADS)

    Yukhno, L. F.

    2007-11-01

    A modification of certain well-known methods of the conjugate direction type is proposed and examined. The modified methods are more stable with respect to the accumulation of round-off errors. Moreover, these methods are applicable for solving ill-conditioned systems of linear algebraic equations that, in particular, arise as approximations of ill-posed problems. Numerical results illustrating the advantages of the proposed modification are presented.

  1. Nonlinear Algebraic Reynolds Stress Model for Two-Phase Turbulent Flows Laden with Small Heavy Particles in Circular Tube

    NASA Astrophysics Data System (ADS)

    Mukin, R. V.; Alipchenkov, V. M.; Zaichik, L. I.; Mukina, L. S.; Strizhov, V. F.

    2011-12-01

    The purpose of the study is to present an explicit algebraic Reynolds stress (nonlinear turbulent viscosity) model combined with modified k - ɛ turbulence model taking into account particles effect on turbulence for calculating the main turbulent characteristics of two-phase flows. For calculating particles distribution in space we used diffusion-inertia model (DIM). The turbulence attenuating in the presence of particles is clearly observed, investigated and compared with the experimental data. The developed model adequately described turbulence anisotropy and the influence of particles inertia and concentration on the turbulence intensity.

  2. A new model for algebraic Rossby solitary waves in rotation fluid and its solution

    NASA Astrophysics Data System (ADS)

    Chen, Yao-Deng; Yang, Hong-Wei; Gao, Yu-Fang; Yin, Bao-Shu; Feng, Xing-Ru

    2015-09-01

    A generalized Boussinesq equation that includes the dissipation effect is derived to describe a kind of algebraic Rossby solitary waves in a rotating fluid by employing perturbation expansions and stretching transformations of time and space. Using this equation, the conservation laws of algebraic Rossby solitary waves are discussed. It is found that the mass, the momentum, the energy, and the velocity of center of gravity of the algebraic solitary waves are conserved in the propagation process. Finally, the analytical solution of the equation is generated. Based on the analytical solution, the properties of the algebraic solitary waves and the dissipation effect are discussed. The results point out that, similar to classic solitary waves, the dissipation can cause the amplitude and the speed of solitary waves to decrease; however, unlike classic solitary waves, the algebraic solitary waves can split during propagation and the decrease of the detuning parameter can accelerate the occurrence of the solitary waves fission phenomenon. Project supported by the Shandong Provincial Key Laboratory of Marine Ecology and Environment and Disaster Prevention and Mitigation Project, China (Grant No. 2012010), the National Natural Science Foundation of China (Grant Nos. 41205082 and 41476019), the Special Funds for Theoretical Physics of the National Natural Science Foundation of China (Grant No. 11447205), and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), China.

  3. Digital Maps, Matrices and Computer Algebra

    ERIC Educational Resources Information Center

    Knight, D. G.

    2005-01-01

    The way in which computer algebra systems, such as Maple, have made the study of complex problems accessible to undergraduate mathematicians with modest computational skills is illustrated by some large matrix calculations, which arise from representing the Earth's surface by digital elevation models. Such problems are often considered to lie in…

  4. NPN fuzzy sets and NPN qualitative algebra: a computational framework for bipolar cognitive modeling and multiagent decision analysis.

    PubMed

    Zhang, W R

    1996-01-01

    An NPN (Negative-Positive-Neutral) fuzzy set theory and an NPN qualitative algebra (Q-algebra) are proposed which form a computational framework for bipolar cognitive modeling and multiagent decision analysis. First a 6-valued NPN logic is introduced which extends the usual 4-valued Q-algebra (S, approximately , plus sign in circle,multiply sign in circle) and S={+,-,0,?} by adding one more level of specification; and then a real-valued NPN fuzzy logic is introduced which extends the 6-valued model to the real space { for all(x,y)|(x,y)in[-1,0]x[0,1]} and adds infinite levels of specifications, As a generalization, a fuzzy set theory is presented that allows beta-level fuzzy number-based NPN variables (x,y) to be substituted into (S, approximately , plus sign in circle,multiply sign in circle) where multiply sign in circle stands for any NPN T-norm; plus sign in circle stands for disjunction (V) or union ( union or logical sum), and beta is the number of alpha-cuts.

  5. Adaptive Algebraic Multigrid Methods

    SciTech Connect

    Brezina, M; Falgout, R; MacLachlan, S; Manteuffel, T; McCormick, S; Ruge, J

    2004-04-09

    Our ability to simulate physical processes numerically is constrained by our ability to solve the resulting linear systems, prompting substantial research into the development of multiscale iterative methods capable of solving these linear systems with an optimal amount of effort. Overcoming the limitations of geometric multigrid methods to simple geometries and differential equations, algebraic multigrid methods construct the multigrid hierarchy based only on the given matrix. While this allows for efficient black-box solution of the linear systems associated with discretizations of many elliptic differential equations, it also results in a lack of robustness due to assumptions made on the near-null spaces of these matrices. This paper introduces an extension to algebraic multigrid methods that removes the need to make such assumptions by utilizing an adaptive process. The principles which guide the adaptivity are highlighted, as well as their application to algebraic multigrid solution of certain symmetric positive-definite linear systems.

  6. Recursive boson system in the Cuntz algebra O{sub {infinity}}

    SciTech Connect

    Kawamura, Katsunori

    2007-09-15

    Bosons and fermions are often written by elements of other algebras. Abe (private communication) gave a realization of bosons by formal infinite sums of the canonical generators of the Cuntz algebra O{sub {infinity}}. We show that such formal infinite sum always makes sense on a certain dense subspace of any permutative representation of O{sub {infinity}}. In this meaning, we can regard as if the algebra B of bosons was a unital *-subalgebra of O{sub {infinity}} on a given permutative representation. According to this relation, we compute branching laws arising from restrictions of representations of O{sub {infinity}} on B. For example, it is shown that the Fock representation of B is given as the restriction of the standard representation of O{sub {infinity}} on B.

  7. Magnetic resonance Spectroscopy with Linear Algebraic Modeling (SLAM) for higher speed and sensitivity

    NASA Astrophysics Data System (ADS)

    Zhang, Yi; Gabr, Refaat E.; Schär, Michael; Weiss, Robert G.; Bottomley, Paul A.

    2012-05-01

    Speed and signal-to-noise ratio (SNR) are critical for localized magnetic resonance spectroscopy (MRS) of low-concentration metabolites. Matching voxels to anatomical compartments a priori yields better SNR than the spectra created by summing signals from constituent chemical-shift-imaging (CSI) voxels post-acquisition. Here, a new method of localized Spectroscopy using Linear Algebraic Modeling (SLAM) is presented, that can realize this additional SNR gain. Unlike prior methods, SLAM generates spectra from C signal-generating anatomic compartments utilizing a CSI sequence wherein essentially only the C central k-space phase-encoding gradient steps with highest SNR are retained. After MRI-based compartment segmentation, the spectra are reconstructed by solving a sub-set of linear simultaneous equations from the standard CSI algorithm. SLAM is demonstrated with one-dimensional CSI surface coil phosphorus MRS in phantoms, the human leg and the heart on a 3T clinical scanner. Its SNR performance, accuracy, sensitivity to registration errors and inhomogeneity, are evaluated. Compared to one-dimensional CSI, SLAM yielded quantitatively the same results 4-times faster in 24 cardiac patients and healthy subjects. SLAM is further extended with fractional phase-encoding gradients that optimize SNR and/or minimize both inter- and intra-compartmental contamination. In proactive cardiac phosphorus MRS of six healthy subjects, both SLAM and fractional-SLAM (fSLAM) produced results indistinguishable from CSI while preserving SNR gains of 36-45% in the same scan-time. Both SLAM and fSLAM are simple to implement and reduce the minimum scan-time for CSI, which otherwise limits the translation of higher SNR achievable at higher field strengths to faster scanning.

  8. The connection-set algebra--a novel formalism for the representation of connectivity structure in neuronal network models.

    PubMed

    Djurfeldt, Mikael

    2012-07-01

    The connection-set algebra (CSA) is a novel and general formalism for the description of connectivity in neuronal network models, from small-scale to large-scale structure. The algebra provides operators to form more complex sets of connections from simpler ones and also provides parameterization of such sets. CSA is expressive enough to describe a wide range of connection patterns, including multiple types of random and/or geometrically dependent connectivity, and can serve as a concise notation for network structure in scientific writing. CSA implementations allow for scalable and efficient representation of connectivity in parallel neuronal network simulators and could even allow for avoiding explicit representation of connections in computer memory. The expressiveness of CSA makes prototyping of network structure easy. A C+ + version of the algebra has been implemented and used in a large-scale neuronal network simulation (Djurfeldt et al., IBM J Res Dev 52(1/2):31-42, 2008b) and an implementation in Python has been publicly released.

  9. Constructing a Coherent Problem Model to Facilitate Algebra Problem Solving in a Chemistry Context

    ERIC Educational Resources Information Center

    Ngu, Bing Hiong; Yeung, Alexander Seeshing; Phan, Huy P.

    2015-01-01

    An experiment using a sample of 11th graders compared text editing and worked examples approaches in learning to solve dilution and molarity algebra word problems in a chemistry context. Text editing requires students to assess the structure of a word problem by specifying whether the problem text contains sufficient, missing, or irrelevant…

  10. Proposing and Testing a Model to Explain Traits of Algebra Preparedness

    ERIC Educational Resources Information Center

    Venenciano, Linda; Heck, Ronald

    2016-01-01

    Early experiences with theoretical thinking and generalization in measurement are hypothesized to develop constructs we name here as logical reasoning and preparedness for algebra. Based on work of V. V. Davydov (1975), the Measure Up (MU) elementary grades experimental mathematics curriculum uses quantities of area, length, volume, and mass to…

  11. Prospective Mathematics Teachers' Sense Making of Polynomial Multiplication and Factorization Modeled with Algebra Tiles

    ERIC Educational Resources Information Center

    Caglayan, Günhan

    2013-01-01

    This study is about prospective secondary mathematics teachers' understanding and sense making of representational quantities generated by algebra tiles, the quantitative units (linear vs. areal) inherent in the nature of these quantities, and the quantitative addition and multiplication operations--referent preserving versus referent…

  12. Developing Pre-Algebraic Thinking in Generalizing Repeating Pattern Using SOLO Model

    ERIC Educational Resources Information Center

    Lian, Lim Hooi; Yew, Wun Thiam

    2011-01-01

    In this paper, researchers discussed the application of the generalization perspective in helping the primary school pupils to develop their pre-algebraic thinking in generalizing repeating pattern. There are two main stages of the generalization perspective had been adapted, namely investigating and generalizing the pattern. Since the Biggs and…

  13. Examinations in the Final Year of Transition to Mathematical Methods Computer Algebra System (CAS)

    ERIC Educational Resources Information Center

    Leigh-Lancaster, David; Les, Magdalena; Evans, Michael

    2010-01-01

    2009 was the final year of parallel implementation for Mathematical Methods Units 3 and 4 and Mathematical Methods (CAS) Units 3 and 4. From 2006-2009 there was a common technology-free short answer examination that covered the same function, algebra, calculus and probability content for both studies with corresponding expectations for key…

  14. Comparison of different algebraic stress models in predicting temperature fluctuations and mean velocity in liquid-metals

    SciTech Connect

    de Lemos, M.J.S.

    1985-01-01

    The present work consists of a numerical investigation comparing three algebraic stress closures for turbulence in predicting the variance of temperature fluctuations and mean velocity for flow of mercury. The models of Ljuboja and Rodi, Sha and Launder, and Lemos and Sesonske are used, as they handle differently the modeling of the dissipation rate of temperature fluctuations, and several terms in the algebraic equations for the turbulent fluxes. A sensitivity analysis on some constants of the latter model is also presented. Pipe flow with constant wall heat flux were the geometry and boundary condition. The range for Re was from 30000 to 60000, and the buoyancy parameter Ra/Re/sup 2/ was varied from 10/sup -5/ to 10/sup -4/, where Ra is the Rayleigh number. The model of Lemos and Sesonske shows a substantial improvement in predicting temperature fluctuations, whereas predictions for the mean velocity show a weak dependence on the model used. Nevertheless, the model of Lemos and Sesonske gives results closer to available experimental data.

  15. Spatial-Operator Algebra For Robotic Manipulators

    NASA Technical Reports Server (NTRS)

    Rodriguez, Guillermo; Kreutz, Kenneth K.; Milman, Mark H.

    1991-01-01

    Report discusses spatial-operator algebra developed in recent studies of mathematical modeling, control, and design of trajectories of robotic manipulators. Provides succinct representation of mathematically complicated interactions among multiple joints and links of manipulator, thereby relieving analyst of most of tedium of detailed algebraic manipulations. Presents analytical formulation of spatial-operator algebra, describes some specific applications, summarizes current research, and discusses implementation of spatial-operator algebra in the Ada programming language.

  16. Multiple solution of linear algebraic systems by an iterative method with recomputed preconditioner in the analysis of microstrip structures

    NASA Astrophysics Data System (ADS)

    Ahunov, Roman R.; Kuksenko, Sergey P.; Gazizov, Talgat R.

    2016-06-01

    A multiple solution of linear algebraic systems with dense matrix by iterative methods is considered. To accelerate the process, the recomputing of the preconditioning matrix is used. A priory condition of the recomputing based on change of the arithmetic mean of the current solution time during the multiple solution is proposed. To confirm the effectiveness of the proposed approach, the numerical experiments using iterative methods BiCGStab and CGS for four different sets of matrices on two examples of microstrip structures are carried out. For solution of 100 linear systems the acceleration up to 1.6 times, compared to the approach without recomputing, is obtained.

  17. A differential algebraic approach for the modeling of polycrystalline ferromagnetic hysteresis with minor loops and frequency dependence

    NASA Astrophysics Data System (ADS)

    Wang, Dan; Wang, Linxiang; Melnik, Roderick

    2016-07-01

    In the current paper, a nonlinear differential algebraic approach is proposed for the modeling of hysteretic dynamics of polycrystalline ferromagnetic materials. The model is constructed by employing a phenomenological theory to the magnetization orientation switching. For the modeling of hysteresis in polycrystalline ferromagnetic materials, the single crystal model is applied to each magnetic domain along its own principal axis. The overall dynamics of the polycrystalline materials is obtained by taking a weighted combination of the dynamics of all magnetic domains. The weight function for the combination is taken as the distribution function of the principal axes. Numerical simulations are performed and comparisons with its experimental counterparts are presented. The hysteretic dynamics caused by orientation switching processes is accurately captured by the proposed model. Minor hysteresis loops associated with partial-amplitude loadings are also captured. Rate dependence of the hysteresis loops are inherently incorporated into the model due to its differential nature.

  18. Thinking Visually about Algebra

    ERIC Educational Resources Information Center

    Baroudi, Ziad

    2015-01-01

    Many introductions to algebra in high school begin with teaching students to generalise linear numerical patterns. This article argues that this approach needs to be changed so that students encounter variables in the context of modelling visual patterns so that the variables have a meaning. The article presents sample classroom activities,…

  19. The Effect of Scheduling Models for Introductory Algebra on 9th-Grade Students, Test Scores and Grades

    ERIC Educational Resources Information Center

    O'Hanlon, Angela L.

    2011-01-01

    The purpose of the study was to determine the effect of pacing and scheduling of algebra coursework on assigned 9th-grade students who traditionally would qualify for pre-algebra instruction and same course 9th-grade students who traditionally would qualify for standard algebra instruction. Students were selected based on completion of first-year…

  20. Genetic hotels for the standard genetic code: evolutionary analysis based upon novel three-dimensional algebraic models.

    PubMed

    José, Marco V; Morgado, Eberto R; Govezensky, Tzipe

    2011-07-01

    Herein, we rigorously develop novel 3-dimensional algebraic models called Genetic Hotels of the Standard Genetic Code (SGC). We start by considering the primeval RNA genetic code which consists of the 16 codons of type RNY (purine-any base-pyrimidine). Using simple algebraic operations, we show how the RNA code could have evolved toward the current SGC via two different intermediate evolutionary stages called Extended RNA code type I and II. By rotations or translations of the subset RNY, we arrive at the SGC via the former (type I) or via the latter (type II), respectively. Biologically, the Extended RNA code type I, consists of all codons of the type RNY plus codons obtained by considering the RNA code but in the second (NYR type) and third (YRN type) reading frames. The Extended RNA code type II, comprises all codons of the type RNY plus codons that arise from transversions of the RNA code in the first (YNY type) and third (RNR) nucleotide bases. Since the dimensions of remarkable subsets of the Genetic Hotels are not necessarily integer numbers, we also introduce the concept of algebraic fractal dimension. A general decoding function which maps each codon to its corresponding amino acid or the stop signals is also derived. The Phenotypic Hotel of amino acids is also illustrated. The proposed evolutionary paths are discussed in terms of the existing theories of the evolution of the SGC. The adoption of 3-dimensional models of the Genetic and Phenotypic Hotels will facilitate the understanding of the biological properties of the SGC.

  1. Middle School Math Acceleration and Equitable Access to Eighth-Grade Algebra: Evidence from the Wake County Public School System

    ERIC Educational Resources Information Center

    Dougherty, Shaun M.; Goodman, Joshua S.; Hill, Darryl V.; Litke, Erica G.; Page, Lindsay C.

    2015-01-01

    Taking algebra by eighth grade is considered an important milestone on the pathway to college readiness. We highlight a collaboration to investigate one district's effort to increase middle school algebra course-taking. In 2010, the Wake County Public Schools began assigning middle school students to accelerated math and eighth-grade algebra based…

  2. Multiple solution of systems of linear algebraic equations by an iterative method with the adaptive recalculation of the preconditioner

    NASA Astrophysics Data System (ADS)

    Akhunov, R. R.; Gazizov, T. R.; Kuksenko, S. P.

    2016-08-01

    The mean time needed to solve a series of systems of linear algebraic equations (SLAEs) as a function of the number of SLAEs is investigated. It is proved that this function has an extremum point. An algorithm for adaptively determining the time when the preconditioner matrix should be recalculated when a series of SLAEs is solved is developed. A numerical experiment with multiply solving a series of SLAEs using the proposed algorithm for computing 100 capacitance matrices with two different structures—microstrip when its thickness varies and a modal filter as the gap between the conductors varies—is carried out. The speedups turned out to be close to the optimal ones.

  3. Algebraic multigrid

    NASA Technical Reports Server (NTRS)

    Ruge, J. W.; Stueben, K.

    1987-01-01

    The state of the art in algebraic multgrid (AMG) methods is discussed. The interaction between the relaxation process and the coarse grid correction necessary for proper behavior of the solution probes is discussed in detail. Sufficient conditions on relaxation and interpolation for the convergence of the V-cycle are given. The relaxation used in AMG, what smoothing means in an algebraic setting, and how it relates to the existing theory are considered. Some properties of the coarse grid operator are discussed, and results on the convergence of two-level and multilevel convergence are given. Details of an algorithm particularly studied for problems obtained by discretizing a single elliptic, second order partial differential equation are given. Results of experiments with such problems using both finite difference and finite element discretizations are presented.

  4. Three-Dimensional Algebraic Models of the tRNA Code and 12 Graphs for Representing the Amino Acids.

    PubMed

    José, Marco V; Morgado, Eberto R; Guimarães, Romeu Cardoso; Zamudio, Gabriel S; de Farías, Sávio Torres; Bobadilla, Juan R; Sosa, Daniela

    2014-01-01

    Three-dimensional algebraic models, also called Genetic Hotels, are developed to represent the Standard Genetic Code, the Standard tRNA Code (S-tRNA-C), and the Human tRNA code (H-tRNA-C). New algebraic concepts are introduced to be able to describe these models, to wit, the generalization of the 2n-Klein Group and the concept of a subgroup coset with a tail. We found that the H-tRNA-C displayed broken symmetries in regard to the S-tRNA-C, which is highly symmetric. We also show that there are only 12 ways to represent each of the corresponding phenotypic graphs of amino acids. The averages of statistical centrality measures of the 12 graphs for each of the three codes are carried out and they are statistically compared. The phenotypic graphs of the S-tRNA-C display a common triangular prism of amino acids in 10 out of the 12 graphs, whilst the corresponding graphs for the H-tRNA-C display only two triangular prisms. The graphs exhibit disjoint clusters of amino acids when their polar requirement values are used. We contend that the S-tRNA-C is in a frozen-like state, whereas the H-tRNA-C may be in an evolving state. PMID:25370377

  5. Three-Dimensional Algebraic Models of the tRNA Code and 12 Graphs for Representing the Amino Acids

    PubMed Central

    José, Marco V.; Morgado, Eberto R.; Guimarães, Romeu Cardoso; Zamudio, Gabriel S.; de Farías, Sávio Torres; Bobadilla, Juan R.; Sosa, Daniela

    2014-01-01

    Three-dimensional algebraic models, also called Genetic Hotels, are developed to represent the Standard Genetic Code, the Standard tRNA Code (S-tRNA-C), and the Human tRNA code (H-tRNA-C). New algebraic concepts are introduced to be able to describe these models, to wit, the generalization of the 2n-Klein Group and the concept of a subgroup coset with a tail. We found that the H-tRNA-C displayed broken symmetries in regard to the S-tRNA-C, which is highly symmetric. We also show that there are only 12 ways to represent each of the corresponding phenotypic graphs of amino acids. The averages of statistical centrality measures of the 12 graphs for each of the three codes are carried out and they are statistically compared. The phenotypic graphs of the S-tRNA-C display a common triangular prism of amino acids in 10 out of the 12 graphs, whilst the corresponding graphs for the H-tRNA-C display only two triangular prisms. The graphs exhibit disjoint clusters of amino acids when their polar requirement values are used. We contend that the S-tRNA-C is in a frozen-like state, whereas the H-tRNA-C may be in an evolving state. PMID:25370377

  6. Three-Dimensional Algebraic Models of the tRNA Code and 12 Graphs for Representing the Amino Acids.

    PubMed

    José, Marco V; Morgado, Eberto R; Guimarães, Romeu Cardoso; Zamudio, Gabriel S; de Farías, Sávio Torres; Bobadilla, Juan R; Sosa, Daniela

    2014-08-11

    Three-dimensional algebraic models, also called Genetic Hotels, are developed to represent the Standard Genetic Code, the Standard tRNA Code (S-tRNA-C), and the Human tRNA code (H-tRNA-C). New algebraic concepts are introduced to be able to describe these models, to wit, the generalization of the 2n-Klein Group and the concept of a subgroup coset with a tail. We found that the H-tRNA-C displayed broken symmetries in regard to the S-tRNA-C, which is highly symmetric. We also show that there are only 12 ways to represent each of the corresponding phenotypic graphs of amino acids. The averages of statistical centrality measures of the 12 graphs for each of the three codes are carried out and they are statistically compared. The phenotypic graphs of the S-tRNA-C display a common triangular prism of amino acids in 10 out of the 12 graphs, whilst the corresponding graphs for the H-tRNA-C display only two triangular prisms. The graphs exhibit disjoint clusters of amino acids when their polar requirement values are used. We contend that the S-tRNA-C is in a frozen-like state, whereas the H-tRNA-C may be in an evolving state.

  7. Algebraic Bethe ansatz for the sℓ (2) Gaudin model with boundary

    NASA Astrophysics Data System (ADS)

    Cirilo António, N.; Manojlović, N.; Ragoucy, E.; Salom, I.

    2015-04-01

    Following Sklyanin's proposal in the periodic case, we derive the generating function of the Gaudin Hamiltonians with boundary terms. Our derivation is based on the quasi-classical expansion of the linear combination of the transfer matrix of the XXX Heisenberg spin chain and the central element, the so-called Sklyanin determinant. The corresponding Gaudin Hamiltonians with boundary terms are obtained as the residues of the generating function. By defining the appropriate Bethe vectors which yield strikingly simple off shell action of the generating function, we fully implement the algebraic Bethe ansatz, obtaining the spectrum of the generating function and the corresponding Bethe equations.

  8. Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz

    NASA Astrophysics Data System (ADS)

    Belliard, Samuel; Crampé, Nicolas

    2013-11-01

    We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes the usual form of a product of operators acting on a particular vector except that the number of operators is equal to the length of the chain. We prove this result for the chains with small length. We obtain also an off-shell equation (i.e. satisfied without the Bethe equations) formally similar to the ones obtained in the periodic case or with diagonal boundaries.

  9. A Deterministic Interfacial Cyclic Oxidation Spalling Model. Part 2; Algebraic Approximation, Descriptive Parameters, and Normalized Universal Curve

    NASA Technical Reports Server (NTRS)

    Smialek, James L.

    2002-01-01

    A cyclic oxidation interfacial spalling model has been developed in Part 1. The governing equations have been simplified here by substituting a new algebraic expression for the series (Good-Smialek approximation). This produced a direct relationship between cyclic oxidation weight change and model input parameters. It also allowed for the mathematical derivation of various descriptive parameters as a function of the inputs. It is shown that the maximum in weight change varies directly with the parabolic rate constant and cycle duration and inversely with the spall fraction, all to the 1/2 power. The number of cycles to reach maximum and zero weight change vary inversely with the spall fraction, and the ratio of these cycles is exactly 1:3 for most oxides. By suitably normalizing the weight change and cycle number, it is shown that all cyclic oxidation weight change model curves can be represented by one universal expression for a given oxide scale.

  10. Cellerator: extending a computer algebra system to include biochemical arrows for signal transduction simulations

    NASA Technical Reports Server (NTRS)

    Shapiro, Bruce E.; Levchenko, Andre; Meyerowitz, Elliot M.; Wold, Barbara J.; Mjolsness, Eric D.

    2003-01-01

    Cellerator describes single and multi-cellular signal transduction networks (STN) with a compact, optionally palette-driven, arrow-based notation to represent biochemical reactions and transcriptional activation. Multi-compartment systems are represented as graphs with STNs embedded in each node. Interactions include mass-action, enzymatic, allosteric and connectionist models. Reactions are translated into differential equations and can be solved numerically to generate predictive time courses or output as systems of equations that can be read by other programs. Cellerator simulations are fully extensible and portable to any operating system that supports Mathematica, and can be indefinitely nested within larger data structures to produce highly scaleable models.

  11. Twisted C⋆-algebra formulation of quantum cosmology with application to the Bianchi I model

    NASA Astrophysics Data System (ADS)

    Rosenbaum, Marcos; Vergara, J. David; Juárez, Román; Minzoni, A. A.

    2014-04-01

    A twisted C⋆-algebra of the extended (noncommutative) Heisenberg-Weyl group has been constructed which takes into account the uncertainty principle for coordinates in the Planck-length regime. This general construction is then used to generate an appropriate Hilbert space and observables for the noncommutative theory which, when applied to the Bianchi I cosmology, leads to a new set of equations that describe the quantum evolution of the Universe. We find that this formulation matches theories based on a reticular Heisenberg-Weyl algebra in the bouncing and expanding regions of a collapsing Bianchi universe. There is, however, an additional effect introduced by the dynamics generated by the noncommutativity. This is an oscillation in the spectrum of the volume operator of the Universe, within the bouncing region of the commutative theories. We show that this effect is generic and produced by the noncommutative momentum exchange between the degrees of freedom in the cosmology. We give asymptotic and numerical solutions which show the above mentioned effects of the noncommutativity.

  12. Computational algebraic geometry for statistical modeling FY09Q2 progress.

    SciTech Connect

    Thompson, David C.; Rojas, Joseph Maurice; Pebay, Philippe Pierre

    2009-03-01

    This is a progress report on polynomial system solving for statistical modeling. This is a progress report on polynomial system solving for statistical modeling. This quarter we have developed our first model of shock response data and an algorithm for identifying the chamber cone containing a polynomial system in n variables with n+k terms within polynomial time - a significant improvement over previous algorithms, all having exponential worst-case complexity. We have implemented and verified the chamber cone algorithm for n+3 and are working to extend the implementation to handle arbitrary k. Later sections of this report explain chamber cones in more detail; the next section provides an overview of the project and how the current progress fits into it.

  13. Static algebraic solitons in Korteweg-de Vries type systems and the Hirota transformation.

    PubMed

    Burde, G I

    2011-08-01

    Some effects in the soliton dynamics governed by higher-order Korteweg-de Vries (KdV) type equations are discussed. This is done based on the exact explicit solutions of the equations derived in the paper. It is shown that some higher order KdV equations possessing multisoliton solutions also admit steady state solutions in terms of algebraic functions describing localized patterns. Solutions including both those static patterns and propagating KdV-like solitons are combinations of algebraic and hyperbolic functions. It is shown that the localized structures behave like static solitons upon collisions with regular moving solitons, with their shape remaining unchanged after the collision and only the position shifted. These phenomena are not revealed in common multisoliton solutions derived using inverse scattering or Hirota's method. The solutions of the higher-order KdV type equations were obtained using a method devised for obtaining soliton solutions of nonlinear evolution equations. This method can be combined with Hirota's method with a modified representation of the solution which allows the results to be extended to multisoliton solutions. The prospects for applying the methods to soliton equations not of KdV type are discussed. PMID:21929136

  14. Coverings of topological semi-abelian algebras

    NASA Astrophysics Data System (ADS)

    Mucuk, Osman; Demir, Serap

    2016-08-01

    In this work, we study on a category of topological semi-abelian algebras which are topological models of given an algebraic theory T whose category of models is semi-abelian; and investigate some results on the coverings of topological models of such theories yielding semi-abelian categories. We also consider the internal groupoid structure in the semi-abelian category of T-algebras, and give a criteria for the lifting of internal groupoid structure to the covering groupoids.

  15. Algebraic trigonometry

    NASA Astrophysics Data System (ADS)

    Vaninsky, Alexander

    2011-04-01

    This article introduces a trigonometric field (TF) that extends the field of real numbers by adding two new elements: sin and cos - satisfying an axiom sin2 + cos2 = 1. It is shown that by assigning meaningful names to particular elements of the field, all known trigonometric identities may be introduced and proved. Two different interpretations of the TF are discussed with many others potentially possible. The main objective of this article is to introduce a broader view of trigonometry that can serve as motivation for mathematics students and teachers to study and teach abstract algebraic structures.

  16. Filiform Lie algebras of order 3

    SciTech Connect

    Navarro, R. M.

    2014-04-15

    The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e., filiform Lie (super)algebras, into the theory of Lie algebras of order F. Thus, the concept of filiform Lie algebras of order F is obtained. In particular, for F = 3 it has been proved that by using infinitesimal deformations of the associated model elementary Lie algebra it can be obtained families of filiform elementary lie algebras of order 3, analogously as that occurs into the theory of Lie algebras [M. Vergne, “Cohomologie des algèbres de Lie nilpotentes. Application à l’étude de la variété des algèbres de Lie nilpotentes,” Bull. Soc. Math. France 98, 81–116 (1970)]. Also we give the dimension, using an adaptation of the sl(2,C)-module Method, and a basis of such infinitesimal deformations in some generic cases.

  17. Hopf algebras of rooted forests, cocyles, and free Rota-Baxter algebras

    NASA Astrophysics Data System (ADS)

    Zhang, Tianjie; Gao, Xing; Guo, Li

    2016-10-01

    The Hopf algebra and the Rota-Baxter algebra are the two algebraic structures underlying the algebraic approach of Connes and Kreimer to renormalization of perturbative quantum field theory. In particular, the Hopf algebra of rooted trees serves as the "baby model" of Feynman graphs in their approach and can be characterized by certain universal properties involving a Hochschild 1-cocycle. Decorated rooted trees have also been applied to study Feynman graphs. We will continue the study of universal properties of various spaces of decorated rooted trees with such a 1-cocycle, leading to the concept of a cocycle Hopf algebra. We further apply the universal properties to equip a free Rota-Baxter algebra with the structure of a cocycle Hopf algebra.

  18. Quantum algebra of N superspace

    SciTech Connect

    Hatcher, Nicolas; Restuccia, A.; Stephany, J.

    2007-08-15

    We identify the quantum algebra of position and momentum operators for a quantum system bearing an irreducible representation of the super Poincare algebra in the N>1 and D=4 superspace, both in the case where there are no central charges in the algebra, and when they are present. This algebra is noncommutative for the position operators. We use the properties of superprojectors acting on the superfields to construct explicit position and momentum operators satisfying the algebra. They act on the projected wave functions associated to the various supermultiplets with defined superspin present in the representation. We show that the quantum algebra associated to the massive superparticle appears in our construction and is described by a supermultiplet of superspin 0. This result generalizes the construction for D=4, N=1 reported recently. For the case N=2 with central charges, we present the equivalent results when the central charge and the mass are different. For the {kappa}-symmetric case when these quantities are equal, we discuss the reduction to the physical degrees of freedom of the corresponding superparticle and the construction of the associated quantum algebra.

  19. Modular properties of doubly extended N = 4 superconformal algebras and their connection to rational torus models (I)

    NASA Astrophysics Data System (ADS)

    Petersen, Jens Lyng; Taormina, Anne

    1991-05-01

    The doubly extended N = 4 superconformal algebra, which contains all conventional extended superconformal algebras, is analyzed when one of the central extensions is set to 1. The modular transformations of the characters are derived, the relation between the characters and those of the N = 2 minimal is clarified, and in the process it is shown how rather simple extensions of the algebra based on rational torus theories, give rise to finite dimensional representations of the modular group.

  20. An algebraic function operator expectation value based eigenstate determinations for quantum systems with one degree of freedom

    SciTech Connect

    Kalay, Berfin; Demiralp, Metin

    2015-12-31

    This proceedings paper aims to show the efficiency of an expectation value identity for a given algebraic function operator which is assumed to be depending pn only position operator. We show that this expectation value formula becomes enabled to determine the eigenstates of the quantum system Hamiltonian as long as it is autonomous and an appropriate basis set in position operator is used. This approach produces a denumerable infinite recursion which may be considered as revisited but at the same time generalized form of the recursions over the natural number powers of the position operator. The content of this short paper is devoted not only to the formulation of the new method but also to show that this novel approach is capable of catching the eigenvalues and eigenfunctions for Hydrogen-like systems, beyond that, it can give a hand to us to reveal the wavefunction structure. So it has also somehow a confirmative nature.

  1. Transformation of time dependence to linear algebra

    NASA Astrophysics Data System (ADS)

    Menšík, Miroslav

    2005-10-01

    Reduced density matrix and memory function in the Nakajima-Zwanzig equation are expanded in properly chosen basis of special functions. This trick completely transforms time dependence to linear algebra. Then, the master equation for memory function is constructed and expanded in the same basis functions. For the model of a simple harmonic oscillator it is shown that this trick introduces infinite partial summation of the memory function in the system-bath interaction.

  2. Hopf algebras and topological recursion

    NASA Astrophysics Data System (ADS)

    Esteves, João N.

    2015-11-01

    We consider a model for topological recursion based on the Hopf algebra of planar binary trees defined by Loday and Ronco (1998 Adv. Math. 139 293-309 We show that extending this Hopf algebra by identifying pairs of nearest neighbor leaves, and thus producing graphs with loops, we obtain the full recursion formula discovered by Eynard and Orantin (2007 Commun. Number Theory Phys. 1 347-452).

  3. A Non-Econometric Analysis with Algebraic Models to Forecast the Numbers of Newly Hired and Retirement of Public Primary School Teachers in Taiwan

    ERIC Educational Resources Information Center

    Lung-Hsing, Kuo; Hung-Jen, Yang; Ying-Wen, Lin; Shang-Ming, Su

    2011-01-01

    In recent years, the "street teachers" issue has caused social concern in Taiwan. This study estimates the retirement of and needs for newly hired and public primary school teachers in 2010 using an algebraic model from the paper by Husssar (1999). This recursive methodology predicts the number of newly hired public primary school teachers due to…

  4. The roles of prefrontal and posterior parietal cortex in algebra problem solving: a case of using cognitive modeling to inform neuroimaging data.

    PubMed

    Danker, Jared F; Anderson, John R

    2007-04-15

    In naturalistic algebra problem solving, the cognitive processes of representation and retrieval are typically confounded, in that transformations of the equations typically require retrieval of mathematical facts. Previous work using cognitive modeling has associated activity in the prefrontal cortex with the retrieval demands of algebra problems and activity in the posterior parietal cortex with the transformational demands of algebra problems, but these regions tend to behave similarly in response to task manipulations (Anderson, J.R., Qin, Y., Sohn, M.-H., Stenger, V.A., Carter, C.S., 2003. An information-processing model of the BOLD response in symbol manipulation tasks. Psychon. Bull. Rev. 10, 241-261; Qin, Y., Carter, C.S., Silk, E.M., Stenger, A., Fissell, K., Goode, A., Anderson, J.R., 2004. The change of brain activation patterns as children learn algebra equation solving. Proc. Natl. Acad. Sci. 101, 5686-5691). With this study we attempt to isolate activity in these two regions by using a multi-step algebra task in which transformation (parietal) is manipulated in the first step and retrieval (prefrontal) is manipulated in the second step. Counter to our initial predictions, both brain regions were differentially active during both steps. We designed two cognitive models, one encompassing our initial assumptions and one in which both processes were engaged during both steps. The first model provided a poor fit to the behavioral and neural data, while the second model fit both well. This simultaneously emphasizes the strong relationship between retrieval and representation in mathematical reasoning and demonstrates that cognitive modeling can serve as a useful tool for understanding task manipulations in neuroimaging experiments. PMID:17355908

  5. The roles of prefrontal and posterior parietal cortex in algebra problem solving: a case of using cognitive modeling to inform neuroimaging data.

    PubMed

    Danker, Jared F; Anderson, John R

    2007-04-15

    In naturalistic algebra problem solving, the cognitive processes of representation and retrieval are typically confounded, in that transformations of the equations typically require retrieval of mathematical facts. Previous work using cognitive modeling has associated activity in the prefrontal cortex with the retrieval demands of algebra problems and activity in the posterior parietal cortex with the transformational demands of algebra problems, but these regions tend to behave similarly in response to task manipulations (Anderson, J.R., Qin, Y., Sohn, M.-H., Stenger, V.A., Carter, C.S., 2003. An information-processing model of the BOLD response in symbol manipulation tasks. Psychon. Bull. Rev. 10, 241-261; Qin, Y., Carter, C.S., Silk, E.M., Stenger, A., Fissell, K., Goode, A., Anderson, J.R., 2004. The change of brain activation patterns as children learn algebra equation solving. Proc. Natl. Acad. Sci. 101, 5686-5691). With this study we attempt to isolate activity in these two regions by using a multi-step algebra task in which transformation (parietal) is manipulated in the first step and retrieval (prefrontal) is manipulated in the second step. Counter to our initial predictions, both brain regions were differentially active during both steps. We designed two cognitive models, one encompassing our initial assumptions and one in which both processes were engaged during both steps. The first model provided a poor fit to the behavioral and neural data, while the second model fit both well. This simultaneously emphasizes the strong relationship between retrieval and representation in mathematical reasoning and demonstrates that cognitive modeling can serve as a useful tool for understanding task manipulations in neuroimaging experiments.

  6. Algebraic Multigrid Benchmark

    SciTech Connect

    2013-05-06

    AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumps and an anisotropy in one part.

  7. Numerical continuation of solution at a singular point of high codimension for systems of nonlinear algebraic or transcendental equations

    NASA Astrophysics Data System (ADS)

    Krasnikov, S. D.; Kuznetsov, E. B.

    2016-09-01

    Numerical continuation of solution through certain singular points of the curve of the set of solutions to a system of nonlinear algebraic or transcendental equations with a parameter is considered. Bifurcation points of codimension two and three are investigated. Algorithms and computer programs are developed that implement the procedure of discrete parametric continuation of the solution and find all branches at simple bifurcation points of codimension two and three. Corresponding theorems are proved, and each algorithm is rigorously justified. A novel algorithm for the estimation of errors of tangential vectors at simple bifurcation points of a finite codimension m is proposed. The operation of the computer programs is demonstrated by test examples, which allows one to estimate their efficiency and confirm the theoretical results.

  8. Comparing the Impact of Traditional and Modeling College Algebra Courses on Student Performance in Survey of Calculus

    ERIC Educational Resources Information Center

    West, Jerry G.

    2013-01-01

    Students in higher education deserve opportunities to succeed and learning environments which maximize success. Mathematics courses can create a barrier for success for some students. College algebra is a course that serves as a gateway to required courses in many bachelor's degree programs. The content in college algebra should serve to…

  9. The smooth entropy formalism for von Neumann algebras

    NASA Astrophysics Data System (ADS)

    Berta, Mario; Furrer, Fabian; Scholz, Volkher B.

    2016-01-01

    We discuss information-theoretic concepts on infinite-dimensional quantum systems. In particular, we lift the smooth entropy formalism as introduced by Renner and collaborators for finite-dimensional systems to von Neumann algebras. For the smooth conditional min- and max-entropy, we recover similar characterizing properties and information-theoretic operational interpretations as in the finite-dimensional case. We generalize the entropic uncertainty relation with quantum side information of Tomamichel and Renner and discuss applications to quantum cryptography. In particular, we prove the possibility to perform privacy amplification and classical data compression with quantum side information modeled by a von Neumann algebra.

  10. The algebras of large N matrix mechanics

    SciTech Connect

    Halpern, M.B.; Schwartz, C.

    1999-09-16

    Extending early work, we formulate the large N matrix mechanics of general bosonic, fermionic and supersymmetric matrix models, including Matrix theory: The Hamiltonian framework of large N matrix mechanics provides a natural setting in which to study the algebras of the large N limit, including (reduced) Lie algebras, (reduced) supersymmetry algebras and free algebras. We find in particular a broad array of new free algebras which we call symmetric Cuntz algebras, interacting symmetric Cuntz algebras, symmetric Bose/Fermi/Cuntz algebras and symmetric Cuntz superalgebras, and we discuss the role of these algebras in solving the large N theory. Most important, the interacting Cuntz algebras are associated to a set of new (hidden!) local quantities which are generically conserved only at large N. A number of other new large N phenomena are also observed, including the intrinsic nonlocality of the (reduced) trace class operators of the theory and a closely related large N field identification phenomenon which is associated to another set (this time nonlocal) of new conserved quantities at large N.

  11. Bethe Ansatz and the Spectral Theory of Affine Lie algebra-Valued Connections II: The Non Simply-Laced Case

    NASA Astrophysics Data System (ADS)

    Masoero, Davide; Raimondo, Andrea; Valeri, Daniele

    2016-09-01

    We assess the ODE/IM correspondence for the quantum g -KdV model, for a non-simply laced Lie algebra g. This is done by studying a meromorphic connection with values in the Langlands dual algebra of the affine Lie algebra g^{(1)} , and constructing the relevant {Ψ} -system among subdominant solutions. We then use the {Ψ} -system to prove that the generalized spectral determinants satisfy the Bethe Ansatz equations of the quantum g -KdV model. We also consider generalized Airy functions for twisted Kac-Moody algebras and we construct new explicit solutions to the Bethe Ansatz equations. The paper is a continuation of our previous work on the ODE/IM correspondence for simply-laced Lie algebras.

  12. Similarity solutions for systems arising from an Aedes aegypti model

    NASA Astrophysics Data System (ADS)

    Freire, Igor Leite; Torrisi, Mariano

    2014-04-01

    In a recent paper a new model for the Aedes aegypti mosquito dispersal dynamics was proposed and its Lie point symmetries were investigated. According to the carried group classification, the maximal symmetry Lie algebra of the nonlinear cases is reached whenever the advection term vanishes. In this work we analyze the family of systems obtained when the wind effects on the proposed model are neglected. Wide new classes of solutions to the systems under consideration are obtained.

  13. Central charge and quasihole scaling dimensions from model wavefunctions: toward relating Jack wavefunctions to {\\cal W} -algebras

    NASA Astrophysics Data System (ADS)

    Bernevig, B. Andrei; Gurarie, Victor; Simon, Steven H.

    2009-06-01

    We present a general method for obtaining the central charge and the quasihole scaling dimension directly from ground-state and quasihole wavefunctions. Our method applies to wavefunctions satisfying specific clustering properties. We then use our method to examine the relation between Jack symmetric functions and certain {\\cal W} -algebras. We add substantially to the evidence that the (k, r) admissible Jack functions correspond to correlators of the conformal field theory {\\cal W}_k(k+1,k+r) by calculating the central charge and scaling dimensions of some of the fields in both cases and showing that they match. For the Jacks described by unitary {\\cal W} -models, the central charge and quasihole exponents match those previously obtained from analyzing the physics of the edge excitations. For the Jacks described by non-unitary {\\cal W} -models the central charge and quasihole scaling dimensions obtained from the wavefunctions differ from those obtained from the edge physics, which instead agree with the 'effective' central charge of the corresponding {\\cal W} -model.

  14. Matrix-algebra-based calculations of the time evolution of the binary spin-bath model for magnetization transfer.

    PubMed

    Müller, Dirk K; Pampel, André; Möller, Harald E

    2013-05-01

    Quantification of magnetization-transfer (MT) experiments are typically based on the assumption of the binary spin-bath model. This model allows for the extraction of up to six parameters (relative pool sizes, relaxation times, and exchange rate constants) for the characterization of macromolecules, which are coupled via exchange processes to the water in tissues. Here, an approach is presented for estimating MT parameters acquired with arbitrary saturation schemes and imaging pulse sequences. It uses matrix algebra to solve the Bloch-McConnell equations without unwarranted simplifications, such as assuming steady-state conditions for pulsed saturation schemes or neglecting imaging pulses. The algorithm achieves sufficient efficiency for voxel-by-voxel MT parameter estimations by using a polynomial interpolation technique. Simulations, as well as experiments in agar gels with continuous-wave and pulsed MT preparation, were performed for validation and for assessing approximations in previous modeling approaches. In vivo experiments in the normal human brain yielded results that were consistent with published data.

  15. Implementation of algebraic stress models in a general 3-D Navier-Stokes method (PAB3D)

    NASA Technical Reports Server (NTRS)

    Abdol-Hamid, Khaled S.

    1995-01-01

    A three-dimensional multiblock Navier-Stokes code, PAB3D, which was developed for propulsion integration and general aerodynamic analysis, has been used extensively by NASA Langley and other organizations to perform both internal (exhaust) and external flow analysis of complex aircraft configurations. This code was designed to solve the simplified Reynolds Averaged Navier-Stokes equations. A two-equation k-epsilon turbulence model has been used with considerable success, especially for attached flows. Accurate predicting of transonic shock wave location and pressure recovery in separated flow regions has been more difficult. Two algebraic Reynolds stress models (ASM) have been recently implemented in the code that greatly improved the code's ability to predict these difficult flow conditions. Good agreement with Direct Numerical Simulation (DNS) for a subsonic flat plate was achieved with ASM's developed by Shih, Zhu, and Lumley and Gatski and Speziale. Good predictions were also achieved at subsonic and transonic Mach numbers for shock location and trailing edge boattail pressure recovery on a single-engine afterbody/nozzle model.

  16. Classical and quantum Kummer shape algebras

    NASA Astrophysics Data System (ADS)

    Odzijewicz, A.; Wawreniuk, E.

    2016-07-01

    We study a family of integrable systems of nonlinearly coupled harmonic oscillators on the classical and quantum levels. We show that the integrability of these systems follows from their symmetry characterized by algebras, here called Kummer shape algebras. The resolution of identity for a wide class of reproducing kernels is found. A number of examples, illustrating this theory, are also presented.

  17. Investigation of quantum phase transitions in the spdf interacting boson model based on dual algebraic structures for the four-level pairing model

    NASA Astrophysics Data System (ADS)

    Jafarizadeh, M. A.; Jalili Majarshin, A.; Fouladi, N.; Ghapanvari, M.

    2016-09-01

    The building blocks of the interacting boson model (IBM) are associated with both s and d bosons for positive parity states. An extension of sd-IBM along these models to spdf-IBM can provide the appropriate framework to describe negative parity states. In this paper, a solvable extended transitional Hamiltonian based on the affine \\widehat{{SU}(1,1)} Lie algebra is proposed to describe low lying positive and negative parity states between the spherical and deformed gamma-unstable shape. Quantum phase transitions (QPTs) are investigated based on dual algebraic structures for the four-level pairing model. Numerical extraction to low-lying energy levels and transition rates within the control parameters of this evaluated Hamiltonian are presented for various N values. By reproducing the experimental results, the method based on the signatures of the phase transition, such as the expectation value of the boson number operators in the lowest excited states, are used to provide a better description of Ru isotopes in this transitional region.

  18. Linear algebra of the permutation invariant Crow-Kimura model of prebiotic evolution.

    PubMed

    Bratus, Alexander S; Novozhilov, Artem S; Semenov, Yuri S

    2014-10-01

    A particular case of the famous quasispecies model - the Crow-Kimura model with a permutation invariant fitness landscape - is investigated. Using the fact that the mutation matrix in the case of a permutation invariant fitness landscape has a special tridiagonal form, a change of the basis is suggested such that in the new coordinates a number of analytical results can be obtained. In particular, using the eigenvectors of the mutation matrix as the new basis, we show that the quasispecies distribution approaches a binomial one and give simple estimates for the speed of convergence. Another consequence of the suggested approach is a parametric solution to the system of equations determining the quasispecies. Using this parametric solution we show that our approach leads to exact asymptotic results in some cases, which are not covered by the existing methods. In particular, we are able to present not only the limit behavior of the leading eigenvalue (mean population fitness), but also the exact formulas for the limit quasispecies eigenvector for special cases. For instance, this eigenvector has a geometric distribution in the case of the classical single peaked fitness landscape. On the biological side, we propose a mathematical definition, based on the closeness of the quasispecies to the binomial distribution, which can be used as an operational definition of the notorious error threshold. Using this definition, we suggest two approximate formulas to estimate the critical mutation rate after which the quasispecies delocalization occurs. PMID:25149562

  19. Linear algebra of the permutation invariant Crow-Kimura model of prebiotic evolution.

    PubMed

    Bratus, Alexander S; Novozhilov, Artem S; Semenov, Yuri S

    2014-10-01

    A particular case of the famous quasispecies model - the Crow-Kimura model with a permutation invariant fitness landscape - is investigated. Using the fact that the mutation matrix in the case of a permutation invariant fitness landscape has a special tridiagonal form, a change of the basis is suggested such that in the new coordinates a number of analytical results can be obtained. In particular, using the eigenvectors of the mutation matrix as the new basis, we show that the quasispecies distribution approaches a binomial one and give simple estimates for the speed of convergence. Another consequence of the suggested approach is a parametric solution to the system of equations determining the quasispecies. Using this parametric solution we show that our approach leads to exact asymptotic results in some cases, which are not covered by the existing methods. In particular, we are able to present not only the limit behavior of the leading eigenvalue (mean population fitness), but also the exact formulas for the limit quasispecies eigenvector for special cases. For instance, this eigenvector has a geometric distribution in the case of the classical single peaked fitness landscape. On the biological side, we propose a mathematical definition, based on the closeness of the quasispecies to the binomial distribution, which can be used as an operational definition of the notorious error threshold. Using this definition, we suggest two approximate formulas to estimate the critical mutation rate after which the quasispecies delocalization occurs.

  20. Statecharts Via Process Algebra

    NASA Technical Reports Server (NTRS)

    Luttgen, Gerald; vonderBeeck, Michael; Cleaveland, Rance

    1999-01-01

    Statecharts is a visual language for specifying the behavior of reactive systems. The Language extends finite-state machines with concepts of hierarchy, concurrency, and priority. Despite its popularity as a design notation for embedded system, precisely defining its semantics has proved extremely challenging. In this paper, a simple process algebra, called Statecharts Process Language (SPL), is presented, which is expressive enough for encoding Statecharts in a structure-preserving and semantic preserving manner. It is establish that the behavioral relation bisimulation, when applied to SPL, preserves Statecharts semantics

  1. An algebraic model on the performance of a direct methanol fuel cell with consideration of methanol crossover

    NASA Astrophysics Data System (ADS)

    Yin, Ken-Ming

    An algebraic one-dimensional model on the membrane-electrode-assembly (MEA) of direct methanol fuel cell (DMFC) is proposed. Non-linear regression procedure was imposed on the model to retrieve important parameters: solid polymer electrolyte conductivity κ m, exchange current density of methanol electro-oxidation at anode catalyst surface i oM,ref, and mass diffusivity of methanol in aqueous phase within the porous electrode D a that correspond to the experimentally measured polarization curves. Although numerical iteration is required for a complete solution, the explicit relationships of methanol concentration, methanol crossover rate, oxygen concentration and cell discharge current density do provide a clear picture of the mass transport and electrochemical kinetics within the various porous media in the MEA. It is shown the cathode mixed potential induced by the parallel reactions of oxygen reduction and oxidation of crossover methanol elucidates the potential drop of the cathode and the decrease of the cell open circuit voltage (OCV). Methanol transport in the membrane is described by the diffusion, electro-osmosis, and pressure induced convection. Detailed accounts of the effects of anode methanol and cathode oxygen feed concentrations on the cell discharge performance are given with correlation to the physical structure and chemical compositions of the catalyst layers (CLs).

  2. Renormalization group flows and continual Lie algebras

    NASA Astrophysics Data System (ADS)

    Bakas, Ioannis

    2003-08-01

    We study the renormalization group flows of two-dimensional metrics in sigma models using the one-loop beta functions, and demonstrate that they provide a continual analogue of the Toda field equations in conformally flat coordinates. In this algebraic setting, the logarithm of the world-sheet length scale, t, is interpreted as Dynkin parameter on the root system of a novel continual Lie algebra, denoted by Script G(d/dt;1), with anti-symmetric Cartan kernel K(t,t') = delta'(t-t'); as such, it coincides with the Cartan matrix of the superalgebra sl(N|N+1) in the large-N limit. The resulting Toda field equation is a non-linear generalization of the heat equation, which is integrable in target space and shares the same dissipative properties in time, t. We provide the general solution of the renormalization group flows in terms of free fields, via Bäcklund transformations, and present some simple examples that illustrate the validity of their formal power series expansion in terms of algebraic data. We study in detail the sausage model that arises as geometric deformation of the O(3) sigma model, and give a new interpretation to its ultra-violet limit by gluing together two copies of Witten's two-dimensional black hole in the asymptotic region. We also provide some new solutions that describe the renormalization group flow of negatively curved spaces in different patches, which look like a cane in the infra-red region. Finally, we revisit the transition of a flat cone C/Zn to the plane, as another special solution, and note that tachyon condensation in closed string theory exhibits a hidden relation to the infinite dimensional algebra Script G(d/dt;1) in the regime of gravity. Its exponential growth holds the key for the construction of conserved currents and their systematic interpretation in string theory, but they still remain unknown.

  3. CULA: hybrid GPU accelerated linear algebra routines

    NASA Astrophysics Data System (ADS)

    Humphrey, John R.; Price, Daniel K.; Spagnoli, Kyle E.; Paolini, Aaron L.; Kelmelis, Eric J.

    2010-04-01

    The modern graphics processing unit (GPU) found in many standard personal computers is a highly parallel math processor capable of nearly 1 TFLOPS peak throughput at a cost similar to a high-end CPU and an excellent FLOPS/watt ratio. High-level linear algebra operations are computationally intense, often requiring O(N3) operations and would seem a natural fit for the processing power of the GPU. Our work is on CULA, a GPU accelerated implementation of linear algebra routines. We present results from factorizations such as LU decomposition, singular value decomposition and QR decomposition along with applications like system solution and least squares. The GPU execution model featured by NVIDIA GPUs based on CUDA demands very strong parallelism, requiring between hundreds and thousands of simultaneous operations to achieve high performance. Some constructs from linear algebra map extremely well to the GPU and others map poorly. CPUs, on the other hand, do well at smaller order parallelism and perform acceptably during low-parallelism code segments. Our work addresses this via hybrid a processing model, in which the CPU and GPU work simultaneously to produce results. In many cases, this is accomplished by allowing each platform to do the work it performs most naturally.

  4. I CAN Learn[R] Pre-Algebra and Algebra. What Works Clearinghouse Intervention Report

    ERIC Educational Resources Information Center

    What Works Clearinghouse, 2009

    2009-01-01

    The I CAN Learn[R] Education System is an interactive, self-paced, mastery-based software system that includes the I CAN Learn[R] Fundamentals of Math (5th-6th grade math) curriculum, the I CAN Learn[R] Pre-Algebra curriculum, and the I CAN Learn[R] Algebra curriculum. College algebra credit is also available to students in participating schools…

  5. A priori direct numerical simulation assessment of algebraic flame surface density models for turbulent premixed flames in the context of large eddy simulation

    NASA Astrophysics Data System (ADS)

    Chakraborty, Nilanjan; Klein, Markus

    2008-08-01

    Flame surface density (FSD) based reaction rate closure is one of the most important approaches in turbulent premixed flame modeling. The algebraic models for FSD based on power laws often require information about the fractal dimension D and the inner cut-off scale ηi. In the present study, two three-dimensional direct numerical simulation (DNS) databases for freely propagating statistically planar turbulent premixed flames are analyzed among which the flame in one case belongs to the corrugated flamelet (CF) regime, whereas the other falls well within the thin reaction zone (TRZ) regime. It is found that D for the flame in the TRZ regime is greater than the value obtained for the flame in the CF regime. For the flame within the TRZ regime, the fractal dimension is found to be 7/3, which is the same as D for a material surface in a turbulent environment. For the flame in the CF regime, ηi is found to scale with the Gibson scale, whereas ηi is found to scale with the Kolmogorov length scale for the flame in the TRZ regime. Based on these observations a new algebraic model for FSD is proposed, where D and ηi are expressed as functions of Karlovitz number. The performances of the new and existing algebraic models for FSD are compared with the corresponding values obtained from DNS databases.

  6. Difficulties in initial algebra learning in Indonesia

    NASA Astrophysics Data System (ADS)

    Jupri, Al; Drijvers, Paul; van den Heuvel-Panhuizen, Marja

    2014-12-01

    Within mathematics curricula, algebra has been widely recognized as one of the most difficult topics, which leads to learning difficulties worldwide. In Indonesia, algebra performance is an important issue. In the Trends in International Mathematics and Science Study (TIMSS) 2007, Indonesian students' achievement in the algebra domain was significantly below the average student performance in other Southeast Asian countries such as Thailand, Malaysia, and Singapore. This fact gave rise to this study which aims to investigate Indonesian students' difficulties in algebra. In order to do so, a literature study was carried out on students' difficulties in initial algebra. Next, an individual written test on algebra tasks was administered, followed by interviews. A sample of 51 grade VII Indonesian students worked the written test, and 37 of them were interviewed afterwards. Data analysis revealed that mathematization, i.e., the ability to translate back and forth between the world of the problem situation and the world of mathematics and to reorganize the mathematical system itself, constituted the most frequently observed difficulty in both the written test and the interview data. Other observed difficulties concerned understanding algebraic expressions, applying arithmetic operations in numerical and algebraic expressions, understanding the different meanings of the equal sign, and understanding variables. The consequences of these findings on both task design and further research in algebra education are discussed.

  7. Algebraic approximations for transcendental equations with applications in nanophysics

    NASA Astrophysics Data System (ADS)

    Barsan, Victor

    2015-09-01

    Using algebraic approximations of trigonometric or hyperbolic functions, a class of transcendental equations can be transformed in tractable, algebraic equations. Studying transcendental equations this way gives the eigenvalues of Sturm-Liouville problems associated to wave equation, mainly to Schroedinger equation; these algebraic approximations provide approximate analytical expressions for the energy of electrons and phonons in quantum wells, quantum dots (QDs) and quantum wires, in the frame of one-particle models of such systems. The advantage of this approach, compared to the numerical calculations, is that the final result preserves the functional dependence on the physical parameters of the problem. The errors of this method, situated between some few percentages and ?, are carefully analysed. Several applications, for quantum wells, QDs and quantum wires, are presented.

  8. Learning Algebra in a Computer Algebra Environment

    ERIC Educational Resources Information Center

    Drijvers, Paul

    2004-01-01

    This article summarises a doctoral thesis entitled "Learning algebra in a computer algebra environment, design research on the understanding of the concept of parameter" (Drijvers, 2003). It describes the research questions, the theoretical framework, the methodology and the results of the study. The focus of the study is on the understanding of…

  9. Reasoning about nondeterministic and concurrent actions: A process algebra approach

    SciTech Connect

    De Giacomo, G.; Chen, Xiao Jun

    1996-12-31

    In this paper, we study reasoning about actions following a model checking approach in contrast to the usual validity checking one. Specifically, we model a dynamic system as a transition graph which represents all the possible system evolutions in terms of state changes caused by actions. Such a transition graph is defined by means of a suitable process algebra associated with an explicit global store. To reason about system properties we introduce an extension of modal {mu}-calculus. This setting, although directly applicable only when complete information on the system is available, has several interesting features for reasoning about actions. On one hand, it inherits from the vast literature on process algebras tools for dealing with complex systems, treating suitably important aspects like parallelism, communications, interruptions, coordinations among agents. On the other hand, reasoning by model checking is typically much easier than more general logical services such as validity checking.

  10. Moving frames and prolongation algebras

    NASA Technical Reports Server (NTRS)

    Estabrook, F. B.

    1982-01-01

    Differential ideals generated by sets of 2-forms which can be written with constant coefficients in a canonical basis of 1-forms are considered. By setting up a Cartan-Ehresmann connection, in a fiber bundle over a base space in which the 2-forms live, one finds an incomplete Lie algebra of vector fields in the fields in the fibers. Conversely, given this algebra (a prolongation algebra), one can derive the differential ideal. The two constructs are thus dual, and analysis of either derives properties of both. Such systems arise in the classical differential geometry of moving frames. Examples of this are discussed, together with examples arising more recently: the Korteweg-de Vries and Harrison-Ernst systems.

  11. LETTER TO THE EDITOR: Exactly solvable quantum spin ladders associated with the orthogonal and symplectic Lie algebras

    NASA Astrophysics Data System (ADS)

    Batchelor, M. T.; de Gier, J.; Links, J.; Maslen, M.

    2000-03-01

    We extend the results of spin ladder models associated with the Lie algebras su (2n ) to the case of the orthogonal and symplectic algebras o (2n ), sp (2n ) where n is the number of legs for the system. Two classes of models are found whose symmetry, either orthogonal or symplectic, has an explicit n dependence. Integrability of these models is shown for an arbitrary coupling of XX -type rung interactions and applied magnetic field term.

  12. Elementary Algebra Connections to Precalculus

    ERIC Educational Resources Information Center

    Lopez-Boada, Roberto; Daire, Sandra Arguelles

    2013-01-01

    This article examines the attitudes of some precalculus students to solve trigonometric and logarithmic equations and systems using the concepts of elementary algebra. With the goal of enticing the students to search for and use connections among mathematical topics, they are asked to solve equations or systems specifically designed to allow…

  13. Algebraic theory of molecules

    NASA Technical Reports Server (NTRS)

    Iachello, Franco

    1995-01-01

    An algebraic formulation of quantum mechanics is presented. In this formulation, operators of interest are expanded onto elements of an algebra, G. For bound state problems in nu dimensions the algebra G is taken to be U(nu + 1). Applications to the structure of molecules are presented.

  14. Profiles of Algebraic Competence

    ERIC Educational Resources Information Center

    Humberstone, J.; Reeve, R.A.

    2008-01-01

    The algebraic competence of 72 12-year-old female students was examined to identify profiles of understanding reflecting different algebraic knowledge states. Beginning algebraic competence (mapping abilities: word-to-symbol and vice versa, classifying, and solving equations) was assessed. One week later, the nature of assistance required to map…

  15. Orientation in operator algebras

    PubMed Central

    Alfsen, Erik M.; Shultz, Frederic W.

    1998-01-01

    A concept of orientation is relevant for the passage from Jordan structure to associative structure in operator algebras. The research reported in this paper bridges the approach of Connes for von Neumann algebras and ourselves for C*-algebras in a general theory of orientation that is of geometric nature and is related to dynamics. PMID:9618457

  16. Developing Thinking in Algebra

    ERIC Educational Resources Information Center

    Mason, John; Graham, Alan; Johnson-Wilder, Sue

    2005-01-01

    This book is for people with an interest in algebra whether as a learner, or as a teacher, or perhaps as both. It is concerned with the "big ideas" of algebra and what it is to understand the process of thinking algebraically. The book has been structured according to a number of pedagogic principles that are exposed and discussed along the way,…

  17. Connecting Arithmetic to Algebra

    ERIC Educational Resources Information Center

    Darley, Joy W.; Leapard, Barbara B.

    2010-01-01

    Algebraic thinking is a top priority in mathematics classrooms today. Because elementary school teachers lay the groundwork to develop students' capacity to think algebraically, it is crucial for teachers to have a conceptual understanding of the connections between arithmetic and algebra and be confident in communicating these connections. Many…

  18. Algebraic Multigrid Benchmark

    2013-05-06

    AMG2013 is a parallel algebraic multigrid solver for linear systems arising from problems on unstructured grids. It has been derived directly from the Boomer AMG solver in the hypre library, a large linear solvers library that is being developed in the Center for Applied Scientific Computing (CASC) at LLNL. The driver provided in the benchmark can build various test problems. The default problem is a Laplace type problem on an unstructured domain with various jumpsmore » and an anisotropy in one part.« less

  19. A new algebra core for the minimal form' problem

    SciTech Connect

    Purtill, M.R. . Center for Communications Research); Oliveira, J.S.; Cook, G.O. Jr. )

    1991-12-20

    The demands of large-scale algebraic computation have led to the development of many new algorithms for manipulating algebraic objects in computer algebra systems. For instance, parallel versions of many important algorithms have been discovered. Simultaneously, more effective symbolic representations of algebraic objects have been sought. Also, while some clever techniques have been found for improving the speed of the algebraic simplification process, little attention has been given to the issue of restructuring expressions, or transforming them into minimal forms.'' By minimal form,'' we mean that form of an expression that involves a minimum number of operations. In a companion paper, we introduce some new algorithms that are very effective at finding minimal forms of expressions. These algorithms require algebraic and combinatorial machinery that is not readily available in most algebra systems. In this paper we describe a new algebra core that begins to provide the necessary capabilities.

  20. Generalized algebraic relation for predicting developing curved channel flow with a k-epsilon model of turbulence

    SciTech Connect

    Humphrey, J.A.C.; Pourahmadi, F.

    1981-06-01

    Using algebraic approximations for the Reynolds stress equations a general expression has been derived for C/sub ..mu../ in ..nu../sub t/ = C/sub ..mu../ k/sup 2//epsilon which accounts simultaneously for the effects of streamline curvature and pressure-strain in the flow, including wall-induced influences on the velocity fluctuations. The expression derived can be shown to encompass similar but more specific formulations proposed by Bradshaw, Rodi, and Leschziner and Rodi. The present formulation has been used in conjunction with k-epsilon model of turbulence to predict developing, two-dimensional, curved channel flows where both curvature and pressure-strain effects can be large. Minor modifications to include the influence of curvature on the length scale of the flow near the walls produces a significant improvement in the calculations. While, in general, predictions are in good agreement with experimental measurements of mildly and strongly curved flows, the model tends to overpredict the kinetic energy of turbulence in the inner-radius (convex) wall region. This is attributed to a breakdown of the assumption that u/sub i/u/sub j/k is a constant in the derivation of the general expression for C/sub ..mu../. Most of the experimental results suggest the presence of a weak cross-stream motion due to Taylor-Goertler vortices which cannot be resolved by the calculation scheme. Despite its limitations the present formulation provides a degree of generality not previously available in two-equation modeling of turbulent flows.

  1. Generalized algebraic relation for predicting developing curved channel flow with a k-epsilon model of turbulence

    SciTech Connect

    Humphrey, J.A.C.; Pourahmadi, F.

    1981-06-01

    Using algebraic approximations for the Reynolds stress equations a general expression has been derived for C/sub ..mu../ in ..nu../sub t/ = C/sub ..mu../ k/sup 2//epsilon which accounts simultaneously for the effects of streamline curvature and pressure-strain in the flow, including wall-induced influences on the velocity fluctuations. The expression derived can be shown to encompass smilar but more specific formulations proposed by Bradshaw, Rodi, and Leschziner and Rodi. The present formulation has been used in conjunction with a k-epsilon model of turbulence to predict developing, two-dimensional, curved channel flows where both curvature and pressure-strain effects can be large. Minor modifications to include the influence of curvature on the length scale of the flow near the walls produce a significant improvement in the calculations. While, in general, predictions are in good agreement with experimental measurements of mildly and strongly curved flows, the model tends to overpredict the kinetic energy of turbulence in the inner-radius (convex) wall region. This is attributed to a breakdown of the assumption that u/sub i/u/sub j//k is a constant in the derivation of the general expression for C/sub ..mu../. Most of the experimental results suggest the presence of a weak cross-stream motion due to Taylor-Goertler vortices which cannot be resolved by the calculation scheme. Despite its limitations the present formulation provides a degree of generality not previously available in two-equation modeling of turbulent flows.

  2. Algebraic multigrid preconditioning within parallel finite-element solvers for 3-D electromagnetic modelling problems in geophysics

    NASA Astrophysics Data System (ADS)

    Koldan, Jelena; Puzyrev, Vladimir; de la Puente, Josep; Houzeaux, Guillaume; Cela, José María

    2014-06-01

    We present an elaborate preconditioning scheme for Krylov subspace methods which has been developed to improve the performance and reduce the execution time of parallel node-based finite-element (FE) solvers for 3-D electromagnetic (EM) numerical modelling in exploration geophysics. This new preconditioner is based on algebraic multigrid (AMG) that uses different basic relaxation methods, such as Jacobi, symmetric successive over-relaxation (SSOR) and Gauss-Seidel, as smoothers and the wave front algorithm to create groups, which are used for a coarse-level generation. We have implemented and tested this new preconditioner within our parallel nodal FE solver for 3-D forward problems in EM induction geophysics. We have performed series of experiments for several models with different conductivity structures and characteristics to test the performance of our AMG preconditioning technique when combined with biconjugate gradient stabilized method. The results have shown that, the more challenging the problem is in terms of conductivity contrasts, ratio between the sizes of grid elements and/or frequency, the more benefit is obtained by using this preconditioner. Compared to other preconditioning schemes, such as diagonal, SSOR and truncated approximate inverse, the AMG preconditioner greatly improves the convergence of the iterative solver for all tested models. Also, when it comes to cases in which other preconditioners succeed to converge to a desired precision, AMG is able to considerably reduce the total execution time of the forward-problem code-up to an order of magnitude. Furthermore, the tests have confirmed that our AMG scheme ensures grid-independent rate of convergence, as well as improvement in convergence regardless of how big local mesh refinements are. In addition, AMG is designed to be a black-box preconditioner, which makes it easy to use and combine with different iterative methods. Finally, it has proved to be very practical and efficient in the

  3. Model approach for simulating the thermodynamic behavior of the MFTF cryogenic cooling systems - a status report

    SciTech Connect

    Sutton, S.B.; Stein, W.; Reitter, T.A.; Hindmarsh, A.C.

    1983-08-31

    A numerical model for calculating the thermodynamic behavior of the MFTF-B cryogenic cooling system is described. Nine component types are discussed with governing equations given. The algorithm for solving the coupled set of algebraic and ordinary differential equations is described. The model and its application to the MFTF-B cryogenic cooling system has not been possible due to lack of funding.

  4. A Theoretical Framework for Research in Algebra: Modification of Janvier's "Star" Model of Function Understanding.

    ERIC Educational Resources Information Center

    Bowman, Anita H.

    A pentagonal model, based on the star model of function understanding of C. Janvier (1987), is presented as a framework for the design and interpretation of research in the area of learning the concept of mathematical function. The five vertices of the pentagon correspond to five common representations of mathematical function: (1) graph; (2)…

  5. A non-linear algebraic model for the turbulent scalar fluxes

    SciTech Connect

    Younis, B.A.; Speziale, C.G.; Clark, T.T.

    1995-09-01

    The need for a new approach to modelling the scalar fluxes stems from the lack of realism in the performance of the simple gradient-transport models and the inadequacy of many of the assumptions underlying the more complicated scalar-flux transport closures. The problems with the simple gradient-transport closures are well known. In models of this type, the scalar fluxes are related to the mean scalar field via a scalar turbulent diffusivity. The purpose of this paper is to report on a novel approach to the modelling of the turbulent scalar fluxes (u{sub i}{theta}) which arise as a consequence of time averaging the transport equation for a mean scalar ({Theta}). The focus of this paper will be on the case where {Theta} is a `passive` scalar; the extension of this approach to cases involving buoyancy and compressibility will be briefly discussed. Models of this type fail badly in complex and strongly-buoyant flows.

  6. Algebraic function operator expectation value based quantum eigenstate determination: A case of twisted or bent Hamiltonian, or, a spatially univariate quantum system on a curved space

    SciTech Connect

    Baykara, N. A.

    2015-12-31

    Recent studies on quantum evolutionary problems in Demiralp’s group have arrived at a stage where the construction of an expectation value formula for a given algebraic function operator depending on only position operator becomes possible. It has also been shown that this formula turns into an algebraic recursion amongst some finite number of consecutive elements in a set of expectation values of an appropriately chosen basis set over the natural number powers of the position operator as long as the function under consideration and the system Hamiltonian are both autonomous. This recursion corresponds to a denumerable infinite number of algebraic equations whose solutions can or can not be obtained analytically. This idea is not completely original. There are many recursive relations amongst the expectation values of the natural number powers of position operator. However, those recursions may not be always efficient to get the system energy values and especially the eigenstate wavefunctions. The present approach is somehow improved and generalized form of those expansions. We focus on this issue for a specific system where the Hamiltonian is defined on the coordinate of a curved space instead of the Cartesian one.

  7. Asymptotic Identity in Min-Plus Algebra: A Report on CPNS

    PubMed Central

    Li, Ming; Zhao, Wei

    2012-01-01

    Network calculus is a theory initiated primarily in computer communication networks, especially in the aspect of real-time communications, where min-plus algebra plays a role. Cyber-physical networking systems (CPNSs) are recently developing fast and models in data flows as well as systems in CPNS are, accordingly, greatly desired. Though min-plus algebra may be a promising tool to linearize any node in CPNS as can be seen from its applications to the Internet computing, there are tough problems remaining unsolved in this regard. The identity in min-plus algebra is one problem we shall address. We shall point out the confusions about the conventional identity in the min-plus algebra and present an analytical expression of the asymptotic identity that may not cause confusions. PMID:21822446

  8. Asymptotic identity in min-plus algebra: a report on CPNS.

    PubMed

    Li, Ming; Zhao, Wei

    2012-01-01

    Network calculus is a theory initiated primarily in computer communication networks, especially in the aspect of real-time communications, where min-plus algebra plays a role. Cyber-physical networking systems (CPNSs) are recently developing fast and models in data flows as well as systems in CPNS are, accordingly, greatly desired. Though min-plus algebra may be a promising tool to linearize any node in CPNS as can be seen from its applications to the Internet computing, there are tough problems remaining unsolved in this regard. The identity in min-plus algebra is one problem we shall address. We shall point out the confusions about the conventional identity in the min-plus algebra and present an analytical expression of the asymptotic identity that may not cause confusions. PMID:21822446

  9. Asymptotic identity in min-plus algebra: a report on CPNS.

    PubMed

    Li, Ming; Zhao, Wei

    2012-01-01

    Network calculus is a theory initiated primarily in computer communication networks, especially in the aspect of real-time communications, where min-plus algebra plays a role. Cyber-physical networking systems (CPNSs) are recently developing fast and models in data flows as well as systems in CPNS are, accordingly, greatly desired. Though min-plus algebra may be a promising tool to linearize any node in CPNS as can be seen from its applications to the Internet computing, there are tough problems remaining unsolved in this regard. The identity in min-plus algebra is one problem we shall address. We shall point out the confusions about the conventional identity in the min-plus algebra and present an analytical expression of the asymptotic identity that may not cause confusions.

  10. Multifractal vector fields and stochastic Clifford algebra

    NASA Astrophysics Data System (ADS)

    Schertzer, Daniel; Tchiguirinskaia, Ioulia

    2015-12-01

    In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.

  11. Multifractal vector fields and stochastic Clifford algebra

    SciTech Connect

    Schertzer, Daniel Tchiguirinskaia, Ioulia

    2015-12-15

    In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.

  12. Multifractal vector fields and stochastic Clifford algebra.

    PubMed

    Schertzer, Daniel; Tchiguirinskaia, Ioulia

    2015-12-01

    In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality. PMID:26723166

  13. Multifractal vector fields and stochastic Clifford algebra.

    PubMed

    Schertzer, Daniel; Tchiguirinskaia, Ioulia

    2015-12-01

    In the mid 1980s, the development of multifractal concepts and techniques was an important breakthrough for complex system analysis and simulation, in particular, in turbulence and hydrology. Multifractals indeed aimed to track and simulate the scaling singularities of the underlying equations instead of relying on numerical, scale truncated simulations or on simplified conceptual models. However, this development has been rather limited to deal with scalar fields, whereas most of the fields of interest are vector-valued or even manifold-valued. We show in this paper that the combination of stable Lévy processes with Clifford algebra is a good candidate to bridge up the present gap between theory and applications. We show that it indeed defines a convenient framework to generate multifractal vector fields, possibly multifractal manifold-valued fields, based on a few fundamental and complementary properties of Lévy processes and Clifford algebra. In particular, the vector structure of these algebra is much more tractable than the manifold structure of symmetry groups while the Lévy stability grants a given statistical universality.

  14. Stirling System Modeling for Space Nuclear Power Systems

    NASA Technical Reports Server (NTRS)

    Lewandowski, Edward J.; Johnson, Paul K.

    2007-01-01

    A dynamic model of a high-power Stirling convertor has been developed for space nuclear power systems modeling. The model is based on the Component Test Power Convertor (CTPC), a 12.5-kWe free-piston Stirling convertor. The model includes the fluid heat source, the Stirling convertor, output power and heat rejection. The Stirling convertor model includes the Stirling cycle thermodynamics, heat flow, mechanical mass-spring damper systems, and the linear alternator. The model was validated against test data. Both nonlinear and linear versions of the model were developed. The linear version algebraically couples two separate linear dynamic models; one model of the Stirling cycle and one model of the thermal system, through the pressure factors. Future possible uses of the Stirling system dynamic model are discussed. A pair of commercially available 1-kWe Stirling convertors is being purchased by NASA Glenn Research Center. The specifications of those convertors may eventually be incorporated into the dynamic model and analysis compared to the convertor test data. Subsequent potential testing could include integrating the convertors into a pumped liquid metal hot-end interface. This test would provide more data for comparison to the dynamic model analysis.

  15. Stirling System Modeling for Space Nuclear Power Systems

    NASA Technical Reports Server (NTRS)

    Lewandowski, Edward J.; Johnson, Paul K.

    2008-01-01

    A dynamic model of a high-power Stirling convertor has been developed for space nuclear power systems modeling. The model is based on the Component Test Power Convertor (CTPC), a 12.5-kWe free-piston Stirling convertor. The model includes the fluid heat source, the Stirling convertor, output power, and heat rejection. The Stirling convertor model includes the Stirling cycle thermodynamics, heat flow, mechanical mass-spring damper systems, and the linear alternator. The model was validated against test data. Both nonlinear and linear versions of the model were developed. The linear version algebraically couples two separate linear dynamic models; one model of the Stirling cycle and one model of the thermal system, through the pressure factors. Future possible uses of the Stirling system dynamic model are discussed. A pair of commercially available 1-kWe Stirling convertors is being purchased by NASA Glenn Research Center. The specifications of those convertors may eventually be incorporated into the dynamic model and analysis compared to the convertor test data. Subsequent potential testing could include integrating the convertors into a pumped liquid metal hot-end interface. This test would provide more data for comparison to the dynamic model analysis.

  16. Computer algebra and operators

    NASA Technical Reports Server (NTRS)

    Fateman, Richard; Grossman, Robert

    1989-01-01

    The symbolic computation of operator expansions is discussed. Some of the capabilities that prove useful when performing computer algebra computations involving operators are considered. These capabilities may be broadly divided into three areas: the algebraic manipulation of expressions from the algebra generated by operators; the algebraic manipulation of the actions of the operators upon other mathematical objects; and the development of appropriate normal forms and simplification algorithms for operators and their actions. Brief descriptions are given of the computer algebra computations that arise when working with various operators and their actions.

  17. Algebraic Lattices in QFT Renormalization

    NASA Astrophysics Data System (ADS)

    Borinsky, Michael

    2016-07-01

    The structure of overlapping subdivergences, which appear in the perturbative expansions of quantum field theory, is analyzed using algebraic lattice theory. It is shown that for specific QFTs the sets of subdivergences of Feynman diagrams form algebraic lattices. This class of QFTs includes the standard model. In kinematic renormalization schemes, in which tadpole diagrams vanish, these lattices are semimodular. This implies that the Hopf algebra of Feynman diagrams is graded by the coradical degree or equivalently that every maximal forest has the same length in the scope of BPHZ renormalization. As an application of this framework, a formula for the counter terms in zero-dimensional QFT is given together with some examples of the enumeration of primitive or skeleton diagrams.

  18. Modelling, Simulation, Animation, and Real-Time Control (Mosart) for a Class of Electromechanical Systems: A System-Theoretic Approach

    ERIC Educational Resources Information Center

    Rodriguez, Armando A.; Metzger, Richard P.; Cifdaloz, Oguzhan; Dhirasakdanon, Thanate; Welfert, Bruno

    2004-01-01

    This paper describes an interactive modelling, simulation, animation, and real-time control (MoSART) environment for a class of 'cart-pendulum' electromechanical systems that may be used to enhance learning within differential equations and linear algebra classes. The environment is useful for conveying fundamental mathematical/systems concepts…

  19. Discrete Minimal Surface Algebras

    NASA Astrophysics Data System (ADS)

    Arnlind, Joakim; Hoppe, Jens

    2010-05-01

    We consider discrete minimal surface algebras (DMSA) as generalized noncommutative analogues of minimal surfaces in higher dimensional spheres. These algebras appear naturally in membrane theory, where sequences of their representations are used as a regularization. After showing that the defining relations of the algebra are consistent, and that one can compute a basis of the enveloping algebra, we give several explicit examples of DMSAs in terms of subsets of sln (any semi-simple Lie algebra providing a trivial example by itself). A special class of DMSAs are Yang-Mills algebras. The representation graph is introduced to study representations of DMSAs of dimension d ≤ 4, and properties of representations are related to properties of graphs. The representation graph of a tensor product is (generically) the Cartesian product of the corresponding graphs. We provide explicit examples of irreducible representations and, for coinciding eigenvalues, classify all the unitary representations of the corresponding algebras.

  20. SDG fermion-pair algebraic SO(12) and Sp(10) models and their boson realizations

    SciTech Connect

    Navatil, P.; Geyer, H.B.; Dobes, J.

    1995-11-01

    It is shown how the boson mapping formalism may be applied as a useful many-body tool to solve a fermion problem. This is done in the context of generalized Ginocchio models for which the authors introduce S-, D-, and G-pairs of fermions and subsequently construct the sdg-boson realizations of the generalized Dyson type. The constructed SO(12) and Sp(10) fermion models are solved beyond the explicit symmetry limits. Phase transitions to rotational structures are obtained also in situations where there is no underlying SU(3) symmetry. 34 refs., 5 figs., 2 tabs.

  1. Algebraic geometric methods for the stabilizability and reliability of multivariable and of multimode systems

    NASA Technical Reports Server (NTRS)

    Anderson, B. D. O.; Brockett, R. W.; Byrnes, C. I.; Ghosh, B. K.; Stevens, P. K.

    1983-01-01

    The extent to which feedback can alter the dynamic characteristics (e.g., instability, oscillations) of a control system, possibly operating in one or more modes (e.g., failure versus nonfailure of one or more components) is examined.

  2. Thermodynamics. [algebraic structure

    NASA Technical Reports Server (NTRS)

    Zeleznik, F. J.

    1976-01-01

    The fundamental structure of thermodynamics is purely algebraic, in the sense of atopological, and it is also independent of partitions, composite systems, the zeroth law, and entropy. The algebraic structure requires the notion of heat, but not the first law. It contains a precise definition of entropy and identifies it as a purely mathematical concept. It also permits the construction of an entropy function from heat measurements alone when appropriate conditions are satisfied. Topology is required only for a discussion of the continuity of thermodynamic properties, and then the weak topology is the relevant topology. The integrability of the differential form of the first law can be examined independently of Caratheodory's theorem and his inaccessibility axiom. Criteria are established by which one can determine when an integrating factor can be made intensive and the pseudopotential extensive and also an entropy. Finally, a realization of the first law is constructed which is suitable for all systems whether they are solids or fluids, whether they do or do not exhibit chemical reactions, and whether electromagnetic fields are or are not present.

  3. Shape Optimization for Navier-Stokes Equations with Algebraic Turbulence Model: Existence Analysis

    SciTech Connect

    Bulicek, Miroslav Haslinger, Jaroslav Malek, Josef Stebel, Jan

    2009-10-15

    We study a shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to an optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by a generalized stationary Navier-Stokes system with nontrivial mixed boundary conditions. In this paper we prove the existence of solutions both to the generalized Navier-Stokes system and to the shape optimization problem.

  4. Algebraic tools for dealing with the atomic shell model. I. Wavefunctions and integrals for hydrogen-like ions

    NASA Astrophysics Data System (ADS)

    Surzhykov, Andrey; Koval, Peter; Fritzsche, Stephan

    2005-01-01

    Today, the 'hydrogen atom model' is known to play its role not only in teaching the basic elements of quantum mechanics but also for building up effective theories in atomic and molecular physics, quantum optics, plasma physics, or even in the design of semiconductor devices. Therefore, the analytical as well as numerical solutions of the hydrogen-like ions are frequently required both, for analyzing experimental data and for carrying out quite advanced theoretical studies. In order to support a fast and consistent access to these (Coulomb-field) solutions, here we present the DIRAC program which has been developed originally for studying the properties and dynamical behavior of the (hydrogen-like) ions. In the present version, a set of MAPLE procedures is provided for the Coulomb wave and Green's functions by applying the (wave) equations from both, the nonrelativistic and relativistic theory. Apart from the interactive access to these functions, moreover, a number of radial integrals are also implemented in the DIRAC program which may help the user to construct transition amplitudes and cross sections as they occur frequently in the theory of ion-atom and ion-photon collisions. Program summaryTitle of program:DIRAC Catalogue number: ADUQ Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUQ Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions: None Computer for which the program is designed and has been tested: All computers with a license of the computer algebra package MAPLE [1] Program language used: Maple 8 and 9 No. of lines in distributed program, including test data, etc.:2186 No. of bytes in distributed program, including test data, etc.: 162 591 Distribution format: tar gzip file CPC Program Library subprograms required: None Nature of the physical problem: Analytical solutions of the hydrogen atom are widely used in very different fields of physics [2,3]. Despite of the rather simple structure

  5. Anatomically accurate high resolution modeling of human whole heart electromechanics: A strongly scalable algebraic multigrid solver method for nonlinear deformation

    PubMed Central

    Augustin, Christoph M.; Neic, Aurel; Liebmann, Manfred; Prassl, Anton J.; Niederer, Steven A.; Haase, Gundolf; Plank, Gernot

    2016-01-01

    Electromechanical (EM) models of the heart have been used successfully to study fundamental mechanisms underlying a heart beat in health and disease. However, in all modeling studies reported so far numerous simplifications were made in terms of representing biophysical details of cellular function and its heterogeneity, gross anatomy and tissue microstructure, as well as the bidirectional coupling between electrophysiology (EP) and tissue distension. One limiting factor is the employed spatial discretization methods which are not sufficiently flexible to accommodate complex geometries or resolve heterogeneities, but, even more importantly, the limited efficiency of the prevailing solver techniques which are not sufficiently scalable to deal with the incurring increase in degrees of freedom (DOF) when modeling cardiac electromechanics at high spatio-temporal resolution. This study reports on the development of a novel methodology for solving the nonlinear equation of finite elasticity using human whole organ models of cardiac electromechanics, discretized at a high para-cellular resolution. Three patient-specific, anatomically accurate, whole heart EM models were reconstructed from magnetic resonance (MR) scans at resolutions of 220 μm, 440 μm and 880 μm, yielding meshes of approximately 184.6, 24.4 and 3.7 million tetrahedral elements and 95.9, 13.2 and 2.1 million displacement DOF, respectively. The same mesh was used for discretizing the governing equations of both electrophysiology (EP) and nonlinear elasticity. A novel algebraic multigrid (AMG) preconditioner for an iterative Krylov solver was developed to deal with the resulting computational load. The AMG preconditioner was designed under the primary objective of achieving favorable strong scaling characteristics for both setup and solution runtimes, as this is key for exploiting current high performance computing hardware. Benchmark results using the 220 μm, 440 μm and 880 μm meshes demonstrate

  6. Anatomically accurate high resolution modeling of human whole heart electromechanics: A strongly scalable algebraic multigrid solver method for nonlinear deformation

    NASA Astrophysics Data System (ADS)

    Augustin, Christoph M.; Neic, Aurel; Liebmann, Manfred; Prassl, Anton J.; Niederer, Steven A.; Haase, Gundolf; Plank, Gernot

    2016-01-01

    Electromechanical (EM) models of the heart have been used successfully to study fundamental mechanisms underlying a heart beat in health and disease. However, in all modeling studies reported so far numerous simplifications were made in terms of representing biophysical details of cellular function and its heterogeneity, gross anatomy and tissue microstructure, as well as the bidirectional coupling between electrophysiology (EP) and tissue distension. One limiting factor is the employed spatial discretization methods which are not sufficiently flexible to accommodate complex geometries or resolve heterogeneities, but, even more importantly, the limited efficiency of the prevailing solver techniques which is not sufficiently scalable to deal with the incurring increase in degrees of freedom (DOF) when modeling cardiac electromechanics at high spatio-temporal resolution. This study reports on the development of a novel methodology for solving the nonlinear equation of finite elasticity using human whole organ models of cardiac electromechanics, discretized at a high para-cellular resolution. Three patient-specific, anatomically accurate, whole heart EM models were reconstructed from magnetic resonance (MR) scans at resolutions of 220 μm, 440 μm and 880 μm, yielding meshes of approximately 184.6, 24.4 and 3.7 million tetrahedral elements and 95.9, 13.2 and 2.1 million displacement DOF, respectively. The same mesh was used for discretizing the governing equations of both electrophysiology (EP) and nonlinear elasticity. A novel algebraic multigrid (AMG) preconditioner for an iterative Krylov solver was developed to deal with the resulting computational load. The AMG preconditioner was designed under the primary objective of achieving favorable strong scaling characteristics for both setup and solution runtimes, as this is key for exploiting current high performance computing hardware. Benchmark results using the 220 μm, 440 μm and 880 μm meshes demonstrate

  7. Putting the Modern in Algebra

    ERIC Educational Resources Information Center

    Bosse, Michael J.; Ries, Heather; Chandler, Kayla

    2012-01-01

    Secondary school mathematics teachers often need to answer the "Why do we do that?" question in such a way that avoids confusion and evokes student interest. Understanding the properties of number systems can provide an avenue to better grasp algebraic structures, which in turn builds students' conceptual knowledge of secondary mathematics. This…

  8. Exploring Algebraic Misconceptions with Technology

    ERIC Educational Resources Information Center

    Sakow, Matthew; Karaman, Ruveyda

    2015-01-01

    Many students struggle with algebra, from simplifying expressions to solving systems of equations. Students also have misconceptions about the meaning of variables. In response to the question "Can x + y + z ever equal x + p + z?" during a student interview, the student claimed, "Never . . . because p has to have a different value…

  9. Inequalities, Assessment and Computer Algebra

    ERIC Educational Resources Information Center

    Sangwin, Christopher J.

    2015-01-01

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

  10. Highly-accelerated quantitative 2D and 3D localized spectroscopy with linear algebraic modeling (SLAM) and sensitivity encoding

    PubMed Central

    Zhang, Yi; Gabr, Refaat E.; Zhou, Jinyuan; Weiss, Robert G.; Bottomley, Paul A.

    2013-01-01

    Noninvasive magnetic resonance spectroscopy (MRS) with chemical shift imaging (CSI) provides valuable metabolic information for research and clinical studies, but is often limited by long scan times. Recently, spectroscopy with linear algebraic modeling (SLAM) was shown to provide compartment-averaged spectra resolved in one spatial dimension with many-fold reductions in scan-time. This was achieved using a small subset of the CSI phase-encoding steps from central image k-space that maximized the signal-to-noise ratio. Here, SLAM is extended to two- and three-dimensions (2D, 3D). In addition, SLAM is combined with sensitivity-encoded (SENSE) parallel imaging techniques, enabling the replacement of even more CSI phase-encoding steps to further accelerate scan-speed. A modified SLAM reconstruction algorithm is introduced that significantly reduces the effects of signal nonuniformity within compartments. Finally, main-field inhomogeneity corrections are provided, analogous to CSI. These methods are all tested on brain proton MRS data from a total of 24 patients with brain tumors, and in a human cardiac phosphorus 3D SLAM study at 3T. Acceleration factors of up to 120-fold versus CSI are demonstrated, including speed-up factors of 5-fold relative to already-accelerated SENSE CSI. Brain metabolites are quantified in SLAM and SENSE SLAM spectra and found to be indistinguishable from CSI measures from the same compartments. The modified reconstruction algorithm demonstrated immunity to maladjusted segmentation and errors from signal heterogeneity in brain data. In conclusion, SLAM demonstrates the potential to supplant CSI in studies requiring compartment-average spectra or large volume coverage, by dramatically reducing scan-time while providing essentially the same quantitative results. PMID:24188921

  11. Highly-accelerated quantitative 2D and 3D localized spectroscopy with linear algebraic modeling (SLAM) and sensitivity encoding

    NASA Astrophysics Data System (ADS)

    Zhang, Yi; Gabr, Refaat E.; Zhou, Jinyuan; Weiss, Robert G.; Bottomley, Paul A.

    2013-12-01

    Noninvasive magnetic resonance spectroscopy (MRS) with chemical shift imaging (CSI) provides valuable metabolic information for research and clinical studies, but is often limited by long scan times. Recently, spectroscopy with linear algebraic modeling (SLAM) was shown to provide compartment-averaged spectra resolved in one spatial dimension with many-fold reductions in scan-time. This was achieved using a small subset of the CSI phase-encoding steps from central image k-space that maximized the signal-to-noise ratio. Here, SLAM is extended to two- and three-dimensions (2D, 3D). In addition, SLAM is combined with sensitivity-encoded (SENSE) parallel imaging techniques, enabling the replacement of even more CSI phase-encoding steps to further accelerate scan-speed. A modified SLAM reconstruction algorithm is introduced that significantly reduces the effects of signal nonuniformity within compartments. Finally, main-field inhomogeneity corrections are provided, analogous to CSI. These methods are all tested on brain proton MRS data from a total of 24 patients with brain tumors, and in a human cardiac phosphorus 3D SLAM study at 3T. Acceleration factors of up to 120-fold versus CSI are demonstrated, including speed-up factors of 5-fold relative to already-accelerated SENSE CSI. Brain metabolites are quantified in SLAM and SENSE SLAM spectra and found to be indistinguishable from CSI measures from the same compartments. The modified reconstruction algorithm demonstrated immunity to maladjusted segmentation and errors from signal heterogeneity in brain data. In conclusion, SLAM demonstrates the potential to supplant CSI in studies requiring compartment-average spectra or large volume coverage, by dramatically reducing scan-time while providing essentially the same quantitative results.

  12. Tests of Predictions of the Algebraic Cluster Model: the Triangular D 3h Symmetry of 12C

    NASA Astrophysics Data System (ADS)

    Gai, Moshe

    2016-07-01

    A new theoretical approach to clustering in the frame of the Algebraic Cluster Model (ACM) has been developed. It predicts rotation-vibration structure with rotational band of an oblate equilateral triangular symmetric spinning top with a D 3h symmetry characterized by the sequence of states: 0+, 2+, 3-, 4±, 5- with a degenerate 4+ and 4- (parity doublet) states. Our measured new 2+ 2 in 12C allows the first study of rotation-vibration structure in 12C. The newly measured 5- state and 4- states fit very well the predicted ground state rotational band structure with the predicted sequence of states: 0+, 2+, 3-, 4±, 5- with almost degenerate 4+ and 4- (parity doublet) states. Such a D 3h symmetry is characteristic of triatomic molecules, but it is observed in the ground state rotational band of 12C for the first time in a nucleus. We discuss predictions of the ACM of other rotation-vibration bands in 12 C such as the (0+) Hoyle band and the (1-) bending mode with prediction of (“missing 3- and 4-”) states that may shed new light on clustering in 12C and light nuclei. In particular, the observation (or non observation) of the predicted (“missing”) states in the Hoyle band will allow us to conclude the geometrical arrangement of the three alpha particles composing the Hoyle state at 7.6542 MeV in 12C. We discuss proposed research programs at the Darmstadt S-DALINAC and at the newly constructed ELI-NP facility near Bucharest to test the predictions of the ACM in isotopes of carbon.

  13. Computer subroutine ISUDS accurately solves large system of simultaneous linear algebraic equations

    NASA Technical Reports Server (NTRS)

    Collier, G.

    1967-01-01

    Computer program, an Iterative Scheme Using a Direct Solution, obtains double precision accuracy using a single-precision coefficient matrix. ISUDS solves a system of equations written in matrix form as AX equals B, where A is a square non-singular coefficient matrix, X is a vector, and B is a vector.

  14. The Effects of Female Mathematician Role Models on Eighth- and Ninth-Grade First-Year Algebra Students.

    ERIC Educational Resources Information Center

    O'Brien, Judith A.; Tracy, Dyanne M.

    In the United States female and male students supposedly have the same educational opportunities. Females continue to score below male students on the mathematics portions of standardized tests and less frequently choose mathematics-oriented careers. In this experimental study (n=95), 47 first-year algebra students participated in a month-long…

  15. Effectiveness of the Mind Research Institute's Algebra Readiness Curriculum on Student Achievement Implemented in a Tiered Response to Intervention Model

    ERIC Educational Resources Information Center

    Quick, Nancy

    2013-01-01

    Algebra is typically the gatekeeper for higher-level math coursework. Low math performance on standardized assessments impedes access to these higher-level math classes. Limited math progress in high school affects future career opportunities and quality of life. High school students who have historically struggled with math need interventions…

  16. Shape Optimization for Navier-Stokes Equations with Algebraic Turbulence Model: Numerical Analysis and Computation

    SciTech Connect

    Haslinger, Jaroslav; Stebel, Jan

    2011-04-15

    We study the shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. The aim is to find a shape which a priori ensures the given velocity profile on the outlet part. The mathematical formulation leads to the optimal control problem in which the control variable is the shape of the domain representing the header, the state problem is represented by the generalized Navier-Stokes system with nontrivial boundary conditions. This paper deals with numerical aspects of the problem.

  17. Heterogenous Acceleration for Linear Algebra in Multi-coprocessor Environments

    SciTech Connect

    Luszczek, Piotr R; Tomov, Stanimire Z; Dongarra, Jack J

    2015-01-01

    We present an efficient and scalable programming model for the development of linear algebra in heterogeneous multi-coprocessor environments. The model incorporates some of the current best design and implementation practices for the heterogeneous acceleration of dense linear algebra (DLA). Examples are given as the basis for solving linear systems' algorithms - the LU, QR, and Cholesky factorizations. To generate the extreme level of parallelism needed for the efficient use of coprocessors, algorithms of interest are redesigned and then split into well-chosen computational tasks. The tasks execution is scheduled over the computational components of a hybrid system of multi-core CPUs and coprocessors using a light-weight runtime system. The use of lightweight runtime systems keeps scheduling overhead low, while enabling the expression of parallelism through otherwise sequential code. This simplifies the development efforts and allows the exploration of the unique strengths of the various hardware components.

  18. Using PROC GLIMMIX to Analyze the Animal Watch, a Web-Based Tutoring System for Algebra Readiness

    ERIC Educational Resources Information Center

    Barbu, Otilia C.

    2012-01-01

    In this study, I investigated how proficiently seventh-grade students enrolled in two Southwestern schools solve algebra word problems. I analyzed various factors that could affect this proficiency and explored the differences between English Learners (ELs) and native English Primary students (EPs). I collected the data as part of the Animal Watch…

  19. Accuracy requirements of optical linear algebra processors in adaptive optics imaging systems.

    PubMed

    Downie, J D; Goodman, J W

    1989-10-15

    A ground-based adaptive optics imaging telescope system attempts to improve image quality by measuring and correcting for atmospherically induced wavefront aberrations. The necessary control computations during each cycle will take a finite amount of time, which adds to the residual error variance since the atmosphere continues to change during that time. Thus an optical processor may be well-suited for this task. This paper investigates this possibility by studying the accuracy requirements in a general optical processor that will make it competitive with, or superior to, a conventional digital computer for adaptive optics use.

  20. Structure of classical affine and classical affine fractional W-algebras

    SciTech Connect

    Suh, Uhi Rinn

    2015-01-15

    We introduce a classical BRST complex (See Definition 3.2.) and show that one can construct a classical affine W-algebra via the complex. This definition clarifies that classical affine W-algebras can be considered as quasi-classical limits of quantum affine W-algebras. We also give a definition of a classical affine fractional W-algebra as a Poisson vertex algebra. As in the classical affine case, a classical affine fractional W-algebra has two compatible λ-brackets and is isomorphic to an algebra of differential polynomials as a differential algebra. When a classical affine fractional W-algebra is associated to a minimal nilpotent, we describe explicit forms of free generators and compute λ-brackets between them. Provided some assumptions on a classical affine fractional W-algebra, we find an infinite sequence of integrable systems related to the algebra, using the generalized Drinfel’d and Sokolov reduction.

  1. A Richer Understanding of Algebra

    ERIC Educational Resources Information Center

    Foy, Michelle

    2008-01-01

    Algebra is one of those hard-to-teach topics where pupils seem to struggle to see it as more than a set of rules to learn, but this author recently used the software "Grid Algebra" from ATM, which engaged her Year 7 pupils in exploring algebraic concepts for themselves. "Grid Algebra" allows pupils to experience number, pre-algebra, and algebra…

  2. Accuracy requirements of optical linear algebra processors in adaptive optics imaging systems

    NASA Technical Reports Server (NTRS)

    Downie, John D.

    1990-01-01

    A ground-based adaptive optics imaging telescope system attempts to improve image quality by detecting and correcting for atmospherically induced wavefront aberrations. The required control computations during each cycle will take a finite amount of time. Longer time delays result in larger values of residual wavefront error variance since the atmosphere continues to change during that time. Thus an optical processor may be well-suited for this task. This paper presents a study of the accuracy requirements in a general optical processor that will make it competitive with, or superior to, a conventional digital computer for the adaptive optics application. An optimization of the adaptive optics correction algorithm with respect to an optical processor's degree of accuracy is also briefly discussed.

  3. Connecting Algebra and Chemistry.

    ERIC Educational Resources Information Center

    O'Connor, Sean

    2003-01-01

    Correlates high school chemistry curriculum with high school algebra curriculum and makes the case for an integrated approach to mathematics and science instruction. Focuses on process integration. (DDR)

  4. Accelerating sparse linear algebra using graphics processing units

    NASA Astrophysics Data System (ADS)

    Spagnoli, Kyle E.; Humphrey, John R.; Price, Daniel K.; Kelmelis, Eric J.

    2011-06-01

    The modern graphics processing unit (GPU) found in many standard personal computers is a highly parallel math processor capable of over 1 TFLOPS of peak computational throughput at a cost similar to a high-end CPU with excellent FLOPS-to-watt ratio. High-level sparse linear algebra operations are computationally intense, often requiring large amounts of parallel operations and would seem a natural fit for the processing power of the GPU. Our work is on a GPU accelerated implementation of sparse linear algebra routines. We present results from both direct and iterative sparse system solvers. The GPU execution model featured by NVIDIA GPUs based on CUDA demands very strong parallelism, requiring between hundreds and thousands of simultaneous operations to achieve high performance. Some constructs from linear algebra map extremely well to the GPU and others map poorly. CPUs, on the other hand, do well at smaller order parallelism and perform acceptably during low-parallelism code segments. Our work addresses this via hybrid a processing model, in which the CPU and GPU work simultaneously to produce results. In many cases, this is accomplished by allowing each platform to do the work it performs most naturally. For example, the CPU is responsible for graph theory portion of the direct solvers while the GPU simultaneously performs the low level linear algebra routines.

  5. Z 2-graded classical r-matrices and algebraic Bethe ansatz: applications to integrable models of quantum optics and nuclear physics

    NASA Astrophysics Data System (ADS)

    Skrypnyk, T.

    2016-09-01

    We consider quantum integrable models based on the Lie algebra gl(n) and non-skew-symmetric classical r-matrices associated with Z 2-gradings of gl(n) of the following type: {gl}(n)={gl}{(n)}\\bar{0}+{gl}{(n)}\\bar{1}, where {gl}{(n)}\\bar{0}={gl}({n}1)\\oplus {gl}(n-{n}1). Among the considered models are Gaudin-type models with an external magnetic field, used in nuclear physics to produce proton–neutron Bardeen–Cooper–Schrieer-type models, n-level many-mode Jaynes–Cummings–Dicke-type models of quantum optics, matrix generalization of Bose–Hubbard dimers, etc. We diagonalize the constructed models by means of the ‘generalized’ nested Bethe ansatz.

  6. Z 2-graded classical r-matrices and algebraic Bethe ansatz: applications to integrable models of quantum optics and nuclear physics

    NASA Astrophysics Data System (ADS)

    Skrypnyk, T.

    2016-09-01

    We consider quantum integrable models based on the Lie algebra gl(n) and non-skew-symmetric classical r-matrices associated with Z 2-gradings of gl(n) of the following type: {gl}(n)={gl}{(n)}\\bar{0}+{gl}{(n)}\\bar{1}, where {gl}{(n)}\\bar{0}={gl}({n}1)\\oplus {gl}(n-{n}1). Among the considered models are Gaudin-type models with an external magnetic field, used in nuclear physics to produce proton-neutron Bardeen-Cooper-Schrieer-type models, n-level many-mode Jaynes-Cummings-Dicke-type models of quantum optics, matrix generalization of Bose-Hubbard dimers, etc. We diagonalize the constructed models by means of the ‘generalized’ nested Bethe ansatz.

  7. Algebraic distance on graphs.

    SciTech Connect

    Chen, J.; Safro, I.

    2011-01-01

    Measuring the connection strength between a pair of vertices in a graph is one of the most important concerns in many graph applications. Simple measures such as edge weights may not be sufficient for capturing the effects associated with short paths of lengths greater than one. In this paper, we consider an iterative process that smooths an associated value for nearby vertices, and we present a measure of the local connection strength (called the algebraic distance; see [D. Ron, I. Safro, and A. Brandt, Multiscale Model. Simul., 9 (2011), pp. 407-423]) based on this process. The proposed measure is attractive in that the process is simple, linear, and easily parallelized. An analysis of the convergence property of the process reveals that the local neighborhoods play an important role in determining the connectivity between vertices. We demonstrate the practical effectiveness of the proposed measure through several combinatorial optimization problems on graphs and hypergraphs.

  8. Imperfect Cloning Operations in Algebraic Quantum Theory

    NASA Astrophysics Data System (ADS)

    Kitajima, Yuichiro

    2015-01-01

    No-cloning theorem says that there is no unitary operation that makes perfect clones of non-orthogonal quantum states. The objective of the present paper is to examine whether an imperfect cloning operation exists or not in a C*-algebraic framework. We define a universal -imperfect cloning operation which tolerates a finite loss of fidelity in the cloned state, and show that an individual system's algebra of observables is abelian if and only if there is a universal -imperfect cloning operation in the case where the loss of fidelity is less than . Therefore in this case no universal -imperfect cloning operation is possible in algebraic quantum theory.

  9. General A 9 × 9 Matrix Representation of Birman—Wenzl—Murakami Algebra and Berry Phase in Yang—Baxter System

    NASA Astrophysics Data System (ADS)

    Gou, Li-Dan; Xue, Kang; Wang, Gang-Cheng

    2011-02-01

    We present a 9 × 9 S-matrix and E-matrix. A representation of specialized Birman—Wenzl—Murakami algebra is obtained. Starting from the given braid group representation S-matrix, we obtain the trigonometric solution of Yang-Baxter equation. A unitary matrix Ř(x, ϕ1,ϕ2) is generated via the Yang—Baxterization approach. Then we construct a Yang—Baxter Hamiltonian through the unitary matrix Ř(x, ϕ1,ϕ2). Berry phase of this Yang—Baxter system is investigated in detail.

  10. Linear-Algebra Programs

    NASA Technical Reports Server (NTRS)

    Lawson, C. L.; Krogh, F. T.; Gold, S. S.; Kincaid, D. R.; Sullivan, J.; Williams, E.; Hanson, R. J.; Haskell, K.; Dongarra, J.; Moler, C. B.

    1982-01-01

    The Basic Linear Algebra Subprograms (BLAS) library is a collection of 38 FORTRAN-callable routines for performing basic operations of numerical linear algebra. BLAS library is portable and efficient source of basic operations for designers of programs involving linear algebriac computations. BLAS library is supplied in portable FORTRAN and Assembler code versions for IBM 370, UNIVAC 1100 and CDC 6000 series computers.

  11. Algebraic Reasoning through Patterns

    ERIC Educational Resources Information Center

    Rivera, F. D.; Becker, Joanne Rossi

    2009-01-01

    This article presents the results of a three-year study that explores students' performance on patterning tasks involving prealgebra and algebra. The findings, insights, and issues drawn from the study are intended to help teach prealgebra and algebra. In the remainder of the article, the authors take a more global view of the three-year study on…

  12. Teaching Structure in Algebra

    ERIC Educational Resources Information Center

    Merlin, Ethan M.

    2013-01-01

    This article describes how the author has developed tasks for students that address the missed "essence of the matter" of algebraic transformations. Specifically, he has found that having students practice "perceiving" algebraic structure--by naming the "glue" in the expressions, drawing expressions using…

  13. Mathematical models for space shuttle ground systems

    NASA Technical Reports Server (NTRS)

    Tory, E. G.

    1985-01-01

    Math models are a series of algorithms, comprised of algebraic equations and Boolean Logic. At Kennedy Space Center, math models for the Space Shuttle Systems are performed utilizing the Honeywell 66/80 digital computers, Modcomp II/45 Minicomputers and special purpose hardware simulators (MicroComputers). The Shuttle Ground Operations Simulator operating system provides the language formats, subroutines, queueing schemes, execution modes and support software to write, maintain and execute the models. The ground systems presented consist primarily of the Liquid Oxygen and Liquid Hydrogen Cryogenic Propellant Systems, as well as liquid oxygen External Tank Gaseous Oxygen Vent Hood/Arm and the Vehicle Assembly Building (VAB) High Bay Cells. The purpose of math modeling is to simulate the ground hardware systems and to provide an environment for testing in a benign mode. This capability allows the engineers to check out application software for loading and launching the vehicle, and to verify the Checkout, Control, & Monitor Subsystem within the Launch Processing System. It is also used to train operators and to predict system response and status in various configurations (normal operations, emergency and contingent operations), including untried configurations or those too dangerous to try under real conditions, i.e., failure modes.

  14. A two-loop sparse matrix numerical integration procedure for the solution of differential/algebraic equations: Application to multibody systems

    NASA Astrophysics Data System (ADS)

    Shabana, Ahmed A.; Hussein, Bassam A.

    2009-11-01

    In this paper, a two-loop implicit sparse matrix numerical integration (TLISMNI) procedure for the solution of constrained rigid and flexible multibody system differential and algebraic equations is proposed. The proposed method ensures that the kinematic constraint equations are satisfied at the position, velocity and acceleration levels. In this method, a sparse Lagrangian augmented form of the equations of motion that ensures that the constraints are satisfied at the acceleration level is first used to solve for all the accelerations and Lagrange multipliers. The independent coordinates and velocities are then identified and integrated using HTT or Newmark formulas, expressed in this paper in terms of the independent accelerations only. The constraint equations at the position level are then used within an iterative Newton-Raphson procedure to determine the dependent coordinates. The dependent velocities are determined by solving a linear system of algebraic equations. In order to effectively exploit efficient sparse matrix techniques and have minimum storage requirements, a two-loop iterative method is proposed. Equally important, the proposed method avoids the use of numerical differentiation which is commonly associated with the use of implicit integration methods in multibody system algorithms. Numerical examples are presented in order to demonstrate the use of the new integration procedure.

  15. C*-algebraic scattering theory and explicitly solvable quantum field theories

    NASA Astrophysics Data System (ADS)

    Warchall, Henry A.

    1985-06-01

    A general theoretical framework is developed for the treatment of a class of quantum field theories that are explicitly exactly solvable, but require the use of C*-algebraic techniques because time-dependent scattering theory cannot be constructed in any one natural representation of the observable algebra. The purpose is to exhibit mechanisms by which inequivalent representations of the observable algebra can arise in quantum field theory, in a setting free of other complications commonly associated with the specification of dynamics. One of two major results is the development of necessary and sufficient conditions for the concurrent unitary implementation of two automorphism groups in a class of quasifree representations of the algebra of the canonical commutation relations (CCR). The automorphism groups considered are induced by one-parameter groups of symplectic transformations on the classical phase space over which the Weyl algebra of the CCR is built; each symplectic group is conjugate by a fixed symplectic transformation to a one-parameter unitary group. The second result, an analog to the Birman-Belopol'skii theorem in two-Hilbert-space scattering theory, gives sufficient conditions for the existence of Mo/ller wave morphisms in theories with time-development automorphism groups of the above type. In a paper which follows, this framework is used to analyze a particular model system for which wave operators fail to exist in any natural representation of the observable algebra, but for which wave morphisms and an associated S matrix are easily constructed.

  16. Communication system modeling

    NASA Technical Reports Server (NTRS)

    Holland, L. D.; Walsh, J. R., Jr.; Wetherington, R. D.

    1971-01-01

    This report presents the results of work on communications systems modeling and covers three different areas of modeling. The first of these deals with the modeling of signals in communication systems in the frequency domain and the calculation of spectra for various modulations. These techniques are applied in determining the frequency spectra produced by a unified carrier system, the down-link portion of the Command and Communications System (CCS). The second modeling area covers the modeling of portions of a communication system on a block basis. A detailed analysis and modeling effort based on control theory is presented along with its application to modeling of the automatic frequency control system of an FM transmitter. A third topic discussed is a method for approximate modeling of stiff systems using state variable techniques.

  17. ALGEBRA IIVer 1.22

    SciTech Connect

    2003-06-03

    The ALGEBRA II program allows the user to manipulate data from a finite element analysis before it is plotted by evaluating algebraic expressions. The equation variables are dependent on the input database variable names. The finite element output data is in the form of variable values (e.g., stress, strain, and velocity components) in an EXODUS II database which can be read by plot programs. Code is written in a portable form as possible. Fortran code is written in ANSI Standard FORTRAN-77. Machine-specific routines are limited in number and are grouped together to minimize the time required to adapt them to a new system. SEACAS codes has been ported to several Unix systems.

  18. ALGEBRA IIVer 1.22

    2003-06-03

    The ALGEBRA II program allows the user to manipulate data from a finite element analysis before it is plotted by evaluating algebraic expressions. The equation variables are dependent on the input database variable names. The finite element output data is in the form of variable values (e.g., stress, strain, and velocity components) in an EXODUS II database which can be read by plot programs. Code is written in a portable form as possible. Fortran codemore » is written in ANSI Standard FORTRAN-77. Machine-specific routines are limited in number and are grouped together to minimize the time required to adapt them to a new system. SEACAS codes has been ported to several Unix systems.« less

  19. Lie algebra extensions of current algebras on S3

    NASA Astrophysics Data System (ADS)

    Kori, Tosiaki; Imai, Yuto

    2015-06-01

    An affine Kac-Moody algebra is a central extension of the Lie algebra of smooth mappings from S1 to the complexification of a Lie algebra. In this paper, we shall introduce a central extension of the Lie algebra of smooth mappings from S3 to the quaternization of a Lie algebra and investigate its root space decomposition. We think this extension of current algebra might give a mathematical tool for four-dimensional conformal field theory as Kac-Moody algebras give it for two-dimensional conformal field theory.

  20. Leibniz algebras associated with representations of filiform Lie algebras

    NASA Astrophysics Data System (ADS)

    Ayupov, Sh. A.; Camacho, L. M.; Khudoyberdiyev, A. Kh.; Omirov, B. A.

    2015-12-01

    In this paper we investigate Leibniz algebras whose quotient Lie algebra is a naturally graded filiform Lie algebra nn,1. We introduce a Fock module for the algebra nn,1 and provide classification of Leibniz algebras L whose corresponding Lie algebra L / I is the algebra nn,1 with condition that the ideal I is a Fock nn,1-module, where I is the ideal generated by squares of elements from L. We also consider Leibniz algebras with corresponding Lie algebra nn,1 and such that the action I ×nn,1 → I gives rise to a minimal faithful representation of nn,1. The classification up to isomorphism of such Leibniz algebras is given for the case of n = 4.

  1. Mathematical circulatory system model

    NASA Technical Reports Server (NTRS)

    Lakin, William D. (Inventor); Stevens, Scott A. (Inventor)

    2010-01-01

    A system and method of modeling a circulatory system including a regulatory mechanism parameter. In one embodiment, a regulatory mechanism parameter in a lumped parameter model is represented as a logistic function. In another embodiment, the circulatory system model includes a compliant vessel, the model having a parameter representing a change in pressure due to contraction of smooth muscles of a wall of the vessel.

  2. Degenerate Sklyanin algebras

    NASA Astrophysics Data System (ADS)

    Smirnov, Andrey

    2010-08-01

    New trigonometric and rational solutions of the quantum Yang-Baxter equation (QYBE) are obtained by applying some singular gauge transformations to the known Belavin-Drinfeld elliptic R-matrix for sl(2;?). These solutions are shown to be related to the standard ones by the quasi-Hopf twist. We demonstrate that the quantum algebras arising from these new R-matrices can be obtained as special limits of the Sklyanin algebra. A representation for these algebras by the difference operators is found. The sl( N;?)-case is discussed.

  3. Degenerate Sklyanin algebras

    NASA Astrophysics Data System (ADS)

    Smirnov, Andrey

    2010-08-01

    New trigonometric and rational solutions of the quantum Yang-Baxter equation (QYBE) are obtained by applying some singular gauge transformations to the known Belavin-Drinfeld elliptic R-matrix for sl(2;?). These solutions are shown to be related to the standard ones by the quasi-Hopf twist. We demonstrate that the quantum algebras arising from these new R-matrices can be obtained as special limits of the Sklyanin algebra. A representation for these algebras by the difference operators is found. The sl(N;?)-case is discussed.

  4. Modular Modeling System Model Builder

    SciTech Connect

    McKim, C.S.; Matthews, M.T.

    1996-12-31

    The latest release of the Modular Modeling System (MMS) Model Builder adds still more time-saving features to an already powerful MMS dynamic-simulation tool set. The Model Builder takes advantage of 32-bit architecture within the Microsoft Windows 95/NT{trademark} Operating Systems to better integrate a mature library of power-plant components. In addition, the MMS Library of components can now be modified and extended with a new tool named MMS CompGen{trademark}. The MMS Model Builder allows the user to quickly build a graphical schematic representation for a plant by selecting from a library of predefined power plant components to dynamically simulate their operation. In addition, each component has a calculation subroutine stored in a dynamic-link library (DLL), which facilitates the determination of a steady-state condition and performance of routine calculations for the component. These calculations, termed auto-parameterization, help avoid repetitive and often tedious hand calculations for model initialization. In striving to meet the needs for large models and increase user productivity, the MMS Model Builder has been completely revamped to make power plant model creation and maintainability easier and more efficient.

  5. Approximate Bisimulation-Based Reduction of Power System Dynamic Models

    SciTech Connect

    Stankovic, AM; Dukic, SD; Saric, AT

    2015-05-01

    In this paper we propose approximate bisimulation relations and functions for reduction of power system dynamic models in differential- algebraic (descriptor) form. The full-size dynamic model is obtained by linearization of the nonlinear transient stability model. We generalize theoretical results on approximate bisimulation relations and bisimulation functions, originally derived for a class of constrained linear systems, to linear systems in descriptor form. An algorithm for transient stability assessment is proposed and used to determine whether the power system is able to maintain the synchronism after a large disturbance. Two benchmark power systems are used to illustrate the proposed algorithm and to evaluate the applicability of approximate bisimulation relations and bisimulation functions for reduction of the power system dynamic models.

  6. Chain modeling for life cycle systems engineering

    SciTech Connect

    Rivera, J.J.; Shapiro, V.

    1997-12-01

    Throughout Sandia`s history, products have been represented by drawings. Solid modeling systems have recently replaced drawings as the preferred means for representing product geometry. These systems are used for product visualization, engineering analysis and manufacturing planning. Unfortunately, solid modeling technology is inadequate for life cycle systems engineering, which requires maintenance of technical history, efficient management of geometric and non-geometric data, and explicit representation of engineering and manufacturing characteristics. Such information is not part of the mathematical foundation of solid modeling. The current state-of-the-art in life cycle engineering is comprised of painstakingly created special purpose tools, which often are incompatible. New research on {open_quotes}chain modeling{close_quotes} provides a method of chaining the functionality of a part to the geometric representation. Chain modeling extends classical solid modeling to include physical, manufacturing, and procedural information required for life cycle engineering. In addition, chain modeling promises to provide the missing theoretical basis for Sandia`s parent/child product realization paradigm. In chain modeling, artifacts and systems are characterized in terms of their combinatorial properties: cell complexes, chains, and their operators. This approach is firmly rooted in algebraic topology and is a natural extension of current technology. The potential benefits of this approach include explicit hierarchical and combinatorial representation of physics, geometry, functionality, test, and legacy data in a common computational framework that supports a rational decision process and partial design automation. Chain modeling will have a significant impact on design preservation, system identification, parameterization, system reliability, and design simplification.

  7. Algebraic Semantics for Narrative

    ERIC Educational Resources Information Center

    Kahn, E.

    1974-01-01

    This paper uses discussion of Edmund Spenser's "The Faerie Queene" to present a theoretical framework for explaining the semantics of narrative discourse. The algebraic theory of finite automata is used. (CK)

  8. Modeling of geothermal systems

    SciTech Connect

    Bodvarsson, G.S.; Pruess, K.; Lippmann, M.J.

    1985-03-01

    During the last decade the use of numerical modeling for geothermal resource evaluation has grown significantly, and new modeling approaches have been developed. In this paper we present a summary of the present status in numerical modeling of geothermal systems, emphasizing recent developments. Different modeling approaches are described and their applicability discussed. The various modeling tasks, including natural-state, exploitation, injection, multi-component and subsidence modeling, are illustrated with geothermal field examples. 99 refs., 14 figs.

  9. Covariant deformed oscillator algebras

    NASA Technical Reports Server (NTRS)

    Quesne, Christiane

    1995-01-01

    The general form and associativity conditions of deformed oscillator algebras are reviewed. It is shown how the latter can be fulfilled in terms of a solution of the Yang-Baxter equation when this solution has three distinct eigenvalues and satisfies a Birman-Wenzl-Murakami condition. As an example, an SU(sub q)(n) x SU(sub q)(m)-covariant q-bosonic algebra is discussed in some detail.

  10. Geometric Algebra for Physicists

    NASA Astrophysics Data System (ADS)

    Doran, Chris; Lasenby, Anthony

    2007-11-01

    Preface; Notation; 1. Introduction; 2. Geometric algebra in two and three dimensions; 3. Classical mechanics; 4. Foundations of geometric algebra; 5. Relativity and spacetime; 6. Geometric calculus; 7. Classical electrodynamics; 8. Quantum theory and spinors; 9. Multiparticle states and quantum entanglement; 10. Geometry; 11. Further topics in calculus and group theory; 12. Lagrangian and Hamiltonian techniques; 13. Symmetry and gauge theory; 14. Gravitation; Bibliography; Index.

  11. Quantum walks, deformed relativity and Hopf algebra symmetries.

    PubMed

    Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo

    2016-05-28

    We show how the Weyl quantum walk derived from principles in D'Ariano & Perinotti (D'Ariano & Perinotti 2014Phys. Rev. A90, 062106. (doi:10.1103/PhysRevA.90.062106)), enjoying a nonlinear Lorentz symmetry of dynamics, allows one to introduce Hopf algebras for position and momentum of the emerging particle. We focus on two special models of Hopf algebras-the usual Poincaré and theκ-Poincaré algebras.

  12. Quantum walks, deformed relativity and Hopf algebra symmetries.

    PubMed

    Bisio, Alessandro; D'Ariano, Giacomo Mauro; Perinotti, Paolo

    2016-05-28

    We show how the Weyl quantum walk derived from principles in D'Ariano & Perinotti (D'Ariano & Perinotti 2014Phys. Rev. A90, 062106. (doi:10.1103/PhysRevA.90.062106)), enjoying a nonlinear Lorentz symmetry of dynamics, allows one to introduce Hopf algebras for position and momentum of the emerging particle. We focus on two special models of Hopf algebras-the usual Poincaré and theκ-Poincaré algebras. PMID:27091171

  13. System Advisor Model

    2010-03-01

    The System Advisor Model (SAM) is a performance and economic model designed to facilitate decision making for people involved in the renewable energy industry, ranging from project managers and engineers to incentive program designers, technology developers, and researchers.

  14. Fundamental Theorems of Algebra for the Perplexes

    ERIC Educational Resources Information Center

    Poodiak, Robert; LeClair, Kevin

    2009-01-01

    The fundamental theorem of algebra for the complex numbers states that a polynomial of degree n has n roots, counting multiplicity. This paper explores the "perplex number system" (also called the "hyperbolic number system" and the "spacetime number system") In this system (which has extra roots of +1 besides the usual [plus or minus]1 of the…

  15. The Algebraic Way

    NASA Astrophysics Data System (ADS)

    Hiley, B. J.

    In this chapter, we examine in detail the non-commutative symplectic algebra underlying quantum dynamics. By using this algebra, we show that it contains both the Weyl-von Neumann and the Moyal quantum algebras. The latter contains the Wigner distribution as the kernel of the density matrix. The underlying non-commutative geometry can be projected into either of two Abelian spaces, so-called `shadow phase spaces'. One of these is the phase space of Bohmian mechanics, showing that it is a fragment of the basic underlying algebra. The algebraic approach is much richer, giving rise to two fundamental dynamical time development equations which reduce to the Liouville equation and the Hamilton-Jacobi equation in the classical limit. They also include the Schrödinger equation and its wave-function, showing that these features are a partial aspect of the more general non-commutative structure. We discuss briefly the properties of this more general mathematical background from which the non-commutative symplectic algebra emerges.

  16. Computing Gröbner Bases within Linear Algebra

    NASA Astrophysics Data System (ADS)

    Suzuki, Akira

    In this paper, we present an alternative algorithm to compute Gröbner bases, which is based on computations on sparse linear algebra. Both of S-polynomial computations and monomial reductions are computed in linear algebra simultaneously in this algorithm. So it can be implemented to any computational system which can handle linear algebra. For a given ideal in a polynomial ring, it calculates a Gröbner basis along with the corresponding term order appropriately.

  17. Algebraic approach to solve tt dilepton equations

    SciTech Connect

    Sonnenschein, Lars

    2005-11-01

    The set of nonlinear equations describing the standard model kinematics of the top quark antiquark production system in the dilepton decay channel has at most a fourfold ambiguity due to two not fully reconstructed neutrinos. Its most precise solution is of major importance for measurements of top quark properties like the top quark mass and tt spin correlations. Simple algebraic operations allow one to transform the nonlinear equations into a system of two polynomial equations with two unknowns. These two polynomials of multidegree eight can in turn be analytically reduced to one polynomial with one unknown by means of resultants. The obtained univariate polynomial is of degree 16. The number of its real solutions is determined analytically by means of Sturm's theorem, which is as well used to isolate each real solution into a unique pairwise disjoint interval. The solutions are polished by seeking the sign change of the polynomial in a given interval through binary bracketing.

  18. A method to convert algebraic boundary representations to CSG representations for three-dimensional solids

    SciTech Connect

    Buchele, S.F.; Ellingson, W.A.

    1997-06-01

    Recent advances in reverse engineering have focused on recovering a boundary representation (b-rep) of an object, often for integration with rapid prototyping. This boundary representation may be a 3-D point cloud, a triangulation of points, or piecewise algebraic or parametric surfaces. This paper presents work in progress to develop an algorithm to extend the current state of the art in reverse engineering of mechanical parts. This algorithm will take algebraic surface representations as input and will produce a constructive solid geometry (CSG) description that uses solid primitives such as rectangular block, pyramid, sphere, cylinder, and cone. The proposed algorithm will automatically generate a CSG solid model of a part given its algebraic b-rep, thus allowing direct input into a CAD system and subsequent CSG model generation.

  19. Cognitive Tutor[R] Algebra I. What Works Clearinghouse Intervention Report

    ERIC Educational Resources Information Center

    What Works Clearinghouse, 2007

    2007-01-01

    "Cognitive Tutor[R] Algebra I," a full year course, delivers instruction in single variable data, simplifying linear expressions, mathematical modeling, solving systems with linear equations, problem solving using proportional reasoning, and powers and exponents. Students work at their own pace to develop problem-solving skills. The duration of…

  20. MLS: Airplane system modeling

    NASA Technical Reports Server (NTRS)

    Thompson, A. D.; Stapleton, B. P.; Walen, D. B.; Rieder, P. F.; Moss, D. G.

    1981-01-01

    Analysis, modeling, and simulations were conducted as part of a multiyear investigation of the more important airplane-system-related items of the microwave landing system (MLS). Particular emphasis was placed upon the airplane RF system, including the antenna radiation distribution, the cabling options from the antenna to the receiver, and the overall impact of the airborne system gains and losses upon the direct-path signal structure. In addition, effort was expended toward determining the impact of the MLS upon the airplane flight management system and developing the initial stages of a fast-time MLS automatic control system simulation model. Results ot these studies are presented.

  1. Spatial-Operator Algebra For Flexible-Link Manipulators

    NASA Technical Reports Server (NTRS)

    Jain, Abhinandan; Rodriguez, Guillermo

    1994-01-01

    Method of computing dynamics of multiple-flexible-link robotic manipulators based on spatial-operator algebra, which originally applied to rigid-link manipulators. Aspects of spatial-operator-algebra approach described in several previous articles in NASA Tech Briefs-most recently "Robot Control Based on Spatial-Operator Algebra" (NPO-17918). In extension of spatial-operator algebra to manipulators with flexible links, each link represented by finite-element model: mass of flexible link apportioned among smaller, lumped-mass rigid bodies, coupling of motions expressed in terms of vibrational modes. This leads to operator expression for modal-mass matrix of link.

  2. Integrated Workforce Modeling System

    NASA Technical Reports Server (NTRS)

    Moynihan, Gary P.

    2000-01-01

    There are several computer-based systems, currently in various phases of development at KSC, which encompass some component, aspect, or function of workforce modeling. These systems may offer redundant capabilities and/or incompatible interfaces. A systems approach to workforce modeling is necessary in order to identify and better address user requirements. This research has consisted of two primary tasks. Task 1 provided an assessment of existing and proposed KSC workforce modeling systems for their functionality and applicability to the workforce planning function. Task 2 resulted in the development of a proof-of-concept design for a systems approach to workforce modeling. The model incorporates critical aspects of workforce planning, including hires, attrition, and employee development.

  3. Quantization maps, algebra representation, and non-commutative Fourier transform for Lie groups

    SciTech Connect

    Guedes, Carlos; Oriti, Daniele; Raasakka, Matti

    2013-08-15

    The phase space given by the cotangent bundle of a Lie group appears in the context of several models for physical systems. A representation for the quantum system in terms of non-commutative functions on the (dual) Lie algebra, and a generalized notion of (non-commutative) Fourier transform, different from standard harmonic analysis, has been recently developed, and found several applications, especially in the quantum gravity literature. We show that this algebra representation can be defined on the sole basis of a quantization map of the classical Poisson algebra, and identify the conditions for its existence. In particular, the corresponding non-commutative star-product carried by this representation is obtained directly from the quantization map via deformation quantization. We then clarify under which conditions a unitary intertwiner between such algebra representation and the usual group representation can be constructed giving rise to the non-commutative plane waves and consequently, the non-commutative Fourier transform. The compact groups U(1) and SU(2) are considered for different choices of quantization maps, such as the symmetric and the Duflo map, and we exhibit the corresponding star-products, algebra representations, and non-commutative plane waves.

  4. On the dimensions of oscillator algebras induced by orthogonal polynomials

    NASA Astrophysics Data System (ADS)

    Honnouvo, G.; Thirulogasanthar, K.

    2014-09-01

    There is a generalized oscillator algebra associated with every class of orthogonal polynomials lbrace Ψ _n(x)rbrace _{n = 0}^{infty }, on the real line, satisfying a three term recurrence relation xΨn(x) = bnΨn+1(x) + bn-1Ψn-1(x), Ψ0(x) = 1, b-1 = 0. This note presents necessary and sufficient conditions on bn for such algebras to be of finite dimension. As examples, we discuss the dimensions of oscillator algebras associated with Hermite, Legendre, and Gegenbauer polynomials. Some remarks on the dimensions of oscillator algebras associated with multi-boson systems are also presented.

  5. Evaluating the structural identifiability of the parameters of the EBPR sub-model in ASM2d by the differential algebra method.

    PubMed

    Zhang, Tian; Zhang, Daijun; Li, Zhenliang; Cai, Qing

    2010-05-01

    The calibration of ASMs is a prerequisite for their application to simulation of a wastewater treatment plant. This work should be made based on the evaluation of structural identifiability of model parameters. An EBPR sub-model including denitrification phosphorus removal has been incorporated in ASM2d. Yet no report is presented on the structural identifiability of the parameters in the EBPR sub-model. In this paper, the differential algebra approach was used to address this issue. The results showed that the structural identifiability of parameters in the EBPR sub-model could be improved by increasing the measured variables. The reduction factor eta(NO)(3) was identifiable when combined data of aerobic process and anoxic process were assumed. For K(PP), X(PAO) and q(PHA) of the anaerobic process to be uniquely identifiable, one of them is needed to be determined by other ways. Likewise, if prior information on one of the parameters, K(PHA), X(PAO) and q(PP) of the aerobic process, is known, all the parameters are identifiable. The above results could be of interest to the parameter estimation of the EBPR sub-model. The algorithm proposed in the paper is also suitable for other sub-models of ASMs.

  6. Model-Based Systems

    NASA Technical Reports Server (NTRS)

    Frisch, Harold P.

    2007-01-01

    Engineers, who design systems using text specification documents, focus their work upon the completed system to meet Performance, time and budget goals. Consistency and integrity is difficult to maintain within text documents for a single complex system and more difficult to maintain as several systems are combined into higher-level systems, are maintained over decades, and evolve technically and in performance through updates. This system design approach frequently results in major changes during the system integration and test phase, and in time and budget overruns. Engineers who build system specification documents within a model-based systems environment go a step further and aggregate all of the data. They interrelate all of the data to insure consistency and integrity. After the model is constructed, the various system specification documents are prepared, all from the same database. The consistency and integrity of the model is assured, therefore the consistency and integrity of the various specification documents is insured. This article attempts to define model-based systems relative to such an environment. The intent is to expose the complexity of the enabling problem by outlining what is needed, why it is needed and how needs are being addressed by international standards writing teams.

  7. Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction

    ERIC Educational Resources Information Center

    Wasserman, Nicholas H.

    2016-01-01

    This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…

  8. Challenges of Algebraic Multigrid across Multicore Architectures

    SciTech Connect

    Baker, A H; Gamblin, T; Schulz, M; Yang, U M

    2010-04-12

    Algebraic multigrid (AMG) is a popular solver for large-scale scientific computing and an essential component of many simulation codes. AMG has shown to be extremely efficient on distributed-memory architectures. However, when executed on modern multicore architectures, we face new challenges that can significantly deteriorate AMG's performance. We examine its performance and scalability on three disparate multicore architectures: a cluster with four AMD Opteron Quad-core processors per node (Hera), a Cray XT5 with two AMD Opteron Hex-core processors per node (Jaguar), and an IBM BlueGene/P system with a single Quad-core processor (Intrepid). We discuss our experiences on these platforms and present results using both an MPI-only and a hybrid MPI/OpenMP model. We also discuss a set of techniques that helped to overcome the associated problems, including thread and process pinning and correct memory associations.

  9. Peer & Parent Encouragement of Early Algebra Enrollment & Mathematics Achievement

    ERIC Educational Resources Information Center

    Filer, Kimberly L.; Chang, Mido

    2008-01-01

    Using data from the National Education Longitudinal Study of 1988 (NELS:88), path analytic procedures were performed to test a model of the effects of parent and peer encouragement to take algebra on the mathematics achievement of eighth grade students. The effects of socio-economic status (SES) on middle school algebra course-taking and…

  10. Computer-Intensive Algebra and Students' Conceptual Knowledge of Functions.

    ERIC Educational Resources Information Center

    O'Callaghan, Brian R.

    1998-01-01

    Describes a research project that examined the effects of the Computer-Intensive Algebra (CIA) and traditional algebra curricula on students' (N=802) understanding of the function concept. Results indicate that CIA students achieved a better understanding of functions and were better at the components of modeling, interpreting, and translating.…

  11. Computer Program For Linear Algebra

    NASA Technical Reports Server (NTRS)

    Krogh, F. T.; Hanson, R. J.

    1987-01-01

    Collection of routines provided for basic vector operations. Basic Linear Algebra Subprogram (BLAS) library is collection from FORTRAN-callable routines for employing standard techniques to perform basic operations of numerical linear algebra.

  12. Algebra for Gifted Third Graders.

    ERIC Educational Resources Information Center

    Borenson, Henry

    1987-01-01

    Elementary school children who are exposed to a concrete, hands-on experience in algebraic linear equations will more readily develop a positive mind-set and expectation for success in later formal, algebraic studies. (CB)

  13. Automatic code generation in SPARK: Applications of computer algebra and compiler-compilers

    SciTech Connect

    Nataf, J.M.; Winkelmann, F.

    1992-09-01

    We show how computer algebra and compiler-compilers are used for automatic code generation in the Simulation Problem Analysis and Research Kernel (SPARK), an object oriented environment for modeling complex physical systems that can be described by differential-algebraic equations. After a brief overview of SPARK, we describe the use of computer algebra in SPARK`s symbolic interface, which generates solution code for equations that are entered in symbolic form. We also describe how the Lex/Yacc compiler-compiler is used to achieve important extensions to the SPARK simulation language, including parametrized macro objects and steady-state resetting of a dynamic simulation. The application of these methods to solving the partial differential equations for two-dimensional heat flow is illustrated.

  14. Automatic code generation in SPARK: Applications of computer algebra and compiler-compilers

    SciTech Connect

    Nataf, J.M.; Winkelmann, F.

    1992-09-01

    We show how computer algebra and compiler-compilers are used for automatic code generation in the Simulation Problem Analysis and Research Kernel (SPARK), an object oriented environment for modeling complex physical systems that can be described by differential-algebraic equations. After a brief overview of SPARK, we describe the use of computer algebra in SPARK's symbolic interface, which generates solution code for equations that are entered in symbolic form. We also describe how the Lex/Yacc compiler-compiler is used to achieve important extensions to the SPARK simulation language, including parametrized macro objects and steady-state resetting of a dynamic simulation. The application of these methods to solving the partial differential equations for two-dimensional heat flow is illustrated.

  15. The algebra of bipartite graphs and Hurwitz numbers of seamed surfaces

    NASA Astrophysics Data System (ADS)

    Alekseevskii, A. V.; Natanzon, S. M.

    2008-08-01

    We extend the definition of Hurwitz numbers to the case of seamed surfaces, which arise in new models of mathematical physics, and prove that they form a system of correlators for a Klein topological field theory in the sense defined in [1]. We find the corresponding Cardy-Frobenius algebras, which yield a method for calculating the Hurwitz numbers. As a by-product, we prove that the vector space generated by the bipartite graphs with n edges possesses a natural binary operation that makes this space into a non-commutative Frobenius algebra isomorphic to the algebra of intertwining operators for a representation of the symmetric group S_n on the space generated by the set of all partitions of a set of n elements.

  16. Parameter optimization in S-system models

    PubMed Central

    Vilela, Marco; Chou, I-Chun; Vinga, Susana; Vasconcelos, Ana Tereza R; Voit, Eberhard O; Almeida, Jonas S

    2008-01-01

    Background The inverse problem of identifying the topology of biological networks from their time series responses is a cornerstone challenge in systems biology. We tackle this challenge here through the parameterization of S-system models. It was previously shown that parameter identification can be performed as an optimization based on the decoupling of the differential S-system equations, which results in a set of algebraic equations. Results A novel parameterization solution is proposed for the identification of S-system models from time series when no information about the network topology is known. The method is based on eigenvector optimization of a matrix formed from multiple regression equations of the linearized decoupled S-system. Furthermore, the algorithm is extended to the optimization of network topologies with constraints on metabolites and fluxes. These constraints rejoin the system in cases where it had been fragmented by decoupling. We demonstrate with synthetic time series why the algorithm can be expected to converge in most cases. Conclusion A procedure was developed that facilitates automated reverse engineering tasks for biological networks using S-systems. The proposed method of eigenvector optimization constitutes an advancement over S-system parameter identification from time series using a recent method called Alternating Regression. The proposed method overcomes convergence issues encountered in alternate regression by identifying nonlinear constraints that restrict the search space to computationally feasible solutions. Because the parameter identification is still performed for each metabolite separately, the modularity and linear time characteristics of the alternating regression method are preserved. Simulation studies illustrate how the proposed algorithm identifies the correct network topology out of a collection of models which all fit the dynamical time series essentially equally well. PMID:18416837

  17. Pseudo Algebraically Closed Extensions

    NASA Astrophysics Data System (ADS)

    Bary-Soroker, Lior

    2009-07-01

    This PhD deals with the notion of pseudo algebraically closed (PAC) extensions of fields. It develops a group-theoretic machinery, based on a generalization of embedding problems, to study these extensions. Perhaps the main result is that although there are many PAC extensions, the Galois closure of a proper PAC extension is separably closed. The dissertation also contains the following subjects. The group theoretical counterpart of pseudo algebraically closed extensions, the so-called projective pairs. Applications to seemingly unrelated subjects, e.g., an analog of Dirichlet's theorem about primes in arithmetic progression for polynomial rings in one variable over infinite fields.

  18. Symmetry algebra of a generalized anisotropic harmonic oscillator

    NASA Technical Reports Server (NTRS)

    Castanos, O.; Lopez-Pena, R.

    1993-01-01

    It is shown that the symmetry Lie algebra of a quantum system with accidental degeneracy can be obtained by means of the Noether's theorem. The procedure is illustrated by considering a generalized anisotropic two dimensional harmonic oscillator, which can have an infinite set of states with the same energy characterized by an u(1,1) Lie algebra.

  19. Intertextuality and Sense Production in the Learning of Algebraic Methods

    ERIC Educational Resources Information Center

    Rojano, Teresa; Filloy, Eugenio; Puig, Luis

    2014-01-01

    In studies carried out in the 1980s the algebraic symbols and expressions are revealed through prealgebraic readers as non-independent texts, as texts that relate to other texts that in some cases belong to the reader's native language or to the arithmetic sign system. Such outcomes suggest that the act of reading algebraic texts submerges…

  20. Factors Influencing Student Academic Performance in Online High School Algebra

    ERIC Educational Resources Information Center

    Liu, Feng; Cavanaugh, Cathy

    2012-01-01

    This paper describes the effect of teacher comments, students' demographic information and learning management system utilisation on student final scores in algebra courses in a K-12 virtual learning environment. Students taking algebra courses in a state virtual school in the Midwestern US region during 2007-2008 participated in this study.…

  1. From geometry to algebra: the Euclidean way with technology

    NASA Astrophysics Data System (ADS)

    Ferrarello, Daniela; Flavia Mammana, Maria; Pennisi, Mario

    2016-05-01

    In this paper, we present the results of an experimental classroom activity, history-based with a phylogenetic approach, to achieve algebra properties through geometry. In particular, we used Euclidean propositions, processed them by a dynamic geometry system and translate them into algebraic special products.

  2. Introduction to Matrix Algebra, Student's Text, Unit 23.

    ERIC Educational Resources Information Center

    Allen, Frank B.; And Others

    Unit 23 in the SMSG secondary school mathematics series is a student text covering the following topics in matrix algebra: matrix operations, the algebra of 2 X 2 matrices, matrices and linear systems, representation of column matrices as geometric vectors, and transformations of the plane. Listed in the appendix are four research exercises in…

  3. Markov-Tree model of intrinsic transport in Hamiltonian systems

    NASA Technical Reports Server (NTRS)

    Meiss, J. D.; Ott, E.

    1985-01-01

    A particle in a chaotic region of phase space can spend a long time near the boundary of a regular region since transport there is slow. This 'stickiness' of regular regions is thought to be responsible for previous observations in numerical experiments of a long-time algebraic decay of the particle survival probability, i.e., survival probability approximately t to the (-z) power for large t. This paper presents a global model for transport in such systems and demonstrates the essential role of the infinite hierarchy of small islands interspersed in the chaotic region. Results for z are discussed.

  4. Stability of Linear Equations--Algebraic Approach

    ERIC Educational Resources Information Center

    Cherif, Chokri; Goldstein, Avraham; Prado, Lucio M. G.

    2012-01-01

    This article could be of interest to teachers of applied mathematics as well as to people who are interested in applications of linear algebra. We give a comprehensive study of linear systems from an application point of view. Specifically, we give an overview of linear systems and problems that can occur with the computed solution when the…

  5. Integrating Map Algebra and Statistical Modeling for Spatio-Temporal Analysis of Monthly Mean Daily Incident Photosynthetically Active Radiation (PAR) over a Complex Terrain

    PubMed Central

    Evrendilek, Fatih

    2007-01-01

    This study aims at quantifying spatio-temporal dynamics of monthly mean daily incident photosynthetically active radiation (PAR) over a vast and complex terrain such as Turkey. The spatial interpolation method of universal kriging, and the combination of multiple linear regression (MLR) models and map algebra techniques were implemented to generate surface maps of PAR with a grid resolution of 500 × 500 m as a function of five geographical and 14 climatic variables. Performance of the geostatistical and MLR models was compared using mean prediction error (MPE), root-mean-square prediction error (RMSPE), average standard prediction error (ASE), mean standardized prediction error (MSPE), root-mean-square standardized prediction error (RMSSPE), and adjusted coefficient of determination (R2adj.). The best-fit MLR- and universal kriging-generated models of monthly mean daily PAR were validated against an independent 37-year observed dataset of 35 climate stations derived from 160 stations across Turkey by the Jackknifing method. The spatial variability patterns of monthly mean daily incident PAR were more accurately reflected in the surface maps created by the MLR-based models than in those created by the universal kriging method, in particular, for spring (May) and autumn (November). The MLR-based spatial interpolation algorithms of PAR described in this study indicated the significance of the multifactor approach to understanding and mapping spatio-temporal dynamics of PAR for a complex terrain over meso-scales.

  6. Canister Model, Systems Analysis

    1993-09-29

    This packges provides a computer simulation of a systems model for packaging nuclear waste and spent nuclear fuel in canisters. The canister model calculates overall programmatic cost, number of canisters, and fuel and waste inventories for the Idaho Chemical Processing Plant (other initial conditions can be entered).

  7. C*-algebras associated with reversible extensions of logistic maps

    NASA Astrophysics Data System (ADS)

    Kwaśniewski, Bartosz K.

    2012-10-01

    The construction of reversible extensions of dynamical systems presented in a previous paper by the author and A.V. Lebedev is enhanced, so that it applies to arbitrary mappings (not necessarily with open range). It is based on calculating the maximal ideal space of C*-algebras that extends endomorphisms to partial automorphisms via partial isometric representations, and involves a new set of 'parameters' (the role of parameters is played by chosen sets or ideals). As model examples, we give a thorough description of reversible extensions of logistic maps and a classification of systems associated with compression of unitaries generating homeomorphisms of the circle. Bibliography: 34 titles.

  8. C*-algebras associated with reversible extensions of logistic maps

    SciTech Connect

    Kwasniewski, Bartosz K

    2012-10-31

    The construction of reversible extensions of dynamical systems presented in a previous paper by the author and A.V. Lebedev is enhanced, so that it applies to arbitrary mappings (not necessarily with open range). It is based on calculating the maximal ideal space of C*-algebras that extends endomorphisms to partial automorphisms via partial isometric representations, and involves a new set of 'parameters' (the role of parameters is played by chosen sets or ideals). As model examples, we give a thorough description of reversible extensions of logistic maps and a classification of systems associated with compression of unitaries generating homeomorphisms of the circle. Bibliography: 34 titles.

  9. Flexible system modeling

    SciTech Connect

    Maragno, M.; Schmid, C.; Schmieg, M.

    1995-04-01

    Stability analysis calculations are typically based on predefined system models, where, in the majority of cases, the well known IEEE definitions for controllers, prime movers, and other associated devices and functions are in use. for planning purposes, this approach might be acceptable, since predefined sets of parameters will allow a favorable and reasonable behavior of the analyzed system to be achieved, thus representing the possibly implementable system behavior. However, this approach is often also applied for system operation analysis purposes, for which typical IEEE models are applicable only in few cases. In quite a number of cases, even manufacturers who perform highly accurate system modeling studies have been asked to deliver block diagrams and parameters according to a list of available IEEE models. Utilities and consultants with an in-depth knowledge and tradition of conducting system operation performance and optimization studies have frequently requested adequate and accurate procedures and tools to tackle this special field of power system analysis appropriately. This need to solve complex operation analysis and special component planning problems has prompted the development of adequate methods and tools at DIgSILENT Systems in cooperation with FICHTNER C.E. This article focuses on various possibilities to approach this problem and to report on the applied strategies and methods. Comprehensive examples are given to demonstrate the capabilities of the implemented procedures.

  10. Formal Formality of the Hypercommutative Algebras of Low Dimensional Calabi-Yau Varieties

    NASA Astrophysics Data System (ADS)

    Drummond-Cole, Gabriel C.

    2014-04-01

    There is a homotopy hypercommutative algebra structure on the cohomology of a Calabi-Yau variety. The truncation of this homotopy hypercommutative algebra to a strict hypercommutative algebra is well-known as a mathematical realization of the genus zero B-model. It is shown that this truncation loses no information for some cases, including all Calabi-Yau 3-folds.

  11. Critical Infrastructure Modeling System

    2004-10-01

    The Critical Infrastructure Modeling System (CIMS) is a 3D modeling and simulation environment designed to assist users in the analysis of dependencies within individual infrastructure and also interdependencies between multiple infrastructures. Through visual cuing and textual displays, a use can evaluate the effect of system perturbation and identify the emergent patterns that evolve. These patterns include possible outage areas from a loss of power, denial of service or access, and disruption of operations. Method ofmore » Solution: CIMS allows the user to model a system, create an overlay of information, and create 3D representative images to illustrate key infrastructure elements. A geo-referenced scene, satellite, aerial images or technical drawings can be incorporated into the scene. Scenarios of events can be scripted, and the user can also interact during run time to alter system characteristics. CIMS operates as a discrete event simulation engine feeding a 3D visualization.« less

  12. College Algebra II.

    ERIC Educational Resources Information Center

    Benjamin, Carl; And Others

    Presented are student performance objectives, a student progress chart, and assignment sheets with objective and diagnostic measures for the stated performance objectives in College Algebra II. Topics covered include: differencing and complements; real numbers; factoring; fractions; linear equations; exponents and radicals; complex numbers,…

  13. Computer Algebra versus Manipulation

    ERIC Educational Resources Information Center

    Zand, Hossein; Crowe, David

    2004-01-01

    In the UK there is increasing concern about the lack of skill in algebraic manipulation that is evident in students entering mathematics courses at university level. In this note we discuss how the computer can be used to ameliorate some of the problems. We take as an example the calculations needed in three dimensional vector analysis in polar…

  14. Algebraic Artful Aids.

    ERIC Educational Resources Information Center

    Glick, David

    1995-01-01

    Presents a technique that helps students concentrate more on the science and less on the mechanics of algebra while dealing with introductory physics formulas. Allows the teacher to do complex problems at a lower level and not be too concerned about the mathematical abilities of the students. (JRH)

  15. Computers in Abstract Algebra

    ERIC Educational Resources Information Center

    Nwabueze, Kenneth K.

    2004-01-01

    The current emphasis on flexible modes of mathematics delivery involving new information and communication technology (ICT) at the university level is perhaps a reaction to the recent change in the objectives of education. Abstract algebra seems to be one area of mathematics virtually crying out for computer instructional support because of the…

  16. On vertex algebra representations of the Schrödinger-Virasoro Lie algebra

    NASA Astrophysics Data System (ADS)

    Unterberger, Jérémie

    2009-12-01

    The Schrödinger-Virasoro Lie algebra sv is an extension of the Virasoro Lie algebra by a nilpotent Lie algebra formed with a bosonic current of weight 3/2 and a bosonic current of weight 1. It is also a natural infinite-dimensional extension of the Schrödinger Lie algebra, which — leaving aside the invariance under time-translation — has been proved to be a symmetry algebra for many statistical physics models undergoing a dynamics with dynamical exponent z=2. We define in this article general Schrödinger-Virasoro primary fields by analogy with conformal field theory, characterized by a 'spin' index and a (non-relativistic) mass, and construct vertex algebra representations of sv out of a charged symplectic boson and a free boson and its associated vertex operators. We also compute two- and three-point functions of still conjectural massive fields that are defined by an analytic continuation with respect to a formal parameter.

  17. Optical systolic solutions of linear algebraic equations

    NASA Technical Reports Server (NTRS)

    Neuman, C. P.; Casasent, D.

    1984-01-01

    The philosophy and data encoding possible in systolic array optical processor (SAOP) were reviewed. The multitude of linear algebraic operations achievable on this architecture is examined. These operations include such linear algebraic algorithms as: matrix-decomposition, direct and indirect solutions, implicit and explicit methods for partial differential equations, eigenvalue and eigenvector calculations, and singular value decomposition. This architecture can be utilized to realize general techniques for solving matrix linear and nonlinear algebraic equations, least mean square error solutions, FIR filters, and nested-loop algorithms for control engineering applications. The data flow and pipelining of operations, design of parallel algorithms and flexible architectures, application of these architectures to computationally intensive physical problems, error source modeling of optical processors, and matching of the computational needs of practical engineering problems to the capabilities of optical processors are emphasized.

  18. An algebra of discrete event processes

    NASA Technical Reports Server (NTRS)

    Heymann, Michael; Meyer, George

    1991-01-01

    This report deals with an algebraic framework for modeling and control of discrete event processes. The report consists of two parts. The first part is introductory, and consists of a tutorial survey of the theory of concurrency in the spirit of Hoare's CSP, and an examination of the suitability of such an algebraic framework for dealing with various aspects of discrete event control. To this end a new concurrency operator is introduced and it is shown how the resulting framework can be applied. It is further shown that a suitable theory that deals with the new concurrency operator must be developed. In the second part of the report the formal algebra of discrete event control is developed. At the present time the second part of the report is still an incomplete and occasionally tentative working paper.

  19. Modeling Sustainable Food Systems

    NASA Astrophysics Data System (ADS)

    Allen, Thomas; Prosperi, Paolo

    2016-05-01

    The processes underlying environmental, economic, and social unsustainability derive in part from the food system. Building sustainable food systems has become a predominating endeavor aiming to redirect our food systems and policies towards better-adjusted goals and improved societal welfare. Food systems are complex social-ecological systems involving multiple interactions between human and natural components. Policy needs to encourage public perception of humanity and nature as interdependent and interacting. The systemic nature of these interdependencies and interactions calls for systems approaches and integrated assessment tools. Identifying and modeling the intrinsic properties of the food system that will ensure its essential outcomes are maintained or enhanced over time and across generations, will help organizations and governmental institutions to track progress towards sustainability, and set policies that encourage positive transformations. This paper proposes a conceptual model that articulates crucial vulnerability and resilience factors to global environmental and socio-economic changes, postulating specific food and nutrition security issues as priority outcomes of food systems. By acknowledging the systemic nature of sustainability, this approach allows consideration of causal factor dynamics. In a stepwise approach, a logical application is schematized for three Mediterranean countries, namely Spain, France, and Italy.

  20. Modeling Sustainable Food Systems.

    PubMed

    Allen, Thomas; Prosperi, Paolo

    2016-05-01

    The processes underlying environmental, economic, and social unsustainability derive in part from the food system. Building sustainable food systems has become a predominating endeavor aiming to redirect our food systems and policies towards better-adjusted goals and improved societal welfare. Food systems are complex social-ecological systems involving multiple interactions between human and natural components. Policy needs to encourage public perception of humanity and nature as interdependent and interacting. The systemic nature of these interdependencies and interactions calls for systems approaches and integrated assessment tools. Identifying and modeling the intrinsic properties of the food system that will ensure its essential outcomes are maintained or enhanced over time and across generations, will help organizations and governmental institutions to track progress towards sustainability, and set policies that encourage positive transformations. This paper proposes a conceptual model that articulates crucial vulnerability and resilience factors to global environmental and socio-economic changes, postulating specific food and nutrition security issues as priority outcomes of food systems. By acknowledging the systemic nature of sustainability, this approach allows consideration of causal factor dynamics. In a stepwise approach, a logical application is schematized for three Mediterranean countries, namely Spain, France, and Italy.