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Sample records for computer algebra systems

  1. Computer Algebra Systems in Undergraduate Instruction.

    Science.gov (United States)

    Small, Don; And Others

    1986-01-01

    Computer algebra systems (such as MACSYMA and muMath) can carry out many of the operations of calculus, linear algebra, and differential equations. Use of them with sketching graphs of rational functions and with other topics is discussed. (MNS)

  2. Algebraic computing

    International Nuclear Information System (INIS)

    MacCallum, M.A.H.

    1990-01-01

    The implementation of a new computer algebra system is time consuming: designers of general purpose algebra systems usually say it takes about 50 man-years to create a mature and fully functional system. Hence the range of available systems and their capabilities changes little between one general relativity meeting and the next, despite which there have been significant changes in the period since the last report. The introductory remarks aim to give a brief survey of capabilities of the principal available systems and highlight one or two trends. The reference to the most recent full survey of computer algebra in relativity and brief descriptions of the Maple, REDUCE and SHEEP and other applications are given. (author)

  3. Nonlinear evolution equations and solving algebraic systems: the importance of computer algebra

    International Nuclear Information System (INIS)

    Gerdt, V.P.; Kostov, N.A.

    1989-01-01

    In the present paper we study the application of computer algebra to solve the nonlinear polynomial systems which arise in investigation of nonlinear evolution equations. We consider several systems which are obtained in classification of integrable nonlinear evolution equations with uniform rank. Other polynomial systems are related with the finding of algebraic curves for finite-gap elliptic potentials of Lame type and generalizations. All systems under consideration are solved using the method based on construction of the Groebner basis for corresponding polynomial ideals. The computations have been carried out using computer algebra systems. 20 refs

  4. Category-theoretic models of algebraic computer systems

    Science.gov (United States)

    Kovalyov, S. P.

    2016-01-01

    A computer system is said to be algebraic if it contains nodes that implement unconventional computation paradigms based on universal algebra. A category-based approach to modeling such systems that provides a theoretical basis for mapping tasks to these systems' architecture is proposed. The construction of algebraic models of general-purpose computations involving conditional statements and overflow control is formally described by a reflector in an appropriate category of algebras. It is proved that this reflector takes the modulo ring whose operations are implemented in the conventional arithmetic processors to the Łukasiewicz logic matrix. Enrichments of the set of ring operations that form bases in the Łukasiewicz logic matrix are found.

  5. ASYS: a computer algebra package for analysis of nonlinear algebraic equations systems

    International Nuclear Information System (INIS)

    Gerdt, V.P.; Khutornoj, N.V.

    1992-01-01

    A program package ASYS for analysis of nonlinear algebraic equations based on the Groebner basis technique is described. The package is written in REDUCE computer algebra language. It has special facilities to treat polynomial ideals of positive dimension, corresponding to algebraic systems with infinitely many solutions. Such systems can be transformed to an equivalent set of subsystems with reduced number of variables in completely automatic way. It often allows to construct the explicit form of a solution set in many problems of practical importance. Some examples and results of comparison with the standard Reduce package GROEBNER and special-purpose systems FELIX and A1PI are given. 21 refs.; 2 tabs

  6. Computer algebra applications

    International Nuclear Information System (INIS)

    Calmet, J.

    1982-01-01

    A survey of applications based either on fundamental algorithms in computer algebra or on the use of a computer algebra system is presented. Recent work in biology, chemistry, physics, mathematics and computer science is discussed. In particular, applications in high energy physics (quantum electrodynamics), celestial mechanics and general relativity are reviewed. (Auth.)

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

    Science.gov (United States)

    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. Copyright © 2010 Elsevier Inc. All rights reserved.

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

    Science.gov (United States)

    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…

  9. Computer algebra and operators

    Science.gov (United States)

    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.

  10. Applications of computer algebra

    CERN Document Server

    1985-01-01

    Today, certain computer software systems exist which surpass the computational ability of researchers when their mathematical techniques are applied to many areas of science and engineering. These computer systems can perform a large portion of the calculations seen in mathematical analysis. Despite this massive power, thousands of people use these systems as a routine resource for everyday calculations. These software programs are commonly called "Computer Algebra" systems. They have names such as MACSYMA, MAPLE, muMATH, REDUCE and SMP. They are receiving credit as a computational aid with in­ creasing regularity in articles in the scientific and engineering literature. When most people think about computers and scientific research these days, they imagine a machine grinding away, processing numbers arithmetically. It is not generally realized that, for a number of years, computers have been performing non-numeric computations. This means, for example, that one inputs an equa­ tion and obtains a closed for...

  11. Microeconomic theory and computation applying the maxima open-source computer algebra system

    CERN Document Server

    Hammock, Michael R

    2014-01-01

    This book provides a step-by-step tutorial for using Maxima, an open-source multi-platform computer algebra system, to examine the economic relationships that form the core of microeconomics in a way that complements traditional modeling techniques.

  12. Waterloo Workshop on Computer Algebra

    CERN Document Server

    Zima, Eugene; WWCA-2016; Advances in computer algebra : in honour of Sergei Abramov's' 70th birthday

    2018-01-01

    This book discusses the latest advances in algorithms for symbolic summation, factorization, symbolic-numeric linear algebra and linear functional equations. It presents a collection of papers on original research topics from the Waterloo Workshop on Computer Algebra (WWCA-2016), a satellite workshop of the International Symposium on Symbolic and Algebraic Computation (ISSAC’2016), which was held at Wilfrid Laurier University (Waterloo, Ontario, Canada) on July 23–24, 2016.   This workshop and the resulting book celebrate the 70th birthday of Sergei Abramov (Dorodnicyn Computing Centre of the Russian Academy of Sciences, Moscow), whose highly regarded and inspirational contributions to symbolic methods have become a crucial benchmark of computer algebra and have been broadly adopted by many Computer Algebra systems.

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

    Science.gov (United States)

    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…

  14. Computational linear and commutative algebra

    CERN Document Server

    Kreuzer, Martin

    2016-01-01

    This book combines, in a novel and general way, an extensive development of the theory of families of commuting matrices with applications to zero-dimensional commutative rings, primary decompositions and polynomial system solving. It integrates the Linear Algebra of the Third Millennium, developed exclusively here, with classical algorithmic and algebraic techniques. Even the experienced reader will be pleasantly surprised to discover new and unexpected aspects in a variety of subjects including eigenvalues and eigenspaces of linear maps, joint eigenspaces of commuting families of endomorphisms, multiplication maps of zero-dimensional affine algebras, computation of primary decompositions and maximal ideals, and solution of polynomial systems. This book completes a trilogy initiated by the uncharacteristically witty books Computational Commutative Algebra 1 and 2 by the same authors. The material treated here is not available in book form, and much of it is not available at all. The authors continue to prese...

  15. Algebraic computing in general relativity

    International Nuclear Information System (INIS)

    D'Inverno, R.A.

    1975-01-01

    The purpose of this paper is to bring to the attention of potential users the existence of algebraic computing systems, and to illustrate their use by reviewing a number of problems for which such a system has been successfully used in General Relativity. In addition, some remarks are included which may be of help in the future design of these systems. (author)

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

    Science.gov (United States)

    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…

  17. An algebra of reversible computation.

    Science.gov (United States)

    Wang, Yong

    2016-01-01

    We design an axiomatization for reversible computation called reversible ACP (RACP). It has four extendible modules: basic reversible processes algebra, algebra of reversible communicating processes, recursion and abstraction. Just like process algebra ACP in classical computing, RACP can be treated as an axiomatization foundation for reversible computation.

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

    Science.gov (United States)

    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.

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

    Science.gov (United States)

    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…

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

    Science.gov (United States)

    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…

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

    Science.gov (United States)

    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…

  2. GRG computer algebra system in gravitation and general relativity theory

    International Nuclear Information System (INIS)

    Zhitnikov, V.V.; Obukhova, I.G.

    1985-01-01

    The main concepts and capabilities of the GRG specialized computer agebra system intended for performing calculations in the gravitation theory are described. The GRG system is written in the STANDARD LISP language. The program consists of two parts: the first one - for setting initial data, the second one - for specifying a consequence of calculations. The system can function in three formalisms: a coordinate, a tetradic with the Lorentz basis and a spinor ones. The major capabilities of the GRG system are the following: calculation of connectivity and curvature according to the specified metrics, tetrad and torsion; metric type determination according to Petrov; calculation of the Bianchi indentities; operation with an electromagnetic field; tetradic rotations; coordinate conversions

  3. Inequalities, Assessment and Computer Algebra

    Science.gov (United States)

    Sangwin, Christopher J.

    2015-01-01

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

  4. Lie algebra in quantum physics by means of computer algebra

    OpenAIRE

    Kikuchi, Ichio; Kikuchi, Akihito

    2017-01-01

    This article explains how to apply the computer algebra package GAP (www.gap-system.org) in the computation of the problems in quantum physics, in which the application of Lie algebra is necessary. The article contains several exemplary computations which readers would follow in the desktop PC: such as, the brief review of elementary ideas of Lie algebra, the angular momentum in quantum mechanics, the quark eight-fold way model, and the usage of Weyl character formula (in order to construct w...

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

    Science.gov (United States)

    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)

  6. Geometric Algebra Computing

    CERN Document Server

    Corrochano, Eduardo Bayro

    2010-01-01

    This book presents contributions from a global selection of experts in the field. This useful text offers new insights and solutions for the development of theorems, algorithms and advanced methods for real-time applications across a range of disciplines. Written in an accessible style, the discussion of all applications is enhanced by the inclusion of numerous examples, figures and experimental analysis. Features: provides a thorough discussion of several tasks for image processing, pattern recognition, computer vision, robotics and computer graphics using the geometric algebra framework; int

  7. Applications of Computer Algebra Conference

    CERN Document Server

    Martínez-Moro, Edgar

    2017-01-01

    The Applications of Computer Algebra (ACA) conference covers a wide range of topics from Coding Theory to Differential Algebra to Quantam Computing, focusing on the interactions of these and other areas with the discipline of Computer Algebra. This volume provides the latest developments in the field as well as its applications in various domains, including communications, modelling, and theoretical physics. The book will appeal to researchers and professors of computer algebra, applied mathematics, and computer science, as well as to engineers and computer scientists engaged in research and development.

  8. Computational aspects of algebraic curves

    CERN Document Server

    Shaska, Tanush

    2005-01-01

    The development of new computational techniques and better computing power has made it possible to attack some classical problems of algebraic geometry. The main goal of this book is to highlight such computational techniques related to algebraic curves. The area of research in algebraic curves is receiving more interest not only from the mathematics community, but also from engineers and computer scientists, because of the importance of algebraic curves in applications including cryptography, coding theory, error-correcting codes, digital imaging, computer vision, and many more.This book cove

  9. ADAM: analysis of discrete models of biological systems using computer algebra.

    Science.gov (United States)

    Hinkelmann, Franziska; Brandon, Madison; Guang, Bonny; McNeill, Rustin; Blekherman, Grigoriy; Veliz-Cuba, Alan; Laubenbacher, Reinhard

    2011-07-20

    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. 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. 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 mathematical algorithms as a web

  10. Applications of symbolic algebraic computation

    International Nuclear Information System (INIS)

    Brown, W.S.; Hearn, A.C.

    1979-01-01

    This paper is a survey of applications of systems for symbomic algebraic computation. In most successful applications, calculations that can be taken to a given order by hand are then extended one or two more orders by computer. Furthermore, with a few notable exceptins, these applications also involve numerical computation in some way. Therefore the authors emphasize the interface between symbolic and numerical computation, including: 1. Computations with both symbolic and numerical phases. 2. Data involving both the unpredictible size and shape that typify symbolic computation and the (usually inexact) numerical values that characterize numerical computation. 3. Applications of one field to the other. It is concluded that the fields of symbolic and numerical computation can advance most fruitfully in harmony rather than in competition. (Auth.)

  11. Development process of in-service training intended for teachers to perform teaching of mathematics with computer algebra systems

    Science.gov (United States)

    Ardıç, Mehmet Alper; Işleyen, Tevfik

    2018-01-01

    In this study, we deal with the development process of in-service training activities designed in order for mathematics teachers of secondary education to realize teaching of mathematics, utilizing computer algebra systems. In addition, the results obtained from the researches carried out during and after the in-service training were summarized. Last section focuses on suggestions any teacher can use to carry out activities aimed at using computer algebra systems in teaching environments.

  12. Computations in finite-dimensional Lie algebras

    Directory of Open Access Journals (Sweden)

    A. M. Cohen

    1997-12-01

    Full Text Available This paper describes progress made in context with the construction of a general library of Lie algebra algorithms, called ELIAS (Eindhoven Lie Algebra System, within the computer algebra package GAP. A first sketch of the package can be found in Cohen and de Graaf[1]. Since then, in a collaborative effort with G. Ivanyos, the authors have continued to develop algorithms which were implemented in ELIAS by the second author. These activities are part of a bigger project, called ACELA and financed by STW, the Dutch Technology Foundation, which aims at an interactive book on Lie algebras (cf. Cohen and Meertens [2]. This paper gives a global description of the main ways in which to present Lie algebras on a computer. We focus on the transition from a Lie algebra abstractly given by an array of structure constants to a Lie algebra presented as a subalgebra of the Lie algebra of n×n matrices. We describe an algorithm typical of the structure analysis of a finite-dimensional Lie algebra: finding a Levi subalgebra of a Lie algebra.

  13. Introduction to computational linear algebra

    CERN Document Server

    Nassif, Nabil; Erhel, Jocelyne

    2015-01-01

    Introduction to Computational Linear Algebra introduces the reader with a background in basic mathematics and computer programming to the fundamentals of dense and sparse matrix computations with illustrating examples. The textbook is a synthesis of conceptual and practical topics in ""Matrix Computations."" The book's learning outcomes are twofold: to understand state-of-the-art computational tools to solve matrix computations problems (BLAS primitives, MATLAB® programming) as well as essential mathematical concepts needed to master the topics of numerical linear algebra. It is suitable for s

  14. Computing one of Victor Moll's irresistible integrals with computer algebra

    Directory of Open Access Journals (Sweden)

    Christoph Koutschan

    2008-04-01

    Full Text Available We investigate a certain quartic integral from V. Moll's book “Irresistible Integrals” and demonstrate how it can be solved by computer algebra methods, namely by using non-commutative Gröbner bases. We present recent implementations in the computer algebra systems SINGULAR and MATHEMATICA.

  15. Inequalities, assessment and computer algebra

    Science.gov (United States)

    Sangwin, Christopher J.

    2015-01-01

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

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

    Science.gov (United States)

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

    2018-01-01

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

  17. Aberration studies and computer algebra

    International Nuclear Information System (INIS)

    Hawkes, P.W.

    1981-01-01

    The labour of calculating expressions for aberration coefficients is considerably lightened if a computer algebra language is used to perform the various substitutions and expansions involved. After a brief discussion of matrix representations of aberration coefficients, a particular language, which has shown itself to be well adapted to particle optics, is described and applied to the study of high frequency cavity lenses. (orig.)

  18. Computational triadic algebras of signs

    Energy Technology Data Exchange (ETDEWEB)

    Zadrozny, W. [T.J. Watson Research Center, Yorktown Heights, NY (United States)

    1996-12-31

    We present a finite model of Peirce`s ten classes of signs. We briefly describe Peirce`s taxonomy of signs; we prove that any finite collection of signs can be extended to a finite algebra of signs in which all interpretants are themselves being interpreted; and we argue that Peirce`s ten classes of signs can be defined using constraints on algebras of signs. The paper opens the possibility of defining multimodal cognitive agents using Peirce`s classes of signs, and is a first step towards building a computational logic of signs based on Peirce`s taxonomies.

  19. Elementary Business Calculus with Computer Algebra.

    Science.gov (United States)

    Judson, Phoebe T.

    1990-01-01

    Described are various ways that a computer algebra system (MAPLE) was used to facilitate the resequencing of skills and applications within an elementary college-level business calculus course. Experimental results confirmed earlier findings that skills acquisition is not a prerequisite to conceptual understanding or problem-solving ability. (JJK)

  20. Computational algebraic geometry of epidemic models

    Science.gov (United States)

    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.

  1. Some Applications of Algebraic System Solving

    Science.gov (United States)

    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…

  2. Computer programs for the solution of systems of linear algebraic equations

    Science.gov (United States)

    Sequi, W. T.

    1973-01-01

    FORTRAN subprograms for the solution of systems of linear algebraic equations are described, listed, and evaluated in this report. Procedures considered are direct solution, iteration, and matrix inversion. Both incore methods and those which utilize auxiliary data storage devices are considered. Some of the subroutines evaluated require the entire coefficient matrix to be in core, whereas others account for banding or sparceness of the system. General recommendations relative to equation solving are made, and on the basis of tests, specific subprograms are recommended.

  3. Computers in nonassociative rings and algebras

    CERN Document Server

    Beck, Robert E

    1977-01-01

    Computers in Nonassociative Rings and Algebras provides information pertinent to the computational aspects of nonassociative rings and algebras. This book describes the algorithmic approaches for solving problems using a computer.Organized into 10 chapters, this book begins with an overview of the concept of a symmetrized power of a group representation. This text then presents data structures and other computational methods that may be useful in the field of computational algebra. Other chapters consider several mathematical ideas, including identity processing in nonassociative algebras, str

  4. Dynamical systems and linear algebra

    OpenAIRE

    Colonius, Fritz (Prof.)

    2007-01-01

    Dynamical systems and linear algebra / F. Colonius, W. Kliemann. - In: Handbook of linear algebra / ed. by Leslie Hogben. - Boca Raton : Chapman & Hall/CRC, 2007. - S. 56,1-56,22. - (Discrete mathematics and its applications)

  5. Computer Program For Linear Algebra

    Science.gov (United States)

    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.

  6. Efficient Adjoint Computation of Hybrid Systems of Differential Algebraic Equations with Applications in Power Systems

    Energy Technology Data Exchange (ETDEWEB)

    Abhyankar, Shrirang [Argonne National Lab. (ANL), Argonne, IL (United States); Anitescu, Mihai [Argonne National Lab. (ANL), Argonne, IL (United States); Constantinescu, Emil [Argonne National Lab. (ANL), Argonne, IL (United States); Zhang, Hong [Argonne National Lab. (ANL), Argonne, IL (United States)

    2016-03-31

    Sensitivity analysis is an important tool to describe power system dynamic behavior in response to parameter variations. It is a central component in preventive and corrective control applications. The existing approaches for sensitivity calculations, namely, finite-difference and forward sensitivity analysis, require a computational effort that increases linearly with the number of sensitivity parameters. In this work, we investigate, implement, and test a discrete adjoint sensitivity approach whose computational effort is effectively independent of the number of sensitivity parameters. The proposed approach is highly efficient for calculating trajectory sensitivities of larger systems and is consistent, within machine precision, with the function whose sensitivity we are seeking. This is an essential feature for use in optimization applications. Moreover, our approach includes a consistent treatment of systems with switching, such as DC exciters, by deriving and implementing the adjoint jump conditions that arise from state and time-dependent discontinuities. The accuracy and the computational efficiency of the proposed approach are demonstrated in comparison with the forward sensitivity analysis approach.

  7. Computer Algebra Recipes for Mathematical Physics

    CERN Document Server

    Enns, Richard H

    2005-01-01

    Over two hundred novel and innovative computer algebra worksheets or "recipes" will enable readers in engineering, physics, and mathematics to easily and rapidly solve and explore most problems they encounter in their mathematical physics studies. While the aim of this text is to illustrate applications, a brief synopsis of the fundamentals for each topic is presented, the topics being organized to correlate with those found in traditional mathematical physics texts. The recipes are presented in the form of stories and anecdotes, a pedagogical approach that makes a mathematically challenging subject easier and more fun to learn. Key features: * Uses the MAPLE computer algebra system to allow the reader to easily and quickly change the mathematical models and the parameters and then generate new answers * No prior knowledge of MAPLE is assumed; the relevant MAPLE commands are introduced on a need-to-know basis * All MAPLE commands are indexed for easy reference * A classroom-tested story/anecdote format is use...

  8. Computer methods in general relativity: algebraic computing

    CERN Document Server

    Araujo, M E; Skea, J E F; Koutras, A; Krasinski, A; Hobill, D; McLenaghan, R G; Christensen, S M

    1993-01-01

    Karlhede & MacCallum [1] gave a procedure for determining the Lie algebra of the isometry group of an arbitrary pseudo-Riemannian manifold, which they intended to im- plement using the symbolic manipulation package SHEEP but never did. We have recently finished making this procedure explicit by giving an algorithm suitable for implemen- tation on a computer [2]. Specifically, we have written an algorithm for determining the isometry group of a spacetime (in four dimensions), and partially implemented this algorithm using the symbolic manipulation package CLASSI, which is an extension of SHEEP.

  9. IV International Conference on Computer Algebra in Physical Research. Collection of abstracts

    International Nuclear Information System (INIS)

    Rostovtsev, V.A.

    1990-01-01

    The abstracts of the reports made on IV International conference on computer algebra in physical research are presented. The capabilities of application of computers for algebraic computations in high energy physics and quantum field theory are discussed. Particular attention is paid to a software for the REDUCE computer algebra system

  10. Using CAMAL for algebraic computations in general relativity

    International Nuclear Information System (INIS)

    Fitch, J.P.

    1979-01-01

    CAMAL is a collection of computer algebra systems developed in Cambridge, England for use mainly in theoretical physics. One of these was designed originally for general relativity calculations, although it is often used in other fields. In a recent paper Cohen, Leringe, and Sundblad compared six systems for algebraic computations applied to general relativity available in Stockholm. Here similar information for CAMAL is given and by using the same tests CAMAL is added to the comparison. (author)

  11. Computer algebra as a research tool in physics

    International Nuclear Information System (INIS)

    Drouffe, J.M.

    1985-04-01

    The progress of computer algebra observed during these last years has had certainly an impact in physics. I want to precise the role of these new techniques in this application domain and to analyze their present limitations. In Section 1, I describe briefly the use of algebraic manipulation programs at the elementary level. The numerical and symbolic solutions of problems are compared in Section 2. Section 3 is devoted to a prospective about the use of computer algebra at the highest level, as an ''intelligent'' system. I recall in Section 4 what is required from a system to be used in physics

  12. Resolution of First- and Second-Order Linear Differential Equations with Periodic Inputs by a Computer Algebra System

    Directory of Open Access Journals (Sweden)

    M. Legua

    2008-01-01

    Full Text Available In signal processing, a pulse means a rapid change in the amplitude of a signal from a baseline value to a higher or lower value, followed by a rapid return to the baseline value. A square wave function may be viewed as a pulse that repeats its occurrence periodically but the return to the baseline value takes some time to happen. When these periodic functions act as inputs in dynamic systems, the standard tool commonly used to solve the associated initial value problem (IVP is Laplace transform and its inverse. We show how a computer algebra system may also provide the solution of these IVP straight forwardly by adequately introducing the periodic input.

  13. High-Speed Computation of the Kleene Star in Max-Plus Algebraic System Using a Cell Broadband Engine

    Science.gov (United States)

    Goto, Hiroyuki

    This research addresses a high-speed computation method for the Kleene star of the weighted adjacency matrix in a max-plus algebraic system. We focus on systems whose precedence constraints are represented by a directed acyclic graph and implement it on a Cell Broadband Engine™ (CBE) processor. Since the resulting matrix gives the longest travel times between two adjacent nodes, it is often utilized in scheduling problem solvers for a class of discrete event systems. This research, in particular, attempts to achieve a speedup by using two approaches: parallelization and SIMDization (Single Instruction, Multiple Data), both of which can be accomplished by a CBE processor. The former refers to a parallel computation using multiple cores, while the latter is a method whereby multiple elements are computed by a single instruction. Using the implementation on a Sony PlayStation 3™ equipped with a CBE processor, we found that the SIMDization is effective regardless of the system's size and the number of processor cores used. We also found that the scalability of using multiple cores is remarkable especially for systems with a large number of nodes. In a numerical experiment where the number of nodes is 2000, we achieved a speedup of 20 times compared with the method without the above techniques.

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

    Science.gov (United States)

    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…

  15. Elements of algebraic coding systems

    CERN Document Server

    Cardoso da Rocha, Jr, Valdemar

    2014-01-01

    Elements of Algebraic Coding Systems is an introductory text to algebraic coding theory. In the first chapter, you'll gain inside knowledge of coding fundamentals, which is essential for a deeper understanding of state-of-the-art coding systems. This book is a quick reference for those who are unfamiliar with this topic, as well as for use with specific applications such as cryptography and communication. Linear error-correcting block codes through elementary principles span eleven chapters of the text. Cyclic codes, some finite field algebra, Goppa codes, algebraic decoding algorithms, and applications in public-key cryptography and secret-key cryptography are discussed, including problems and solutions at the end of each chapter. Three appendices cover the Gilbert bound and some related derivations, a derivation of the Mac- Williams' identities based on the probability of undetected error, and two important tools for algebraic decoding-namely, the finite field Fourier transform and the Euclidean algorithm f...

  16. Partially ordered algebraic systems

    CERN Document Server

    Fuchs, Laszlo

    2011-01-01

    Originally published in an important series of books on pure and applied mathematics, this monograph by a distinguished mathematician explores a high-level area in algebra. It constitutes the first systematic summary of research concerning partially ordered groups, semigroups, rings, and fields. The self-contained treatment features numerous problems, complete proofs, a detailed bibliography, and indexes. It presumes some knowledge of abstract algebra, providing necessary background and references where appropriate. This inexpensive edition of a hard-to-find systematic survey will fill a gap i

  17. Algebraic Systems and Pushdown Automata

    Science.gov (United States)

    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.

  18. Multilinear Computing and Multilinear Algebraic Geometry

    Science.gov (United States)

    2016-08-10

    algebra : linear systems, least squares, eigevalue problems, singular value problems, determinant evaluation, low-rank approximations, etc — problems...intractability to move beyond linear algebra , substantiating what the PI had proposed. High-resolution MRI with tensors: In another piece of work... applications . One reason is that we found out that many statistical estimation problems ( linear regression, errors-in-variables regression, principal components

  19. Algebraic Modeling of Topological and Computational Structures and Applications

    CERN Document Server

    Theodorou, Doros; Stefaneas, Petros; Kauffman, Louis

    2017-01-01

    This interdisciplinary book covers a wide range of subjects, from pure mathematics (knots, braids, homotopy theory, number theory) to more applied mathematics (cryptography, algebraic specification of algorithms, dynamical systems) and concrete applications (modeling of polymers and ionic liquids, video, music and medical imaging). The main mathematical focus throughout the book is on algebraic modeling with particular emphasis on braid groups. The research methods include algebraic modeling using topological structures, such as knots, 3-manifolds, classical homotopy groups, and braid groups. The applications address the simulation of polymer chains and ionic liquids, as well as the modeling of natural phenomena via topological surgery. The treatment of computational structures, including finite fields and cryptography, focuses on the development of novel techniques. These techniques can be applied to the design of algebraic specifications for systems modeling and verification. This book is the outcome of a w...

  20. Implementing Computer Algebra Enabled Questions for the Assessment and Learning of Mathematics

    Science.gov (United States)

    Sangwin, Christopher J.; Naismith, Laura

    2008-01-01

    We present principles for the design of an online system to support computer algebra enabled questions for use within the teaching and learning of mathematics in higher education. The introduction of a computer algebra system (CAS) into a computer aided assessment (CAA) system affords sophisticated response processing of student provided answers.…

  1. Projects Using a Computer Algebra System in First-Year Undergraduate Mathematics

    Science.gov (United States)

    Rosenzweig, Martin

    2007-01-01

    This paper illustrates the use of computer-based projects in two one-semester first-year undergraduate mathematics classes. Developed over a period of years, the approach is one in which the classes are organised into work-groups, with computer-based projects being undertaken periodically to illustrate the class material. These projects are…

  2. Using Computer Symbolic Algebra to Solve Differential Equations.

    Science.gov (United States)

    Mathews, John H.

    1989-01-01

    This article illustrates that mathematical theory can be incorporated into the process to solve differential equations by a computer algebra system, muMATH. After an introduction to functions of muMATH, several short programs for enhancing the capabilities of the system are discussed. Listed are six references. (YP)

  3. Dynamical systems of algebraic origin

    CERN Document Server

    Schmidt, Klaus

    1995-01-01

    Although much of classical ergodic theory is concerned with single transformations and one-parameter flows, the subject inherits from statistical mechanics not only its name, but also an obligation to analyze spatially extended systems with multidimensional symmetry groups. However, the wealth of concrete and natural examples which has contributed so much to the appeal and development of classical dynamics, is noticeably absent in this more general theory. The purpose of this book is to help remedy this scarcity of explicit examples by introducing a class of continuous Zd-actions diverse enough to exhibit many of the new phenomena encountered in the transition from Z to Zd, but which nevertheless lends itself to systematic study: the Zd-actions by automorphisms of compact, abelian groups. One aspect of these actions, not surprising in itself but quite striking in its extent and depth nonetheless, is the connection with commutative algebra and arithmetical algebraic geometry. The algebraic framework resulting...

  4. Algebraic methods in system theory

    Science.gov (United States)

    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.

  5. Classical versus Computer Algebra Methods in Elementary Geometry

    Science.gov (United States)

    Pech, Pavel

    2005-01-01

    Computer algebra methods based on results of commutative algebra like Groebner bases of ideals and elimination of variables make it possible to solve complex, elementary and non elementary problems of geometry, which are difficult to solve using a classical approach. Computer algebra methods permit the proof of geometric theorems, automatic…

  6. ALAM/CLAM and some applications of computer algebra systems to problems in general relativity

    International Nuclear Information System (INIS)

    Russell-Clark, R.A.

    1973-01-01

    This paper is divided into three parts. Part A presents a historical survey of the development of the system, a brief description of its features and, finally, a critical assessment. ALAM and CLAM have been used in many problems in General Relativity; the vast majority of these belong to a set of standard calculations termed ''metric applications''. However, four large non-standard applications have been attempted successfully and these are described in Part B. CAMAL is the only other system which has been used extensively for work in relativity. CAMAL has played an important role in two research projects and details of these are given in Part C

  7. Algebra

    CERN Document Server

    Flanders, Harley

    1975-01-01

    Algebra presents the essentials of algebra with some applications. The emphasis is on practical skills, problem solving, and computational techniques. Topics covered range from equations and inequalities to functions and graphs, polynomial and rational functions, and exponentials and logarithms. Trigonometric functions and complex numbers are also considered, together with exponentials and logarithms.Comprised of eight chapters, this book begins with a discussion on the fundamentals of algebra, each topic explained, illustrated, and accompanied by an ample set of exercises. The proper use of a

  8. Clifford algebras, noncommutative tori and universal quantum computers

    OpenAIRE

    Vlasov, Alexander Yu.

    2001-01-01

    Recently author suggested [quant-ph/0010071] an application of Clifford algebras for construction of a "compiler" for universal binary quantum computer together with later development [quant-ph/0012009] of the similar idea for a non-binary base. The non-binary case is related with application of some extension of idea of Clifford algebras. It is noncommutative torus defined by polynomial algebraic relations of order l. For l=2 it coincides with definition of Clifford algebra. Here is presente...

  9. Ideals, varieties, and algorithms an introduction to computational algebraic geometry and commutative algebra

    CERN Document Server

    Cox, David A; O'Shea, Donal

    2015-01-01

    This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book. A comprehensive chart in the preface illustrates a variety of ways to proceed with the material once these chapters are covered. In addition to the fundamentals of algebraic geometry—the elimination theorem, the extension theorem, the closure theorem, and the Nullstellensatz—this new edition incorporates several substantial changes, all of which are listed in the Preface. The largest revision incorporates a new chapter (ten), which presents some of the essentials of progress made over the last decades in computing Gröbner bases. The book also includes current computer algebra material in Appendix C and updated independent projects (Appendix D). The book may serve as a first or second course in undergraduate abstract algebra and, with some supplementation perhaps, for beginning graduate level courses in algebraic geom...

  10. Algebraic computability and enumeration models recursion theory and descriptive complexity

    CERN Document Server

    Nourani, Cyrus F

    2016-01-01

    This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories and functorial models, with Kleene algebra examples for languages. Functorial models for Peano arithmetic are described toward important computational complexity areas on a Hilbert program, leading to computability with initial models. Infinite language categories are also introduced to explain descriptive complexity with recursive computability with admissible sets and urelements. Algebraic and categorical realizability is staged on several levels, addressing new computability questions with omitting types realizably. Further applications to computing with ultrafilters on sets and Turing degree computability are examined. Functorial models computability is presented with algebraic trees realizing intuitionistic type...

  11. Discrete event systems in dioid algebra and conventional algebra

    CERN Document Server

    Declerck, Philippe

    2013-01-01

    This book concerns the use of dioid algebra as (max, +) algebra to treat the synchronization of tasks expressed by the maximum of the ends of the tasks conditioning the beginning of another task - a criterion of linear programming. A classical example is the departure time of a train which should wait for the arrival of other trains in order to allow for the changeover of passengers.The content focuses on the modeling of a class of dynamic systems usually called "discrete event systems" where the timing of the events is crucial. Events are viewed as sudden changes in a process which i

  12. Homogeneous Buchberger algorithms and Sullivant's computational commutative algebra challenge

    DEFF Research Database (Denmark)

    Lauritzen, Niels

    2005-01-01

    We give a variant of the homogeneous Buchberger algorithm for positively graded lattice ideals. Using this algorithm we solve the Sullivant computational commutative algebra challenge.......We give a variant of the homogeneous Buchberger algorithm for positively graded lattice ideals. Using this algorithm we solve the Sullivant computational commutative algebra challenge....

  13. Algebraic Varieties and System Design

    DEFF Research Database (Denmark)

    Aabrandt, Andreas

    of cover ideals of hypergraphs, the topological ranking demonstrates the non-trivial decisions that needs to be considered in system design. All the methods developed here have an underlying common structure, namely that they all appear at solution sets for systems of polynomials. These solution sets......Design and analysis of networks have many applications in the engineering sciences. This dissertation seeks to contribute to the methods used in the analysis of networks with a view towards assisting decision making processes. Networks are initially considered as objects in the category of graphs...... and later as objects in the category of hypergraphs. The connection with the category of simplicial pairs become apparent when the topology is analyzed using homological algebra. A topological ranking is developed that measures the ability of the network to stay path-connected. Combined with the analysis...

  14. Computer programs for nonlinear algebraic equations

    International Nuclear Information System (INIS)

    Asaoka, Takumi

    1977-10-01

    We have provided principal computer subroutines for obtaining numerical solutions of nonlinear algebraic equations through a review of the various methods. Benchmark tests were performed on these subroutines to grasp the characteristics of them compared to the existing subroutines. As computer programs based on the secant method, subroutines of the Muller's method using the Chambers' algorithm were newly developed, in addition to the equipment of subroutines of the Muller's method itself. The programs based on the Muller-Chambers' method are useful especially for low-order polynomials with complex coefficients except for the case of finding the triple roots, three close roots etc. In addition, we have equipped subroutines based on the Madsen's algorithm, a variant of the Newton's method. The subroutines have revealed themselves very useful as standard programs because all the roots are found accurately for every case though they take longer computing time than other subroutines for low-order polynomials. It is shown also that an existing subroutine of the Bairstow's method gives the fastest algorithm for polynomials with complex coefficients, except for the case of finding the triple roots etc. We have provided also subroutines to estimate error bounds for all the roots produced with the various algorithms. (auth.)

  15. A Comparison of Success and Failure Rates between Computer-Assisted and Traditional College Algebra Sections

    Science.gov (United States)

    Herron, Sherry; Gandy, Rex; Ye, Ningjun; Syed, Nasser

    2012-01-01

    A unique aspect of the implementation of a computer algebra system (CAS) at a comprehensive university in the U.S. allowed us to compare the student success and failure rates to the traditional method of teaching college algebra. Due to space limitations, the university offered sections of both CAS and traditional simultaneously and, upon…

  16. Q-systems as cluster algebras

    International Nuclear Information System (INIS)

    Kedem, Rinat

    2008-01-01

    Q-systems first appeared in the analysis of the Bethe equations for the XXX model and generalized Heisenberg spin chains (Kirillov and Reshetikhin 1987 Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Steklov. 160 211-21, 301). Such systems are known to exist for any simple Lie algebra and many other Kac-Moody algebras. We formulate the Q-system associated with any simple, simply-laced Lie algebras g in the language of cluster algebras (Fomin and Zelevinsky 2002 J. Am. Math. Soc. 15 497-529), and discuss the relation of the polynomiality property of the solutions of the Q-system in the initial variables, which follows from the representation-theoretical interpretation, to the Laurent phenomenon in cluster algebras (Fomin and Zelevinsky 2002 Adv. Appl. Math. 28 119-44)

  17. Computational commutative and non-commutative algebraic geometry

    CERN Document Server

    Cojocaru, S; Ufnarovski, V

    2005-01-01

    This publication gives a good insight in the interplay between commutative and non-commutative algebraic geometry. The theoretical and computational aspects are the central theme in this study. The topic is looked at from different perspectives in over 20 lecture reports. It emphasizes the current trends in commutative and non-commutative algebraic geometry and algebra. The contributors to this publication present the most recent and state-of-the-art progresses which reflect the topic discussed in this publication. Both researchers and graduate students will find this book a good source of information on commutative and non-commutative algebraic geometry.

  18. Introduction to applied algebraic systems

    CERN Document Server

    Reilly, Norman R

    2009-01-01

    This upper-level undergraduate textbook provides a modern view of algebra with an eye to new applications that have arisen in recent years. A rigorous introduction to basic number theory, rings, fields, polynomial theory, groups, algebraic geometry and elliptic curves prepares students for exploring their practical applications related to storing, securing, retrieving and communicating information in the electronic world. It will serve as a textbook for an undergraduate course in algebra with a strong emphasis on applications. The book offers a brief introduction to elementary number theory as

  19. Lie Algebras and Integrable Systems

    International Nuclear Information System (INIS)

    Zhang Yufeng; Mei Jianqin

    2012-01-01

    A 3 × 3 matrix Lie algebra is first introduced, its subalgebras and the generated Lie algebras are obtained, respectively. Applications of a few Lie subalgebras give rise to two integrable nonlinear hierarchies of evolution equations from their reductions we obtain the nonlinear Schrödinger equations, the mKdV equations, the Broer-Kaup (BK) equation and its generalized equation, etc. The linear and nonlinear integrable couplings of one integrable hierarchy presented in the paper are worked out by casting a 3 × 3 Lie subalgebra into a 2 × 2 matrix Lie algebra. Finally, we discuss the elliptic variable solutions of a generalized BK equation. (general)

  20. Solving algebraic computational problems in geodesy and geoinformatics the answer to modern challenges

    CERN Document Server

    Awange, Joseph L

    2004-01-01

    While preparing and teaching 'Introduction to Geodesy I and II' to - dergraduate students at Stuttgart University, we noticed a gap which motivated the writing of the present book: Almost every topic that we taughtrequiredsomeskillsinalgebra,andinparticular,computeral- bra! From positioning to transformation problems inherent in geodesy and geoinformatics, knowledge of algebra and application of computer algebra software were required. In preparing this book therefore, we haveattemptedtoputtogetherbasicconceptsofabstractalgebra which underpin the techniques for solving algebraic problems. Algebraic c- putational algorithms useful for solving problems which require exact solutions to nonlinear systems of equations are presented and tested on various problems. Though the present book focuses mainly on the two ?elds,theconceptsand techniquespresented hereinarenonetheless- plicable to other ?elds where algebraic computational problems might be encountered. In Engineering for example, network densi?cation and robo...

  1. ASYS2: a new version of computer algebra package ASYS for analysis and simplification of polynomial systems

    International Nuclear Information System (INIS)

    Gerdt, V.P.; Khutornoj, N.V.

    1993-01-01

    In this paper a new version of a package ASYS for analysis of nonlinear algebraic equations based on the Groebner basis technique is described. In addition to the first version ASYS1 of the package, the current one has a number of new facilities which provide its higher efficiency. Some examples and results of comparison between ASYS2, ASYS1 and two other REDUCE packages GROEBNER and CALI included in REDUCE 3.5, are given. 16 refs., 4 tabs

  2. Computer algebra simulation - what can it do?; Was leistet Computer-Algebra-Simulation?

    Energy Technology Data Exchange (ETDEWEB)

    Braun, S. [Visual Analysis AG, Muenchen (Germany)

    2001-07-01

    Shortened development times require new and improved calculation methods. Numeric methods have long become state of the art. However, although numeric simulations provide a better understanding of process parameters, they do not give a feast overview of the interdependences between parameters. Numeric simulations are effective only if all physical parameters are sufficiently known; otherwise, the efficiency will decrease due to the large number of variant calculations required. Computer algebra simulation closes this gap and provides a deeper understanding of the physical fundamentals of technical processes. [German] Neue und verbesserte Berechnungsmethoden sind notwendig, um die staendige Verkuerzung der Entwicklungszyklen zu ermoeglichen. Herkoemmliche Methoden, die auf einem rein numerischen Ansatz basieren, haben sich in vielen Anwendungsbereichen laengst zum Standard entwickelt. Aber nicht nur die staendig kuerzer werdenden Entwicklungszyklen, sondern auch die weiterwachsende Komplexitaet machen es notwendig, ein besseres Verstaendnis der beteiligten Prozessparameter zu gewinnen. Die numerische Simulation besticht zwar durch Detailloesungen, selbst bei komplexen Strukturen und Prozessen, allerdings liefert sie keine schnelle Abschaetzung ueber die Zusammenhaenge zwischen den einzelnen Parametern. Die numerische Simulation ist nur dann effektiv, wenn alle physikalischen Parameter hinreichend bekannt sind; andernfalls sinkt die Effizienz durch die notwendige Anzahl von notwendigen Variantenrechnungen sehr stark. Die Computer-Algebra-Simulation schliesst diese Luecke in dem sie es erlaubt, sich einen tieferen Einblick in die physikalische Funktionsweise technischer Prozesse zu verschaffen. (orig.)

  3. Titration Calculations with Computer Algebra Software

    Science.gov (United States)

    Lachance, Russ; Biaglow, Andrew

    2012-01-01

    This article examines the symbolic algebraic solution of the titration equations for a diprotic acid, as obtained using "Mathematica," "Maple," and "Mathcad." The equilibrium and conservation equations are solved symbolically by the programs to eliminate the approximations that normally would be performed by the student. Of the three programs,…

  4. Matrix algebra theory, computations and applications in statistics

    CERN Document Server

    Gentle, James E

    2017-01-01

    This textbook for graduate and advanced undergraduate students presents the theory of matrix algebra for statistical applications, explores various types of matrices encountered in statistics, and covers numerical linear algebra. Matrix algebra is one of the most important areas of mathematics in data science and in statistical theory, and the second edition of this very popular textbook provides essential updates and comprehensive coverage on critical topics in mathematics in data science and in statistical theory. Part I offers a self-contained description of relevant aspects of the theory of matrix algebra for applications in statistics. It begins with fundamental concepts of vectors and vector spaces; covers basic algebraic properties of matrices and analytic properties of vectors and matrices in multivariate calculus; and concludes with a discussion on operations on matrices in solutions of linear systems and in eigenanalysis. Part II considers various types of matrices encountered in statistics, such as...

  5. Application of Computer Algebra Systems to the Construction of the Collocations and Least Residuals Method for Solving the 3D Navier–Stokes Equations

    Directory of Open Access Journals (Sweden)

    V. P. Shapeev

    2014-01-01

    Full Text Available The method of collocations and least residuals (CLR, which was proposed previously for the numerical solution of two-dimensional Navier–Stokes equations governing the stationary flows of a viscous incompressible fluid, is extended here for the three-dimensional case. The solution is sought in the implemented version of the method in the form of an expansion in the basis solenoidal functions. At all stages of the CLR method construction, a computer algebra system (CAS is applied for the derivation and verification of the formulas of the method and for their translation into arithmetic operators of the Fortran language. For accelerating the convergence of iterations a sufficiently universal algorithm is proposed, which is simple in its implementation and is based on the use of the Krylov’s subspaces. The obtained computational formulas of the CLR method were verified on the exact analytic solution of a test problem. Comparisons with the published numerical results of solving the benchmark problem of the 3D driven cubic cavity flow show that the accuracy of the results obtained by the CLR method corresponds to the known high-accuracy solutions.

  6. The Simulation of an Oxidation-Reduction Titration Curve with Computer Algebra

    Science.gov (United States)

    Whiteley, Richard V., Jr.

    2015-01-01

    Although the simulation of an oxidation/reduction titration curve is an important exercise in an undergraduate course in quantitative analysis, that exercise is frequently simplified to accommodate computational limitations. With the use of readily available computer algebra systems, however, such curves for complicated systems can be generated…

  7. Computer-Aided College Algebra: Learning Components that Students Find Beneficial

    Science.gov (United States)

    Aichele, Douglas B.; Francisco, Cynthia; Utley, Juliana; Wescoatt, Benjamin

    2011-01-01

    A mixed-method study was conducted during the Fall 2008 semester to better understand the experiences of students participating in computer-aided instruction of College Algebra using the software MyMathLab. The learning environment included a computer learning system for the majority of the instruction, a support system via focus groups (weekly…

  8. The algebraic manipulation program DIRAC on IBM personal computers

    International Nuclear Information System (INIS)

    Grozin, A.G.; Perlt, H.

    1989-01-01

    The version DIRAC (2.2) for IBM compatible personal computers is described. It is designed to manipulate algebraically with polynomials and tensors. After a short introduction concerning implementation and usage on personal computers an example program is given. It contains a detailed user's guide to DIRAC (2.2) and, additionally some useful applications. 4 refs

  9. Singularities and computer algebra festschrift for Gert-Martin Greuel on the occasion of his 70th birthday

    CERN Document Server

    Pfister, Gerhard; Schulze, Mathias

    2017-01-01

    This book arose from a conference on “Singularities and Computer Algebra” which was held at the Pfalz-Akademie Lambrecht in June 2015 in honor of Gert-Martin Greuel’s 70th birthday. This unique volume presents a collection of recent original research by some of the leading figures in singularity theory on a broad range of topics including topological and algebraic aspects, classification problems, deformation theory and resolution of singularities. At the same time, the articles highlight a variety of techniques, ranging from theoretical methods to practical tools from computer algebra. Greuel himself made major contributions to the development of both singularity theory and computer algebra. With Gerhard Pfister and Hans Schönemann, he developed the computer algebra system SINGULAR, which has since become the computational tool of choice for many singularity theorists. The book addresses researchers whose work involves singularity theory and computer algebra from the PhD to expert level.

  10. Proton computed tomography images with algebraic reconstruction

    Energy Technology Data Exchange (ETDEWEB)

    Bruzzi, M. [Physics and Astronomy Department, University of Florence, Florence (Italy); Civinini, C.; Scaringella, M. [INFN - Florence Division, Florence (Italy); Bonanno, D. [INFN - Catania Division, Catania (Italy); Brianzi, M. [INFN - Florence Division, Florence (Italy); Carpinelli, M. [INFN - Laboratori Nazionali del Sud, Catania (Italy); Chemistry and Pharmacy Department, University of Sassari, Sassari (Italy); Cirrone, G.A.P.; Cuttone, G. [INFN - Laboratori Nazionali del Sud, Catania (Italy); Presti, D. Lo [INFN - Catania Division, Catania (Italy); Physics and Astronomy Department, University of Catania, Catania (Italy); Maccioni, G. [INFN – Cagliari Division, Cagliari (Italy); Pallotta, S. [INFN - Florence Division, Florence (Italy); Department of Biomedical, Experimental and Clinical Sciences, University of Florence, Florence (Italy); SOD Fisica Medica, Azienda Ospedaliero-Universitaria Careggi, Firenze (Italy); Randazzo, N. [INFN - Catania Division, Catania (Italy); Romano, F. [INFN - Laboratori Nazionali del Sud, Catania (Italy); Sipala, V. [INFN - Laboratori Nazionali del Sud, Catania (Italy); Chemistry and Pharmacy Department, University of Sassari, Sassari (Italy); Talamonti, C. [INFN - Florence Division, Florence (Italy); Department of Biomedical, Experimental and Clinical Sciences, University of Florence, Florence (Italy); SOD Fisica Medica, Azienda Ospedaliero-Universitaria Careggi, Firenze (Italy); Vanzi, E. [Fisica Sanitaria, Azienda Ospedaliero-Universitaria Senese, Siena (Italy)

    2017-02-11

    A prototype of proton Computed Tomography (pCT) system for hadron-therapy has been manufactured and tested in a 175 MeV proton beam with a non-homogeneous phantom designed to simulate high-contrast material. BI-SART reconstruction algorithms have been implemented with GPU parallelism, taking into account of most likely paths of protons in matter. Reconstructed tomography images with density resolutions r.m.s. down to ~1% and spatial resolutions <1 mm, achieved within processing times of ~15′ for a 512×512 pixels image prove that this technique will be beneficial if used instead of X-CT in hadron-therapy.

  11. A Comparison of Equality in Computer Algebra and Correctness in Mathematical Pedagogy (II)

    Science.gov (United States)

    Bradford, Russell; Davenport, James H.; Sangwin, Chris

    2010-01-01

    A perennial problem in computer-aided assessment is that "a right answer", pedagogically speaking, is not the same thing as "a mathematically correct expression", as verified by a computer algebra system, or indeed other techniques such as random evaluation. Paper I in this series considered the difference in cases where there was "the right…

  12. Algebraic Functions, Computer Programming, and the Challenge of Transfer

    Science.gov (United States)

    Schanzer, Emmanuel Tanenbaum

    2015-01-01

    Students' struggles with algebra are well documented. Prior to the introduction of functions, mathematics is typically focused on applying a set of arithmetic operations to compute an answer. The introduction of functions, however, marks the point at which mathematics begins to focus on building up abstractions as a way to solve complex problems.…

  13. Computing with impure numbers - Automatic consistency checking and units conversion using computer algebra

    Science.gov (United States)

    Stoutemyer, D. R.

    1977-01-01

    The computer algebra language MACSYMA enables the programmer to include symbolic physical units in computer calculations, and features automatic detection of dimensionally-inhomogeneous formulas and conversion of inconsistent units in a dimensionally homogeneous formula. Some examples illustrate these features.

  14. Algebraic limit cycles in polynomial systems of differential equations

    International Nuclear Information System (INIS)

    Llibre, Jaume; Zhao Yulin

    2007-01-01

    Using elementary tools we construct cubic polynomial systems of differential equations with algebraic limit cycles of degrees 4, 5 and 6. We also construct a cubic polynomial system of differential equations having an algebraic homoclinic loop of degree 3. Moreover, we show that there are polynomial systems of differential equations of arbitrary degree that have algebraic limit cycles of degree 3, as well as give an example of a cubic polynomial system of differential equations with two algebraic limit cycles of degree 4

  15. Algebra

    CERN Document Server

    Tabak, John

    2004-01-01

    Looking closely at algebra, its historical development, and its many useful applications, Algebra examines in detail the question of why this type of math is so important that it arose in different cultures at different times. The book also discusses the relationship between algebra and geometry, shows the progress of thought throughout the centuries, and offers biographical data on the key figures. Concise and comprehensive text accompanied by many illustrations presents the ideas and historical development of algebra, showcasing the relevance and evolution of this branch of mathematics.

  16. Continuous analog of multiplicative algebraic reconstruction technique for computed tomography

    Science.gov (United States)

    Tateishi, Kiyoko; Yamaguchi, Yusaku; Abou Al-Ola, Omar M.; Kojima, Takeshi; Yoshinaga, Tetsuya

    2016-03-01

    We propose a hybrid dynamical system as a continuous analog to the block-iterative multiplicative algebraic reconstruction technique (BI-MART), which is a well-known iterative image reconstruction algorithm for computed tomography. The hybrid system is described by a switched nonlinear system with a piecewise smooth vector field or differential equation and, for consistent inverse problems, the convergence of non-negatively constrained solutions to a globally stable equilibrium is guaranteed by the Lyapunov theorem. Namely, we can prove theoretically that a weighted Kullback-Leibler divergence measure can be a common Lyapunov function for the switched system. We show that discretizing the differential equation by using the first-order approximation (Euler's method) based on the geometric multiplicative calculus leads to the same iterative formula of the BI-MART with the scaling parameter as a time-step of numerical discretization. The present paper is the first to reveal that a kind of iterative image reconstruction algorithm is constructed by the discretization of a continuous-time dynamical system for solving tomographic inverse problems. Iterative algorithms with not only the Euler method but also the Runge-Kutta methods of lower-orders applied for discretizing the continuous-time system can be used for image reconstruction. A numerical example showing the characteristics of the discretized iterative methods is presented.

  17. A comparison of equality in computer algebra and correctness in mathematical pedagogy (II)

    OpenAIRE

    Bradford, Russell; Davenport, James H; Sangwin, C

    2010-01-01

    A perennial problem in computer-aided assessment is that “a right answer”, pedagogically speaking, is not the same thing as “a mathematically correct expression”, as verified by a computer algebra system, or indeed other techniques such as random evaluation. Paper I in this series considered the difference in cases where there was “the right answer”, typically calculus questions. Here we look at some other cases, notably in linear algebra, where there can be many “right answers”, but still th...

  18. INPUT-OUTPUT STRUCTURE OF LINEAR-DIFFERENTIAL ALGEBRAIC SYSTEMS

    NARCIS (Netherlands)

    KUIJPER, M; SCHUMACHER, JM

    Systems of linear differential and algebraic equations occur in various ways, for instance, as a result of automated modeling procedures and in problems involving algebraic constraints, such as zero dynamics and exact model matching. Differential/algebraic systems may represent an input-output

  19. Algebraic computing program for studying the gauge theory

    International Nuclear Information System (INIS)

    Zet, G.

    2005-01-01

    An algebraic computing program running on Maple V platform is presented. The program is devoted to the study of the gauge theory with an internal Lie group as local symmetry. The physical quantities (gauge potentials, strength tensors, dual tensors etc.) are introduced either as equations in terms of previous defined quantities (tensors), or by manual entry of the component values. The components of the strength tensor and of its dual are obtained with respect to a given metric of the space-time used for describing the gauge theory. We choose a Minkowski space-time endowed with spherical symmetry and give some example of algebraic computing that are adequate for studying electroweak or gravitational interactions. The field equations are also obtained and their solutions are determined using the DEtools facilities of the Maple V computing program. (author)

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

    Science.gov (United States)

    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.

  1. Coexistence of algebraic and non-algebraic limit cycles for quintic polynomial differential systems

    Directory of Open Access Journals (Sweden)

    Ahmed Bendjeddou

    2017-03-01

    Full Text Available In the work by Gine and Grau [11], a planar differential system of degree nine admitting a nested configuration formed by an algebraic and a non-algebraic limit cycles explicitly given was presented. As an improvement, we obtain by a new method a similar result for a family of quintic polynomial differential systems.

  2. Algebraic Structure of Dynamical Systems

    Science.gov (United States)

    2017-05-22

    determine three coordinates of the particle’s location at all times. So we can split the container into two discrete halves. Next we label one half of...each discrete time step, this can thought of as the whole magentic tape shifting over to the left. However the computer is not able to accurately...to suggest that the mathematics performed in this research will have such profound 10 implications, but just to demonstrate that studying math for

  3. The Automation of Stochastization Algorithm with Use of SymPy Computer Algebra Library

    Science.gov (United States)

    Demidova, Anastasya; Gevorkyan, Migran; Kulyabov, Dmitry; Korolkova, Anna; Sevastianov, Leonid

    2018-02-01

    SymPy computer algebra library is used for automatic generation of ordinary and stochastic systems of differential equations from the schemes of kinetic interaction. Schemes of this type are used not only in chemical kinetics but also in biological, ecological and technical models. This paper describes the automatic generation algorithm with an emphasis on application details.

  4. Revisiting Newtonian and Non-Newtonian Fluid Mechanics Using Computer Algebra

    Science.gov (United States)

    Knight, D. G.

    2006-01-01

    This article illustrates how a computer algebra system, such as Maple[R], can assist in the study of theoretical fluid mechanics, for both Newtonian and non-Newtonian fluids. The continuity equation, the stress equations of motion, the Navier-Stokes equations, and various constitutive equations are treated, using a full, but straightforward,…

  5. Algebras of Random Operators Associated to Delone Dynamical Systems

    International Nuclear Information System (INIS)

    Lenz, Daniel; Stollmann, Peter

    2003-01-01

    We carry out a careful study of operator algebras associated with Delone dynamical systems. A von Neumann algebra is defined using noncommutative integration theory. Features of these algebras and the operators they contain are discussed. We restrict our attention to a certain C*-subalgebra to discuss a Shubin trace formula

  6. Image reconstruction of computed tomograms using functional algebra

    International Nuclear Information System (INIS)

    Bradaczek, M.; Bradaczek, H.

    1997-01-01

    A detailed presentation of the process for calculating computed tomograms from the measured data by means of functional algebra is given and an attempt is made to demonstrate the relationships to those inexperienced in mathematics. Suggestions are also made to the manufacturers for improving tomography software although the authors cannot exclude the possibility that some of the recommendations may have already been realized. An interpolation in Fourier space to right-angled coordinates was not employed so that additional computer time and errors resulting from the interpolation are avoided. The savings in calculation time can only be estimated but should amount to about 25%. The error-correction calculation is merely a suggestion since it depends considerably on the apparatus used. Functional algebra is introduced here because it is not so well known but does provide appreciable simplifications in comparison to an explicit presentation. Didactic reasons as well as the possibility for reducing calculation time provided the foundation for this work. (orig.) [de

  7. Prime factorization using quantum annealing and computational algebraic geometry

    Science.gov (United States)

    Dridi, Raouf; Alghassi, Hedayat

    2017-02-01

    We investigate prime factorization from two perspectives: quantum annealing and computational algebraic geometry, specifically Gröbner bases. We present a novel autonomous algorithm which combines the two approaches and leads to the factorization of all bi-primes up to just over 200000, the largest number factored to date using a quantum processor. We also explain how Gröbner bases can be used to reduce the degree of Hamiltonians.

  8. Prime factorization using quantum annealing and computational algebraic geometry

    OpenAIRE

    Dridi, Raouf; Alghassi, Hedayat

    2017-01-01

    We investigate prime factorization from two perspectives: quantum annealing and computational algebraic geometry, specifically Gr?bner bases. We present a novel autonomous algorithm which combines the two approaches and leads to the factorization of all bi-primes up to just over 200000, the largest number factored to date using a quantum processor. We also explain how Gr?bner bases can be used to reduce the degree of Hamiltonians.

  9. Polynomial algebra of discrete models in systems biology.

    Science.gov (United States)

    Veliz-Cuba, Alan; Jarrah, Abdul Salam; Laubenbacher, Reinhard

    2010-07-01

    An increasing number of discrete mathematical models are being published in Systems Biology, ranging from Boolean network models to logical models and Petri nets. They are used to model a variety of biochemical networks, such as metabolic networks, gene regulatory networks and signal transduction networks. There is increasing evidence that such models can capture key dynamic features of biological networks and can be used successfully for hypothesis generation. This article provides a unified framework that can aid the mathematical analysis of Boolean network models, logical models and Petri nets. They can be represented as polynomial dynamical systems, which allows the use of a variety of mathematical tools from computer algebra for their analysis. Algorithms are presented for the translation into polynomial dynamical systems. Examples are given of how polynomial algebra can be used for the model analysis. alanavc@vt.edu Supplementary data are available at Bioinformatics online.

  10. The combinatorics computation for Casimir operators of the symplectic Lie algebra and the application for determining the center of the enveloping algebra of a semidirect product

    International Nuclear Information System (INIS)

    Le Van Hop.

    1989-12-01

    The combinatorics computation is used to describe the Casimir operators of the symplectic Lie Algebra. This result is applied for determining the Center of the enveloping Algebra of the semidirect Product of the Heisenberg Lie Algebra and the symplectic Lie Algebra. (author). 10 refs

  11. The Cuntz algebra Q_N and C*-algebras of product systems

    DEFF Research Database (Denmark)

    Hong, Jeong Hee; Larsen, Nadia S.; Szymanski, Wojciech

    2011-01-01

    We consider a product system over the multiplicative group semigroup N^x of Hilbert bimodules which is implicit in work of S. Yamashita and of the second named author. We prove directly, using universal properties, that the associated Nica-Toeplitz algebra is an extension of the C*-algebra Q...

  12. Logic and algebraic structures in quantum computing

    CERN Document Server

    Eskandarian, Ali; Harizanov, Valentina S

    2016-01-01

    Arising from a special session held at the 2010 North American Annual Meeting of the Association for Symbolic Logic, this volume is an international cross-disciplinary collaboration with contributions from leading experts exploring connections across their respective fields. Themes range from philosophical examination of the foundations of physics and quantum logic, to exploitations of the methods and structures of operator theory, category theory, and knot theory in an effort to gain insight into the fundamental questions in quantum theory and logic. The book will appeal to researchers and students working in related fields, including logicians, mathematicians, computer scientists, and physicists. A brief introduction provides essential background on quantum mechanics and category theory, which, together with a thematic selection of articles, may also serve as the basic material for a graduate course or seminar.

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

    Science.gov (United States)

    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 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.

  14. Kronecker Algebra-based Deadlock Analysis for Railway Systems

    Directory of Open Access Journals (Sweden)

    Robert Mittermayr

    2012-09-01

    Full Text Available Deadlock analysis for railway systems differs in several aspects from deadlock analysis in computer science. While the problem of deadlock analysis for standard computer systems is well-understood, multi-threaded embedded computer systems pose new challenges. A novel approach in this area can easily be applied to deadlock analysis in the domain of railway systems. The approach is based on Kronecker algebra. A lazy implementation of the matrix operations even allows analysing exponentially sized systems in a very efficient manner. The running time of the algorithm does not depend on the problem size but on the size of the solution. While other approaches suffer from the fact that additional constraints make the problem and its solution harder, our approach delivers its results faster if constraints are added. In addition, our approach is complete and sound for railway systems, i.e., it generates neither false positives nor false negatives.

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

    Science.gov (United States)

    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.

  16. Algebra

    CERN Document Server

    Sepanski, Mark R

    2010-01-01

    Mark Sepanski's Algebra is a readable introduction to the delightful world of modern algebra. Beginning with concrete examples from the study of integers and modular arithmetic, the text steadily familiarizes the reader with greater levels of abstraction as it moves through the study of groups, rings, and fields. The book is equipped with over 750 exercises suitable for many levels of student ability. There are standard problems, as well as challenging exercises, that introduce students to topics not normally covered in a first course. Difficult problems are broken into manageable subproblems

  17. On Numerical Stability in Large Scale Linear Algebraic Computations

    Czech Academy of Sciences Publication Activity Database

    Strakoš, Zdeněk; Liesen, J.

    2005-01-01

    Roč. 85, č. 5 (2005), s. 307-325 ISSN 0044-2267 R&D Projects: GA AV ČR 1ET400300415 Institutional research plan: CEZ:AV0Z10300504 Keywords : linear algebraic systems * eigenvalue problems * convergence * numerical stability * backward error * accuracy * Lanczos method * conjugate gradient method * GMRES method Subject RIV: BA - General Mathematics Impact factor: 0.351, year: 2005

  18. Study on time of flight property of electron optical systems by differential algebraic method

    International Nuclear Information System (INIS)

    Cheng Min; Tang Tiantong; Yao Zhenhua

    2002-01-01

    Differential algebraic method is a powerful and promising technique in computer numerical analysis. When applied to nonlinear dynamics systems, the arbitrary high-order transfer properties of the systems can be computed directly with high precision. In this paper, the principle of differential algebra is applied to study on the time of flight (TOF) property of electron optical systems and their arbitrary order TOF transfer properties can be numerically calculated out. As an example, TOF transfer properties of a uniform magnetic sector field analyzer have been studied by differential algebraic method. Relative errors of the first-order and second-order TOF transfer coefficients of the magnetic sector field analyzer are of the order 10 -11 or smaller compared with the analytic solutions. It is proved that differential algebraic TOF method is of high accuracy and very helpful for high-order TOF transfer property analysis of electron optical systems. (author)

  19. Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear partial differential evolution equations of dynamical systems

    Institute of Scientific and Technical Information of China (English)

    2008-01-01

    Using functional derivative technique in quantum field theory, the algebraic dy-namics approach for solution of ordinary differential evolution equations was gen-eralized to treat partial differential evolution equations. The partial differential evo-lution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynam-ics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new nu-merical algorithm—algebraic dynamics algorithm was proposed for partial differ-ential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experi-ments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically.

  20. Assessing Elementary Algebra with STACK

    Science.gov (United States)

    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…

  1. Integrability of dynamical systems algebra and analysis

    CERN Document Server

    Zhang, Xiang

    2017-01-01

    This is the first book to systematically state the fundamental theory of integrability and its development of ordinary differential equations with emphasis on the Darboux theory of integrability and local integrability together with their applications. It summarizes the classical results of Darboux integrability and its modern development together with their related Darboux polynomials and their applications in the reduction of Liouville and elementary integrabilty and in the center—focus problem, the weakened Hilbert 16th problem on algebraic limit cycles and the global dynamical analysis of some realistic models in fields such as physics, mechanics and biology. Although it can be used as a textbook for graduate students in dynamical systems, it is intended as supplementary reading for graduate students from mathematics, physics, mechanics and engineering in courses related to the qualitative theory, bifurcation theory and the theory of integrability of dynamical systems.

  2. Affine.m—Mathematica package for computations in representation theory of finite-dimensional and affine Lie algebras

    Science.gov (United States)

    Nazarov, Anton

    2012-11-01

    In this paper we present Affine.m-a program for computations in representation theory of finite-dimensional and affine Lie algebras and describe implemented algorithms. The algorithms are based on the properties of weights and Weyl symmetry. Computation of weight multiplicities in irreducible and Verma modules, branching of representations and tensor product decomposition are the most important problems for us. These problems have numerous applications in physics and we provide some examples of these applications. The program is implemented in the popular computer algebra system Mathematica and works with finite-dimensional and affine Lie algebras. Catalogue identifier: AENA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENB_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, UK Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 24 844 No. of bytes in distributed program, including test data, etc.: 1 045 908 Distribution format: tar.gz Programming language: Mathematica. Computer: i386-i686, x86_64. Operating system: Linux, Windows, Mac OS, Solaris. RAM: 5-500 Mb Classification: 4.2, 5. Nature of problem: Representation theory of finite-dimensional Lie algebras has many applications in different branches of physics, including elementary particle physics, molecular physics, nuclear physics. Representations of affine Lie algebras appear in string theories and two-dimensional conformal field theory used for the description of critical phenomena in two-dimensional systems. Also Lie symmetries play a major role in a study of quantum integrable systems. Solution method: We work with weights and roots of finite-dimensional and affine Lie algebras and use Weyl symmetry extensively. Central problems which are the computations of weight multiplicities, branching and fusion coefficients are solved using one general recurrent

  3. An algebraic substructuring using multiple shifts for eigenvalue computations

    International Nuclear Information System (INIS)

    Ko, Jin Hwan; Jung, Sung Nam; Byun, Do Young; Bai, Zhaojun

    2008-01-01

    Algebraic substructuring (AS) is a state-of-the-art method in eigenvalue computations, especially for large-sized problems, but originally it was designed to calculate only the smallest eigenvalues. Recently, an updated version of AS has been introduced to calculate the interior eigenvalues over a specified range by using a shift concept that is referred to as the shifted AS. In this work, we propose a combined method of both AS and the shifted AS by using multiple shifts for solving a considerable number of eigensolutions in a large-sized problem, which is an emerging computational issue of noise or vibration analysis in vehicle design. In addition, we investigated the accuracy of the shifted AS by presenting an error criterion. The proposed method has been applied to the FE model of an automobile body. The combined method yielded a higher efficiency without loss of accuracy in comparison to the original AS

  4. Calculation of heat-kernel coefficients and usage of computer algebra

    International Nuclear Information System (INIS)

    Bel'kov, A.A.; Lanev, A.V.; Schaale, A.

    1995-01-01

    The calculation of heat-kernel coefficients with the classical De Witt algorithm has been discussed. We present the explicit form of the coefficients up to h 5 in the general case and up to h 7 min for the minimal parts. The results are compared with the expressions in other papers. A method to optimize the usage of memory for working with large expressions on universal computer algebra systems has been proposed. 20 refs

  5. Construction Example for Algebra System Using Harmony Search Algorithm

    Directory of Open Access Journals (Sweden)

    FangAn Deng

    2015-01-01

    Full Text Available The construction example of algebra system is to verify the existence of a complex algebra system, and it is a NP-hard problem. In this paper, to solve this kind of problems, firstly, a mathematical optimization model for construction example of algebra system is established. Secondly, an improved harmony search algorithm based on NGHS algorithm (INGHS is proposed to find as more solutions as possible for the optimization model; in the proposed INGHS algorithm, to achieve the balance between exploration power and exploitation power in the search process, a global best strategy and parameters dynamic adjustment method are present. Finally, nine construction examples of algebra system are used to evaluate the optimization model and performance of INGHS. The experimental results show that the proposed algorithm has strong performance for solving complex construction example problems of algebra system.

  6. Deformations of classical Lie algebras with homogeneous root system in characteristic two. I

    International Nuclear Information System (INIS)

    Chebochko, N G

    2005-01-01

    Spaces of local deformations of classical Lie algebras with a homogeneous root system over a field K of characteristic 2 are studied. By a classical Lie algebra over a field K we mean the Lie algebra of a simple algebraic Lie group or its quotient algebra by the centre. The description of deformations of Lie algebras is interesting in connection with the classification of the simple Lie algebras.

  7. Quantum integrable systems related to lie algebras

    International Nuclear Information System (INIS)

    Olshanetsky, M.A.; Perelomov, A.M.

    1983-01-01

    Some quantum integrable finite-dimensional systems related to Lie algebras are considered. This review continues the previous review of the same authors (1981) devoted to the classical aspects of these systems. The dynamics of some of these systems is closely related to free motion in symmetric spaces. Using this connection with the theory of symmetric spaces some results such as the forms of spectra, wave functions, S-matrices, quantum integrals of motion are derived. In specific cases the considered systems describe the one-dimensional n-body systems interacting pairwise via potentials g 2 v(q) of the following 5 types: vsub(I)(q)=q - 2 , vsub(II)(q)=sinh - 2 q, vsub(III)(q)=sin - 2 q, vsub(IV)(q)=P(q), vsub(V)(q)=q - 2 +#betta# 2 q 2 . Here P(q) is the Weierstrass function, so that the first three cases are merely subcases on the fourth. The system characterized by the Toda nearest-neighbour potential exp(qsub(j)-qsub(j+1)) is moreover considered. This review presents from a general and universal point of view results obtained mainly over the past fifteen years. Besides, it contains some new results both of physical and mathematical interest. (orig.)

  8. Notes on algebraic invariants for non-commutative dynamical systems

    Energy Technology Data Exchange (ETDEWEB)

    Longo, R [Rome Univ. (Italy). Istituto di Matematica

    1979-11-01

    We consider an algebraic invariant for non-commutative dynamical systems naturally arising as the spectrum of the modular operator associated to an invariant state, provided certain conditions of mixing type are present. This invariant turns out to be exactly the annihilator of the invariant T of Connes. Further comments are included, in particular on the type of certain algebras of local observables

  9. Application of Computer Graphics to Graphing in Algebra and Trigonometry. Final Report.

    Science.gov (United States)

    Morris, J. Richard

    This project was designed to improve the graphing competency of students in elementary algebra, intermediate algebra, and trigonometry courses at Virginia Commonwealth University. Computer graphics programs were designed using an Apple II Plus computer and implemented using Pascal. The software package is interactive and gives students control…

  10. Computer-aided tool for the teaching of relational algebra in data base courses

    Directory of Open Access Journals (Sweden)

    Johnny Villalobos Murillo

    2016-03-01

    Full Text Available This article describes the design and implementation of computer-aided tool called Relational Algebra Translator (RAT in data base courses, for the teaching of relational algebra. There was a problem when introducing the relational algebra topic in the course EIF 211 Design and Implementation of Databases, which belongs to the career of Engineering in Information Systems of the National University of Costa Rica, because students attending this course were lacking profound mathematical knowledge, which led to a learning problem, being this an important subject to understand what the data bases search and request do RAT comes along to enhance the teaching-learning process. It introduces the architectural and design principles required for its implementation, such as: the language symbol table, the gramatical rules and the basic algorithms that RAT uses to translate from relational algebra to SQL language. This tool has been used for one periods and has demonstrated to be effective in the learning-teaching process.  This urged investigators to publish it in the web site: www.slinfo.una.ac.cr in order for this tool to be used in other university courses.

  11. Algebraic and computational aspects of real tensor ranks

    CERN Document Server

    Sakata, Toshio; Miyazaki, Mitsuhiro

    2016-01-01

    This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of tensor ranks, maximal ranks, and typical ranks, over the real number field. Although tensor ranks have been often argued in the complex number field, it should be emphasized that this book treats real tensor ranks, which have direct applications in statistics. The book provides several interesting ideas, including determinant polynomials, determinantal ideals, absolutely nonsingular tensors, absolutely full column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. In addition to reviews of methods to determine real tensor ranks in details, global theories such as the Jacobian method are also reviewed in details. The book includes as well an accessible and comprehensive introduction of mathematical backgrounds, with basics of positive polynomials and calculations by using the Groebner basis. Furthermore, this book provides insights into numerical methods of finding tensor ranks through...

  12. Robust algebraic image enhancement for intelligent control systems

    Science.gov (United States)

    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.

  13. Crossed product algebras associated with topological dynamical systems

    NARCIS (Netherlands)

    Svensson, Pär Christian

    2009-01-01

    We study connections between topological dynamical systems and associated algebras of crossed product type. We derive equivalences between structural properties of a crossed product and dynamical properties of the associated system and furthermore derive qualitative results concerning the crossed

  14. Entropic and algebraic K-systems: A comparison

    International Nuclear Information System (INIS)

    Benatti, F.

    1990-01-01

    In the quantum, i.e. non-commutative case, algebraic K-systems and entropic K-systems must be distinguished. The similarities and differences between them are considered, especially with regard to clustering- and mixing properties. 14 refs

  15. INdAM Meeting on Homological and Computational Methods in Commutative Algebra

    CERN Document Server

    Gubeladze, Joseph; Römer, Tim

    2017-01-01

    This volume collects contributions by leading experts in the area of commutative algebra related to the  INdAM meeting “Homological and Computational Methods in Commutative Algebra” held in Cortona (Italy) from May 30 to  June 3, 2016 . The conference and this volume are dedicated to Winfried Bruns on the occasion of his 70th birthday. In particular, the topics of this book strongly reflect the variety of Winfried Bruns’ research interests and his great impact on commutative algebra as well as its applications to related fields. The authors discuss recent and relevant developments in algebraic geometry, commutative algebra, computational algebra, discrete geometry and homological algebra. The book offers a unique resource, both for young and more experienced researchers seeking comprehensive overviews and extensive bibliographic references.

  16. Remarks on second-order quadratic systems in algebras

    Directory of Open Access Journals (Sweden)

    Art Sagle

    2017-10-01

    Full Text Available This paper is an addendum to our earlier paper [8], where a systematic study of quadratic systems of second order ordinary differential equations defined in commutative algebras was presented. Here we concentrate on special solutions and energy considerations of some quadratic systems defined in algebras which need not be commutative, however, we shall throughout assume the algebra to be associative. We here also give a positive answer to an open question, concerning periodic motions of such systems, posed in our earlier paper.

  17. On W1+∞ 3-algebra and integrable system

    Directory of Open Access Journals (Sweden)

    Min-Ru Chen

    2015-02-01

    Full Text Available We construct the W1+∞ 3-algebra and investigate its connection with the integrable systems. Since the W1+∞ 3-algebra with a fixed generator W00 in the operator Nambu 3-bracket recovers the W1+∞ algebra, it is intrinsically related to the KP hierarchy. For the general case of the W1+∞ 3-algebra, we directly derive the KP and KdV equations from the Nambu–Poisson evolution equation with the different Hamiltonian pairs of the KP hierarchy. Due to the Nambu–Poisson evolution equation involves two Hamiltonians, the deep relationship between the Hamiltonian pairs of KP hierarchy is revealed. Furthermore we give a realization of the W1+∞ 3-algebra in terms of a complex bosonic field. Based on the Nambu 3-brackets of the complex bosonic field, we derive the (generalized nonlinear Schrödinger equation and give an application in optical soliton.

  18. Algebraic polynomial system solving and applications

    NARCIS (Netherlands)

    Bleylevens, I.W.M.

    2010-01-01

    The problem of computing the solutions of a system of multivariate polynomial equations can be approached by the Stetter-Möller matrix method which casts the problem into a large eigenvalue problem. This Stetter-Möller matrix method forms the starting point for the development of computational

  19. Global identifiability of linear compartmental models--a computer algebra algorithm.

    Science.gov (United States)

    Audoly, S; D'Angiò, L; Saccomani, M P; Cobelli, C

    1998-01-01

    A priori global identifiability deals with the uniqueness of the solution for the unknown parameters of a model and is, thus, a prerequisite for parameter estimation of biological dynamic models. Global identifiability is however difficult to test, since it requires solving a system of algebraic nonlinear equations which increases both in nonlinearity degree and number of terms and unknowns with increasing model order. In this paper, a computer algebra tool, GLOBI (GLOBal Identifiability) is presented, which combines the topological transfer function method with the Buchberger algorithm, to test global identifiability of linear compartmental models. GLOBI allows for the automatic testing of a priori global identifiability of general structure compartmental models from general multi input-multi output experiments. Examples of usage of GLOBI to analyze a priori global identifiability of some complex biological compartmental models are provided.

  20. Study on Differential Algebraic Method of Aberrations up to Arbitrary Order for Combined Electromagnetic Focusing Systems

    Institute of Scientific and Technical Information of China (English)

    CHENG Min; TANG Tiantong; YAO Zhenhua; ZHU Jingping

    2001-01-01

    Differential algebraic method is apowerful technique in computer numerical analysisbased on nonstandard analysis and formal series the-ory. It can compute arbitrary high order derivativeswith excellent accuracy. The principle of differentialalgebraic method is applied to calculate high orderaberrations of combined electromagnetic focusing sys-tems. As an example, third-order geometric aberra-tion coefficients of an actual combined electromagneticfocusing system were calculated. The arbitrary highorder aberrations are conveniently calculated by dif-ferential algebraic method and the fifth-order aberra-tion diagrams are given.

  1. Discrete integrable systems and deformations of associative algebras

    International Nuclear Information System (INIS)

    Konopelchenko, B G

    2009-01-01

    Interrelations between discrete deformations of the structure constants for associative algebras and discrete integrable systems are reviewed. Theory of deformations for associative algebras is presented. Closed left ideal generated by the elements representing the multiplication table plays a central role in this theory. Deformations of the structure constants are generated by the deformation driving algebra and governed by the central system of equations. It is demonstrated that many discrete equations such as discrete Boussinesq equation, discrete WDVV equation, discrete Schwarzian KP and BKP equations, discrete Hirota-Miwa equations for KP and BKP hierarchies are particular realizations of the central system. An interaction between the theories of discrete integrable systems and discrete deformations of associative algebras is reciprocal and fruitful. An interpretation of the Menelaus relation (discrete Schwarzian KP equation), discrete Hirota-Miwa equation for KP hierarchy, consistency around the cube as the associativity conditions and the concept of gauge equivalence, for instance, between the Menelaus and KP configurations are particular examples.

  2. KMS states on Nica-Toeplitz algebras of product systems

    DEFF Research Database (Denmark)

    Hong, Jeong Hee; Larsen, Nadia S.; Szymanski, Wojciech

    2012-01-01

    We investigate KMS states of Fowler's Nica-Toeplitz algebra NT(X) associated to a compactly aligned product system X over a semigroup P of Hilbert bimodules. This analysis relies on restrictions of these states to the core algebra which satisfy appropriate scaling conditions. The concept of product...... system of finite type is introduced. If (G, P) is a lattice ordered group and X is a product system of finite type over P satisfying certain coherence properties, we construct KMS_beta states of NT(X) associated to a scalar dynamics from traces on the coefficient algebra of the product system. Our...... results were motivated by, and generalize some of the results of Laca and Raeburn obtained for the Toeplitz algebra of the affine semigroup over the natural numbers....

  3. Principles of linear algebra with Mathematica

    CERN Document Server

    Shiskowski, Kenneth M

    2013-01-01

    A hands-on introduction to the theoretical and computational aspects of linear algebra using Mathematica® Many topics in linear algebra are simple, yet computationally intensive, and computer algebra systems such as Mathematica® are essential not only for learning to apply the concepts to computationally challenging problems, but also for visualizing many of the geometric aspects within this field of study. Principles of Linear Algebra with Mathematica uniquely bridges the gap between beginning linear algebra and computational linear algebra that is often encountered in applied settings,

  4. A Computer Algebra Approach to Solving Chemical Equilibria in General Chemistry

    Science.gov (United States)

    Kalainoff, Melinda; Lachance, Russ; Riegner, Dawn; Biaglow, Andrew

    2012-01-01

    In this article, we report on a semester-long study of the incorporation into our general chemistry course, of advanced algebraic and computer algebra techniques for solving chemical equilibrium problems. The method presented here is an alternative to the commonly used concentration table method for describing chemical equilibria in general…

  5. Changes in Pre-Service Teachers' Algebraic Misconceptions by Using Computer-Assisted Instruction

    Science.gov (United States)

    Lin, ByCheng-Yao; Ko, Yi-Yin; Kuo, Yu-Chun

    2014-01-01

    In order to carry out current reforms regarding algebra and technology in elementary school mathematics successfully, pre-service elementary mathematics teachers must be equipped with adequate understandings of algebraic concepts and self-confidence in using computers for their future teaching. This paper examines the differences in preservice…

  6. The algebraic criteria for the stability of control systems

    Science.gov (United States)

    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.

  7. Rosen's (M,R) system in process algebra.

    Science.gov (United States)

    Gatherer, Derek; Galpin, Vashti

    2013-11-17

    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. 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. We argue that the behaviour of (M,R) in Bio-PEPA shows life-like properties.

  8. Quadratic algebra approach to relativistic quantum Smorodinsky-Winternitz systems

    International Nuclear Information System (INIS)

    Marquette, Ian

    2011-01-01

    There exists a relation between the Klein-Gordon and the Dirac equations with scalar and vector potentials of equal magnitude and the Schroedinger equation. We obtain the relativistic energy spectrum for the four relativistic quantum Smorodinsky-Winternitz systems from their quasi-Hamiltonian and the quadratic algebras studied by Daskaloyannis in the nonrelativistic context. We also apply the quadratic algebra approach directly to the initial Dirac equation for these four systems and show that the quadratic algebras obtained are the same than those obtained from the quasi-Hamiltonians. We point out how results obtained in context of quantum superintegrable systems and their polynomial algebras can be applied to the quantum relativistic case.

  9. The lie-algebraic structures and integrability of differential and differential-difference nonlinear dynamical systems

    International Nuclear Information System (INIS)

    Prykarpatsky, A.K.; Blackmore, D.L.; Bogolubov, N.N. Jr.

    2007-05-01

    The infinite-dimensional operator Lie algebras of the related integrable nonlocal differential-difference dynamical systems are treated as their hidden symmetries. As a result of their dimerization the Lax type representations for both local differential-difference equations and nonlocal ones are obtained. An alternative approach to the Lie-algebraic interpretation of the integrable local differential-difference systems is also proposed. The Hamiltonian representation for a hierarchy of Lax type equations on a dual space to the centrally extended Lie algebra of integro-differential operators with matrix-valued coefficients coupled with suitable eigenfunctions and adjoint eigenfunctions evolutions of associated spectral problems is obtained by means of a specially constructed Baecklund transformation. The Hamiltonian description for the corresponding set of additional symmetry hierarchies is represented. The relation of these hierarchies with Lax type integrable (3+1)-dimensional nonlinear dynamical systems and their triple Lax type linearizations is analyzed. The Lie-algebraic structures, related with centrally extended current operator Lie algebras are discussed with respect to constructing new nonlinear integrable dynamical systems on functional manifolds and super-manifolds. Special Poisson structures and related with them factorized integrable operator dynamical systems having interesting applications in modern mathematical physics, quantum computing mathematics and other fields are constructed. The previous purely computational results are explained within the approach developed. (author)

  10. Algebraic quantization of systems with a gauge degeneracy

    International Nuclear Information System (INIS)

    Grundling, H.B.G.S.; Hurst, C.A.

    1985-01-01

    Systems with a gauge degeneracy are characterized either by supplementary conditions, or by a set of generators of gauge transformations, or by a set of constraints deriving from Dirac's canonical constraint method. These constraints can be expressed either as conditions on the field algebra F, or on the states on F. In a Csup(*)-algebra framework, we show that the state conditions give rise to a factor algebra of a subalgebra of the field algebra F. This factor algebra R, is free of state conditions. In this formulation we show also that the algebraic conditions can be treated in the same way as the state conditions. The connection between states on F and states on R is investigated further within this framework, as is also the set of transformations which are compatible with the set of constraints. It is also shown that not every set of constraints can give rise to a nontrivial system. Finally as an example, the abstract theory is applied to the electromagnetic field, and this treatment can be generalized to all systems of bosons with linear constraints. The question of dynamics is not discussed. (orig.)

  11. Monomial algebras

    CERN Document Server

    Villarreal, Rafael

    2015-01-01

    The book stresses the interplay between several areas of pure and applied mathematics, emphasizing the central role of monomial algebras. It unifies the classical results of commutative algebra with central results and notions from graph theory, combinatorics, linear algebra, integer programming, and combinatorial optimization. The book introduces various methods to study monomial algebras and their presentation ideals, including Stanley-Reisner rings, subrings and blowup algebra-emphasizing square free quadratics, hypergraph clutters, and effective computational methods.

  12. 2nd EACA International School on Computer Algebra and its Applications

    CERN Document Server

    Gimenez, Philippe; Sáenz-de-Cabezón, Eduardo

    2017-01-01

    Featuring up-to-date coverage of three topics lying at the intersection of combinatorics and commutative algebra, namely Koszul algebras, primary decompositions and subdivision operations in simplicial complexes, this book has its focus on computations. "Computations and combinatorics in commutative algebra" has been written by experts in both theoretical and computational aspects of these three subjects and is aimed at a broad audience, from experienced researchers who want to have an easy but deep review of the topics covered to postgraduate students who need a quick introduction to the techniques. The computational treatment of the material, including plenty of examples and code, will be useful for a wide range of professionals interested in the connections between commutative algebra and combinatorics.

  13. Process algebras for hybrid systems : comparison and development

    NARCIS (Netherlands)

    Khadim, U.

    2008-01-01

    Our research is about formal speci¯cation and analysis of hybrid systems. The formalism used is process algebra. Hybrid systems are systems that exhibit both discrete and continuous behaviour. An example of a hybrid system is a digital controller controlling a physical device such as present in

  14. Vertex algebras and algebraic curves

    CERN Document Server

    Frenkel, Edward

    2004-01-01

    Vertex algebras are algebraic objects that encapsulate the concept of operator product expansion from two-dimensional conformal field theory. Vertex algebras are fast becoming ubiquitous in many areas of modern mathematics, with applications to representation theory, algebraic geometry, the theory of finite groups, modular functions, topology, integrable systems, and combinatorics. This book is an introduction to the theory of vertex algebras with a particular emphasis on the relationship with the geometry of algebraic curves. The notion of a vertex algebra is introduced in a coordinate-independent way, so that vertex operators become well defined on arbitrary smooth algebraic curves, possibly equipped with additional data, such as a vector bundle. Vertex algebras then appear as the algebraic objects encoding the geometric structure of various moduli spaces associated with algebraic curves. Therefore they may be used to give a geometric interpretation of various questions of representation theory. The book co...

  15. Analytical solution using computer algebra of a biosensor for detecting toxic substances in water

    Science.gov (United States)

    Rúa Taborda, María. Isabel

    2014-05-01

    In a relatively recent paper an electrochemical biosensor for water toxicity detection based on a bio-chip as a whole cell was proposed and numerically solved and analyzed. In such paper the kinetic processes in a miniaturized electrochemical biosensor system was described using the equations for specific enzymatic reaction and the diffusion equation. The numerical solution shown excellent agreement with the measured data but such numerical solution is not enough to design efficiently the corresponding bio-chip. For this reason an analytical solution is demanded. The object of the present work is to provide such analytical solution and then to give algebraic guides to design the bio-sensor. The analytical solution is obtained using computer algebra software, specifically Maple. The method of solution is the Laplace transform, with Bromwich integral and residue theorem. The final solution is given as a series of Bessel functions and the effective time for the bio-sensor is computed. It is claimed that the analytical solutions that were obtained will be very useful to predict further current variations in similar systems with different geometries, materials and biological components. Beside of this the analytical solution that we provide is very useful to investigate the relationship between different chamber parameters such as cell radius and height; and electrode radius.

  16. Exact distributions of two-sample rank statistics and block rank statistics using computer algebra

    NARCIS (Netherlands)

    Wiel, van de M.A.

    1998-01-01

    We derive generating functions for various rank statistics and we use computer algebra to compute the exact null distribution of these statistics. We present various techniques for reducing time and memory space used by the computations. We use the results to write Mathematica notebooks for

  17. Identification of control targets in Boolean molecular network models via computational algebra.

    Science.gov (United States)

    Murrugarra, David; Veliz-Cuba, Alan; Aguilar, Boris; Laubenbacher, Reinhard

    2016-09-23

    Many problems in biomedicine and other areas of the life sciences can be characterized as control problems, with the goal of finding strategies to change a disease or otherwise undesirable state of a biological system into another, more desirable, state through an intervention, such as a drug or other therapeutic treatment. The identification of such strategies is typically based on a mathematical model of the process to be altered through targeted control inputs. This paper focuses on processes at the molecular level that determine the state of an individual cell, involving signaling or gene regulation. The mathematical model type considered is that of Boolean networks. The potential control targets can be represented by a set of nodes and edges that can be manipulated to produce a desired effect on the system. This paper presents a method for the identification of potential intervention targets in Boolean molecular network models using algebraic techniques. The approach exploits an algebraic representation of Boolean networks to encode the control candidates in the network wiring diagram as the solutions of a system of polynomials equations, and then uses computational algebra techniques to find such controllers. The control methods in this paper are validated through the identification of combinatorial interventions in the signaling pathways of previously reported control targets in two well studied systems, a p53-mdm2 network and a blood T cell lymphocyte granular leukemia survival signaling network. Supplementary data is available online and our code in Macaulay2 and Matlab are available via http://www.ms.uky.edu/~dmu228/ControlAlg . This paper presents a novel method for the identification of intervention targets in Boolean network models. The results in this paper show that the proposed methods are useful and efficient for moderately large networks.

  18. Study of solving a Toda dynamic system with loop algebra

    International Nuclear Information System (INIS)

    Zhu Qiao; Yang Zhanying; Shi Kangjie; Wen Junqing

    2006-01-01

    The authors construct a Toda system with Loop algebra, and prove that the Lax equation L=[L,M] can be solved by means of solving a regular Riemann-Hilbert problem. In our system, M in Lax pair is an antisymmetrical matrix, while L=L + + M, and L + is a quasi-upper triangular matrix of loop algebra. In order to check our result, the authors exactly solve an R-H problem under a given initial condition as an example. (authors)

  19. Calculating three loop ladder and V-topologies for massive operator matrix elements by computer algebra

    International Nuclear Information System (INIS)

    Ablinger, J.; Schneider, C.; Manteuffel, A. von

    2015-09-01

    Three loop ladder and V-topology diagrams contributing to the massive operator matrix element A Qg are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable N and the dimensional parameter ε. Given these representations, the desired Laurent series expansions in ε can be obtained with the help of our computer algebra toolbox. Here we rely on generalized hypergeometric functions and Mellin-Barnes representations, on difference ring algorithms for symbolic summation, on an optimized version of the multivariate Almkvist-Zeilberger algorithm for symbolic integration, and on new methods to calculate Laurent series solutions of coupled systems of differential equations. The solutions can be computed for general coefficient matrices directly for any basis also performing the expansion in the dimensional parameter in case it is expressible in terms of indefinite nested product-sum expressions. This structural result is based on new results of our difference ring theory. In the cases discussed we deal with iterative sum- and integral-solutions over general alphabets. The final results are expressed in terms of special sums, forming quasi-shuffle algebras, such as nested harmonic sums, generalized harmonic sums, and nested binomially weighted (cyclotomic) sums. Analytic continuations to complex values of N are possible through the recursion relations obeyed by these quantities and their analytic asymptotic expansions. The latter lead to a host of new constants beyond the multiple zeta values, the infinite generalized harmonic and cyclotomic sums in the case of V-topologies.

  20. Calculating three loop ladder and V-topologies for massive operator matrix elements by computer algebra

    Science.gov (United States)

    Ablinger, J.; Behring, A.; Blümlein, J.; De Freitas, A.; von Manteuffel, A.; Schneider, C.

    2016-05-01

    Three loop ladder and V-topology diagrams contributing to the massive operator matrix element AQg are calculated. The corresponding objects can all be expressed in terms of nested sums and recurrences depending on the Mellin variable N and the dimensional parameter ε. Given these representations, the desired Laurent series expansions in ε can be obtained with the help of our computer algebra toolbox. Here we rely on generalized hypergeometric functions and Mellin-Barnes representations, on difference ring algorithms for symbolic summation, on an optimized version of the multivariate Almkvist-Zeilberger algorithm for symbolic integration, and on new methods to calculate Laurent series solutions of coupled systems of differential equations. The solutions can be computed for general coefficient matrices directly for any basis also performing the expansion in the dimensional parameter in case it is expressible in terms of indefinite nested product-sum expressions. This structural result is based on new results of our difference ring theory. In the cases discussed we deal with iterative sum- and integral-solutions over general alphabets. The final results are expressed in terms of special sums, forming quasi-shuffle algebras, such as nested harmonic sums, generalized harmonic sums, and nested binomially weighted (cyclotomic) sums. Analytic continuations to complex values of N are possible through the recursion relations obeyed by these quantities and their analytic asymptotic expansions. The latter lead to a host of new constants beyond the multiple zeta values, the infinite generalized harmonic and cyclotomic sums in the case of V-topologies.

  1. Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates.

    Science.gov (United States)

    Dovlo, Edem; Baddour, Natalie

    2015-01-01

    The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. The advantages of our method include: •The implementation of the 2D Fourier transform in polar coordinates within the toolbox via the combination of two significantly simpler transforms.•The modular approach along with the idea of lookup tables implemented help avoid the issue of indeterminate results which may occur when attempting to directly evaluate the transform.•The concept also helps prevent unnecessary computation of already known transforms thereby saving memory and processing time.

  2. Yang-Baxter algebra - Integrable systems - Conformal quantum field theories

    International Nuclear Information System (INIS)

    Karowski, M.

    1989-01-01

    This series of lectures is based on investigations [1,2] of finite-size corrections for the six-vertex model by means of Bethe ansatz methods. In addition a review on applications of Yang-Baxter algebras and an introduction to the theory of integrable systems and the algebraic Bethe ansatz is presented. A Θ-vacuum like angle appearing in the RSOS-models is discussed. The continuum limit in the critical case of these statistical models is performed to obtain the minimal models of conformal quantum field theory. (author)

  3. Multidimensional analysis algebras and systems for science and engineering

    CERN Document Server

    Hart, George W

    1995-01-01

    This book deals with the mathematical properties of dimensioned quantities, such as length, mass, voltage, and viscosity. Beginning with a careful examination of how one expresses the numerical results of a measurement and uses these results in subsequent manipulations, the author rigorously constructs the notion of dimensioned numbers and discusses their algebraic structure. The result is a unification of linear algebra and traditional dimensional analysis that can be extended from the scalars to which the traditional analysis is perforce restricted to multidimensional vectors of the sort frequently encountered in engineering, systems theory, economics, and other applications.

  4. On the economical solution method for a system of linear algebraic equations

    Directory of Open Access Journals (Sweden)

    Jan Awrejcewicz

    2004-01-01

    Full Text Available The present work proposes a novel optimal and exact method of solving large systems of linear algebraic equations. In the approach under consideration, the solution of a system of algebraic linear equations is found as a point of intersection of hyperplanes, which needs a minimal amount of computer operating storage. Two examples are given. In the first example, the boundary value problem for a three-dimensional stationary heat transfer equation in a parallelepiped in ℝ3 is considered, where boundary value problems of first, second, or third order, or their combinations, are taken into account. The governing differential equations are reduced to algebraic ones with the help of the finite element and boundary element methods for different meshes applied. The obtained results are compared with known analytical solutions. The second example concerns computation of a nonhomogeneous shallow physically and geometrically nonlinear shell subject to transversal uniformly distributed load. The partial differential equations are reduced to a system of nonlinear algebraic equations with the error of O(hx12+hx22. The linearization process is realized through either Newton method or differentiation with respect to a parameter. In consequence, the relations of the boundary condition variations along the shell side and the conditions for the solution matching are reported.

  5. On Split Lie Algebras with Symmetric Root Systems

    Indian Academy of Sciences (India)

    ... and any I j a well described ideal of , satisfying [ I j , I k ] = 0 if j ≠ k . Under certain conditions, the simplicity of is characterized and it is shown that is the direct sum of the family of its minimal ideals, each one being a simple split Lie algebra with a symmetric root system and having all its nonzero roots connected.

  6. On split Lie algebras with symmetric root systems

    Indian Academy of Sciences (India)

    ideal of L, satisfying [Ij ,Ik] = 0 if j = k. Under certain conditions, the simplicity of L is characterized and it is shown that L is the direct sum of the family of its minimal ideals, each one being a simple split Lie algebra with a symmetric root system and having all its nonzero roots connected. Keywords. Infinite dimensional Lie ...

  7. Computing algebraic transfer entropy and coupling directions via transcripts

    Science.gov (United States)

    Amigó, José M.; Monetti, Roberto; Graff, Beata; Graff, Grzegorz

    2016-11-01

    Most random processes studied in nonlinear time series analysis take values on sets endowed with a group structure, e.g., the real and rational numbers, and the integers. This fact allows to associate with each pair of group elements a third element, called their transcript, which is defined as the product of the second element in the pair times the first one. The transfer entropy of two such processes is called algebraic transfer entropy. It measures the information transferred between two coupled processes whose values belong to a group. In this paper, we show that, subject to one constraint, the algebraic transfer entropy matches the (in general, conditional) mutual information of certain transcripts with one variable less. This property has interesting practical applications, especially to the analysis of short time series. We also derive weak conditions for the 3-dimensional algebraic transfer entropy to yield the same coupling direction as the corresponding mutual information of transcripts. A related issue concerns the use of mutual information of transcripts to determine coupling directions in cases where the conditions just mentioned are not fulfilled. We checked the latter possibility in the lowest dimensional case with numerical simulations and cardiovascular data, and obtained positive results.

  8. Relational Algebra in Spatial Decision Support Systems Ontologies.

    Science.gov (United States)

    Diomidous, Marianna; Chardalias, Kostis; Koutonias, Panagiotis; Magnita, Adrianna; Andrianopoulos, Charalampos; Zimeras, Stelios; Mechili, Enkeleint Aggelos

    2017-01-01

    Decision Support Systems (DSS) is a powerful tool, for facilitates researchers to choose the correct decision based on their final results. Especially in medical cases where doctors could use these systems, to overcome the problem with the clinical misunderstanding. Based on these systems, queries must be constructed based on the particular questions that doctors must answer. In this work, combination between questions and queries would be presented via relational algebra.

  9. Integrable finite-dimensional systems related to Lie algebras

    International Nuclear Information System (INIS)

    Olshanetsky, M.A.; Perelomov, A.M.

    1979-01-01

    Some solvable finite-dimensional classical and quantum systems related to the Lie algebras are considered. The dynamics of these systems is closely related to free motion on symmetric spaces. In specific cases the systems considered describe the one-dimensional n-body problem recently considered by many authors. The review represents from general and universal point of view the results obtained during the last few years. Besides, it contains some results both of physical and mathematical type

  10. Color Algebras

    Science.gov (United States)

    Mulligan, Jeffrey B.

    2017-01-01

    A color algebra refers to a system for computing sums and products of colors, analogous to additive and subtractive color mixtures. The difficulty addressed here is the fact that, because of metamerism, we cannot know with certainty the spectrum that produced a particular color solely on the basis of sensory data. Knowledge of the spectrum is not required to compute additive mixture of colors, but is critical for subtractive (multiplicative) mixture. Therefore, we cannot predict with certainty the multiplicative interactions between colors based solely on sensory data. There are two potential applications of a color algebra: first, to aid modeling phenomena of human visual perception, such as color constancy and transparency; and, second, to provide better models of the interactions of lights and surfaces for computer graphics rendering.

  11. Templates for Linear Algebra Problems

    NARCIS (Netherlands)

    Bai, Z.; Day, D.; Demmel, J.; Dongarra, J.; Gu, M.; Ruhe, A.; Vorst, H.A. van der

    1995-01-01

    The increasing availability of advanced-architecture computers is having a very signicant eect on all spheres of scientic computation, including algorithm research and software development in numerical linear algebra. Linear algebra {in particular, the solution of linear systems of equations and

  12. Lukasiewicz-Moisil Many-Valued Logic Algebra of Highly-Complex Systems

    Directory of Open Access Journals (Sweden)

    James F. Glazebrook

    2010-06-01

    Full Text Available The fundamentals of Lukasiewicz-Moisil logic algebras and their applications to complex genetic network dynamics and highly complex systems are presented in the context of a categorical ontology theory of levels, Medical Bioinformatics and self-organizing, highly complex systems. Quantum Automata were defined in refs.[2] and [3] as generalized, probabilistic automata with quantum state spaces [1]. Their next-state functions operate through transitions between quantum states defined by the quantum equations of motions in the SchrÄodinger representation, with both initial and boundary conditions in space-time. A new theorem is proven which states that the category of quantum automata and automata-homomorphisms has both limits and colimits. Therefore, both categories of quantum automata and classical automata (sequential machines are bicomplete. A second new theorem establishes that the standard automata category is a subcategory of the quantum automata category. The quantum automata category has a faithful representation in the category of Generalized (M,R-Systems which are open, dynamic biosystem networks [4] with de¯ned biological relations that represent physiological functions of primordial(s, single cells and the simpler organisms. A new category of quantum computers is also defined in terms of reversible quantum automata with quantum state spaces represented by topological groupoids that admit a local characterization through unique, quantum Lie algebroids. On the other hand, the category of n-Lukasiewicz algebras has a subcategory of centered n-Lukasiewicz algebras (as proven in ref. [2] which can be employed to design and construct subcategories of quantum automata based on n-Lukasiewicz diagrams of existing VLSI. Furthermore, as shown in ref. [2] the category of centered n-Lukasiewicz algebras and the category of Boolean algebras are naturally equivalent. A `no-go' conjecture is also proposed which states that Generalized (M,R-Systems

  13. Conformal algebras of two-dimensional disordered systems

    International Nuclear Information System (INIS)

    Gurarie, Victor; Ludwig, Andreas W.W.

    2002-01-01

    We discuss the structure of two-dimensional conformal field theories at a central charge c=0 describing critical disordered systems, polymers and percolation. We construct a novel extension of the c=0 Virasoro algebra, characterized by a number b measuring the effective number of massless degrees of freedom, and by a logarithmic partner of the stress tensor. It is argued to be present at a generic random critical point, lacking super Kac-Moody, or other higher symmetries, and is a tool to describe and classify such theories. Interestingly, this algebra is not only consistent with, but indeed naturally accommodates in general an underlying global supersymmetry. Polymers and percolation realize this algebra. Unexpectedly, we find that the c=0 Kac table of the degenerate fields contains two distinct theories with b=5/6 and b=-5/8 which we conjecture to correspond to percolation and polymers, respectively. A given Kac-table field can be degenerate only in one of them. Remarkably, we also find this algebra, and thereby an ensuing hidden supersymmetry, realized at general replica-averaged critical points, for which we derive an explicit formula for b. (author). Letter-to-the-editor

  14. On the algebraic reconstruction of the Duffing's mechanical system

    International Nuclear Information System (INIS)

    Aguilar-Ibanez, Carlos; Sanchez H, Jorge; Suarez C, Miguel S.; Martinez C, Juan

    2008-01-01

    The identification of the unknown parameters of the Duffing's mechanical system, based on an algebraic approach, is presented. This approach is fast, accurate, and simple to numerically implement. Also, the method, combined with a suitable invariant filter, can became robust against high frequency output measurement noises. Our method uses the availability of one measurable output and produces an exact formula for the unknown parameters, which may be realized in terms of iterated convolutions. First, we show that the Duffing's system parameters are linearly identifiable with respect to the position variable, then we obtain a linear system where the unknowns are the unavailable parameters. Suitable algebraic operations on the output differential equations makes the identification schema independent of the unavailable initial conditions of the underlying nonlinear dynamical system

  15. Understanding geometric algebra Hamilton, Grassmann, and Clifford for computer vision and graphics

    CERN Document Server

    Kanatani, Kenichi

    2015-01-01

    Introduction PURPOSE OF THIS BOOK ORGANIZATION OF THIS BOOK OTHER FEATURES 3D Euclidean Geometry VECTORS BASIS AND COMPONENTS INNER PRODUCT AND NORM VECTOR PRODUCTS SCALAR TRIPLE PRODUCT PROJECTION, REJECTION, AND REFLECTION ROTATION PLANES LINES PLANES AND LINES Oblique Coordinate Systems RECIPROCAL BASIS RECIPROCAL COMPONENTS INNER, VECTOR, AND SCALAR TRIPLE PRODUCTS METRIC TENSOR RECIPROCITY OF EXPRESSIONS COORDINATE TRANSFORMATIONSHamilton's Quaternion Algebra QUATERNIONS ALGEBRA OF QUATERNIONS CONJUGATE, NORM, AND INVERSE REPRESENTATION OF ROTATION BY QUATERNION Grassmann's Outer Product

  16. Algebraic and adaptive learning in neural control systems

    Science.gov (United States)

    Ferrari, Silvia

    A systematic approach is developed for designing adaptive and reconfigurable nonlinear control systems that are applicable to plants modeled by ordinary differential equations. The nonlinear controller comprising a network of neural networks is taught using a two-phase learning procedure realized through novel techniques for initialization, on-line training, and adaptive critic design. A critical observation is that the gradients of the functions defined by the neural networks must equal corresponding linear gain matrices at chosen operating points. On-line training is based on a dual heuristic adaptive critic architecture that improves control for large, coupled motions by accounting for actual plant dynamics and nonlinear effects. An action network computes the optimal control law; a critic network predicts the derivative of the cost-to-go with respect to the state. Both networks are algebraically initialized based on prior knowledge of satisfactory pointwise linear controllers and continue to adapt on line during full-scale simulations of the plant. On-line training takes place sequentially over discrete periods of time and involves several numerical procedures. A backpropagating algorithm called Resilient Backpropagation is modified and successfully implemented to meet these objectives, without excessive computational expense. This adaptive controller is as conservative as the linear designs and as effective as a global nonlinear controller. The method is successfully implemented for the full-envelope control of a six-degree-of-freedom aircraft simulation. The results show that the on-line adaptation brings about improved performance with respect to the initialization phase during aircraft maneuvers that involve large-angle and coupled dynamics, and parameter variations.

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

    International Nuclear Information System (INIS)

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

    2015-01-01

    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 A n 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 A n , we produce new integrable Hamiltonian systems. (paper)

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

    Science.gov (United States)

    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.

  19. Advanced computer algebra algorithms for the expansion of Feynman integrals

    International Nuclear Information System (INIS)

    Ablinger, Jakob; Round, Mark; Schneider, Carsten

    2012-10-01

    Two-point Feynman parameter integrals, with at most one mass and containing local operator insertions in 4+ε-dimensional Minkowski space, can be transformed to multi-integrals or multi-sums over hyperexponential and/or hypergeometric functions depending on a discrete parameter n. Given such a specific representation, we utilize an enhanced version of the multivariate Almkvist-Zeilberger algorithm (for multi-integrals) and a common summation framework of the holonomic and difference field approach (for multi-sums) to calculate recurrence relations in n. Finally, solving the recurrence we can decide efficiently if the first coefficients of the Laurent series expansion of a given Feynman integral can be expressed in terms of indefinite nested sums and products; if yes, the all n solution is returned in compact representations, i.e., no algebraic relations exist among the occurring sums and products.

  20. Advanced computer algebra algorithms for the expansion of Feynman integrals

    Energy Technology Data Exchange (ETDEWEB)

    Ablinger, Jakob; Round, Mark; Schneider, Carsten [Johannes Kepler Univ., Linz (Austria). Research Inst. for Symbolic Computation; Bluemlein, Johannes [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany)

    2012-10-15

    Two-point Feynman parameter integrals, with at most one mass and containing local operator insertions in 4+{epsilon}-dimensional Minkowski space, can be transformed to multi-integrals or multi-sums over hyperexponential and/or hypergeometric functions depending on a discrete parameter n. Given such a specific representation, we utilize an enhanced version of the multivariate Almkvist-Zeilberger algorithm (for multi-integrals) and a common summation framework of the holonomic and difference field approach (for multi-sums) to calculate recurrence relations in n. Finally, solving the recurrence we can decide efficiently if the first coefficients of the Laurent series expansion of a given Feynman integral can be expressed in terms of indefinite nested sums and products; if yes, the all n solution is returned in compact representations, i.e., no algebraic relations exist among the occurring sums and products.

  1. Analytical SN solutions in heterogeneous slabs using symbolic algebra computer programs

    International Nuclear Information System (INIS)

    Warsa, J.S.

    2002-01-01

    A modern symbolic algebra computer program, MAPLE, is used to compute solutions to the well-known analytical discrete ordinates, or S N , solutions in one-dimensional, slab geometry. Symbolic algebra programs compute the solutions with arbitrary precision and are free of spatial discretization error so they can be used to investigate new discretizations for one-dimensional slab, geometry S N methods. Pointwise scalar flux solutions are computed for several sample calculations of interest. Sample MAPLE command scripts are provided to illustrate how easily the theory can be translated into a working solution and serve as a complete tool capable of computing analytical S N solutions for mono-energetic, one-dimensional transport problems

  2. Solution of the Schrodinger Equation for a Diatomic Oscillator Using Linear Algebra: An Undergraduate Computational Experiment

    Science.gov (United States)

    Gasyna, Zbigniew L.

    2008-01-01

    Computational experiment is proposed in which a linear algebra method is applied to the solution of the Schrodinger equation for a diatomic oscillator. Calculations of the vibration-rotation spectrum for the HCl molecule are presented and the results show excellent agreement with experimental data. (Contains 1 table and 1 figure.)

  3. ACE - an algebraic compiler and encoder for the Chalk River datatron computer

    International Nuclear Information System (INIS)

    Kennedy, J.M.; Okazaki, E.A.; Millican, M.

    1960-03-01

    ACE is a program written for the Chalk River Datatron (Burroughs 205) Computer to enable the machine to compile a program for solving a problem from instructions supplied by the user in a notation related much more closely to algebra than to the machine's own code. (author)

  4. An Algebraic Criterion of Zero Solutions of Some Dynamic Systems

    Directory of Open Access Journals (Sweden)

    Ying Wang

    2012-01-01

    Full Text Available We establish some algebraic results on the zeros of some exponential polynomials and a real coefficient polynomial. Based on the basic theorem, we develop a decomposition technique to investigate the stability of two coupled systems and their discrete versions, that is, to find conditions under which all zeros of the exponential polynomials have negative real parts and the moduli of all roots of a real coefficient polynomial are less than 1.

  5. Algebraic structure of a generalized coupled dispersionless system

    International Nuclear Information System (INIS)

    Victor, Kuetche Kamgang; Thomas, Bouetou Bouetou; Kofane, Timoleon Crepin

    2006-01-01

    We study a physical model of the O(3)-invariant coupled integrable dispersionless equations that describes the dynamic of a focused system within the background of a plane gravitational field. The investigation is carried out both numerically and analytically, and realized beneath some assumptions superseding the structure constant with the structure function implemented in Lie algebra and quasigroup theory, respectively. The energy density and topological structures such as loop soliton are examined

  6. Model Checking Process Algebra of Communicating Resources for Real-time Systems

    DEFF Research Database (Denmark)

    Boudjadar, Jalil; Kim, Jin Hyun; Larsen, Kim Guldstrand

    2014-01-01

    This paper presents a new process algebra, called PACOR, for real-time systems which deals with resource constrained timed behavior as an improved version of the ACSR algebra. We define PACOR as a Process Algebra of Communicating Resources which allows to express preemptiveness, urgent ness...

  7. Model checking process algebra of communicating resources for real-time systems

    DEFF Research Database (Denmark)

    Boudjadar, Jalil; Kim, Jin Hyun; Larsen, Kim Guldstrand

    2014-01-01

    This paper presents a new process algebra, called PACoR, for real-time systems which deals with resource- constrained timed behavior as an improved version of the ACSR algebra. We define PACoR as a Process Algebra of Communicating Resources which allows to explicitly express preemptiveness...

  8. Two Types of Expanding Lie Algebra and New Expanding Integrable Systems

    International Nuclear Information System (INIS)

    Dong Huanhe; Yang Jiming; Wang Hui

    2010-01-01

    From a new Lie algebra proposed by Zhang, two expanding Lie algebras and its corresponding loop algebras are obtained. Two expanding integrable systems are produced with the help of the generalized zero curvature equation. One of them has complex Hamiltion structure with the help of generalized Tu formula (GTM). (general)

  9. Projection computation based on pixel in simultaneous algebraic reconstruction technique

    International Nuclear Information System (INIS)

    Wang Xu; Chen Zhiqiang; Xiong Hua; Zhang Li

    2005-01-01

    SART is an important arithmetic of image reconstruction, in which the projection computation takes over half of the reconstruction time. An efficient way to compute projection coefficient matrix together with memory optimization is presented in this paper. Different from normal method, projection lines are located based on every pixel, and the following projection coefficient computation can make use of the results. Correlation of projection lines and pixels can be used to optimize the computation. (authors)

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

    Science.gov (United States)

    Downie, John D.; Goodman, Joseph W.

    1989-10-01

    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.

  11. Obstructions to Clifford system extensions of algebras

    Indian Academy of Sciences (India)

    Springer Verlag Heidelberg #4 2048 1996 Dec 15 10:16:45

    group character, and then we give a classification of Clifford systems in terms of suitable low-dimensional ... Introduction. The problem of ... Clifford's theory axiomatically, and which can be referred to for general background. In §2, we state a ...

  12. Dynamical systems and algebra associated with seperated graphs

    DEFF Research Database (Denmark)

    Lolk, Matias

    In this thesis, we study partial dynamical systems and graph algebras arising from nitely separated graphs. The thesis consists of an introduction followed by three papers, the rst of which is joint work with Pere Ara. In Article [A], we introduce convex subshifts, an abstract generalisation...... of the partial dynamical systems associated with nite separated graphs. We dene notions of a nite and innite type convex subshift and show that all such dynamical systems arise from a nite bipartite separated graph up to a suitable type of equivalence. We then study various aspects of the ideal structure...

  13. Software Applications on the Peregrine System | High-Performance Computing

    Science.gov (United States)

    Algebraic Modeling System (GAMS) Statistics and analysis High-level modeling system for mathematical reactivity. Gurobi Optimizer Statistics and analysis Solver for mathematical programming LAMMPS Chemistry and , reactivities, and vibrational, electronic and NMR spectra. R Statistical Computing Environment Statistics and

  14. An Algebra-Based Introductory Computational Neuroscience Course with Lab.

    Science.gov (United States)

    Fink, Christian G

    2017-01-01

    A course in computational neuroscience has been developed at Ohio Wesleyan University which requires no previous experience with calculus or computer programming, and which exposes students to theoretical models of neural information processing and techniques for analyzing neural data. The exploration of theoretical models of neural processes is conducted in the classroom portion of the course, while data analysis techniques are covered in lab. Students learn to program in MATLAB and are offered the opportunity to conclude the course with a final project in which they explore a topic of their choice within computational neuroscience. Results from a questionnaire administered at the beginning and end of the course indicate significant gains in student facility with core concepts in computational neuroscience, as well as with analysis techniques applied to neural data.

  15. Edix: A Software for Editing Algebraic Expressions.

    OpenAIRE

    Bouhineau , Denis; Nicaud , Jean-François; Pavard , X.

    2001-01-01

    International audience; The paper presents a computer software, called Edix, devoted to the edition of algebraic expressions in their usual 2D representation. At present, many systems display fine algebraic expressions, but the edition of such expressions is weak. Systems like Word and FrameMaker place sub-expressions in too many boxes so that many editing actions are not simple, while usual CAS (computer algebra systems) just use a 1D representation for the edition. Furthermore, Edix allows ...

  16. Prolongation Loop Algebras for a Solitonic System of Equations

    Directory of Open Access Journals (Sweden)

    Maria A. Agrotis

    2006-11-01

    Full Text Available We consider an integrable system of reduced Maxwell-Bloch equations that describes the evolution of an electromagnetic field in a two-level medium that is inhomogeneously broadened. We prove that the relevant Bäcklund transformation preserves the reality of the n-soliton potentials and establish their pole structure with respect to the broadening parameter. The natural phase space of the model is embedded in an infinite dimensional loop algebra. The dynamical equations of the model are associated to an infinite family of higher order Hamiltonian systems that are in involution. We present the Hamiltonian functions and the Poisson brackets between the extended potentials.

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

    Science.gov (United States)

    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.

  18. Analytical solutions for systems of partial differential-algebraic equations.

    Science.gov (United States)

    Benhammouda, Brahim; Vazquez-Leal, Hector

    2014-01-01

    This work presents the application of the power series method (PSM) to find solutions of partial differential-algebraic equations (PDAEs). Two systems of index-one and index-three are solved to show that PSM can provide analytical solutions of PDAEs in convergent series form. What is more, we present the post-treatment of the power series solutions with the Laplace-Padé (LP) resummation method as a useful strategy to find exact solutions. The main advantage of the proposed methodology is that the procedure is based on a few straightforward steps and it does not generate secular terms or depends of a perturbation parameter.

  19. Solution of systems of linear algebraic equations by the method of summation of divergent series

    International Nuclear Information System (INIS)

    Kirichenko, G.A.; Korovin, Ya.S.; Khisamutdinov, M.V.; Shmojlov, V.I.

    2015-01-01

    A method for solving systems of linear algebraic equations has been proposed on the basis on the summation of the corresponding continued fractions. The proposed algorithm for solving systems of linear algebraic equations is classified as direct algorithms providing an exact solution in a finite number of operations. Examples of solving systems of linear algebraic equations have been presented and the effectiveness of the algorithm has been estimated [ru

  20. On differential operators generating iterative systems of linear ODEs of maximal symmetry algebra

    Science.gov (United States)

    Ndogmo, J. C.

    2017-06-01

    Although every iterative scalar linear ordinary differential equation is of maximal symmetry algebra, the situation is different and far more complex for systems of linear ordinary differential equations, and an iterative system of linear equations need not be of maximal symmetry algebra. We illustrate these facts by examples and derive families of vector differential operators whose iterations are all linear systems of equations of maximal symmetry algebra. Some consequences of these results are also discussed.

  1. Recent Developments in Complex Analysis and Computer Algebra

    CERN Document Server

    Kajiwara, Joji; Xu, Yongzhi

    1999-01-01

    This volume consists of papers presented in the special sessions on "Complex and Numerical Analysis", "Value Distribution Theory and Complex Domains", and "Use of Symbolic Computation in Mathematics Education" of the ISAAC'97 Congress held at the University of Delaware, during June 2-7, 1997. The ISAAC Congress coincided with a U.S.-Japan Seminar also held at the University of Delaware. The latter was supported by the National Science Foundation through Grant INT-9603029 and the Japan Society for the Promotion of Science through Grant MTCS-134. It was natural that the participants of both meetings should interact and consequently several persons attending the Congress also presented papers in the Seminar. The success of the ISAAC Congress and the U.S.-Japan Seminar has led to the ISAAC'99 Congress being held in Fukuoka, Japan during August 1999. Many of the same participants will return to this Seminar. Indeed, it appears that the spirit of the U.S.-Japan Seminar will be continued every second year as part of...

  2. Computer algebra in quantum field theory integration, summation and special functions

    CERN Document Server

    Schneider, Carsten

    2013-01-01

    The book focuses on advanced computer algebra methods and special functions that have striking applications in the context of quantum field theory. It presents the state of the art and new methods for (infinite) multiple sums, multiple integrals, in particular Feynman integrals, difference and differential equations in the format of survey articles. The presented techniques emerge from interdisciplinary fields: mathematics, computer science and theoretical physics; the articles are written by mathematicians and physicists with the goal that both groups can learn from the other field, including

  3. Hom-Novikov algebras

    International Nuclear Information System (INIS)

    Yau, Donald

    2011-01-01

    We study a twisted generalization of Novikov algebras, called Hom-Novikov algebras, in which the two defining identities are twisted by a linear map. It is shown that Hom-Novikov algebras can be obtained from Novikov algebras by twisting along any algebra endomorphism. All algebra endomorphisms on complex Novikov algebras of dimensions 2 or 3 are computed, and their associated Hom-Novikov algebras are described explicitly. Another class of Hom-Novikov algebras is constructed from Hom-commutative algebras together with a derivation, generalizing a construction due to Dorfman and Gel'fand. Two other classes of Hom-Novikov algebras are constructed from Hom-Lie algebras together with a suitable linear endomorphism, generalizing a construction due to Bai and Meng.

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

    Energy Technology Data Exchange (ETDEWEB)

    Vanek, P.; Mandel, J.; Brezina, M. [Univ. of Colorado, Denver, CO (United States)

    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. Canonical formulation of the self-dual Yang-Mills system: Algebras and hierarchies

    International Nuclear Information System (INIS)

    Chau, L.; Yamanaka, I.

    1992-01-01

    We construct a canonical formulation of the self-dual Yang-Mills system formulated in the gauge-invariant group-valued J fields and derive their Hamiltonian and the quadratic algebras of the fundamental Dirac brackets. We also show that the quadratic algebras satisfy Jacobi identities and their structure matrices satisfy modified Yang-Baxter equations. From these quadratic algebras, we construct Kac-Moody-like and Virasoro-like algebras. We also discuss their related symmetries, involutive conserved quantities, and hierarchies of nonlinear and linear equations

  6. Computer programming and computer systems

    CERN Document Server

    Hassitt, Anthony

    1966-01-01

    Computer Programming and Computer Systems imparts a "reading knowledge? of computer systems.This book describes the aspects of machine-language programming, monitor systems, computer hardware, and advanced programming that every thorough programmer should be acquainted with. This text discusses the automatic electronic digital computers, symbolic language, Reverse Polish Notation, and Fortran into assembly language. The routine for reading blocked tapes, dimension statements in subroutines, general-purpose input routine, and efficient use of memory are also elaborated.This publication is inten

  7. Some experience in applying the REDUCE algebraic system to the calculation of scattering processes in QED and QCD

    International Nuclear Information System (INIS)

    Mohring, H.J.; Schiller, A.

    1980-01-01

    The problems arising in the use of the REDUCE algebraic system for calculating traces of the Dirac matrix products describing scattering processes in quantum electrodynamics (QED) and quantum chromodynamics (QCD) are considered. Application of the REDUCE system for describing two-photon processes in e + e - reactions is discussed. An example of using the REDUCE system for calculating matrix elements of elementary processes of hard scattering is described. The calculations were performed by means of the REDUCE2 version on an EC1040 computer. The computations take almost 10 minutes of machine time and computer storage capacity of abo t 800 kiuobites

  8. Donaldson invariants in algebraic geometry

    International Nuclear Information System (INIS)

    Goettsche, L.

    2000-01-01

    In these lectures I want to give an introduction to the relation of Donaldson invariants with algebraic geometry: Donaldson invariants are differentiable invariants of smooth compact 4-manifolds X, defined via moduli spaces of anti-self-dual connections. If X is an algebraic surface, then these moduli spaces can for a suitable choice of the metric be identified with moduli spaces of stable vector bundles on X. This can be used to compute Donaldson invariants via methods of algebraic geometry and has led to a lot of activity on moduli spaces of vector bundles and coherent sheaves on algebraic surfaces. We will first recall the definition of the Donaldson invariants via gauge theory. Then we will show the relation between moduli spaces of anti-self-dual connections and moduli spaces of vector bundles on algebraic surfaces, and how this makes it possible to compute Donaldson invariants via algebraic geometry methods. Finally we concentrate on the case that the number b + of positive eigenvalues of the intersection form on the second homology of the 4-manifold is 1. In this case the Donaldson invariants depend on the metric (or in the algebraic geometric case on the polarization) via a system of walls and chambers. We will study the change of the invariants under wall-crossing, and use this in particular to compute the Donaldson invariants of rational algebraic surfaces. (author)

  9. Integrable N dimensional systems on the Hopf algebra and q deformations

    International Nuclear Information System (INIS)

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

    2000-01-01

    The class of integrable classic and quantum systems on the Hopf algebra, describing the n of interacting particles, is plotted. The general structure of the integrable Hamiltonian system for the Hopf algebra A(g) of the Lee simple algebra g is obtained, wherefrom it follows, that motion integrals depend on the linear combinations k of the phase space coordinates. The q-deformation standard procedure is carried out and the corresponding integrable system is obtained. The general scheme is illustrated by the examples of the sl(2), sl(3) and o(3, 1) algebras. The exact solution is achieved for the N-dimensional Hamiltonian system quantum analog on the Hopf algebra A (sl(2)) through the method of noncommutative integration of linear differential equations [ru

  10. Mastering algebra retrains the visual system to perceive hierarchical structure in equations.

    Science.gov (United States)

    Marghetis, Tyler; Landy, David; Goldstone, Robert L

    2016-01-01

    Formal mathematics is a paragon of abstractness. It thus seems natural to assume that the mathematical expert should rely more on symbolic or conceptual processes, and less on perception and action. We argue instead that mathematical proficiency relies on perceptual systems that have been retrained to implement mathematical skills. Specifically, we investigated whether the visual system-in particular, object-based attention-is retrained so that parsing algebraic expressions and evaluating algebraic validity are accomplished by visual processing. Object-based attention occurs when the visual system organizes the world into discrete objects, which then guide the deployment of attention. One classic signature of object-based attention is better perceptual discrimination within, rather than between, visual objects. The current study reports that object-based attention occurs not only for simple shapes but also for symbolic mathematical elements within algebraic expressions-but only among individuals who have mastered the hierarchical syntax of algebra. Moreover, among these individuals, increased object-based attention within algebraic expressions is associated with a better ability to evaluate algebraic validity. These results suggest that, in mastering the rules of algebra, people retrain their visual system to represent and evaluate abstract mathematical structure. We thus argue that algebraic expertise involves the regimentation and reuse of evolutionarily ancient perceptual processes. Our findings implicate the visual system as central to learning and reasoning in mathematics, leading us to favor educational approaches to mathematics and related STEM fields that encourage students to adapt, not abandon, their use of perception.

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

    Science.gov (United States)

    Veliz-Cuba, Alan; Aguilar, Boris; Hinkelmann, Franziska; Laubenbacher, Reinhard

    2014-06-26

    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. 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. 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 connectivity. The problem for

  12. Simple skew category algebras associated with minimal partially defined dynamical systems

    DEFF Research Database (Denmark)

    Nystedt, Patrik; Öinert, Per Johan

    2013-01-01

    In this article, we continue our study of category dynamical systems, that is functors s from a category G to Topop, and their corresponding skew category algebras. Suppose that the spaces s(e), for e∈ob(G), are compact Hausdorff. We show that if (i) the skew category algebra is simple, then (ii) G...

  13. Amenable crossed product Banach algebras associated with a class of C*-dynamical systems

    NARCIS (Netherlands)

    Jeu, de M.F.E.; Elharti, R.; Pinto, P.R.

    2017-01-01

    We prove that the crossed product Banach algebra ℓ1(G,A;α) that is associated with a C∗-dynamical system (A,G,α) is amenable if G is a discrete amenable group and A is a commutative or finite dimensional C∗-algebra. Perspectives for further developments are indicated.

  14. Improved Linear Algebra Methods for Redshift Computation from Limited Spectrum Data - II

    Science.gov (United States)

    Foster, Leslie; Waagen, Alex; Aijaz, Nabella; Hurley, Michael; Luis, Apolo; Rinsky, Joel; Satyavolu, Chandrika; Gazis, Paul; Srivastava, Ashok; Way, Michael

    2008-01-01

    Given photometric broadband measurements of a galaxy, Gaussian processes may be used with a training set to solve the regression problem of approximating the redshift of this galaxy. However, in practice solving the traditional Gaussian processes equation is too slow and requires too much memory. We employed several methods to avoid this difficulty using algebraic manipulation and low-rank approximation, and were able to quickly approximate the redshifts in our testing data within 17 percent of the known true values using limited computational resources. The accuracy of one method, the V Formulation, is comparable to the accuracy of the best methods currently used for this problem.

  15. Thermodiffusion in Multicomponent Mixtures Thermodynamic, Algebraic, and Neuro-Computing Models

    CERN Document Server

    Srinivasan, Seshasai

    2013-01-01

    Thermodiffusion in Multicomponent Mixtures presents the computational approaches that are employed in the study of thermodiffusion in various types of mixtures, namely, hydrocarbons, polymers, water-alcohol, molten metals, and so forth. We present a detailed formalism of these methods that are based on non-equilibrium thermodynamics or algebraic correlations or principles of the artificial neural network. The book will serve as single complete reference to understand the theoretical derivations of thermodiffusion models and its application to different types of multi-component mixtures. An exhaustive discussion of these is used to give a complete perspective of the principles and the key factors that govern the thermodiffusion process.

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

    International Nuclear Information System (INIS)

    Zhang Yu-Feng; Tam, Honwah

    2016-01-01

    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 A_1 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 A_1, 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. (paper)

  17. A Lie algebraic condition for exponential stability of discrete hybrid systems and application to hybrid synchronization.

    Science.gov (United States)

    Zhao, Shouwei

    2011-06-01

    A Lie algebraic condition for global exponential stability of linear discrete switched impulsive systems is presented in this paper. By considering a Lie algebra generated by all subsystem matrices and impulsive matrices, when not all of these matrices are Schur stable, we derive new criteria for global exponential stability of linear discrete switched impulsive systems. Moreover, simple sufficient conditions in terms of Lie algebra are established for the synchronization of nonlinear discrete systems using a hybrid switching and impulsive control. As an application, discrete chaotic system's synchronization is investigated by the proposed method.

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

    International Nuclear Information System (INIS)

    Dey, Sanjib; Fring, Andreas; Mathanaranjan, Thilagarajah

    2014-01-01

    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. -- 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

  19. 3D algebraic iterative reconstruction for cone-beam x-ray differential phase-contrast computed tomography.

    Science.gov (United States)

    Fu, Jian; Hu, Xinhua; Velroyen, Astrid; Bech, Martin; Jiang, Ming; Pfeiffer, Franz

    2015-01-01

    Due to the potential of compact imaging systems with magnified spatial resolution and contrast, cone-beam x-ray differential phase-contrast computed tomography (DPC-CT) has attracted significant interest. The current proposed FDK reconstruction algorithm with the Hilbert imaginary filter will induce severe cone-beam artifacts when the cone-beam angle becomes large. In this paper, we propose an algebraic iterative reconstruction (AIR) method for cone-beam DPC-CT and report its experiment results. This approach considers the reconstruction process as the optimization of a discrete representation of the object function to satisfy a system of equations that describes the cone-beam DPC-CT imaging modality. Unlike the conventional iterative algorithms for absorption-based CT, it involves the derivative operation to the forward projections of the reconstructed intermediate image to take into account the differential nature of the DPC projections. This method is based on the algebraic reconstruction technique, reconstructs the image ray by ray, and is expected to provide better derivative estimates in iterations. This work comprises a numerical study of the algorithm and its experimental verification using a dataset measured with a three-grating interferometer and a mini-focus x-ray tube source. It is shown that the proposed method can reduce the cone-beam artifacts and performs better than FDK under large cone-beam angles. This algorithm is of interest for future cone-beam DPC-CT applications.

  20. Algebraic invariant curves of plane polynomial differential systems

    Science.gov (United States)

    Tsygvintsev, Alexei

    2001-01-01

    We consider a plane polynomial vector field P(x,y) dx + Q(x,y) dy of degree m>1. With each algebraic invariant curve of such a field we associate a compact Riemann surface with the meromorphic differential ω = dx/P = dy/Q. The asymptotic estimate of the degree of an arbitrary algebraic invariant curve is found. In the smooth case this estimate has already been found by Cerveau and Lins Neto in a different way.

  1. Skew category algebras associated with partially defined dynamical systems

    DEFF Research Database (Denmark)

    Lundström, Patrik; Öinert, Per Johan

    2012-01-01

    We introduce partially defined dynamical systems defined on a topological space. To each such system we associate a functor s from a category G to Topop and show that it defines what we call a skew category algebra A ⋊σ G. We study the connection between topological freeness of s and, on the one...... hand, ideal properties of A ⋊σ G and, on the other hand, maximal commutativity of A in A ⋊σ G. In particular, we show that if G is a groupoid and for each e ∈ ob(G) the group of all morphisms e → e is countable and the topological space s(e) is Tychonoff and Baire. Then the following assertions...... are equivalent: (i) s is topologically free; (ii) A has the ideal intersection property, i.e. if I is a nonzero ideal of A ⋊σ G, then I ∩ A ≠ {0}; (iii) the ring A is a maximal abelian complex subalgebra of A ⋊σ G. Thereby, we generalize a result by Svensson, Silvestrov and de Jeu from the additive group...

  2. An algebraic approach to linear-optical schemes for deterministic quantum computing

    International Nuclear Information System (INIS)

    Aniello, Paolo; Cagli, Ruben Coen

    2005-01-01

    Linear-optical passive (LOP) devices and photon counters are sufficient to implement universal quantum computation with single photons, and particular schemes have already been proposed. In this paper we discuss the link between the algebraic structure of LOP transformations and quantum computing. We first show how to decompose the Fock space of N optical modes in finite-dimensional subspaces that are suitable for encoding strings of qubits and invariant under LOP transformations (these subspaces are related to the spaces of irreducible unitary representations of U (N). Next we show how to design in algorithmic fashion LOP circuits which implement any quantum circuit deterministically. We also present some simple examples, such as the circuits implementing a cNOT gate and a Bell state generator/analyser

  3. Contribution to the minimization of time for the solution of algebraic differential equations system

    International Nuclear Information System (INIS)

    Michael, Samir.

    1982-11-01

    This note deals with the solution of large algebraic-differential systems involved in physical sciences specially in electronics and nuclear physics. The theoretical aspects for the stability of multistep methods is presented in detail. The stability condition is developed and we present our own conditions of stability. These conditions give rise to many new formulae that have very small truncation error. However for a real time simulation, it is necessary to obtain a very high computation speed. For this purpose, we have considered a multiprocessor machine and we have investigated the parallelization of the algorithm of generalized GEAR method. For a linear system, the method of GAUSS-JORDAN is used with some modifications. A new algorithm is presented for parallel matrix multiplication. This research work has been applied to the resolution of a system of equations corresponding to an experiment of gamma thermometry in a nuclear reactor (four thermometers in this case) [fr

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

    Science.gov (United States)

    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.

  5. An algebraic method for system reduction of stationary Gaussian systems

    NARCIS (Netherlands)

    D. Jibetean; J.H. van Schuppen (Jan)

    2003-01-01

    textabstractSystem identification for a particular approach reduces to system reduction, determining for a system with a high state-space dimension a system of low state-space dimension. For Gaussian systems the problem of system reduction is considered with the divergence rate criterion. The

  6. Refined algebraic quantisation in a system with nonconstant gauge invariant structure functions

    International Nuclear Information System (INIS)

    Martínez-Pascual, Eric

    2013-01-01

    In a previous work [J. Louko and E. Martínez-Pascual, “Constraint rescaling in refined algebraic quantisation: Momentum constraint,” J. Math. Phys. 52, 123504 (2011)], refined algebraic quantisation (RAQ) within a family of classically equivalent constrained Hamiltonian systems that are related to each other by rescaling one momentum-type constraint was investigated. In the present work, the first steps to generalise this analysis to cases where more constraints occur are developed. The system under consideration contains two momentum-type constraints, originally abelian, where rescalings of these constraints by a non-vanishing function of the coordinates are allowed. These rescalings induce structure functions at the level of the gauge algebra. Providing a specific parametrised family of real-valued scaling functions, the implementation of the corresponding rescaled quantum momentum-type constraints is performed using RAQ when the gauge algebra: (i) remains abelian and (ii) undergoes into an algebra of a nonunimodular group with nonconstant gauge invariant structure functions. Case (ii) becomes the first example known to the author where an open algebra is handled in refined algebraic quantisation. Challenging issues that arise in the presence of non-gauge invariant structure functions are also addressed

  7. Cubic and quartic planar differential systems with exact algebraic limit cycles

    Directory of Open Access Journals (Sweden)

    Ahmed Bendjeddou

    2011-01-01

    Full Text Available We construct cubic and quartic polynomial planar differential systems with exact limit cycles that are ovals of algebraic real curves of degree four. The result obtained for the cubic case generalizes a proposition of [9]. For the quartic case, we deduce for the first time a class of systems with four algebraic limit cycles and another for which nested configurations of limit cycles occur.

  8. Novel algebraic aspects of Liouvillian integrability for two-dimensional polynomial dynamical systems

    Science.gov (United States)

    Demina, Maria V.

    2018-05-01

    The general structure of irreducible invariant algebraic curves for a polynomial dynamical system in C2 is found. Necessary conditions for existence of exponential factors related to an invariant algebraic curve are derived. As a consequence, all the cases when the classical force-free Duffing and Duffing-van der Pol oscillators possess Liouvillian first integrals are obtained. New exact solutions for the force-free Duffing-van der Pol system are constructed.

  9. College algebra

    CERN Document Server

    Kolman, Bernard

    1985-01-01

    College Algebra, Second Edition is a comprehensive presentation of the fundamental concepts and techniques of algebra. The book incorporates some improvements from the previous edition to provide a better learning experience. It provides sufficient materials for use in the study of college algebra. It contains chapters that are devoted to various mathematical concepts, such as the real number system, the theory of polynomial equations, exponential and logarithmic functions, and the geometric definition of each conic section. Progress checks, warnings, and features are inserted. Every chapter c

  10. Research Progress in Mathematical Analysis of Map Projection by Computer Algebra

    Directory of Open Access Journals (Sweden)

    BIAN Shaofeng

    2017-10-01

    Full Text Available Map projection is an important component of modern cartography, and involves many fussy mathematical analysis processes, such as the power series expansions of elliptical functions, differential of complex and implicit functions, elliptical integral and the operation of complex numbers. The derivation of these problems by hand not only consumes much time and energy but also makes mistake easily, and sometimes can not be realized at all because of the impossible complexity. The research achievements in mathematical analysis of map projection by computer algebra are systematically reviewed in five aspects, i.e., the symbolic expressions of forward and inverse solution of ellipsoidal latitudes, the direct transformations between map projections with different distortion properties, expressions of Gauss projection by complex function, mathematical analysis of oblique Mercator projection, polar chart projection with its transformation. Main problems that need to be further solved in this research field are analyzed. It will be helpful to promote the development of map projection.

  11. An algebraic iterative reconstruction technique for differential X-ray phase-contrast computed tomography.

    Science.gov (United States)

    Fu, Jian; Schleede, Simone; Tan, Renbo; Chen, Liyuan; Bech, Martin; Achterhold, Klaus; Gifford, Martin; Loewen, Rod; Ruth, Ronald; Pfeiffer, Franz

    2013-09-01

    Iterative reconstruction has a wide spectrum of proven advantages in the field of conventional X-ray absorption-based computed tomography (CT). In this paper, we report on an algebraic iterative reconstruction technique for grating-based differential phase-contrast CT (DPC-CT). Due to the differential nature of DPC-CT projections, a differential operator and a smoothing operator are added to the iterative reconstruction, compared to the one commonly used for absorption-based CT data. This work comprises a numerical study of the algorithm and its experimental verification using a dataset measured at a two-grating interferometer setup. Since the algorithm is easy to implement and allows for the extension to various regularization possibilities, we expect a significant impact of the method for improving future medical and industrial DPC-CT applications. Copyright © 2012. Published by Elsevier GmbH.

  12. Recurrence approach and higher order polynomial algebras for superintegrable monopole systems

    Science.gov (United States)

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

    2018-05-01

    We revisit the MIC-harmonic oscillator in flat space with monopole interaction and derive the polynomial algebra satisfied by the integrals of motion and its energy spectrum using the ad hoc recurrence approach. We introduce a superintegrable monopole system in a generalized Taub-Newman-Unti-Tamburino (NUT) space. The Schrödinger equation of this model is solved in spherical coordinates in the framework of Stäckel transformation. It is shown that wave functions of the quantum system can be expressed in terms of the product of Laguerre and Jacobi polynomials. We construct ladder and shift operators based on the corresponding wave functions and obtain the recurrence formulas. By applying these recurrence relations, we construct higher order algebraically independent integrals of motion. We show that the integrals form a polynomial algebra. We construct the structure functions of the polynomial algebra and obtain the degenerate energy spectra of the model.

  13. Two dissimilar approaches to dynamical systems on hyper MV -algebras and their information entropy

    Science.gov (United States)

    Mehrpooya, Adel; Ebrahimi, Mohammad; Davvaz, Bijan

    2017-09-01

    Measuring the flow of information that is related to the evolution of a system which is modeled by applying a mathematical structure is of capital significance for science and usually for mathematics itself. Regarding this fact, a major issue in concern with hyperstructures is their dynamics and the complexity of the varied possible dynamics that exist over them. Notably, the dynamics and uncertainty of hyper MV -algebras which are hyperstructures and extensions of a central tool in infinite-valued Lukasiewicz propositional calculus that models many valued logics are of primary concern. Tackling this problem, in this paper we focus on the subject of dynamical systems on hyper MV -algebras and their entropy. In this respect, we adopt two varied approaches. One is the set-based approach in which hyper MV -algebra dynamical systems are developed by employing set functions and set partitions. By the other method that is based on points and point partitions, we establish the concept of hyper injective dynamical systems on hyper MV -algebras. Next, we study the notion of entropy for both kinds of systems. Furthermore, we consider essential ergodic characteristics of those systems and their entropy. In particular, we introduce the concept of isomorphic hyper injective and hyper MV -algebra dynamical systems, and we demonstrate that isomorphic systems have the same entropy. We present a couple of theorems in order to help calculate entropy. In particular, we prove a contemporary version of addition and Kolmogorov-Sinai Theorems. Furthermore, we provide a comparison between the indispensable properties of hyper injective and semi-independent dynamical systems. Specifically, we present and prove theorems that draw comparisons between the entropies of such systems. Lastly, we discuss some possible relationships between the theories of hyper MV -algebra and MV -algebra dynamical systems.

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

    International Nuclear Information System (INIS)

    McWilliams, J C

    2000-01-01

    -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. Lukasiewicz-Moisil algebras

    CERN Document Server

    Boicescu, V; Georgescu, G; Rudeanu, S

    1991-01-01

    The Lukasiewicz-Moisil algebras were created by Moisil as an algebraic counterpart for the many-valued logics of Lukasiewicz. The theory of LM-algebras has developed to a considerable extent both as an algebraic theory of intrinsic interest and in view of its applications to logic and switching theory.This book gives an overview of the theory, comprising both classical results and recent contributions, including those of the authors. N-valued and &THgr;-valued algebras are presented, as well as &THgr;-algebras with negation.Mathematicians interested in lattice theory or symbolic logic, and computer scientists, will find in this monograph stimulating material for further research.

  16. Algebraic features of some generalizations of the Lotka-Volterra system

    Science.gov (United States)

    Bibik, Yu. V.; Sarancha, D. A.

    2010-10-01

    For generalizations of the Lotka-Volterra system, an integration method is proposed based on the nontrivial algebraic structure of these generalizations. The method makes use of an auxiliary first-order differential equation derived from the phase curve equation with the help of this algebraic structure. Based on this equation, a Hamiltonian approach can be developed and canonical variables (moreover, action-angle variables) can be constructed.

  17. Gauss Elimination: Workhorse of Linear Algebra.

    Science.gov (United States)

    1995-08-05

    linear algebra computation for solving systems, computing determinants and determining the rank of matrix. All of these are discussed in varying contexts. These include different arithmetic or algebraic setting such as integer arithmetic or polynomial rings as well as conventional real (floating-point) arithmetic. These have effects on both accuracy and complexity analyses of the algorithm. These, too, are covered here. The impact of modern parallel computer architecture on GE is also

  18. Linear algebra

    CERN Document Server

    Edwards, Harold M

    1995-01-01

    In his new undergraduate textbook, Harold M Edwards proposes a radically new and thoroughly algorithmic approach to linear algebra Originally inspired by the constructive philosophy of mathematics championed in the 19th century by Leopold Kronecker, the approach is well suited to students in the computer-dominated late 20th century Each proof is an algorithm described in English that can be translated into the computer language the class is using and put to work solving problems and generating new examples, making the study of linear algebra a truly interactive experience Designed for a one-semester course, this text adopts an algorithmic approach to linear algebra giving the student many examples to work through and copious exercises to test their skills and extend their knowledge of the subject Students at all levels will find much interactive instruction in this text while teachers will find stimulating examples and methods of approach to the subject

  19. Basic linear algebra

    CERN Document Server

    Blyth, T S

    2002-01-01

    Basic Linear Algebra is a text for first year students leading from concrete examples to abstract theorems, via tutorial-type exercises. More exercises (of the kind a student may expect in examination papers) are grouped at the end of each section. The book covers the most important basics of any first course on linear algebra, explaining the algebra of matrices with applications to analytic geometry, systems of linear equations, difference equations and complex numbers. Linear equations are treated via Hermite normal forms which provides a successful and concrete explanation of the notion of linear independence. Another important highlight is the connection between linear mappings and matrices leading to the change of basis theorem which opens the door to the notion of similarity. This new and revised edition features additional exercises and coverage of Cramer's rule (omitted from the first edition). However, it is the new, extra chapter on computer assistance that will be of particular interest to readers:...

  20. PRELIMINARY STUDY ON APPLICATION OF MAX PLUS ALGEBRA IN DISTRIBUTED STORAGE SYSTEM THROUGH NETWORK CODING

    Directory of Open Access Journals (Sweden)

    Agus Maman Abadi

    2016-04-01

    Full Text Available The increasing need in techniques of storing big data presents a new challenge. One way to address this challenge is the use of distributed storage systems. One strategy that implemented in distributed data storage systems is the use of Erasure Code which applied to network coding. The code used in this technique is based on the algebraic structure which is called as vector space. Some studies have also been carried out to create code that is based on other algebraic structures such as module.  In this study, we are going to try to set up a code based on the algebraic structure which is a generalization of the module that is semimodule by utilizing the max operations and sum operations at max plus algebra. The results of this study indicate that the max operation and the addition operation on max plus algebra cannot be used to establish a semimodule code, but by modifying the operation "+" as "min", we get a code based on semimodule. Keywords:   code, distributed storage systems, network coding, semimodule, max plus algebra

  1. Linear algebra meets Lie algebra: the Kostant-Wallach theory

    OpenAIRE

    Shomron, Noam; Parlett, Beresford N.

    2008-01-01

    In two languages, Linear Algebra and Lie Algebra, we describe the results of Kostant and Wallach on the fibre of matrices with prescribed eigenvalues of all leading principal submatrices. In addition, we present a brief introduction to basic notions in Algebraic Geometry, Integrable Systems, and Lie Algebra aimed at specialists in Linear Algebra.

  2. Individual differences in algebraic cognition: Relation to the approximate number and semantic memory systems.

    Science.gov (United States)

    Geary, David C; Hoard, Mary K; Nugent, Lara; Rouder, Jeffrey N

    2015-12-01

    The relation between performance on measures of algebraic cognition and acuity of the approximate number system (ANS) and memory for addition facts was assessed for 171 ninth graders (92 girls) while controlling for parental education, sex, reading achievement, speed of numeral processing, fluency of symbolic number processing, intelligence, and the central executive component of working memory. The algebraic tasks assessed accuracy in placing x,y pairs in the coordinate plane, speed and accuracy of expression evaluation, and schema memory for algebra equations. ANS acuity was related to accuracy of placements in the coordinate plane and expression evaluation but not to schema memory. Frequency of fact retrieval errors was related to schema memory but not to coordinate plane or expression evaluation accuracy. The results suggest that the ANS may contribute to or be influenced by spatial-numerical and numerical-only quantity judgments in algebraic contexts, whereas difficulties in committing addition facts to long-term memory may presage slow formation of memories for the basic structure of algebra equations. More generally, the results suggest that different brain and cognitive systems are engaged during the learning of different components of algebraic competence while controlling for demographic and domain general abilities. Copyright © 2015 Elsevier Inc. All rights reserved.

  3. Topos-Based Logic for Quantum Systems and Bi-Heyting Algebras

    OpenAIRE

    Doering, Andreas

    2012-01-01

    Comment: 22 pages, no figures; v2: improved presentation, minor correction, all main results unchanged, added example. Accepted for publication in Logic & Algebra in Quantum Computing, Lecture Notes in Logic, published by the Association for Symbolic Logic in conjunction with Cambridge University Press

  4. Introduction to relation algebras relation algebras

    CERN Document Server

    Givant, Steven

    2017-01-01

    The first volume of a pair that charts relation algebras from novice to expert level, this text offers a comprehensive grounding for readers new to the topic. Upon completing this introduction, mathematics students may delve into areas of active research by progressing to the second volume, Advanced Topics in Relation Algebras; computer scientists, philosophers, and beyond will be equipped to apply these tools in their own field. The careful presentation establishes first the arithmetic of relation algebras, providing ample motivation and examples, then proceeds primarily on the basis of algebraic constructions: subalgebras, homomorphisms, quotient algebras, and direct products. Each chapter ends with a historical section and a substantial number of exercises. The only formal prerequisite is a background in abstract algebra and some mathematical maturity, though the reader will also benefit from familiarity with Boolean algebra and naïve set theory. The measured pace and outstanding clarity are particularly ...

  5. Identification of dynamical Lie algebras for finite-level quantum control systems

    Energy Technology Data Exchange (ETDEWEB)

    Schirmer, S.G.; Pullen, I.C.H.; Solomon, A.I. [Quantum Processes Group and Department of Applied Maths, Open University, Milton Keynes (United Kingdom)]. E-mails: S.G.Schirmer@open.ac.uk; I.C.H.Pullen@open.ac.uk; A.I.Solomon@open.ac.uk

    2002-03-08

    The problem of identifying the dynamical Lie algebras of finite-level quantum systems subject to external control is considered, with special emphasis on systems that are not completely controllable. In particular, it is shown that the dynamical Lie algebra for an N-level system with symmetrically coupled transitions, such as a system with equally spaced energy levels and uniform transition dipole moments, is a subalgebra of so(N) if N=2l+1, and a subalgebra of sp(l) if N=2l. General criteria for obtaining either so(2l+1) or sp(l) are established. (author)

  6. An automatic formulation of inverse free second moment method for algebraic systems

    International Nuclear Information System (INIS)

    Shakshuki, Elhadi; Ponnambalam, Kumaraswamy

    2002-01-01

    In systems with probabilistic uncertainties, an estimation of reliability requires at least the first two moments. In this paper, we focus on probabilistic analysis of linear systems. The important tasks in this analysis are the formulation and the automation of the moment equations. The main objective of the formulation is to provide at least means and variances of the output variables with at least a second-order accuracy. The objective of the automation is to reduce the storage and computational complexities required for implementing (automating) those formulations. This paper extends the recent work done to calculate the first two moments of a set of random algebraic linear equations by developing a stamping procedure to facilitate its automation. The new method has an additional advantage of being able to solve problems when the mean matrix of a system is singular. Lastly, from storage and computational complexities and accuracy point of view, a comparison between the new method and another recently developed first order second moment method is made with numerical examples

  7. Linear algebra

    CERN Document Server

    Liesen, Jörg

    2015-01-01

    This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exerc...

  8. Incomplete projection reconstruction of computed tomography based on the modified discrete algebraic reconstruction technique

    Science.gov (United States)

    Yang, Fuqiang; Zhang, Dinghua; Huang, Kuidong; Gao, Zongzhao; Yang, YaFei

    2018-02-01

    Based on the discrete algebraic reconstruction technique (DART), this study aims to address and test a new improved algorithm applied to incomplete projection data to generate a high quality reconstruction image by reducing the artifacts and noise in computed tomography. For the incomplete projections, an augmented Lagrangian based on compressed sensing is first used in the initial reconstruction for segmentation of the DART to get higher contrast graphics for boundary and non-boundary pixels. Then, the block matching 3D filtering operator was used to suppress the noise and to improve the gray distribution of the reconstructed image. Finally, simulation studies on the polychromatic spectrum were performed to test the performance of the new algorithm. Study results show a significant improvement in the signal-to-noise ratios (SNRs) and average gradients (AGs) of the images reconstructed from incomplete data. The SNRs and AGs of the new images reconstructed by DART-ALBM were on average 30%-40% and 10% higher than the images reconstructed by DART algorithms. Since the improved DART-ALBM algorithm has a better robustness to limited-view reconstruction, which not only makes the edge of the image clear but also makes the gray distribution of non-boundary pixels better, it has the potential to improve image quality from incomplete projections or sparse projections.

  9. Lectures on algebraic statistics

    CERN Document Server

    Drton, Mathias; Sullivant, Seth

    2009-01-01

    How does an algebraic geometer studying secant varieties further the understanding of hypothesis tests in statistics? Why would a statistician working on factor analysis raise open problems about determinantal varieties? Connections of this type are at the heart of the new field of "algebraic statistics". In this field, mathematicians and statisticians come together to solve statistical inference problems using concepts from algebraic geometry as well as related computational and combinatorial techniques. The goal of these lectures is to introduce newcomers from the different camps to algebraic statistics. The introduction will be centered around the following three observations: many important statistical models correspond to algebraic or semi-algebraic sets of parameters; the geometry of these parameter spaces determines the behaviour of widely used statistical inference procedures; computational algebraic geometry can be used to study parameter spaces and other features of statistical models.

  10. Algebraic partial Boolean algebras

    International Nuclear Information System (INIS)

    Smith, Derek

    2003-01-01

    Partial Boolean algebras, first studied by Kochen and Specker in the 1960s, provide the structure for Bell-Kochen-Specker theorems which deny the existence of non-contextual hidden variable theories. In this paper, we study partial Boolean algebras which are 'algebraic' in the sense that their elements have coordinates in an algebraic number field. Several of these algebras have been discussed recently in a debate on the validity of Bell-Kochen-Specker theorems in the context of finite precision measurements. The main result of this paper is that every algebraic finitely-generated partial Boolean algebra B(T) is finite when the underlying space H is three-dimensional, answering a question of Kochen and showing that Conway and Kochen's infinite algebraic partial Boolean algebra has minimum dimension. This result contrasts the existence of an infinite (non-algebraic) B(T) generated by eight elements in an abstract orthomodular lattice of height 3. We then initiate a study of higher-dimensional algebraic partial Boolean algebras. First, we describe a restriction on the determinants of the elements of B(T) that are generated by a given set T. We then show that when the generating set T consists of the rays spanning the minimal vectors in a real irreducible root lattice, B(T) is infinite just if that root lattice has an A 5 sublattice. Finally, we characterize the rays of B(T) when T consists of the rays spanning the minimal vectors of the root lattice E 8

  11. Algebraic calculations for spectrum of superintegrable system from exceptional orthogonal polynomials

    Science.gov (United States)

    Hoque, Md. Fazlul; Marquette, Ian; Post, Sarah; Zhang, Yao-Zhong

    2018-04-01

    We introduce an extended Kepler-Coulomb quantum model in spherical coordinates. The Schrödinger equation of this Hamiltonian is solved in these coordinates and it is shown that the wave functions of the system can be expressed in terms of Laguerre, Legendre and exceptional Jacobi polynomials (of hypergeometric type). We construct ladder and shift operators based on the corresponding wave functions and obtain their recurrence formulas. These recurrence relations are used to construct higher-order, algebraically independent integrals of motion to prove superintegrability of the Hamiltonian. The integrals form a higher rank polynomial algebra. By constructing the structure functions of the associated deformed oscillator algebras we derive the degeneracy of energy spectrum of the superintegrable system.

  12. LCM and MCM: Specification of a control system using dynamic logic and process algebra

    NARCIS (Netherlands)

    Wieringa, Roelf J.; Lewerentz, Claus; Lindner, Thomas

    1994-01-01

    LCM 3.0 is a specification language based on dynamic logic and process algebra, and can be used to specify systems of dynamic objects that communicate synchronously. LCM 3.0 was developed for the specification of object-oriented information systems, but contains sufficient facilities for the

  13. Classification of all solutions of the algebraic Riccati equations for infinite-dimensional systems

    NARCIS (Netherlands)

    Iftime, O; Curtain, R; Zwart, H

    2003-01-01

    We obtain a complete classification of all self-adjoint solution of the control algebraic Riccati equation for infinite-dimensional systems under the following assumptions: the system is output stabilizable, strongly detectable and the filter Riccati equation has an invertible self-adjoint

  14. Algorithms in Algebraic Geometry

    CERN Document Server

    Dickenstein, Alicia; Sommese, Andrew J

    2008-01-01

    In the last decade, there has been a burgeoning of activity in the design and implementation of algorithms for algebraic geometric computation. Some of these algorithms were originally designed for abstract algebraic geometry, but now are of interest for use in applications and some of these algorithms were originally designed for applications, but now are of interest for use in abstract algebraic geometry. The workshop on Algorithms in Algebraic Geometry that was held in the framework of the IMA Annual Program Year in Applications of Algebraic Geometry by the Institute for Mathematics and Its

  15. Second-Order Systems of ODEs Admitting Three-Dimensional Lie Algebras and Integrability

    Directory of Open Access Journals (Sweden)

    Muhammad Ayub

    2013-01-01

    the case of k≥3. We discuss the singular invariant representations of canonical forms for systems of two second-order ODEs admitting three-dimensional Lie algebras. Furthermore, we give an integration procedure for canonical forms for systems of two second-order ODEs admitting three-dimensional Lie algebras which comprises of two approaches, namely, division into four types I, II, III, and IV and that of integrability of the invariant representations. We prove that if a system of two second-order ODEs has a three-dimensional solvable Lie algebra, then, its general solution can be obtained from a partially linear, partially coupled or reduced invariantly represented system of equations. A natural extension of this result is provided for a system of two kth-order (k≥3 ODEs. We present illustrative examples of familiar integrable physical systems which admit three-dimensional Lie algebras such as the classical Kepler problem and the generalized Ermakov systems that give rise to closed trajectories.

  16. Computer Operating System Maintenance.

    Science.gov (United States)

    1982-06-01

    FACILITY The Computer Management Information Facility ( CMIF ) system was developed by Rapp Systems to fulfill the need at the CRF to record and report on...computer center resource usage and utilization. The foundation of the CMIF system is a System 2000 data base (CRFMGMT) which stores and permits access

  17. An algebraic approach to the inverse eigenvalue problem for a quantum system with a dynamical group

    International Nuclear Information System (INIS)

    Wang, S.J.

    1993-04-01

    An algebraic approach to the inverse eigenvalue problem for a quantum system with a dynamical group is formulated for the first time. One dimensional problem is treated explicitly in detail for both the finite dimensional and infinite dimensional Hilbert spaces. For the finite dimensional Hilbert space, the su(2) algebraic representation is used; while for the infinite dimensional Hilbert space, the Heisenberg-Weyl algebraic representation is employed. Fourier expansion technique is generalized to the generator space, which is suitable for analysis of irregular spectra. The polynormial operator basis is also used for complement, which is appropriate for analysis of some simple Hamiltonians. The proposed new approach is applied to solve the classical inverse Sturn-Liouville problem and to study the problems of quantum regular and irregular spectra. (orig.)

  18. Structural analysis and design of multivariable control systems: An algebraic approach

    Science.gov (United States)

    Tsay, Yih Tsong; Shieh, Leang-San; Barnett, Stephen

    1988-01-01

    The application of algebraic system theory to the design of controllers for multivariable (MV) systems is explored analytically using an approach based on state-space representations and matrix-fraction descriptions. Chapters are devoted to characteristic lambda matrices and canonical descriptions of MIMO systems; spectral analysis, divisors, and spectral factors of nonsingular lambda matrices; feedback control of MV systems; and structural decomposition theories and their application to MV control systems.

  19. GPU TECHNOLOGIES EMBODIED IN PARALLEL SOLVERS OF LINEAR ALGEBRAIC EQUATION SYSTEMS

    Directory of Open Access Journals (Sweden)

    Sidorov Alexander Vladimirovich

    2012-10-01

    Full Text Available The author reviews existing shareware solvers that are operated by graphical computer devices. The purpose of this review is to explore the opportunities and limitations of the above parallel solvers applicable for resolution of linear algebraic problems that arise at Research and Educational Centre of Computer Modeling at MSUCE, and Research and Engineering Centre STADYO. The author has explored new applications of the GPU in the PETSc suite and compared them with the results generated absent of the GPU. The research is performed within the CUSP library developed to resolve the problems of linear algebra through the application of GPU. The author has also reviewed the new MAGMA project which is analogous to LAPACK for the GPU.

  20. Dynamics of number systems computation with arbitrary precision

    CERN Document Server

    Kurka, Petr

    2016-01-01

    This book is a source of valuable and useful information on the topics of dynamics of number systems and scientific computation with arbitrary precision. It is addressed to scholars, scientists and engineers, and graduate students. The treatment is elementary and self-contained with relevance both for theory and applications. The basic prerequisite of the book is linear algebra and matrix calculus. .

  1. Linear-Algebra Programs

    Science.gov (United States)

    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.

  2. Guaranteed Cost H∞ Controller Synthesis for Switched Systems Defined on Semi-algebraic Sets

    DEFF Research Database (Denmark)

    Ahmadi, Mohamadreza; Mojallali, Hamed; Wisniewski, Rafael

    2014-01-01

    of Filippov solutions which subsumes solutions with infinite switching in finite time and sliding modes. Firstly, conditions assuring asymptotic stability of Filippov solutions pertained to a switched system defined on semi-algebraic sets are formulated. Accordingly, we derive a set of sum of squares...

  3. Fractal Shapes Description with Parametric L-systems and Turtle Algebra

    OpenAIRE

    Ikbal Zammouri; Béchir Ayeb

    2007-01-01

    In this paper, we propose a new method to describe fractal shapes using parametric l-systems. First we introduce scaling factors in the production rules of the parametric l-systems grammars. Then we decorticate these grammars with scaling factors using turtle algebra to show the mathematical relation between l-systems and iterated function systems (IFS). We demonstrate that with specific values of the scaling factors, we find the exact relationship established by Prusinkiewicz and Hammel betw...

  4. Reliable computer systems.

    Science.gov (United States)

    Wear, L L; Pinkert, J R

    1993-11-01

    In this article, we looked at some decisions that apply to the design of reliable computer systems. We began with a discussion of several terms such as testability, then described some systems that call for highly reliable hardware and software. The article concluded with a discussion of methods that can be used to achieve higher reliability in computer systems. Reliability and fault tolerance in computers probably will continue to grow in importance. As more and more systems are computerized, people will want assurances about the reliability of these systems, and their ability to work properly even when sub-systems fail.

  5. A Structural Model of Algebra Achievement: Computational Fluency and Spatial Visualisation as Mediators of the Effect of Working Memory on Algebra Achievement

    Science.gov (United States)

    Tolar, Tammy Daun; Lederberg, Amy R.; Fletcher, Jack M.

    2009-01-01

    The goal of this study was to develop and evaluate a structural model of the relations among cognitive abilities and arithmetic skills and college students' algebra achievement. The model of algebra achievement was compared to a model of performance on the Scholastic Assessment in Mathematics (SAT-M) to determine whether the pattern of relations…

  6. Parallel Programming Application to Matrix Algebra in the Spectral Method for Control Systems Analysis, Synthesis and Identification

    Directory of Open Access Journals (Sweden)

    V. Yu. Kleshnin

    2016-01-01

    Full Text Available The article describes the matrix algebra libraries based on the modern technologies of parallel programming for the Spectrum software, which can use a spectral method (in the spectral form of mathematical description to analyse, synthesise and identify deterministic and stochastic dynamical systems. The developed matrix algebra libraries use the following technologies for the GPUs: OmniThreadLibrary, OpenMP, Intel Threading Building Blocks, Intel Cilk Plus for CPUs nVidia CUDA, OpenCL, and Microsoft Accelerated Massive Parallelism.The developed libraries support matrices with real elements (single and double precision. The matrix dimensions are limited by 32-bit or 64-bit memory model and computer configuration. These libraries are general-purpose and can be used not only for the Spectrum software. They can also find application in the other projects where there is a need to perform operations with large matrices.The article provides a comparative analysis of the libraries developed for various matrix operations (addition, subtraction, scalar multiplication, multiplication, powers of matrices, tensor multiplication, transpose, inverse matrix, finding a solution of the system of linear equations through the numerical experiments using different CPU and GPU. The article contains sample programs and performance test results for matrix multiplication, which requires most of all computational resources in regard to the other operations.

  7. Solving differential–algebraic equation systems by means of index reduction methodology

    DEFF Research Database (Denmark)

    Sørensen, Kim; Houbak, Niels; Condra, Thomas

    2006-01-01

    of a number of differential equations and algebraic equations — a so called DAE system. Two of the DAE systems are of index 1 and they can be solved by means of standard DAE-solvers. For the actual application, the equation systems are integrated by means of MATLAB’s solver: ode23t, that solves moderately...... stiff ODEs and index 1 DAEs by means of the trapezoidal rule. The last sub-model that models the boilers steam drum consist of two differential and three algebraic equations. The index of this model is greater than 1, which means that ode23t cannot integrate this equation system. In this paper......, it is shown how the equation system, by means of an index reduction methodology, can be reduced to a system of ordinary differential equations — ODEs....

  8. Solving differential-algebraic equation systems by means of index reduction methodology

    DEFF Research Database (Denmark)

    Sørensen, Kim; Houbak, Niels; Condra, Thomas Joseph

    2006-01-01

    of a number of differential equations and algebraic equations - a so called DAE system. Two of the DAE systems are of index 1 and they can be solved by means of standard DAE-solvers. For the actual application, the equation systems are integrated by means of MATLAB’s solver: ode23t, that solves moderately...... stiff ODE’s and index 1 DAE’s by means of the trapezoidal rule. The last sub-model that models the boilers steam drum consist of two differential and three algebraic equations. The index of this model is greater than 1, which means that ode23t cannot integrate this equation system. In this paper......, it is shown how the equation system, by means of an index reduction methodology, can be reduced to a system of Ordinary- Differential-Equations - ODE’s....

  9. Fault tolerant computing systems

    International Nuclear Information System (INIS)

    Randell, B.

    1981-01-01

    Fault tolerance involves the provision of strategies for error detection damage assessment, fault treatment and error recovery. A survey is given of the different sorts of strategies used in highly reliable computing systems, together with an outline of recent research on the problems of providing fault tolerance in parallel and distributed computing systems. (orig.)

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

    Science.gov (United States)

    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.

  11. Algebraic topological entropy

    International Nuclear Information System (INIS)

    Hudetz, T.

    1989-01-01

    As a 'by-product' of the Connes-Narnhofer-Thirring theory of dynamical entropy for (originally non-Abelian) nuclear C * -algebras, the well-known variational principle for topological entropy is eqivalently reformulated in purly algebraically defined terms for (separable) Abelian C * -algebras. This 'algebraic variational principle' should not only nicely illustrate the 'feed-back' of methods developed for quantum dynamical systems to the classical theory, but it could also be proved directly by 'algebraic' methods and could thus further simplify the original proof of the variational principle (at least 'in principle'). 23 refs. (Author)

  12. Algebraic geometry

    CERN Document Server

    Lefschetz, Solomon

    2005-01-01

    An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.

  13. Grassmann algebras

    International Nuclear Information System (INIS)

    Garcia, R.L.

    1983-11-01

    The Grassmann algebra is presented briefly. Exponential and logarithm of matrices functions, whose elements belong to this algebra, are studied with the help of the SCHOONSCHIP and REDUCE 2 algebraic manipulators. (Author) [pt

  14. NCT-ART - a neutron computer tomography code based on the algebraic reconstruction technique

    International Nuclear Information System (INIS)

    Krueger, A.

    1988-01-01

    A computer code is presented, which calculates two-dimensional cuts of material assemblies from a number of neutron radiographic projections. Mathematically, the reconstruction is performed by an iterative solution of a system of linear equations. If the system is fully determined, clear pictures are obtained. Even for an underdetermined system (low number of projections) reasonable pictures are reconstructed, but then picture artefacts and convergence problems occur increasingly. (orig.) With 37 figs [de

  15. A Continuous Formulation for Logical Decisions in Differential Algebraic Systems using Mathematical Programs with Complementarity Constraints

    Directory of Open Access Journals (Sweden)

    Kody M. Powell

    2016-03-01

    Full Text Available This work presents a methodology to represent logical decisions in differential algebraic equation simulation and constrained optimization problems using a set of continuous algebraic equations. The formulations may be used when state variables trigger a change in process dynamics, and introduces a pseudo-binary decision variable, which is continuous, but should only have valid solutions at values of either zero or one within a finite time horizon. This formulation enables dynamic optimization problems with logical disjunctions to be solved by simultaneous solution methods without using methods such as mixed integer programming. Several case studies are given to illustrate the value of this methodology including nonlinear model predictive control of a chemical reactor using a surge tank with overflow to buffer disturbances in feed flow rate. Although this work contains novel methodologies for solving dynamic algebraic equation (DAE constrained problems where the system may experience an abrupt change in dynamics that may otherwise require a conditional statement, there remain substantial limitations to this methodology, including a limited domain where problems may converge and the possibility for ill-conditioning. Although the problems presented use only continuous algebraic equations, the formulation has inherent non-smoothness. Hence, these problems must be solved with care and only in select circumstances, such as in simulation or situations when the solution is expected to be near the solver’s initial point.

  16. Transforming an Introductory Linear Algebra Course with a TI-92 Hand-Held Computer.

    Science.gov (United States)

    Quesada, Antonio R.

    2003-01-01

    Describes how the introduction of the TI-92 transformed a traditional first semester linear algebra course into a matrix-oriented course that emphasized conceptual understanding, relevant applications, and numerical issues. Indicates an increase in students' overall performance as they found the calculator very useful, believed it helped them…

  17. On the Use of an Algebraic Signature Analyzer for Mixed-Signal Systems Testing

    Directory of Open Access Journals (Sweden)

    Vadim Geurkov

    2014-01-01

    Full Text Available We propose an approach to design of an algebraic signature analyzer that can be used for mixed-signal systems testing. The analyzer does not contain carry propagating circuitry, which improves its performance as well as fault tolerance. The common design technique of a signature analyzer for mixed-signal systems is based on the rules of an arithmetic finite field. The application of this technique to the systems with an arbitrary radix is a challenging task and the devices designed possess high hardware complexity. The proposed technique is simple and applicable to systems of any size and radix. The hardware complexity is low. The technique can also be used in arithmetic/algebraic coding and cryptography.

  18. Dynamical scaling and crossover from algebraic to logarithmic growth in dilute systems

    DEFF Research Database (Denmark)

    Mouritsen, Ole G.; Shah, Peter Jivan

    1989-01-01

    The ordering dynamics of the two-dimensional Ising antiferromagnet with mobile vacancies and nonconserved order parameter is studied by Monte Carlo temperature-quenching experiments. The domain-size distribution function is shown to obey dynamical scaling. A crossover is found from an algebraic...... growth law for the pure system to effectively logarithmic growth behavior in the dilute system, in accordance with recent experiments on ordering kinetics in impure chemisorbed overlayers and off-stoichiometric alloys....

  19. Computer information systems framework

    International Nuclear Information System (INIS)

    Shahabuddin, S.

    1989-01-01

    Management information systems (MIS) is a commonly used term in computer profession. The new information technology has caused management to expect more from computer. The process of supplying information follows a well defined procedure. MIS should be capable for providing usable information to the various areas and levels of organization. MIS is different from data processing. MIS and business hierarchy provides a good framework for many organization which are using computers. (A.B.)

  20. Priority in Process Algebras

    Science.gov (United States)

    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.

  1. Attacks on computer systems

    Directory of Open Access Journals (Sweden)

    Dejan V. Vuletić

    2012-01-01

    Full Text Available Computer systems are a critical component of the human society in the 21st century. Economic sector, defense, security, energy, telecommunications, industrial production, finance and other vital infrastructure depend on computer systems that operate at local, national or global scales. A particular problem is that, due to the rapid development of ICT and the unstoppable growth of its application in all spheres of the human society, their vulnerability and exposure to very serious potential dangers increase. This paper analyzes some typical attacks on computer systems.

  2. Petascale Computational Systems

    OpenAIRE

    Bell, Gordon; Gray, Jim; Szalay, Alex

    2007-01-01

    Computational science is changing to be data intensive. Super-Computers must be balanced systems; not just CPU farms but also petascale IO and networking arrays. Anyone building CyberInfrastructure should allocate resources to support a balanced Tier-1 through Tier-3 design.

  3. Advances in Statistical Control, Algebraic Systems Theory, and Dynamic Systems Characteristics A Tribute to Michael K Sain

    CERN Document Server

    Won, Chang-Hee; Michel, Anthony N

    2008-01-01

    This volume - dedicated to Michael K. Sain on the occasion of his seventieth birthday - is a collection of chapters covering recent advances in stochastic optimal control theory and algebraic systems theory. Written by experts in their respective fields, the chapters are thematically organized into four parts: Part I focuses on statistical control theory, where the cost function is viewed as a random variable and performance is shaped through cost cumulants. In this respect, statistical control generalizes linear-quadratic-Gaussian and H-infinity control. Part II addresses algebraic systems th

  4. Cohomology of Effect Algebras

    Directory of Open Access Journals (Sweden)

    Frank Roumen

    2017-01-01

    Full Text Available We will define two ways to assign cohomology groups to effect algebras, which occur in the algebraic study of quantum logic. The first way is based on Connes' cyclic cohomology. The resulting cohomology groups are related to the state space of the effect algebra, and can be computed using variations on the Kunneth and Mayer-Vietoris sequences. The second way involves a chain complex of ordered abelian groups, and gives rise to a cohomological characterization of state extensions on effect algebras. This has applications to no-go theorems in quantum foundations, such as Bell's theorem.

  5. Resilient computer system design

    CERN Document Server

    Castano, Victor

    2015-01-01

    This book presents a paradigm for designing new generation resilient and evolving computer systems, including their key concepts, elements of supportive theory, methods of analysis and synthesis of ICT with new properties of evolving functioning, as well as implementation schemes and their prototyping. The book explains why new ICT applications require a complete redesign of computer systems to address challenges of extreme reliability, high performance, and power efficiency. The authors present a comprehensive treatment for designing the next generation of computers, especially addressing safety-critical, autonomous, real time, military, banking, and wearable health care systems.   §  Describes design solutions for new computer system - evolving reconfigurable architecture (ERA) that is free from drawbacks inherent in current ICT and related engineering models §  Pursues simplicity, reliability, scalability principles of design implemented through redundancy and re-configurability; targeted for energy-,...

  6. Numerical linear algebra theory and applications

    CERN Document Server

    Beilina, Larisa; Karchevskii, Mikhail

    2017-01-01

    This book combines a solid theoretical background in linear algebra with practical algorithms for numerical solution of linear algebra problems. Developed from a number of courses taught repeatedly by the authors, the material covers topics like matrix algebra, theory for linear systems of equations, spectral theory, vector and matrix norms combined with main direct and iterative numerical methods, least squares problems, and eigen problems. Numerical algorithms illustrated by computer programs written in MATLAB® are also provided as supplementary material on SpringerLink to give the reader a better understanding of professional numerical software for the solution of real-life problems. Perfect for a one- or two-semester course on numerical linear algebra, matrix computation, and large sparse matrices, this text will interest students at the advanced undergraduate or graduate level.

  7. Algorithms of estimation for nonlinear systems a differential and algebraic viewpoint

    CERN Document Server

    Martínez-Guerra, Rafael

    2017-01-01

    This book acquaints readers with recent developments in dynamical systems theory and its applications, with a strong focus on the control and estimation of nonlinear systems. Several algorithms are proposed and worked out for a set of model systems, in particular so-called input-affine or bilinear systems, which can serve to approximate a wide class of nonlinear control systems. These can either take the form of state space models or be represented by an input-output equation. The approach taken here further highlights the role of modern mathematical and conceptual tools, including differential algebraic theory, observer design for nonlinear systems and generalized canonical forms.

  8. New computer systems

    International Nuclear Information System (INIS)

    Faerber, G.

    1975-01-01

    Process computers have already become indespensable technical aids for monitoring and automation tasks in nuclear power stations. Yet there are still some problems connected with their use whose elimination should be the main objective in the development of new computer systems. In the paper, some of these problems are summarized, new tendencies in hardware development are outlined, and finally some new systems concepts made possible by the hardware development are explained. (orig./AK) [de

  9. A Pharmacy Computer System

    OpenAIRE

    Claudia CIULCA-VLADAIA; Călin MUNTEAN

    2009-01-01

    Objective: Describing a model of evaluation seen from a customer’s point of view for the current needed pharmacy computer system. Data Sources: literature research, ATTOFARM, WINFARM P.N.S., NETFARM, Info World - PHARMACY MANAGER and HIPOCRATE FARMACIE. Study Selection: Five Pharmacy Computer Systems were selected due to their high rates of implementing at a national level. We used the new criteria recommended by EUROREC Institute in EHR that modifies the model of data exchanges between the E...

  10. Simple relation algebras

    CERN Document Server

    Givant, Steven

    2017-01-01

    This monograph details several different methods for constructing simple relation algebras, many of which are new with this book. By drawing these seemingly different methods together, all are shown to be aspects of one general approach, for which several applications are given. These tools for constructing and analyzing relation algebras are of particular interest to mathematicians working in logic, algebraic logic, or universal algebra, but will also appeal to philosophers and theoretical computer scientists working in fields that use mathematics. The book is written with a broad audience in mind and features a careful, pedagogical approach; an appendix contains the requisite background material in relation algebras. Over 400 exercises provide ample opportunities to engage with the material, making this a monograph equally appropriate for use in a special topics course or for independent study. Readers interested in pursuing an extended background study of relation algebras will find a comprehensive treatme...

  11. Continuum analogues of contragredient Lie algebras

    International Nuclear Information System (INIS)

    Saveliev, M.V.; Vershik, A.M.

    1989-03-01

    We present an axiomatic formulation of a new class of infinite-dimensional Lie algebras - the generalizations of Z-graded Lie algebras with, generally speaking, an infinite-dimensional Cartan subalgebra and a contiguous set of roots. We call such algebras ''continuum Lie algebras''. The simple Lie algebras of constant growth are encapsulated in our formulation. We pay particular attention to the case when the local algebra is parametrized by a commutative algebra while the Cartan operator (the generalization of the Cartan matrix) is a linear operator. Special examples of these algebras are the Kac-Moody algebras, algebras of Poisson brackets, algebras of vector fields on a manifold, current algebras, and algebras with differential or integro-differential Cartan operator. The nonlinear dynamical systems associated with the continuum contragredient Lie algebras are also considered. (author). 9 refs

  12. Algebraic and structural automata theory

    CERN Document Server

    Mikolajczak, B

    1991-01-01

    Automata Theory is part of computability theory which covers problems in computer systems, software, activity of nervous systems (neural networks), and processes of live organisms development.The result of over ten years of research, this book presents work in the following areas of Automata Theory: automata morphisms, time-varying automata, automata realizations and relationships between automata and semigroups.Aimed at those working in discrete mathematics and computer science, parts of the book are suitable for use in graduate courses in computer science, electronics, telecommunications, and control engineering. It is assumed that the reader is familiar with the basic concepts of algebra and graph theory.

  13. Max plus at work modeling and analysis of synchronized systems a course on max-plus algebra and its applications

    CERN Document Server

    Heidergott, Bernd; van der Woude, Jacob

    2014-01-01

    Trains pull into a railroad station and must wait for each other before leaving again in order to let passengers change trains. How do mathematicians then calculate a railroad timetable that accurately reflects their comings and goings? One approach is to use max-plus algebra, a framework used to model Discrete Event Systems, which are well suited to describe the ordering and timing of events. This is the first textbook on max-plus algebra, providing a concise and self-contained introduction to the topic. Applications of max-plus algebra abound in the world around us. Traffic systems, compu

  14. Fault detection and diagnosis in nonlinear systems a differential and algebraic viewpoint

    CERN Document Server

    Martinez-Guerra, Rafael

    2014-01-01

    The high reliability required in industrial processes has created the necessity of detecting abnormal conditions, called faults, while processes are operating. The term fault generically refers to any type of process degradation, or degradation in equipment performance because of changes in the process's physical characteristics, process inputs or environmental conditions. This book is about the fundamentals of fault detection and diagnosis in a variety of nonlinear systems which are represented by ordinary differential equations. The fault detection problem is approached from a differential algebraic viewpoint, using residual generators based upon high-gain nonlinear auxiliary systems (‘observers’). A prominent role is played by the type of mathematical tools that will be used, requiring knowledge of differential algebra and differential equations. Specific theorems tailored to the needs of the problem-solving procedures are developed and proved. Applications to real-world problems, both with constant an...

  15. Flocking of Second-Order Multiagent Systems With Connectivity Preservation Based on Algebraic Connectivity Estimation.

    Science.gov (United States)

    Fang, Hao; Wei, Yue; Chen, Jie; Xin, Bin

    2017-04-01

    The problem of flocking of second-order multiagent systems with connectivity preservation is investigated in this paper. First, for estimating the algebraic connectivity as well as the corresponding eigenvector, a new decentralized inverse power iteration scheme is formulated. Then, based on the estimation of the algebraic connectivity, a set of distributed gradient-based flocking control protocols is built with a new class of generalized hybrid potential fields which could guarantee collision avoidance, desired distance stabilization, and the connectivity of the underlying communication network simultaneously. What is important is that the proposed control scheme allows the existing edges to be broken without violation of connectivity constraints, and thus yields more flexibility of motions and reduces the communication cost for the multiagent system. In the end, nontrivial comparative simulations and experimental results are performed to demonstrate the effectiveness of the theoretical results and highlight the advantages of the proposed estimation scheme and control algorithm.

  16. Generalized Heisenberg algebra and algebraic method: The example of an infinite square-well potential

    International Nuclear Information System (INIS)

    Curado, E.M.F.; Hassouni, Y.; Rego-Monteiro, M.A.; Rodrigues, Ligia M.C.S.

    2008-01-01

    We discuss the role of generalized Heisenberg algebras (GHA) in obtaining an algebraic method to describe physical systems. The method consists in finding the GHA associated to a physical system and the relations between its generators and the physical observables. We choose as an example the infinite square-well potential for which we discuss the representations of the corresponding GHA. We suggest a way of constructing a physical realization of the generators of some GHA and apply it to the square-well potential. An expression for the position operator x in terms of the generators of the algebra is given and we compute its matrix elements

  17. Shape optimization for Navier-Stokes equations with algebraic turbulence model : numerical analysis and computation

    Czech Academy of Sciences Publication Activity Database

    Haslinger, J.; Stebel, Jan

    2011-01-01

    Roč. 63, č. 2 (2011), s. 277-308 ISSN 0095-4616 R&D Projects: GA MŠk LC06052 Institutional research plan: CEZ:AV0Z10190503 Keywords : optimal shape design * paper machine headbox * incompressible non-Newtonian fluid * algebraic turbulence model Subject RIV: BA - General Mathematics Impact factor: 0.952, year: 2011 http://link.springer.com/article/10.1007%2Fs00245-010-9121-x

  18. Topics in quaternion linear algebra

    CERN Document Server

    Rodman, Leiba

    2014-01-01

    Quaternions are a number system that has become increasingly useful for representing the rotations of objects in three-dimensional space and has important applications in theoretical and applied mathematics, physics, computer science, and engineering. This is the first book to provide a systematic, accessible, and self-contained exposition of quaternion linear algebra. It features previously unpublished research results with complete proofs and many open problems at various levels, as well as more than 200 exercises to facilitate use by students and instructors. Applications presented in the book include numerical ranges, invariant semidefinite subspaces, differential equations with symmetries, and matrix equations. Designed for researchers and students across a variety of disciplines, the book can be read by anyone with a background in linear algebra, rudimentary complex analysis, and some multivariable calculus. Instructors will find it useful as a complementary text for undergraduate linear algebra courses...

  19. Bicovariant quantum algebras and quantum Lie algebras

    International Nuclear Information System (INIS)

    Schupp, P.; Watts, P.; Zumino, B.

    1993-01-01

    A bicovariant calculus of differential operators on a quantum group is constructed in a natural way, using invariant maps from Fun(G q ) to U q g, given by elements of the pure braid group. These operators - the 'reflection matrix' Y= triple bond L + SL - being a special case - generate algebras that linearly close under adjoint actions, i.e. they form generalized Lie algebras. We establish the connection between the Hopf algebra formulation of the calculus and a formulation in compact matrix form which is quite powerful for actual computations and as applications we find the quantum determinant and an orthogonality relation for Y in SO q (N). (orig.)

  20. Implicative Algebras

    African Journals Online (AJOL)

    Tadesse

    In this paper we introduce the concept of implicative algebras which is an equivalent definition of lattice implication algebra of Xu (1993) and further we prove that it is a regular Autometrized. Algebra. Further we remark that the binary operation → on lattice implicative algebra can never be associative. Key words: Implicative ...

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

    NARCIS (Netherlands)

    Igonine, Sergei

    2002-01-01

    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

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

    NARCIS (Netherlands)

    Igonin, S.

    2002-01-01

    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

  3. On Robust Stability of Systems of Differential-Algebraic Equations

    Directory of Open Access Journals (Sweden)

    A. Shcheglova

    2016-06-01

    The sufficient conditions of robust stability for index-one and index-two systems are obtained. We use the values of real and complex stability radii obtained for system of ordinary differential equations solved with respect to the derivatives. We consider the example illustrating the obtained results.

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

    International Nuclear Information System (INIS)

    Igonin, Sergei

    2002-01-01

    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=A t S and SA=-A t S for a quadratic matrix A and its transpose A t , which may be of independent interest

  5. Coherent population transfer in multilevel systems with magnetic sublevels. II. Algebraic analysis

    International Nuclear Information System (INIS)

    Martin, J.; Shore, B.W.; Bergmann, K.

    1995-01-01

    We extend previous theoretical work on coherent population transfer by stimulated Raman adiabatic passage for states involving nonzero angular momentum. The pump and Stokes fields are either copropagating or counterpropagating with the corresponding linearly polarized electric-field vectors lying in a common plane with the magnetic-field direction. Zeeman splitting lifts the magnetic sublevel degeneracy. We present an algebraic analysis of dressed-state properties to explain the behavior noted in numerical studies. In particular, we discuss conditions which are likely to lead to a failure of complete population transfer. The applied strategy, based on simple methods of linear algebra, will also be successful for other types of discrete multilevel systems, provided the rotating-wave and adiabatic approximation are valid

  6. Coherent population transfer in multilevel systems with magnetic sublevels. II. Algebraic analysis

    Science.gov (United States)

    Martin, J.; Shore, B. W.; Bergmann, K.

    1995-07-01

    We extend previous theoretical work on coherent population transfer by stimulated Raman adiabatic passage for states involving nonzero angular momentum. The pump and Stokes fields are either copropagating or counterpropagating with the corresponding linearly polarized electric-field vectors lying in a common plane with the magnetic-field direction. Zeeman splitting lifts the magnetic sublevel degeneracy. We present an algebraic analysis of dressed-state properties to explain the behavior noted in numerical studies. In particular, we discuss conditions which are likely to lead to a failure of complete population transfer. The applied strategy, based on simple methods of linear algebra, will also be successful for other types of discrete multilevel systems, provided the rotating-wave and adiabatic approximation are valid.

  7. Analytical-Algebraic Approach to Solving Chaotic System

    Czech Academy of Sciences Publication Activity Database

    Beran, Zdeněk; Čelikovský, Sergej

    2016-01-01

    Roč. 26, č. 3 (2016), č. článku 1650051. ISSN 0218-1274 R&D Projects: GA ČR GA13-20433S Institutional support: RVO:67985556 Keywords : Laplace transform * Laplace-Adomian decomposition * Adomian polynomials * nonlinear systems * chaos Subject RIV: BC - Control Systems Theory Impact factor: 1.329, year: 2016 http://library.utia.cas.cz/separaty/2016/TR/beran-0458430.pdf

  8. Computer network defense system

    Science.gov (United States)

    Urias, Vincent; Stout, William M. S.; Loverro, Caleb

    2017-08-22

    A method and apparatus for protecting virtual machines. A computer system creates a copy of a group of the virtual machines in an operating network in a deception network to form a group of cloned virtual machines in the deception network when the group of the virtual machines is accessed by an adversary. The computer system creates an emulation of components from the operating network in the deception network. The components are accessible by the group of the cloned virtual machines as if the group of the cloned virtual machines was in the operating network. The computer system moves network connections for the group of the virtual machines in the operating network used by the adversary from the group of the virtual machines in the operating network to the group of the cloned virtual machines, enabling protecting the group of the virtual machines from actions performed by the adversary.

  9. (m,n-Semirings and a Generalized Fault-Tolerance Algebra of Systems

    Directory of Open Access Journals (Sweden)

    Syed Eqbal Alam

    2013-01-01

    Full Text Available We propose a new class of mathematical structures called (m,n-semirings (which generalize the usual semirings and describe their basic properties. We define partial ordering and generalize the concepts of congruence, homomorphism, and so forth, for (m,n-semirings. Following earlier work by Rao (2008, we consider systems made up of several components whose failures may cause them to fail and represent the set of such systems algebraically as an (m,n-semiring. Based on the characteristics of these components, we present a formalism to compare the fault-tolerance behavior of two systems using our framework of a partially ordered (m,n-semiring.

  10. Computer system operation

    International Nuclear Information System (INIS)

    Lee, Young Jae; Lee, Hae Cho; Lee, Ho Yeun; Kim, Young Taek; Lee, Sung Kyu; Park, Jeong Suk; Nam, Ji Wha; Kim, Soon Kon; Yang, Sung Un; Sohn, Jae Min; Moon, Soon Sung; Park, Bong Sik; Lee, Byung Heon; Park, Sun Hee; Kim, Jin Hee; Hwang, Hyeoi Sun; Lee, Hee Ja; Hwang, In A.

    1993-12-01

    The report described the operation and the trouble shooting of main computer and KAERINet. The results of the project are as follows; 1. The operation and trouble shooting of the main computer system. (Cyber 170-875, Cyber 960-31, VAX 6320, VAX 11/780). 2. The operation and trouble shooting of the KAERINet. (PC to host connection, host to host connection, file transfer, electronic-mail, X.25, CATV etc.). 3. The development of applications -Electronic Document Approval and Delivery System, Installation the ORACLE Utility Program. 22 tabs., 12 figs. (Author) .new

  11. Computer system operation

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Young Jae; Lee, Hae Cho; Lee, Ho Yeun; Kim, Young Taek; Lee, Sung Kyu; Park, Jeong Suk; Nam, Ji Wha; Kim, Soon Kon; Yang, Sung Un; Sohn, Jae Min; Moon, Soon Sung; Park, Bong Sik; Lee, Byung Heon; Park, Sun Hee; Kim, Jin Hee; Hwang, Hyeoi Sun; Lee, Hee Ja; Hwang, In A [Korea Atomic Energy Research Institute, Taejon (Korea, Republic of)

    1993-12-01

    The report described the operation and the trouble shooting of main computer and KAERINet. The results of the project are as follows; 1. The operation and trouble shooting of the main computer system. (Cyber 170-875, Cyber 960-31, VAX 6320, VAX 11/780). 2. The operation and trouble shooting of the KAERINet. (PC to host connection, host to host connection, file transfer, electronic-mail, X.25, CATV etc.). 3. The development of applications -Electronic Document Approval and Delivery System, Installation the ORACLE Utility Program. 22 tabs., 12 figs. (Author) .new.

  12. New families of superintegrable systems from k-step rational extensions, polynomial algebras and degeneracies

    International Nuclear Information System (INIS)

    Marquette, Ian

    2015-01-01

    Four new families of two-dimensional quantum superintegrable systems are constructed from k-step extension of the harmonic oscillator and the radial oscillator. Their wavefunctions are related with Hermite and Laguerre exceptional orthogonal polynomials (EOP) of type III. We show that ladder operators obtained from alternative construction based on combinations of supercharges in the Krein-Adler and Darboux Crum (or state deleting and creating) approaches can be used to generate a set of integrals of motion and a corresponding polynomial algebra that provides an algebraic derivation of the full spectrum and total number of degeneracies. Such derivation is based on finite dimensional unitary representations (unirreps) and doesn't work for integrals build from standard ladder operators in supersymmetric quantum mechanics (SUSYQM) as they contain singlets isolated from excited states. In this paper, we also rely on a novel approach to obtain the finite dimensional unirreps based on the action of the integrals of motion on the wavefunctions given in terms of these EOP. We compare the results with those obtained from the Daskaloyannis approach and the realizations in terms of deformed oscillator algebras for one of the new families in the case of 1-step extension. This communication is a review of recent works. (paper)

  13. Quadratic algebras

    CERN Document Server

    Polishchuk, Alexander

    2005-01-01

    Quadratic algebras, i.e., algebras defined by quadratic relations, often occur in various areas of mathematics. One of the main problems in the study of these (and similarly defined) algebras is how to control their size. A central notion in solving this problem is the notion of a Koszul algebra, which was introduced in 1970 by S. Priddy and then appeared in many areas of mathematics, such as algebraic geometry, representation theory, noncommutative geometry, K-theory, number theory, and noncommutative linear algebra. The book offers a coherent exposition of the theory of quadratic and Koszul algebras, including various definitions of Koszulness, duality theory, Poincar�-Birkhoff-Witt-type theorems for Koszul algebras, and the Koszul deformation principle. In the concluding chapter of the book, they explain a surprising connection between Koszul algebras and one-dependent discrete-time stochastic processes.

  14. Adaptive algebraic reconstruction technique

    International Nuclear Information System (INIS)

    Lu Wenkai; Yin Fangfang

    2004-01-01

    Algebraic reconstruction techniques (ART) are iterative procedures for reconstructing objects from their projections. It is proven that ART can be computationally efficient by carefully arranging the order in which the collected data are accessed during the reconstruction procedure and adaptively adjusting the relaxation parameters. In this paper, an adaptive algebraic reconstruction technique (AART), which adopts the same projection access scheme in multilevel scheme algebraic reconstruction technique (MLS-ART), is proposed. By introducing adaptive adjustment of the relaxation parameters during the reconstruction procedure, one-iteration AART can produce reconstructions with better quality, in comparison with one-iteration MLS-ART. Furthermore, AART outperforms MLS-ART with improved computational efficiency

  15. Algebraic Verification Method for SEREs Properties via Groebner Bases Approaches

    Directory of Open Access Journals (Sweden)

    Ning Zhou

    2013-01-01

    Full Text Available This work presents an efficient solution using computer algebra system to perform linear temporal properties verification for synchronous digital systems. The method is essentially based on both Groebner bases approaches and symbolic simulation. A mechanism for constructing canonical polynomial set based symbolic representations for both circuit descriptions and assertions is studied. We then present a complete checking algorithm framework based on these algebraic representations by using Groebner bases. The computational experience result in this work shows that the algebraic approach is a quite competitive checking method and will be a useful supplement to the existent verification methods based on simulation.

  16. Comparison of algebraic and analytical approaches to the formulation of the statistical model-based reconstruction problem for X-ray computed tomography.

    Science.gov (United States)

    Cierniak, Robert; Lorent, Anna

    2016-09-01

    The main aim of this paper is to investigate properties of our originally formulated statistical model-based iterative approach applied to the image reconstruction from projections problem which are related to its conditioning, and, in this manner, to prove a superiority of this approach over ones recently used by other authors. The reconstruction algorithm based on this conception uses a maximum likelihood estimation with an objective adjusted to the probability distribution of measured signals obtained from an X-ray computed tomography system with parallel beam geometry. The analysis and experimental results presented here show that our analytical approach outperforms the referential algebraic methodology which is explored widely in the literature and exploited in various commercial implementations. Copyright © 2016 Elsevier Ltd. All rights reserved.

  17. Belle computing system

    International Nuclear Information System (INIS)

    Adachi, Ichiro; Hibino, Taisuke; Hinz, Luc; Itoh, Ryosuke; Katayama, Nobu; Nishida, Shohei; Ronga, Frederic; Tsukamoto, Toshifumi; Yokoyama, Masahiko

    2004-01-01

    We describe the present status of the computing system in the Belle experiment at the KEKB e+e- asymmetric-energy collider. So far, we have logged more than 160fb-1 of data, corresponding to the world's largest data sample of 170M BB-bar pairs at the -bar (4S) energy region. A large amount of event data has to be processed to produce an analysis event sample in a timely fashion. In addition, Monte Carlo events have to be created to control systematic errors accurately. This requires stable and efficient usage of computing resources. Here, we review our computing model and then describe how we efficiently proceed DST/MC productions in our system

  18. QuBiLS-MIDAS: a parallel free-software for molecular descriptors computation based on multilinear algebraic maps.

    Science.gov (United States)

    García-Jacas, César R; Marrero-Ponce, Yovani; Acevedo-Martínez, Liesner; Barigye, Stephen J; Valdés-Martiní, José R; Contreras-Torres, Ernesto

    2014-07-05

    The present report introduces the QuBiLS-MIDAS software belonging to the ToMoCoMD-CARDD suite for the calculation of three-dimensional molecular descriptors (MDs) based on the two-linear (bilinear), three-linear, and four-linear (multilinear or N-linear) algebraic forms. Thus, it is unique software that computes these tensor-based indices. These descriptors, establish relations for two, three, and four atoms by using several (dis-)similarity metrics or multimetrics, matrix transformations, cutoffs, local calculations and aggregation operators. The theoretical background of these N-linear indices is also presented. The QuBiLS-MIDAS software was developed in the Java programming language and employs the Chemical Development Kit library for the manipulation of the chemical structures and the calculation of the atomic properties. This software is composed by a desktop user-friendly interface and an Abstract Programming Interface library. The former was created to simplify the configuration of the different options of the MDs, whereas the library was designed to allow its easy integration to other software for chemoinformatics applications. This program provides functionalities for data cleaning tasks and for batch processing of the molecular indices. In addition, it offers parallel calculation of the MDs through the use of all available processors in current computers. The studies of complexity of the main algorithms demonstrate that these were efficiently implemented with respect to their trivial implementation. Lastly, the performance tests reveal that this software has a suitable behavior when the amount of processors is increased. Therefore, the QuBiLS-MIDAS software constitutes a useful application for the computation of the molecular indices based on N-linear algebraic maps and it can be used freely to perform chemoinformatics studies. Copyright © 2014 Wiley Periodicals, Inc.

  19. Lie algebras and applications

    CERN Document Server

    Iachello, Francesco

    2015-01-01

    This course-based primer provides an introduction to Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. In the first part, it concisely presents the basic concepts of Lie algebras, their representations and their invariants. The second part includes a description of how Lie algebras are used in practice in the treatment of bosonic and fermionic systems. Physical applications considered include rotations and vibrations of molecules (vibron model), collective modes in nuclei (interacting boson model), the atomic shell model, the nuclear shell model, and the quark model of hadrons. One of the key concepts in the application of Lie algebraic methods in physics, that of spectrum generating algebras and their associated dynamic symmetries, is also discussed. The book highlights a number of examples that help to illustrate the abstract algebraic definitions and includes a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators...

  20. Genetic coding and united-hypercomplex systems in the models of algebraic biology.

    Science.gov (United States)

    Petoukhov, Sergey V

    2017-08-01

    Structured alphabets of DNA and RNA in their matrix form of representations are connected with Walsh functions and a new type of systems of multidimensional numbers. This type generalizes systems of complex numbers and hypercomplex numbers, which serve as the basis of mathematical natural sciences and many technologies. The new systems of multi-dimensional numbers have interesting mathematical properties and are called in a general case as "systems of united-hypercomplex numbers" (or briefly "U-hypercomplex numbers"). They can be widely used in models of multi-parametrical systems in the field of algebraic biology, artificial life, devices of biological inspired artificial intelligence, etc. In particular, an application of U-hypercomplex numbers reveals hidden properties of genetic alphabets under cyclic permutations in their doublets and triplets. A special attention is devoted to the author's hypothesis about a multi-linguistic in DNA-sequences in a relation with an ensemble of U-numerical sub-alphabets. Genetic multi-linguistic is considered as an important factor to provide noise-immunity properties of the multi-channel genetic coding. Our results attest to the conformity of the algebraic properties of the U-numerical systems with phenomenological properties of the DNA-alphabets and with the complementary device of the double DNA-helix. It seems that in the modeling field of algebraic biology the genetic-informational organization of living bodies can be considered as a set of united-hypercomplex numbers in some association with the famous slogan of Pythagoras "the numbers rule the world". Copyright © 2017 Elsevier B.V. All rights reserved.

  1. An algorithm to construct the basic algebra of a skew group algebra

    NARCIS (Netherlands)

    Horobeţ, E.

    2016-01-01

    We give an algorithm for the computation of the basic algebra Morita equivalent to a skew group algebra of a path algebra by obtaining formulas for the number of vertices and arrows of the new quiver Qb. We apply this algorithm to compute the basic algebra corresponding to all simple quaternion

  2. Computer Based Expert Systems.

    Science.gov (United States)

    Parry, James D.; Ferrara, Joseph M.

    1985-01-01

    Claims knowledge-based expert computer systems can meet needs of rural schools for affordable expert advice and support and will play an important role in the future of rural education. Describes potential applications in prediction, interpretation, diagnosis, remediation, planning, monitoring, and instruction. (NEC)

  3. Mining Department computer systems

    Energy Technology Data Exchange (ETDEWEB)

    1979-09-01

    Describes the main computer systems currently available, or being developed by the Mining Department of the UK National Coal Board. They are primarily for the use of mining and specialist engineers, but some of them have wider applications, particularly in the research and development and management statistics fields.

  4. DYMAC computer system

    International Nuclear Information System (INIS)

    Hagen, J.; Ford, R.F.

    1979-01-01

    The DYnamic Materials ACcountability program (DYMAC) has been monitoring nuclear material at the Los Alamos Scientific Laboratory plutonium processing facility since January 1978. This paper presents DYMAC's features and philosophy, especially as reflected in its computer system design. Early decisions and tradeoffs are evaluated through the benefit of a year's operating experience

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

    International Nuclear Information System (INIS)

    Konopelchenko, B G; Ortenzi, G

    2011-01-01

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

  6. A Type System for the Vectorial Aspect of the Linear-Algebraic Lambda-Calculus

    Directory of Open Access Journals (Sweden)

    Pablo Arrighi

    2012-07-01

    Full Text Available We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms resulting from the reduction of programs. This gives rise to an original type theory where types, in the same way as terms, can be superposed into linear combinations. We show that the resulting typed lambda-calculus is strongly normalizing and features a weak subject-reduction.

  7. Study on generalized Toda mechanics system with loop algebra L(Dr)

    International Nuclear Information System (INIS)

    Zhu Qiao; Yang Zhanying; Shi Kangjie

    2005-01-01

    The authors generalize the Toda mechanics system with long range interaction to the case of Loop algebra L(D r ). By using a pair of ordered positive integer (X, Y) to describe Toda chains, authors extract the equation of motion and the Hamiltonian structure of this system for (3, 2) Toda chain. It turns out that both extra coordinates and standard Toda variables are Poisson non-commutative in the case of nontrivial generalization, and for some case, extra variables appear linearly on the right hand side of the Poisson bracket. (authors)

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

    Science.gov (United States)

    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.

  9. Differential Privacy for Relational Algebra: Improving the Sensitivity Bounds via Constraint Systems

    Directory of Open Access Journals (Sweden)

    Catuscia Palamidessi

    2012-07-01

    Full Text Available Differential privacy is a modern approach in privacy-preserving data analysis to control the amount of information that can be inferred about an individual by querying a database. The most common techniques are based on the introduction of probabilistic noise, often defined as a Laplacian parametric on the sensitivity of the query. In order to maximize the utility of the query, it is crucial to estimate the sensitivity as precisely as possible. In this paper we consider relational algebra, the classical language for queries in relational databases, and we propose a method for computing a bound on the sensitivity of queries in an intuitive and compositional way. We use constraint-based techniques to accumulate the information on the possible values for attributes provided by the various components of the query, thus making it possible to compute tight bounds on the sensitivity.

  10. Linear algebra as an alternative approach to the synthesis of digital devices of automation and control systems

    Directory of Open Access Journals (Sweden)

    Nikolay Chernov

    2018-01-01

    Full Text Available The article considers linear algebra as an alternative mathematical tool of logic synthesis of digital structures to Boolean algebra and synthesis methods of digital electronic component base (ECB on its ground. The methods of solving the applied problems of logic synthesis are shown, including the expansion of an arbitrary logic function by means of monotonic functions. The proposed mathematical apparatus actually provides the creation of digital structures on the principles of analog circuitry. It can find application in the design of multivalued digital ECB, specialized system-on-chip and analog-digital sensors with current output. The examples of synthesis of the combinational and sequential two-valued and multivalued digital devices are given. In conclusion, the advantages of linear algebra in comparison with Boolean algebra are formulated.

  11. Applied linear algebra and matrix analysis

    CERN Document Server

    Shores, Thomas S

    2018-01-01

    In its second edition, this textbook offers a fresh approach to matrix and linear algebra. Its blend of theory, computational exercises, and analytical writing projects is designed to highlight the interplay between these aspects of an application. This approach places special emphasis on linear algebra as an experimental science that provides tools for solving concrete problems. The second edition’s revised text discusses applications of linear algebra like graph theory and network modeling methods used in Google’s PageRank algorithm. Other new materials include modeling examples of diffusive processes, linear programming, image processing, digital signal processing, and Fourier analysis. These topics are woven into the core material of Gaussian elimination and other matrix operations; eigenvalues, eigenvectors, and discrete dynamical systems; and the geometrical aspects of vector spaces. Intended for a one-semester undergraduate course without a strict calculus prerequisite, Applied Linear Algebra and M...

  12. Computation of focal values and stability analysis of 4-dimensional systems

    Directory of Open Access Journals (Sweden)

    Bo Sang

    2015-08-01

    Full Text Available This article presents a recursive formula for computing the n-th singular point values of a class of 4-dimensional autonomous systems, and establishes the algebraic equivalence between focal values and singular point values. The formula is linear and then avoids complicated integrating operations, therefore the calculation can be carried out by computer algebra system such as Maple. As an application of the formula, bifurcation analysis is made for a quadratic system with a Hopf equilibrium, which can have three small limit cycles around an equilibrium point. The theory and methodology developed in this paper can be used for higher-dimensional systems.

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

    International Nuclear Information System (INIS)

    Hanlon, J.; Ziock, H.

    1997-01-01

    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

  14. Rationality problem for algebraic tori

    CERN Document Server

    Hoshi, Akinari

    2017-01-01

    The authors give the complete stably rational classification of algebraic tori of dimensions 4 and 5 over a field k. In particular, the stably rational classification of norm one tori whose Chevalley modules are of rank 4 and 5 is given. The authors show that there exist exactly 487 (resp. 7, resp. 216) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension 4, and there exist exactly 3051 (resp. 25, resp. 3003) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension 5. The authors make a procedure to compute a flabby resolution of a G-lattice effectively by using the computer algebra system GAP. Some algorithms may determine whether the flabby class of a G-lattice is invertible (resp. zero) or not. Using the algorithms, the suthors determine all the flabby and coflabby G-lattices of rank up to 6 and verify that they are stably permutation. The authors also show that the Krull-Schmidt theorem for G-...

  15. New simple algebraic root locus method for design of feedback control systems

    Directory of Open Access Journals (Sweden)

    Cingara Aleksandar M.

    2008-01-01

    Full Text Available New concept of algebraic characteristic equation decomposition method is presented to simplify the design of closed-loop systems for practical applications. The method consists of two decompositions. The first one, decomposition of the characteristic equation into two lower order equations, was performed in order to simplify the analysis and design of closed loop systems. The second is the decomposition of Laplace variable, s, into two variables, damping coefficient, ζ, and natural frequency, ω n. Those two decompositions reduce the design of any order feedback systems to setting of two complex dominant poles in the desired position. In the paper, we derived explicit equations for six cases: first, second and third order system with P and PI. We got the analytical solutions for the case of fourth and fifth order characteristic equations with the P and PI controller; one may obtain a complete analytical solution of controller gain as a function of the desired damping coefficient. The complete derivation is given for the third order equation with P and PI controller. We can extend the number of specified poles to the highest order of the characteristic equation working in a similar way, so we can specify the position of each pole. The concept is similar to the root locus but root locus is implicit, which makes it more complicated and this is simpler explicit root locus. Standard procedures, root locus and Bode diagrams or Nichol Charts, are neither algebraic nor explicit. We basically change controller parameters and observe the change of some function until we get the desired specifications. The derived method has three important advantage over the standard procedures. It is general, algebraic and explicit. Those are the best poles design results possible; it is not possible to get better controller design results.

  16. Current algebras, measures quasi-invariant under diffeomorphism groups, and infinite quantum systems with accumulation points

    Science.gov (United States)

    Sakuraba, Takao

    The approach to quantum physics via current algebra and unitary representations of the diffeomorphism group is established. This thesis studies possible infinite Bose gas systems using this approach. Systems of locally finite configurations and systems of configurations with accumulation points are considered, with the main emphasis on the latter. In Chapter 2, canonical quantization, quantization via current algebra and unitary representations of the diffeomorphism group are reviewed. In Chapter 3, a new definition of the space of configurations is proposed and an axiom for general configuration spaces is abstracted. Various subsets of the configuration space, including those specifying the number of points in a Borel set and those specifying the number of accumulation points in a Borel set are proved to be measurable using this axiom. In Chapter 4, known results on the space of locally finite configurations and Poisson measure are reviewed in the light of the approach developed in Chapter 3, including the approach to current algebra in the Poisson space by Albeverio, Kondratiev, and Rockner. Goldin and Moschella considered unitary representations of the group of diffeomorphisms of the line based on self-similar random processes, which may describe infinite quantum gas systems with clusters. In Chapter 5, the Goldin-Moschella theory is developed further. Their construction of measures quasi-invariant under diffeomorphisms is reviewed, and a rigorous proof of their conjectures is given. It is proved that their measures with distinct correlation parameters are mutually singular. A quasi-invariant measure constructed by Ismagilov on the space of configurations with accumulation points on the circle is proved to be singular with respect to the Goldin-Moschella measures. Finally a generalization of the Goldin-Moschella measures to the higher-dimensional case is studied, where the notion of covariance matrix and the notion of condition number play important roles. A

  17. Method of computer algebraic calculation of the matrix elements in the second quantization language

    International Nuclear Information System (INIS)

    Gotoh, Masashi; Mori, Kazuhide; Itoh, Reikichi

    1995-01-01

    An automated method by the algebraic programming language REDUCE3 for specifying the matrix elements expressed in second quantization language is presented and then applied to the case of the matrix elements in the TDHF theory. This program works in a very straightforward way by commuting the electron creation and annihilation operator (a † and a) until these operators have completely vanished from the expression of the matrix element under the appropriate elimination conditions. An improved method using singlet generators of unitary transformations in the place of the electron creation and annihilation operators is also presented. This improvement reduces the time and memory required for the calculation. These methods will make programming in the field of quantum chemistry much easier. 11 refs., 1 tab

  18. A linear process-algebraic format for probabilistic systems with data (extended version)

    NARCIS (Netherlands)

    Katoen, Joost P.; van de Pol, Jan Cornelis; Stoelinga, Mariëlle Ida Antoinette; Timmer, Mark

    2010-01-01

    This paper presents a novel linear process-algebraic format for probabilistic automata. The key ingredient is a symbolic transformation of probabilistic process algebra terms that incorporate data into this linear format while preserving strong probabilistic bisimulation. This generalises similar

  19. Language Analysis and Generation in Algebra Tutorial Dialogues for Language-Based Intelligent Tutoring Systems

    National Research Council Canada - National Science Library

    Kim, Jung

    2004-01-01

    The North Carolina A&T State University algebra tutoring dialogue project collects and analyzes algebra tutoring dialogues with the aim of describing tutoring strategies and language with enough rigor that they may...

  20. A linear process-algebraic format for probabilistic systems with data

    NARCIS (Netherlands)

    Katoen, Joost P.; van de Pol, Jan Cornelis; Stoelinga, Mariëlle Ida Antoinette; Timmer, Mark; Gomes, L.; Khomenko, V.; Fernandes, J.M.

    This paper presents a novel linear process algebraic format for probabilistic automata. The key ingredient is a symbolic transformation of probabilistic process algebra terms that incorporate data into this linear format while preserving strong probabilistic bisimulation. This generalises similar

  1. Stability of Linear Equations--Algebraic Approach

    Science.gov (United States)

    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…

  2. Boolean algebra

    CERN Document Server

    Goodstein, R L

    2007-01-01

    This elementary treatment by a distinguished mathematician employs Boolean algebra as a simple medium for introducing important concepts of modern algebra. Numerous examples appear throughout the text, plus full solutions.

  3. Universal algebra

    CERN Document Server

    Grätzer, George

    1979-01-01

    Universal Algebra, heralded as ". . . the standard reference in a field notorious for the lack of standardization . . .," has become the most authoritative, consistently relied on text in a field with applications in other branches of algebra and other fields such as combinatorics, geometry, and computer science. Each chapter is followed by an extensive list of exercises and problems. The "state of the art" account also includes new appendices (with contributions from B. Jónsson, R. Quackenbush, W. Taylor, and G. Wenzel) and a well-selected additional bibliography of over 1250 papers and books which makes this a fine work for students, instructors, and researchers in the field. "This book will certainly be, in the years to come, the basic reference to the subject." --- The American Mathematical Monthly (First Edition) "In this reviewer's opinion [the author] has more than succeeded in his aim. The problems at the end of each chapter are well-chosen; there are more than 650 of them. The book is especially sui...

  4. Ready, Set, Algebra?

    Science.gov (United States)

    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 dissertation,…

  5. Learning Activity Package, Algebra.

    Science.gov (United States)

    Evans, Diane

    A set of ten teacher-prepared Learning Activity Packages (LAPs) in beginning algebra and nine in intermediate algebra, these units cover sets, properties of operations, number systems, open expressions, solution sets of equations and inequalities in one and two variables, exponents, factoring and polynomials, relations and functions, radicals,…

  6. Jordan algebras versus C*- algebras

    International Nuclear Information System (INIS)

    Stormer, E.

    1976-01-01

    The axiomatic formulation of quantum mechanics and the problem of whether the observables form self-adjoint operators on a Hilbert space, are discussed. The relation between C*- algebras and Jordan algebras is studied using spectral theory. (P.D.)

  7. PEP computer control system

    International Nuclear Information System (INIS)

    1979-03-01

    This paper describes the design and performance of the computer system that will be used to control and monitor the PEP storage ring. Since the design is essentially complete and much of the system is operational, the system is described as it is expected to 1979. Section 1 of the paper describes the system hardware which includes the computer network, the CAMAC data I/O system, and the operator control consoles. Section 2 describes a collection of routines that provide general services to applications programs. These services include a graphics package, data base and data I/O programs, and a director programm for use in operator communication. Section 3 describes a collection of automatic and semi-automatic control programs, known as SCORE, that contain mathematical models of the ring lattice and are used to determine in real-time stable paths for changing beam configuration and energy and for orbit correction. Section 4 describes a collection of programs, known as CALI, that are used for calibration of ring elements

  8. Semi-infinite Weil complex and the Virasoro algebra

    International Nuclear Information System (INIS)

    Feigin, B.; Frenkel, E.

    1991-01-01

    We define a semi-infinite analogue of the Weil algebra associated with an infinite-dimensional Lie algebra. It can be used for the definition of semi-infinite characteristic classes by analogy with the Chern-Weil construction. The second term of a spectral sequence of this Weil complex consists of the semi-infinite cohomology of the Lie algebra with coefficients in its 'adjoint semi-infinite symmetric powers'. We compute this cohomology for the Virasoro algebra. This is just the BRST cohomology of the bosonic βγ-system with the central charge 26. We give a complete description of the Fock representations of this bosonic system as modules over the Virasoro algebra, using Friedan-Martinec-Shenker bosonization. We derive a combinatorial identity from this result. (orig.)

  9. Algebraic Methods to Design Signals

    Science.gov (United States)

    2015-08-27

    to date on designing signals using algebraic and combinatorial methods. Mathematical tools from algebraic number theory, representation theory and... combinatorial objects in designing signals for communication purposes. Sequences and arrays with desirable autocorrelation properties have many...multiple access methods in mobile radio communication systems. We continue our mathematical framework based on group algebras, character theory

  10. Commutative algebra with a view toward algebraic geometry

    CERN Document Server

    Eisenbud, David

    1995-01-01

    Commutative Algebra is best understood with knowledge of the geometric ideas that have played a great role in its formation, in short, with a view towards algebraic geometry. The author presents a comprehensive view of commutative algebra, from basics, such as localization and primary decomposition, through dimension theory, differentials, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. Many exercises illustrate and sharpen the theory and extended exercises give the reader an active part in complementing the material presented in the text. One novel feature is a chapter devoted to a quick but thorough treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Applications of the theory and even suggestions for computer algebra projects are included. This book will appeal to readers from beginners to advanced students of commutative algebra or algeb...

  11. Algebraic solutions of shape-invariant position-dependent effective mass systems

    Energy Technology Data Exchange (ETDEWEB)

    Amir, Naila, E-mail: naila.amir@live.com, E-mail: naila.amir@seecs.edu.pk [School of Electrical Engineering and Computer Sciences, National University of Sciences and Technology, Islamabad (Pakistan); Iqbal, Shahid, E-mail: sic80@hotmail.com, E-mail: siqbal@sns.nust.edu.pk [School of Natural Sciences, National University of Sciences and Technology, Islamabad (Pakistan)

    2016-06-15

    Keeping in view the ordering ambiguity that arises due to the presence of position-dependent effective mass in the kinetic energy term of the Hamiltonian, a general scheme for obtaining algebraic solutions of quantum mechanical systems with position-dependent effective mass is discussed. We quantize the Hamiltonian of the pertaining system by using symmetric ordering of the operators concerning momentum and the spatially varying mass, initially proposed by von Roos and Lévy-Leblond. The algebraic method, used to obtain the solutions, is based on the concepts of supersymmetric quantum mechanics and shape invariance. In order to exemplify the general formalism a class of non-linear oscillators has been considered. This class includes the particular example of a one-dimensional oscillator with different position-dependent effective mass profiles. Explicit expressions for the eigenenergies and eigenfunctions in terms of generalized Hermite polynomials are presented. Moreover, properties of these modified Hermite polynomials, like existence of generating function and recurrence relations among the polynomials have also been studied. Furthermore, it has been shown that in the harmonic limit, all the results for the linear harmonic oscillator are recovered.

  12. Modeling Stochastic Complexity in Complex Adaptive Systems: Non-Kolmogorov Probability and the Process Algebra Approach.

    Science.gov (United States)

    Sulis, William H

    2017-10-01

    Walter Freeman III pioneered the application of nonlinear dynamical systems theories and methodologies in his work on mesoscopic brain dynamics.Sadly, mainstream psychology and psychiatry still cling to linear correlation based data analysis techniques, which threaten to subvert the process of experimentation and theory building. In order to progress, it is necessary to develop tools capable of managing the stochastic complexity of complex biopsychosocial systems, which includes multilevel feedback relationships, nonlinear interactions, chaotic dynamics and adaptability. In addition, however, these systems exhibit intrinsic randomness, non-Gaussian probability distributions, non-stationarity, contextuality, and non-Kolmogorov probabilities, as well as the absence of mean and/or variance and conditional probabilities. These properties and their implications for statistical analysis are discussed. An alternative approach, the Process Algebra approach, is described. It is a generative model, capable of generating non-Kolmogorov probabilities. It has proven useful in addressing fundamental problems in quantum mechanics and in the modeling of developing psychosocial systems.

  13. How to Produce S-Tense Operators on Lattice Effect Algebras

    Science.gov (United States)

    Chajda, Ivan; Janda, Jiří; Paseka, Jan

    2014-07-01

    Tense operators in effect algebras play a key role for the representation of the dynamics of formally described physical systems. For this, it is important to know how to construct them on a given effect algebra and how to compute all possible pairs of tense operators on . However, we firstly need to derive a time frame which enables these constructions and computations. Hence, we usually apply a suitable set of states of the effect algebra in question. To approximate physical reality in quantum mechanics, we use only the so-called Jauch-Piron states on in our paper. To realize our constructions, we are restricted on lattice effect algebras only.

  14. Fundamentals of algebraic graph transformation

    CERN Document Server

    Ehrig, Hartmut; Prange, Ulrike; Taentzer, Gabriele

    2006-01-01

    Graphs are widely used to represent structural information in the form of objects and connections between them. Graph transformation is the rule-based manipulation of graphs, an increasingly important concept in computer science and related fields. This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. Part I is an introduction to the classical case of graph and typed graph transformation. In Part II basic and advanced results are first shown for an abstract form of replacement systems, so-called adhesive high-level replacement systems based on category theory, and are then instantiated to several forms of graph and Petri net transformation systems. Part III develops typed attributed graph transformation, a technique of key relevance in the modeling of visual languages and in model transformation. Part IV contains a practical case study on model transformation and a presentation of the AGG (attributed graph grammar) tool envir...

  15. Tensor spaces and exterior algebra

    CERN Document Server

    Yokonuma, Takeo

    1992-01-01

    This book explains, as clearly as possible, tensors and such related topics as tensor products of vector spaces, tensor algebras, and exterior algebras. You will appreciate Yokonuma's lucid and methodical treatment of the subject. This book is useful in undergraduate and graduate courses in multilinear algebra. Tensor Spaces and Exterior Algebra begins with basic notions associated with tensors. To facilitate understanding of the definitions, Yokonuma often presents two or more different ways of describing one object. Next, the properties and applications of tensors are developed, including the classical definition of tensors and the description of relative tensors. Also discussed are the algebraic foundations of tensor calculus and applications of exterior algebra to determinants and to geometry. This book closes with an examination of algebraic systems with bilinear multiplication. In particular, Yokonuma discusses the theory of replicas of Chevalley and several properties of Lie algebras deduced from them.

  16. Providing Feedback on Computer-Based Algebra Homework in Middle-School Classrooms

    Science.gov (United States)

    Fyfe, Emily R.

    2016-01-01

    Homework is transforming at a rapid rate with continuous advances in educational technology. Computer-based homework, in particular, is gaining popularity across a range of schools, with little empirical evidence on how to optimize student learning. The current aim was to test the effects of different types of feedback on computer-based homework.…

  17. Ubiquitous Computing Systems

    DEFF Research Database (Denmark)

    Bardram, Jakob Eyvind; Friday, Adrian

    2009-01-01

    . While such growth is positive, the newest generation of ubicomp practitioners and researchers, isolated to specific tasks, are in danger of losing their sense of history and the broader perspective that has been so essential to the field’s creativity and brilliance. Under the guidance of John Krumm...... applications Privacy protection in systems that connect personal devices and personal information Moving from the graphical to the ubiquitous computing user interface Techniques that are revolutionizing the way we determine a person’s location and understand other sensor measurements While we needn’t become...

  18. Hopf algebras in noncommutative geometry

    International Nuclear Information System (INIS)

    Varilly, Joseph C.

    2001-10-01

    We give an introductory survey to the use of Hopf algebras in several problems of non- commutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We show its relation to the algebra of transverse differential operators introduced by Connes and Moscovici in order to compute a local index formula in cyclic cohomology, and to the several Hopf algebras defined by Connes and Kreimer to simplify the combinatorics of perturbative renormalization. We explain how characteristic classes for a Hopf module algebra can be obtained from the cyclic cohomology of the Hopf algebra which acts on it. Finally, we discuss the theory of non- commutative spherical manifolds and show how they arise as homogeneous spaces of certain compact quantum groups. (author)

  19. A brief history of process algebra

    NARCIS (Netherlands)

    Baeten, J.C.M.

    2005-01-01

    This note addresses the history of process algebra as an area of research in concurrency theory, the theory of parallel and distributed systems in computer science. Origins are traced back to the early seventies of the twentieth century, and developments since that time are sketched. The author

  20. A brief history of process algebra

    NARCIS (Netherlands)

    Baeten, J.C.M.

    2004-01-01

    Abstract. This note addresses the history of process algebra as an area of research in concurrency theory, the theory of parallel and distributed systems in computer science. Origins are traced back to the early seventies of the twentieth century, and developments since that time are sketched. The

  1. Finite-Time Stabilization for a Class of Nonlinear Differential-Algebraic Systems Subject to Disturbance

    Directory of Open Access Journals (Sweden)

    Xiaohui Mo

    2017-01-01

    Full Text Available In this paper, finite-time stabilization problem for a class of nonlinear differential-algebraic systems (NDASs subject to external disturbance is investigated via a composite control manner. A composite finite-time controller (CFTC is proposed with a three-stage design procedure. Firstly, based on the adding a power integrator technique, a finite-time control (FTC law is explicitly designed for the nominal NDAS by only using differential variables. Then, by using homogeneous system theory, a continuous finite-time disturbance observer (CFTDO is constructed to estimate the disturbance generated by an exogenous system. Finally, a composite controller which consists of a feedforward compensation part based on CFTDO and the obtained FTC law is proposed. Rigorous analysis demonstrates that not only the proposed composite controller can stabilize the NDAS in finite time, but also the proposed control scheme exhibits nominal performance recovery property. Simulation examples are provided to illustrate the effectiveness of the proposed control approach.

  2. Multicore Performance of Block Algebraic Iterative Reconstruction Methods

    DEFF Research Database (Denmark)

    Sørensen, Hans Henrik B.; Hansen, Per Christian

    2014-01-01

    Algebraic iterative methods are routinely used for solving the ill-posed sparse linear systems arising in tomographic image reconstruction. Here we consider the algebraic reconstruction technique (ART) and the simultaneous iterative reconstruction techniques (SIRT), both of which rely on semiconv......Algebraic iterative methods are routinely used for solving the ill-posed sparse linear systems arising in tomographic image reconstruction. Here we consider the algebraic reconstruction technique (ART) and the simultaneous iterative reconstruction techniques (SIRT), both of which rely...... on semiconvergence. Block versions of these methods, based on a partitioning of the linear system, are able to combine the fast semiconvergence of ART with the better multicore properties of SIRT. These block methods separate into two classes: those that, in each iteration, access the blocks in a sequential manner...... a fixed relaxation parameter in each method, namely, the one that leads to the fastest semiconvergence. Computational results show that for multicore computers, the sequential approach is preferable....

  3. Kac-Moody algebras derived from linearization systems using Zsub(N) reduction and extended to supersymmetry

    International Nuclear Information System (INIS)

    Bohr, H.; Roy Chowdhury, A.

    1984-10-01

    The hidden symmetries in various integrable models are derived by applying a newly developed method that uses the Riemann-Hilbert transform in a Zsub(N)-reduction of the linearization systems. The method is extended to linearization systems with higher algebras and with supersymmetry. (author)

  4. Toda lattice field theories, discrete W algebras, Toda lattice hierarchies and quantum groups

    International Nuclear Information System (INIS)

    Bonora, L.; Colatto, L.P.; Constantinidis, C.P.

    1996-05-01

    In analogy with the Liouville case, we study the sl 3 Toda theory on the lattice and define the relevant quadratic algebra and out of it we recover the discrete W 3 algebra. We define an integrable system with respect to the latter and establish the relation with the Toda lattice hierarchy. We compute the relevant continuum limits. Finally we find the quantum version of the quadratic algebra. (author). 16 refs

  5. Separable algebras

    CERN Document Server

    Ford, Timothy J

    2017-01-01

    This book presents a comprehensive introduction to the theory of separable algebras over commutative rings. After a thorough introduction to the general theory, the fundamental roles played by separable algebras are explored. For example, Azumaya algebras, the henselization of local rings, and Galois theory are rigorously introduced and treated. Interwoven throughout these applications is the important notion of étale algebras. Essential connections are drawn between the theory of separable algebras and Morita theory, the theory of faithfully flat descent, cohomology, derivations, differentials, reflexive lattices, maximal orders, and class groups. The text is accessible to graduate students who have finished a first course in algebra, and it includes necessary foundational material, useful exercises, and many nontrivial examples.

  6. Intermediate algebra & analytic geometry

    CERN Document Server

    Gondin, William R

    1967-01-01

    Intermediate Algebra & Analytic Geometry Made Simple focuses on the principles, processes, calculations, and methodologies involved in intermediate algebra and analytic geometry. The publication first offers information on linear equations in two unknowns and variables, functions, and graphs. Discussions focus on graphic interpretations, explicit and implicit functions, first quadrant graphs, variables and functions, determinate and indeterminate systems, independent and dependent equations, and defective and redundant systems. The text then examines quadratic equations in one variable, system

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

    International Nuclear Information System (INIS)

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

    2014-01-01

    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. (paper)

  8. Numerical algebra, matrix theory, differential-algebraic equations and control theory festschrift in honor of Volker Mehrmann

    CERN Document Server

    Bollhöfer, Matthias; Kressner, Daniel; Mehl, Christian; Stykel, Tatjana

    2015-01-01

    This edited volume highlights the scientific contributions of Volker Mehrmann, a leading expert in the area of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory. These mathematical research areas are strongly related and often occur in the same real-world applications. The main areas where such applications emerge are computational engineering and sciences, but increasingly also social sciences and economics. This book also reflects some of Volker Mehrmann's major career stages. Starting out working in the areas of numerical linear algebra (his first full professorship at TU Chemnitz was in "Numerical Algebra," hence the title of the book) and matrix theory, Volker Mehrmann has made significant contributions to these areas ever since. The highlights of these are discussed in Parts I and II of the present book. Often the development of new algorithms in numerical linear algebra is motivated by problems in system and control theory. These and his later major work on ...

  9. Coherent states for a polynomial su(1, 1) algebra and a conditionally solvable system

    International Nuclear Information System (INIS)

    Sadiq, Muhammad; Inomata, Akira; Junker, Georg

    2009-01-01

    In a previous paper (2007 J. Phys. A: Math. Theor. 40 11105), we constructed a class of coherent states for a polynomially deformed su(2) algebra. In this paper, we first prepare the discrete representations of the nonlinearly deformed su(1, 1) algebra. Then we extend the previous procedure to construct a discrete class of coherent states for a polynomial su(1, 1) algebra which contains the Barut-Girardello set and the Perelomov set of the SU(1, 1) coherent states as special cases. We also construct coherent states for the cubic algebra related to the conditionally solvable radial oscillator problem.

  10. The Computational Sensorimotor Systems Laboratory

    Data.gov (United States)

    Federal Laboratory Consortium — The Computational Sensorimotor Systems Lab focuses on the exploration, analysis, modeling and implementation of biological sensorimotor systems for both scientific...

  11. Located actions in process algebra with timing

    NARCIS (Netherlands)

    Bergstra, J.A.; Middelburg, C.A.

    2004-01-01

    We propose a process algebra obtained by adapting the process algebra with continuous relative timing from Baeten and Middelburg [Process Algebra with Timing, Springer, 2002, Chap. 4] to spatially located actions. This process algebra makes it possible to deal with the behaviour of systems with a

  12. Categorical Algebra and its Applications

    CERN Document Server

    1988-01-01

    Categorical algebra and its applications contain several fundamental papers on general category theory, by the top specialists in the field, and many interesting papers on the applications of category theory in functional analysis, algebraic topology, algebraic geometry, general topology, ring theory, cohomology, differential geometry, group theory, mathematical logic and computer sciences. The volume contains 28 carefully selected and refereed papers, out of 96 talks delivered, and illustrates the usefulness of category theory today as a powerful tool of investigation in many other areas.

  13. Quartic Poisson algebras and quartic associative algebras and realizations as deformed oscillator algebras

    International Nuclear Information System (INIS)

    Marquette, Ian

    2013-01-01

    We introduce the most general quartic Poisson algebra generated by a second and a fourth order integral of motion of a 2D superintegrable classical system. We obtain the corresponding quartic (associative) algebra for the quantum analog, extend Daskaloyannis construction obtained in context of quadratic algebras, and also obtain the realizations as deformed oscillator algebras for this quartic algebra. We obtain the Casimir operator and discuss how these realizations allow to obtain the finite-dimensional unitary irreducible representations of quartic algebras and obtain algebraically the degenerate energy spectrum of superintegrable systems. We apply the construction and the formula obtained for the structure function on a superintegrable system related to type I Laguerre exceptional orthogonal polynomials introduced recently

  14. A Web-Based Authoring Tool for Algebra-Related Intelligent Tutoring Systems

    Directory of Open Access Journals (Sweden)

    Maria Virvou

    2000-01-01

    Full Text Available This paper describes the development of a web-based authoring tool for Intelligent Tutoring Systems. The tool aims to be useful to teachers and students of domains that make use of algebraic equations. The initial input to the tool is a "description" of a specific domain given by a human teacher. In return the tool provides assistance at the construction of exercises by the human teacher and then monitors the students while they are solving the exercises and provides appropriate feedback. The tool incorporates intelligence in its diagnostic component, which performs error diagnosis to students’ errors. It also handles the teaching material in a flexible and individualised way.

  15. Linear algebra

    CERN Document Server

    Said-Houari, Belkacem

    2017-01-01

    This self-contained, clearly written textbook on linear algebra is easily accessible for students. It begins with the simple linear equation and generalizes several notions from this equation for the system of linear equations and introduces the main ideas using matrices. It then offers a detailed chapter on determinants and introduces the main ideas with detailed proofs. The third chapter introduces the Euclidean spaces using very simple geometric ideas and discusses various major inequalities and identities. These ideas offer a solid basis for understanding general Hilbert spaces in functional analysis. The following two chapters address general vector spaces, including some rigorous proofs to all the main results, and linear transformation: areas that are ignored or are poorly explained in many textbooks. Chapter 6 introduces the idea of matrices using linear transformation, which is easier to understand than the usual theory of matrices approach. The final two chapters are more advanced, introducing t...

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

    Science.gov (United States)

    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…

  17. Teaching the "Diagonalization Concept" in Linear Algebra with Technology: A Case Study at Galatasaray University

    Science.gov (United States)

    Yildiz Ulus, Aysegul

    2013-01-01

    This paper examines experimental and algorithmic contributions of advanced calculators (graphing and computer algebra system, CAS) in teaching the concept of "diagonalization," one of the key topics in Linear Algebra courses taught at the undergraduate level. Specifically, the proposed hypothesis of this study is to assess the effective…

  18. Searching dependency between algebraic equations: An algorithm applied to automated reasoning

    International Nuclear Information System (INIS)

    Yang Lu; Zhang Jingzhong

    1990-01-01

    An efficient computer algorithm is given to decide how many branches of the solution to a system of algebraic also solve another equation. As one of the applications, this can be used in practice to verify a conjecture with hypotheses and conclusion expressed by algebraic equations, despite the variety of reducible or irreducible. (author). 10 refs

  19. Applied algebra codes, ciphers and discrete algorithms

    CERN Document Server

    Hardy, Darel W; Walker, Carol L

    2009-01-01

    This book attempts to show the power of algebra in a relatively simple setting.-Mathematical Reviews, 2010… The book supports learning by doing. In each section we can find many examples which clarify the mathematics introduced in the section and each section is followed by a series of exercises of which approximately half are solved in the end of the book. Additional the book comes with a CD-ROM containing an interactive version of the book powered by the computer algebra system Scientific Notebook. … the mathematics in the book are developed as needed and the focus of the book lies clearly o

  20. Matrices and linear algebra

    CERN Document Server

    Schneider, Hans

    1989-01-01

    Linear algebra is one of the central disciplines in mathematics. A student of pure mathematics must know linear algebra if he is to continue with modern algebra or functional analysis. Much of the mathematics now taught to engineers and physicists requires it.This well-known and highly regarded text makes the subject accessible to undergraduates with little mathematical experience. Written mainly for students in physics, engineering, economics, and other fields outside mathematics, the book gives the theory of matrices and applications to systems of linear equations, as well as many related t

  1. Linear Algebra and Smarandache Linear Algebra

    OpenAIRE

    Vasantha, Kandasamy

    2003-01-01

    The present book, on Smarandache linear algebra, not only studies the Smarandache analogues of linear algebra and its applications, it also aims to bridge the need for new research topics pertaining to linear algebra, purely in the algebraic sense. We have introduced Smarandache semilinear algebra, Smarandache bilinear algebra and Smarandache anti-linear algebra and their fuzzy equivalents. Moreover, in this book, we have brought out the study of linear algebra and vector spaces over finite p...

  2. Computer systems a programmer's perspective

    CERN Document Server

    Bryant, Randal E

    2016-01-01

    Computer systems: A Programmer’s Perspective explains the underlying elements common among all computer systems and how they affect general application performance. Written from the programmer’s perspective, this book strives to teach readers how understanding basic elements of computer systems and executing real practice can lead them to create better programs. Spanning across computer science themes such as hardware architecture, the operating system, and systems software, the Third Edition serves as a comprehensive introduction to programming. This book strives to create programmers who understand all elements of computer systems and will be able to engage in any application of the field--from fixing faulty software, to writing more capable programs, to avoiding common flaws. It lays the groundwork for readers to delve into more intensive topics such as computer architecture, embedded systems, and cybersecurity. This book focuses on systems that execute an x86-64 machine code, and recommends th...

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

    Science.gov (United States)

    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.

  4. Flexibility of Bricard's linkages and other structures via resultants and computer algebra.

    Science.gov (United States)

    Lewis, Robert H; Coutsias, Evangelos A

    2016-07-01

    Flexibility of structures is extremely important for chemistry and robotics. Following our earlier work, we study flexibility using polynomial equations, resultants, and a symbolic algorithm of our creation that analyzes the resultant. We show that the software solves a classic arrangement of quadrilaterals in the plane due to Bricard. We fill in several gaps in Bricard's work and discover new flexible arrangements that he was apparently unaware of. This provides strong evidence for the maturity of the software, and is a wonderful example of mathematical discovery via computer assisted experiment.

  5. Chiral algebras for trinion theories

    International Nuclear Information System (INIS)

    Lemos, Madalena; Peelaers, Wolfger

    2015-01-01

    It was recently understood that one can identify a chiral algebra in any four-dimensional N=2 superconformal theory. In this note, we conjecture the full set of generators of the chiral algebras associated with the T n theories. The conjecture is motivated by making manifest the critical affine module structure in the graded partition function of the chiral algebras, which is computed by the Schur limit of the superconformal index for T n theories. We also explicitly construct the chiral algebra arising from the T 4 theory. Its null relations give rise to new T 4 Higgs branch chiral ring relations.

  6. Linear Algebra and Image Processing

    Science.gov (United States)

    Allali, Mohamed

    2010-01-01

    We use the computing technology digital image processing (DIP) to enhance the teaching of linear algebra so as to make the course more visual and interesting. Certainly, this visual approach by using technology to link linear algebra to DIP is interesting and unexpected to both students as well as many faculty. (Contains 2 tables and 11 figures.)

  7. The cell method a purely algebraic computational method in physics and engineering

    CERN Document Server

    Ferretti, Elena

    2014-01-01

    The Cell Method (CM) is a computational tool that maintains critical multidimensional attributes of physical phenomena in analysis. This information is neglected in the differential formulations of the classical approaches of finite element, boundary element, finite volume, and finite difference analysis, often leading to numerical instabilities and spurious results. This book highlights the central theoretical concepts of the CM that preserve a more accurate and precise representation of the geometric and topological features of variables for practical problem solving. Important applications occur in fields such as electromagnetics, electrodynamics, solid mechanics and fluids. CM addresses non-locality in continuum mechanics, an especially important circumstance in modeling heterogeneous materials. Professional engineers and scientists, as well as graduate students, are offered: A general overview of physics and its mathematical descriptions; Guidance on how to build direct, discrete formulations; Coverag...

  8. Space-time algebra

    CERN Document Server

    Hestenes, David

    2015-01-01

    This small book started a profound revolution in the development of mathematical physics, one which has reached many working physicists already, and which stands poised to bring about far-reaching change in the future. At its heart is the use of Clifford algebra to unify otherwise disparate mathematical languages, particularly those of spinors, quaternions, tensors and differential forms. It provides a unified approach covering all these areas and thus leads to a very efficient ‘toolkit’ for use in physical problems including quantum mechanics, classical mechanics, electromagnetism and relativity (both special and general) – only one mathematical system needs to be learned and understood, and one can use it at levels which extend right through to current research topics in each of these areas. These same techniques, in the form of the ‘Geometric Algebra’, can be applied in many areas of engineering, robotics and computer science, with no changes necessary – it is the same underlying mathematics, a...

  9. Numerical and algebraic studies for the control of finite-dimensional quantum systems

    International Nuclear Information System (INIS)

    Sander, Uwe

    2010-01-01

    In this thesis, two aspects of control theory, namely controllability and optimal control, are applied to quantum systems. The presented results are based on group theoretical techniques and numerical studies. By Lie-algebraic analysis, the controllability properties of systems with an arbitrary topology are described and related to the symmetries existing in these systems. We find that symmetry precludes full controllability. Our work investigates well-known control systems and gives rules for the design of new systems. Furthermore, theoretical and numerical concepts are instrumental to studying quantum channels: Their capacities are optimised using gradient flows on the unitary group in order to find counterexamples to a long-established additivity conjecture. The last part of this thesis presents and benchmarks a modular optimal control algorithm known as GRAPE. Numerical tests show how the interplay of its modules can be optimised for higher performance, and how the algorithm performs in comparison to a Krotov-type optimal control algorithm. It is found that GRAPE performs particularly well when aiming for high qualities. (orig.)

  10. Numerical and algebraic studies for the control of finite-dimensional quantum systems

    Energy Technology Data Exchange (ETDEWEB)

    Sander, Uwe

    2010-11-18

    In this thesis, two aspects of control theory, namely controllability and optimal control, are applied to quantum systems. The presented results are based on group theoretical techniques and numerical studies. By Lie-algebraic analysis, the controllability properties of systems with an arbitrary topology are described and related to the symmetries existing in these systems. We find that symmetry precludes full controllability. Our work investigates well-known control systems and gives rules for the design of new systems. Furthermore, theoretical and numerical concepts are instrumental to studying quantum channels: Their capacities are optimised using gradient flows on the unitary group in order to find counterexamples to a long-established additivity conjecture. The last part of this thesis presents and benchmarks a modular optimal control algorithm known as GRAPE. Numerical tests show how the interplay of its modules can be optimised for higher performance, and how the algorithm performs in comparison to a Krotov-type optimal control algorithm. It is found that GRAPE performs particularly well when aiming for high qualities. (orig.)

  11. Extended Kac-Moody algebras and applications

    International Nuclear Information System (INIS)

    Ragoucy, E.; Sorba, P.

    1991-04-01

    The notion of a Kac-Moody algebra defined on the S 1 circle is extended to super Kac-Moody algebras defined on MxG N , M being a smooth closed compact manifold of dimension greater than one, and G N the Grassman algebra with N generators. All the central extensions of these algebras are computed. Then, for each such algebra the derivation algebra constructed from the MxG N diffeomorphism is determined. The twists of such super Kac-Moody algebras as well as the generalization to non-compact surfaces are partially studied. Finally, the general construction is applied to the study of conformal and superconformal algebras, as well as area-preserving diffeomorphisms algebra and its supersymmetric extension. (author) 65 refs

  12. Computational algebraic geometry for statistical modeling FY09Q2 progress.

    Energy Technology Data Exchange (ETDEWEB)

    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. Generating a New Higher-Dimensional Coupled Integrable Dispersionless System: Algebraic Structures, Bäcklund Transformation and Hidden Structural Symmetries

    International Nuclear Information System (INIS)

    Abbagari, Souleymanou; Bouetou, Thomas B.; Kofane, Timoleon C.

    2013-01-01

    The prolongation structure methodologies of Wahlquist—Estabrook [H.D. Wahlquist and F.B. Estabrook, J. Math. Phys. 16 (1975) 1] for nonlinear differential equations are applied to a more general set of coupled integrable dispersionless system. Based on the obtained prolongation structure, a Lie-Algebra valued connection of a closed ideal of exterior differential forms related to the above system is constructed. A Lie-Algebra representation of some hidden structural symmetries of the previous system, its Bäcklund transformation using the Riccati form of the linear eigenvalue problem and their general corresponding Lax-representation are derived. In the wake of the previous results, we extend the above prolongation scheme to higher-dimensional systems from which a new (2 + 1)-dimensional coupled integrable dispersionless system is unveiled along with its inverse scattering formulation, which applications are straightforward in nonlinear optics where additional propagating dimension deserves some attention. (general)

  14. Abstract algebra

    CERN Document Server

    Garrett, Paul B

    2007-01-01

    Designed for an advanced undergraduate- or graduate-level course, Abstract Algebra provides an example-oriented, less heavily symbolic approach to abstract algebra. The text emphasizes specifics such as basic number theory, polynomials, finite fields, as well as linear and multilinear algebra. This classroom-tested, how-to manual takes a more narrative approach than the stiff formalism of many other textbooks, presenting coherent storylines to convey crucial ideas in a student-friendly, accessible manner. An unusual feature of the text is the systematic characterization of objects by universal

  15. Core status computing system

    International Nuclear Information System (INIS)

    Yoshida, Hiroyuki.

    1982-01-01

    Purpose: To calculate power distribution, flow rate and the like in the reactor core with high accuracy in a BWR type reactor. Constitution: Total flow rate signals, traverse incore probe (TIP) signals as the neutron detector signals, thermal power signals and pressure signals are inputted into a process computer, where the power distribution and the flow rate distribution in the reactor core are calculated. A function generator connected to the process computer calculates the absolute flow rate passing through optional fuel assemblies using, as variables, flow rate signals from the introduction part for fuel assembly flow rate signals, data signals from the introduction part for the geometrical configuration data at the flow rate measuring site of fuel assemblies, total flow rate signals for the reactor core and the signals from the process computer. Numerical values thus obtained are given to the process computer as correction signals to perform correction for the experimental data. (Moriyama, K.)

  16. Capability-based computer systems

    CERN Document Server

    Levy, Henry M

    2014-01-01

    Capability-Based Computer Systems focuses on computer programs and their capabilities. The text first elaborates capability- and object-based system concepts, including capability-based systems, object-based approach, and summary. The book then describes early descriptor architectures and explains the Burroughs B5000, Rice University Computer, and Basic Language Machine. The text also focuses on early capability architectures. Dennis and Van Horn's Supervisor; CAL-TSS System; MIT PDP-1 Timesharing System; and Chicago Magic Number Machine are discussed. The book then describes Plessey System 25

  17. QUANTUM: A Wolfram Mathematica add-on for Dirac Bra-Ket Notation, Non-Commutative Algebra, and Simulation of Quantum Computing Circuits

    International Nuclear Information System (INIS)

    Muñoz, J L Gómez; Delgado, F

    2016-01-01

    This paper introduces QUANTUM, a free library of commands of Wolfram Mathematica that can be used to perform calculations directly in Dirac braket and operator notation. Its development started several years ago, in order to study quantum random walks. Later, many other features were included, like operator and commutator algebra, simulation and graphing of quantum computing circuits, generation and solution of Heisenberg equations of motion, among others. To the best of our knowledge, QUANTUM remains a unique tool in its use of Dirac notation, because it is used both in the input and output of the calculations. This work depicts its usage and features in Quantum Computing and Quantum Hamilton Dynamics. (paper)

  18. An LISP interpreter for a PDP-15 computer system

    International Nuclear Information System (INIS)

    Gonzalez Navidad, R.

    1974-01-01

    LISP processor for a PDP-15 computer system. The object of this work is to use the LISP language as an integral part of a PDP-15 computer system. LISP is a programming language designed for processing lists, and from this it gets its name (LIST-PROCESSING). The most important aspects of LISP are as follows: (1) It is a formal mathematical language based on the theory of recursive functions; (2) It is geared to processing symbolic rather than numerical data; (3) Programs written in LISP are themselves lists. The techniques employed for this application were based on the characteristics and capabilities of the PDP-15 system. It offers a basic minimum system of LISP functions with which more complex functions can be constructed. A detailed description of each of the units comprising the interpreter provides the reader with a useful introduction to the LISP language. Among the results that have been obtained with this interpreter we can quote the following: construction of a set of auxiliary functions for the system and simulation of a Turing machine based on this set of auxiliary functions written in LISP, with which a beginning has been made in setting up a function library, utilizing the capacity of LISP as a self-generating function language. Hence the LISP processor can be used to resolve problems of algebraic manipulation, system simulation, group theory, modern algebra, data classification and processing, and other common logical problems. (author)

  19. Asymptotic Analysis of a System of Algebraic Equations Arising in Dislocation Theory

    KAUST Repository

    Hall, Cameron L.; Chapman, S. Jonathan; Ockendon, John R.

    2010-01-01

    The system of algebraic equations given by σn j=0, j≠=i sgn(xi-xj )|xi-xj|a = 1, i = 1, 2, ⋯ , n, x0 = 0, appears in dislocation theory in models of dislocation pile-ups. Specifically, the case a = 1 corresponds to the simple situation where n dislocations are piled up against a locked dislocation, while the case a = 3 corresponds to n dislocation dipoles piled up against a locked dipole. We present a general analysis of systems of this type for a > 0 and n large. In the asymptotic limit n→∞, it becomes possible to replace the system of discrete equations with a continuum equation for the particle density. For 0 < a < 2, this takes the form of a singular integral equation, while for a > 2 it is a first-order differential equation. The critical case a = 2 requires special treatment, but, up to corrections of logarithmic order, it also leads to a differential equation. The continuum approximation is valid only for i neither too small nor too close to n. The boundary layers at either end of the pile-up are also analyzed, which requires matching between discrete and continuum approximations to the main problem. © 2010 Society for Industrial and Applied Mathematics.

  20. Infinite dimension algebra and conformal symmetry

    International Nuclear Information System (INIS)

    Ragoucy-Aubezon, E.

    1991-04-01

    A generalisation of Kac-Moody algebras (current algebras defined on a circle) to algebras defined on a compact supermanifold of any dimension and with any number of supersymmetries is presented. For such a purpose, we compute all the central extensions of loop algebras defined on this supermanifold, i.e. all the cohomology classes of these loop algebras. Then, we try to extend the relation (i.e. semi-direct sum) that exists between the two dimensional conformal algebras (called Virasoro algebra) and the usual Kac-Moody algebras, by considering the derivation algebra of our extended Kac-Moody algebras. The case of superconformal algebras (used in superstrings theories) is treated, as well as the cases of area-preserving diffeomorphisms (used in membranes theories), and Krichever-Novikov algebras (used for interacting strings). Finally, we present some generalizations of the Sugawara construction to the cases of extended Kac-Moody algebras, and Kac-Moody of superalgebras. These constructions allow us to get new realizations of the Virasoro, and Ramond, Neveu-Schwarz algebras

  1. Secure computing on reconfigurable systems

    OpenAIRE

    Fernandes Chaves, R.J.

    2007-01-01

    This thesis proposes a Secure Computing Module (SCM) for reconfigurable computing systems. SC provides a protected and reliable computational environment, where data security and protection against malicious attacks to the system is assured. SC is strongly based on encryption algorithms and on the attestation of the executed functions. The use of SC on reconfigurable devices has the advantage of being highly adaptable to the application and the user requirements, while providing high performa...

  2. Computer Security Systems Enable Access.

    Science.gov (United States)

    Riggen, Gary

    1989-01-01

    A good security system enables access and protects information from damage or tampering, but the most important aspects of a security system aren't technical. A security procedures manual addresses the human element of computer security. (MLW)

  3. Real space process algebra

    NARCIS (Netherlands)

    Bergstra, J.A.; Baeten, J.C.M.

    1993-01-01

    The real time process algebra of Baeten and Bergstra [Formal Aspects of Computing, 3, 142-188 (1991)] is extended to real space by requiring the presence of spatial coordinates for each atomic action, in addition to the required temporal attribute. It is found that asynchronous communication

  4. COMPUTER ALGEBRA, VIRTUAL LEARNING ENVIRONMENT AND MEANINGFUL LEARNING: IS IT POSSIBLE?

    Directory of Open Access Journals (Sweden)

    Celina A. A. P. Abar

    2011-03-01

    Full Text Available A major challenge faced by teachers nowadays relates to the usage of proper educational technology to achieve a true and meaningful learning experience involving time for reflection. Teachers constantly seek new ways to improve instruction, but in virtual learning environments they often find themselves in a new role, interacting in a dynamic system with students and simultaneously acquiring new skills related to the tools in use. In this paper we address this question by conducting an online course aimed at primary and secondary school mathematics teachers, designed to investigate the effective use of GeoGebra and Moodle. The tools selected for the course are free and easy to use, an important factor for the new technology to be incorporated into teaching practice. The course results show that a well-constructed proposal is able to meet the expectations of teachers. Furthermore, the usage of new technologies involves, beyond technical issues, changes in the behavior and in the relationships between the actors involved.

  5. Computable Types for Dynamic Systems

    NARCIS (Netherlands)

    P.J. Collins (Pieter); K. Ambos-Spies; B. Loewe; W. Merkle

    2009-01-01

    textabstractIn this paper, we develop a theory of computable types suitable for the study of dynamic systems in discrete and continuous time. The theory uses type-two effectivity as the underlying computational model, but we quickly develop a type system which can be manipulated abstractly, but for

  6. Computed tomography system

    International Nuclear Information System (INIS)

    Lambert, T.W.; Blake, J.E.

    1981-01-01

    This invention relates to computed tomography and is particularly concerned with determining the CT numbers of zones of interest in an image displayed on a cathode ray tube which zones lie in the so-called level or center of the gray scale window. (author)

  7. Parallel algorithms for numerical linear algebra

    CERN Document Server

    van der Vorst, H

    1990-01-01

    This is the first in a new series of books presenting research results and developments concerning the theory and applications of parallel computers, including vector, pipeline, array, fifth/future generation computers, and neural computers.All aspects of high-speed computing fall within the scope of the series, e.g. algorithm design, applications, software engineering, networking, taxonomy, models and architectural trends, performance, peripheral devices.Papers in Volume One cover the main streams of parallel linear algebra: systolic array algorithms, message-passing systems, algorithms for p

  8. Principles of algebraic geometry

    CERN Document Server

    Griffiths, Phillip A

    1994-01-01

    A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special top

  9. Helmholtz algebraic solitons

    Energy Technology Data Exchange (ETDEWEB)

    Christian, J M; McDonald, G S [Joule Physics Laboratory, School of Computing, Science and Engineering, Materials and Physics Research Centre, University of Salford, Salford M5 4WT (United Kingdom); Chamorro-Posada, P, E-mail: j.christian@salford.ac.u [Departamento de Teoria de la Senal y Comunicaciones e Ingenieria Telematica, Universidad de Valladolid, ETSI Telecomunicacion, Campus Miguel Delibes s/n, 47011 Valladolid (Spain)

    2010-02-26

    We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the propagation and interaction of broad scalar beams. New conservation laws are presented, and the recovery of paraxial results is discussed in detail. The stability properties of the new solitons are investigated by combining semi-analytical methods and computer simulations. In particular, new general stability regimes are reported for algebraic bright solitons.

  10. Helmholtz algebraic solitons

    International Nuclear Information System (INIS)

    Christian, J M; McDonald, G S; Chamorro-Posada, P

    2010-01-01

    We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the propagation and interaction of broad scalar beams. New conservation laws are presented, and the recovery of paraxial results is discussed in detail. The stability properties of the new solitons are investigated by combining semi-analytical methods and computer simulations. In particular, new general stability regimes are reported for algebraic bright solitons.

  11. Handbook of linear algebra

    CERN Document Server

    Hogben, Leslie

    2013-01-01

    With a substantial amount of new material, the Handbook of Linear Algebra, Second Edition provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use format. It guides you from the very elementary aspects of the subject to the frontiers of current research. Along with revisions and updates throughout, the second edition of this bestseller includes 20 new chapters.New to the Second EditionSeparate chapters on Schur complements, additional types of canonical forms, tensors, matrix polynomials, matrix equations, special types of

  12. Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear ordinary differential equations

    Institute of Scientific and Technical Information of China (English)

    WANG; Shunjin; ZHANG; Hua

    2006-01-01

    The problem of preserving fidelity in numerical computation of nonlinear ordinary differential equations is studied in terms of preserving local differential structure and approximating global integration structure of the dynamical system.The ordinary differential equations are lifted to the corresponding partial differential equations in the framework of algebraic dynamics,and a new algorithm-algebraic dynamics algorithm is proposed based on the exact analytical solutions of the ordinary differential equations by the algebraic dynamics method.In the new algorithm,the time evolution of the ordinary differential system is described locally by the time translation operator and globally by the time evolution operator.The exact analytical piece-like solution of the ordinary differential equations is expressd in terms of Taylor series with a local convergent radius,and its finite order truncation leads to the new numerical algorithm with a controllable precision better than Runge Kutta Algorithm and Symplectic Geometric Algorithm.

  13. Ada Linear-Algebra Program

    Science.gov (United States)

    Klumpp, A. R.; Lawson, C. L.

    1988-01-01

    Routines provided for common scalar, vector, matrix, and quaternion operations. Computer program extends Ada programming language to include linear-algebra capabilities similar to HAS/S programming language. Designed for such avionics applications as software for Space Station.

  14. Energy efficient distributed computing systems

    CERN Document Server

    Lee, Young-Choon

    2012-01-01

    The energy consumption issue in distributed computing systems raises various monetary, environmental and system performance concerns. Electricity consumption in the US doubled from 2000 to 2005.  From a financial and environmental standpoint, reducing the consumption of electricity is important, yet these reforms must not lead to performance degradation of the computing systems.  These contradicting constraints create a suite of complex problems that need to be resolved in order to lead to 'greener' distributed computing systems.  This book brings together a group of outsta

  15. Fast computation of the Maslov index for hyperbolic linear systems with periodic coefficients

    International Nuclear Information System (INIS)

    Chardard, F; Dias, F; Bridges, T J

    2006-01-01

    The Maslov index is a topological property of periodic orbits of finite-dimensional Hamiltonian systems that is widely used in semiclassical quantization, quantum chaology, stability of waves and classical mechanics. The Maslov index is determined from the analysis of a linear Hamiltonian system with periodic coefficients. In this paper, a numerical scheme is devised to compute the Maslov index for hyperbolic linear systems when the phase space has a low dimension. The idea is to compute on the exterior algebra of the ambient vector space, where the Lagrangian subspace representing the unstable subspace is reduced to a line. When the exterior algebra is projectified the Lagrangian subspace always forms a closed loop. The idea is illustrated by application to Hamiltonian systems on a phase space of dimension 4. The theory is used to compute the Maslov index for the spectral problem associated with periodic solutions of the fifth-order Korteweg de Vries equation

  16. Algebraic entropy for algebraic maps

    International Nuclear Information System (INIS)

    Hone, A N W; Ragnisco, Orlando; Zullo, Federico

    2016-01-01

    We propose an extension of the concept of algebraic entropy, as introduced by Bellon and Viallet for rational maps, to algebraic maps (or correspondences) of a certain kind. The corresponding entropy is an index of the complexity of the map. The definition inherits the basic properties from the definition of entropy for rational maps. We give an example with positive entropy, as well as two examples taken from the theory of Bäcklund transformations. (letter)

  17. Computational Systems Chemical Biology

    OpenAIRE

    Oprea, Tudor I.; May, Elebeoba E.; Leitão, Andrei; Tropsha, Alexander

    2011-01-01

    There is a critical need for improving the level of chemistry awareness in systems biology. The data and information related to modulation of genes and proteins by small molecules continue to accumulate at the same time as simulation tools in systems biology and whole body physiologically-based pharmacokinetics (PBPK) continue to evolve. We called this emerging area at the interface between chemical biology and systems biology systems chemical biology, SCB (Oprea et al., 2007).

  18. The algebraic collective model

    International Nuclear Information System (INIS)

    Rowe, D.J.; Turner, P.S.

    2005-01-01

    A recently proposed computationally tractable version of the Bohr collective model is developed to the extent that we are now justified in describing it as an algebraic collective model. The model has an SU(1,1)xSO(5) algebraic structure and a continuous set of exactly solvable limits. Moreover, it provides bases for mixed symmetry collective model calculations. However, unlike the standard realization of SU(1,1), used for computing beta wave functions and their matrix elements in a spherical basis, the algebraic collective model makes use of an SU(1,1) algebra that generates wave functions appropriate for deformed nuclei with intrinsic quadrupole moments ranging from zero to any large value. A previous paper focused on the SO(5) wave functions, as SO(5) (hyper-)spherical harmonics, and computation of their matrix elements. This paper gives analytical expressions for the beta matrix elements needed in applications of the model and illustrative results to show the remarkable gain in efficiency that is achieved by using such a basis in collective model calculations for deformed nuclei

  19. Mathematical Modeling and Algebraic Technique for Resolving a Single-Producer Multi-Retailer Integrated Inventory System with Scrap

    OpenAIRE

    Yuan-Shyi Peter Chiu; Chien-Hua Lee; Nong Pan; Singa Wang Chiu

    2013-01-01

    This study uses mathematical modeling along with an algebraic technique to resolve the production-distribution policy for a single-producer multi-retailer integrated inventory system with scrap in production. We assume that a product is manufactured through an imperfect production process where all nonconforming items will be picked up and scrapped in each production cycle. After the entire lot is quality assured, multiple shipments will be delivered synchronously to m different retailers in ...

  20. Automorphic Lie algebras with dihedral symmetry

    International Nuclear Information System (INIS)

    Knibbeler, V; Lombardo, S; A Sanders, J

    2014-01-01

    The concept of automorphic Lie algebras arises in the context of reduction groups introduced in the early 1980s in the field of integrable systems. automorphic Lie algebras are obtained by imposing a discrete group symmetry on a current algebra of Krichever–Novikov type. Past work shows remarkable uniformity between algebras associated to different reduction groups. For example, if the base Lie algebra is sl 2 (C) and the poles of the automorphic Lie algebra are restricted to an exceptional orbit of the symmetry group, changing the reduction group does not affect the Lie algebra structure. In this research we fix the reduction group to be the dihedral group and vary the orbit of poles as well as the group action on the base Lie algebra. We find a uniform description of automorphic Lie algebras with dihedral symmetry, valid for poles at exceptional and generic orbits. (paper)

  1. Students "Hacking" School Computer Systems

    Science.gov (United States)

    Stover, Del

    2005-01-01

    This article deals with students hacking school computer systems. School districts are getting tough with students "hacking" into school computers to change grades, poke through files, or just pit their high-tech skills against district security. Dozens of students have been prosecuted recently under state laws on identity theft and unauthorized…

  2. Equationally Noetherian property of Ershov algebras

    OpenAIRE

    Dvorzhetskiy, Yuriy

    2014-01-01

    This article is about equationally Noetherian and weak equationally Noetherian property of Ershov algebras. Here we show two canonical forms of the system of equations over Ershov algebras and two criteria of equationally Noetherian and weak equationally Noetherian properties.

  3. On the algebraic characterization of aperiodic tilings related to ADE-root systems

    International Nuclear Information System (INIS)

    Kellendonk, J.

    1992-09-01

    The algebraic characterization of sets of locally equivalent aperiodic tilings, being examples of quantum spaces, is conducted for a certain type of tilings in a manner proposed by A. Connes. These 2-dimensional tilings are obtained by application of the strip method to the root lattice of an ADE-Coxeter group. The plane along which the strip is constructed is determined by the canonical Coxeter element leading to the result that a 2- dimensional tiling decomposes into a cartesian product of two 1- dimensional tilings. The properties of the tilings are investigated, including selfsimilarity, and the determination of the relevant algebraic is considered, namely the ordered K 0 -group of an algebra naturaly assigned to the quantum space. The result also yields an application of the 2-dimensional abstract gap labelling theorem. (orig.)

  4. Pole-placement Predictive Functional Control for under-damped systems with real numbers algebra.

    Science.gov (United States)

    Zabet, K; Rossiter, J A; Haber, R; Abdullah, M

    2017-11-01

    This paper presents the new algorithm of PP-PFC (Pole-placement Predictive Functional Control) for stable, linear under-damped higher-order processes. It is shown that while conventional PFC aims to get first-order exponential behavior, this is not always straightforward with significant under-damped modes and hence a pole-placement PFC algorithm is proposed which can be tuned more precisely to achieve the desired dynamics, but exploits complex number algebra and linear combinations in order to deliver guarantees of stability and performance. Nevertheless, practical implementation is easier by avoiding complex number algebra and hence a modified formulation of the PP-PFC algorithm is also presented which utilises just real numbers while retaining the key attributes of simple algebra, coding and tuning. The potential advantages are demonstrated with numerical examples and real-time control of a laboratory plant. Copyright © 2017 ISA. All rights reserved.

  5. Graded Fock-like representations for a system of algebraically interacting paraparticles

    International Nuclear Information System (INIS)

    Kanakoglou, Konstantinos; Herrera-Aguilar, Alfredo

    2011-01-01

    We will present and study an algebra describing a mixed paraparticle model, known in the bibliography as 'The Relative Parabose Set (RPBS)'. Focusing in the special case of a single parabosonic and a single parafermionic degree of freedom P (1,1) BF , we will construct a class of Fock-like representations of this algebra, dependent on a positive parameter p a kind of generalized parastatistics order. Mathematical properties of the Fock-like modules will be investigated for all values of p and constructions such as ladder operators, irreducibility (for the carrier spaces) and (Z 2 x Z 2 )-gradings (for both the carrier spaces and the algebra itself) will be established.

  6. The Differential-Algebraic Analysis of Symplectic and Lax Structures Related with New Riemann-Type Hydrodynamic Systems

    Science.gov (United States)

    Prykarpatsky, Yarema A.; Artemovych, Orest D.; Pavlov, Maxim V.; Prykarpatski, Anatolij K.

    2013-06-01

    A differential-algebraic approach to studying the Lax-type integrability of the generalized Riemann-type hydrodynamic hierarchy, proposed recently by O. D. Artemovych, M. V. Pavlov, Z. Popowicz and A. K. Prykarpatski, is developed. In addition to the Lax-type representation, found before by Z. Popowicz, a closely related representation is constructed in exact form by means of a new differential-functional technique. The bi-Hamiltonian integrability and compatible Poisson structures of the generalized Riemann type hierarchy are analyzed by means of the symplectic and gradient-holonomic methods. An application of the devised differential-algebraic approach to other Riemann and Vakhnenko type hydrodynamic systems is presented.

  7. Algorithmic algebraic geometry and flux vacua

    International Nuclear Information System (INIS)

    Gray, James; He Yanghui; Lukas, Andre

    2006-01-01

    We develop a new and efficient method to systematically analyse four dimensional effective supergravities which descend from flux compactifications. The issue of finding vacua of such systems, both supersymmetric and non-supersymmetric, is mapped into a problem in computational algebraic geometry. Using recent developments in computer algebra, the problem can then be rapidly dealt with in a completely algorithmic fashion. Two main results are (1) a procedure for calculating constraints which the flux parameters must satisfy in these models if any given type of vacuum is to exist; (2) a stepwise process for finding all of the isolated vacua of such systems and their physical properties. We illustrate our discussion with several concrete examples, some of which have eluded conventional methods so far

  8. On Elementary and Algebraic Cellular Automata

    Science.gov (United States)

    Gulak, Yuriy

    In this paper we study elementary cellular automata from an algebraic viewpoint. The goal is to relate the emergent complex behavior observed in such systems with the properties of corresponding algebraic structures. We introduce algebraic cellular automata as a natural generalization of elementary ones and discuss their applications as generic models of complex systems.

  9. Symbolic derivation of high-order Rayleigh-Schroedinger perturbation energies using computer algebra: Application to vibrational-rotational analysis of diatomic molecules

    Energy Technology Data Exchange (ETDEWEB)

    Herbert, John M. [Kansas State Univ., Manhattan, KS (United States). Dept. of Chemistry

    1997-01-01

    Rayleigh-Schroedinger perturbation theory is an effective and popular tool for describing low-lying vibrational and rotational states of molecules. This method, in conjunction with ab initio techniques for computation of electronic potential energy surfaces, can be used to calculate first-principles molecular vibrational-rotational energies to successive orders of approximation. Because of mathematical complexities, however, such perturbation calculations are rarely extended beyond the second order of approximation, although recent work by Herbert has provided a formula for the nth-order energy correction. This report extends that work and furnishes the remaining theoretical details (including a general formula for the Rayleigh-Schroedinger expansion coefficients) necessary for calculation of energy corrections to arbitrary order. The commercial computer algebra software Mathematica is employed to perform the prohibitively tedious symbolic manipulations necessary for derivation of generalized energy formulae in terms of universal constants, molecular constants, and quantum numbers. As a pedagogical example, a Hamiltonian operator tailored specifically to diatomic molecules is derived, and the perturbation formulae obtained from this Hamiltonian are evaluated for a number of such molecules. This work provides a foundation for future analyses of polyatomic molecules, since it demonstrates that arbitrary-order perturbation theory can successfully be applied with the aid of commercially available computer algebra software.

  10. Linear algebra

    CERN Document Server

    Stoll, R R

    1968-01-01

    Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understand

  11. Lie algebras

    CERN Document Server

    Jacobson, Nathan

    1979-01-01

    Lie group theory, developed by M. Sophus Lie in the 19th century, ranks among the more important developments in modern mathematics. Lie algebras comprise a significant part of Lie group theory and are being actively studied today. This book, by Professor Nathan Jacobson of Yale, is the definitive treatment of the subject and can be used as a textbook for graduate courses.Chapter I introduces basic concepts that are necessary for an understanding of structure theory, while the following three chapters present the theory itself: solvable and nilpotent Lie algebras, Carlan's criterion and its

  12. Basic algebra

    CERN Document Server

    Jacobson, Nathan

    2009-01-01

    A classic text and standard reference for a generation, this volume and its companion are the work of an expert algebraist who taught at Yale for two decades. Nathan Jacobson's books possess a conceptual and theoretical orientation, and in addition to their value as classroom texts, they serve as valuable references.Volume I explores all of the topics typically covered in undergraduate courses, including the rudiments of set theory, group theory, rings, modules, Galois theory, polynomials, linear algebra, and associative algebra. Its comprehensive treatment extends to such rigorous topics as L

  13. Computer systems and nuclear industry

    International Nuclear Information System (INIS)

    Nkaoua, Th.; Poizat, F.; Augueres, M.J.

    1999-01-01

    This article deals with computer systems in nuclear industry. In most nuclear facilities it is necessary to handle a great deal of data and of actions in order to help plant operator to drive, to control physical processes and to assure the safety. The designing of reactors requires reliable computer codes able to simulate neutronic or mechanical or thermo-hydraulic behaviours. Calculations and simulations play an important role in safety analysis. In each of these domains, computer systems have progressively appeared as efficient tools to challenge and master complexity. (A.C.)

  14. A brief history of process algebra

    OpenAIRE

    Baeten, J.C.M.

    2005-01-01

    This note addresses the history of process algebra as an area of research in concurrency theory, the theory of parallel and distributed systems in computer science. Origins are traced back to the early seventies of the twentieth century, and developments since that time are sketched. The author gives his personal views on these matters. He also considers the present situation, and states some challenges for the future.

  15. A brief history of process algebra

    OpenAIRE

    Baeten, J.C.M.

    2004-01-01

    Abstract. This note addresses the history of process algebra as an area of research in concurrency theory, the theory of parallel and distributed systems in computer science. Origins are traced back to the early seventies of the twentieth century, and developments since that time are sketched. The author gives his personal views on these matters. He also considers the present situation, and states some challenges for the future.

  16. Algebra & trigonometry super review

    CERN Document Server

    2012-01-01

    Get all you need to know with Super Reviews! Each Super Review is packed with in-depth, student-friendly topic reviews that fully explain everything about the subject. The Algebra and Trigonometry Super Review includes sets and set operations, number systems and fundamental algebraic laws and operations, exponents and radicals, polynomials and rational expressions, equations, linear equations and systems of linear equations, inequalities, relations and functions, quadratic equations, equations of higher order, ratios, proportions, and variations. Take the Super Review quizzes to see how much y

  17. Operating systems. [of computers

    Science.gov (United States)

    Denning, P. J.; Brown, R. L.

    1984-01-01

    A counter operating system creates a hierarchy of levels of abstraction, so that at a given level all details concerning lower levels can be ignored. This hierarchical structure separates functions according to their complexity, characteristic time scale, and level of abstraction. The lowest levels include the system's hardware; concepts associated explicitly with the coordination of multiple tasks appear at intermediate levels, which conduct 'primitive processes'. Software semaphore is the mechanism controlling primitive processes that must be synchronized. At higher levels lie, in rising order, the access to the secondary storage devices of a particular machine, a 'virtual memory' scheme for managing the main and secondary memories, communication between processes by way of a mechanism called a 'pipe', access to external input and output devices, and a hierarchy of directories cataloguing the hardware and software objects to which access must be controlled.

  18. Retrofitting of NPP Computer systems

    International Nuclear Information System (INIS)

    Pettersen, G.

    1994-01-01

    Retrofitting of nuclear power plant control rooms is a continuing process for most utilities. This involves introducing and/or extending computer-based solutions for surveillance and control as well as improving the human-computer interface. The paper describes typical requirements when retrofitting NPP process computer systems, and focuses on the activities of Institute for energieteknikk, OECD Halden Reactor project with respect to such retrofitting, using examples from actual delivery projects. In particular, a project carried out for Forsmarksverket in Sweden comprising upgrade of the operator system in the control rooms of units 1 and 2 is described. As many of the problems of retrofitting NPP process computer systems are similar to such work in other kinds of process industries, an example from a non-nuclear application area is also given

  19. Galois Connections for Flow Algebras

    DEFF Research Database (Denmark)

    Filipiuk, Piotr; Terepeta, Michal Tomasz; Nielson, Hanne Riis

    2011-01-01

    to the approach taken by Monotone Frameworks and other classical analyses. We present a generic framework for static analysis based on flow algebras and program graphs. Program graphs are often used in Model Checking to model concurrent and distributed systems. The framework allows to induce new flow algebras...

  20. Computer System Design System-on-Chip

    CERN Document Server

    Flynn, Michael J

    2011-01-01

    The next generation of computer system designers will be less concerned about details of processors and memories, and more concerned about the elements of a system tailored to particular applications. These designers will have a fundamental knowledge of processors and other elements in the system, but the success of their design will depend on the skills in making system-level tradeoffs that optimize the cost, performance and other attributes to meet application requirements. This book provides a new treatment of computer system design, particularly for System-on-Chip (SOC), which addresses th

  1. Regular Riemann-Hilbert transforms, Baecklund transformations and hidden symmetry algebra for some linearization systems

    International Nuclear Information System (INIS)

    Chau Ling-Lie; Ge Mo-Lin; Teh, Rosy.

    1984-09-01

    The Baecklund Transformations and the hidden symmetry algebra for Self-Dual Yang-Mills Equations, Landau-Lifshitz equations and the Extended Super Yang-Mills fields (N>2) are discussed on the base of the Regular Riemann-Hilbert Transform and the linearization equations. (author)

  2. Algebraic properties of first integrals for systems of second-order ...

    African Journals Online (AJOL)

    Symmetries of the rst integrals for scalar linear or linearizable second- order ordinary differential equations (ODEs) have already been derived and shown to exhibit interesting properties. One of these is that the symmetry algebra sl(3; R ) is generated by the three triplets of symmetries of the functionally independent first ...

  3. ALGEBRAIC TOPOLOGY

    Indian Academy of Sciences (India)

    tion - 6. How Architectural Features Affect. Building During Earthquakes? C VRMurty. 48 Turbulence and Dispersion. K 5 Gandhi. BOOK REVIEWS. 86 Algebraic Topology. Siddhartha Gadgil. Front Cover. - .. ..-.......... -. Back Cover. Two-dimensional vertical section through a turbulent plume. (Courtesy: G S Shat, CAOS, IISc.).

  4. Algebraic stacks

    Indian Academy of Sciences (India)

    Deligne, Mumford and Artin [DM, Ar2]) and consider algebraic stacks, then we can cons- truct the 'moduli ... the moduli scheme and the moduli stack of vector bundles. First I will give ... 1–31. © Printed in India. 1 ...... Cultura, Spain. References.

  5. Algebraic proofs for shallow water bi-Hamiltonian systems for three cocycle of the semi-direct product of Kac-Moody and Virasoro Lie algebras

    Czech Academy of Sciences Publication Activity Database

    Zuevsky, Alexander

    2018-01-01

    Roč. 16, č. 1 (2018), s. 1-8 ISSN 2391-5455 Institutional support: RVO:67985840 Keywords : Kac-Moody Lie algebras * cocycles Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.682, year: 2016 https://www.degruyter.com/view/j/math.2018.16.issue-1/math-2018-0002/math-2018-0002. xml

  6. Algebraic proofs for shallow water bi-Hamiltonian systems for three cocycle of the semi-direct product of Kac-Moody and Virasoro Lie algebras

    Czech Academy of Sciences Publication Activity Database

    Zuevsky, Alexander

    2018-01-01

    Roč. 16, č. 1 (2018), s. 1-8 ISSN 2391-5455 Institutional support: RVO:67985840 Keywords : Kac-Moody Lie algebras * cocycles Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.682, year: 2016 https://www.degruyter.com/view/j/math.2018.16.issue-1/math-2018-0002/math-2018-0002.xml

  7. Computer control system of TRISTAN

    International Nuclear Information System (INIS)

    Kurokawa, Shin-ichi; Shinomoto, Manabu; Kurihara, Michio; Sakai, Hiroshi.

    1984-01-01

    For the operation of a large accelerator, it is necessary to connect an enormous quantity of electro-magnets, power sources, vacuum equipment, high frequency accelerator and so on and to control them harmoniously. For the purpose, a number of computers are adopted, and connected with a network, in this way, a large computer system for laboratory automation which integrates and controls the whole system is constructed. As a distributed system of large scale, the functions such as electro-magnet control, file processing and operation control are assigned to respective computers, and the total control is made feasible by network connection, at the same time, as the interface with controlled equipment, the CAMAC (computer-aided measurement and control) is adopted to ensure the flexibility and the possibility of expansion of the system. Moreover, the language ''NODAL'' having network support function was developed so as to easily make software without considering the composition of more complex distributed system. The accelerator in the TRISTAN project is composed of an electron linear accelerator, an accumulation ring of 6 GeV and a main ring of 30 GeV. Two ring type accelerators must be synchronously operated as one body, and are controlled with one computer system. The hardware and software are outlined. (Kako, I.)

  8. Computer controlled high voltage system

    Energy Technology Data Exchange (ETDEWEB)

    Kunov, B; Georgiev, G; Dimitrov, L [and others

    1996-12-31

    A multichannel computer controlled high-voltage power supply system is developed. The basic technical parameters of the system are: output voltage -100-3000 V, output current - 0-3 mA, maximum number of channels in one crate - 78. 3 refs.

  9. The ALICE Magnetic System Computation.

    CERN Document Server

    Klempt, W; CERN. Geneva; Swoboda, Detlef

    1995-01-01

    In this note we present the first results from the ALICE magnetic system computation performed in the 3-dimensional way with the Vector Fields TOSCA code (version 6.5) [1]. To make the calculations we have used the IBM RISC System 6000-370 and 6000-550 machines combined in the CERN PaRC UNIX cluster.

  10. Introduction to algebra and trigonometry

    CERN Document Server

    Kolman, Bernard

    1981-01-01

    Introduction to Algebra and Trigonometry provides a complete and self-contained presentation of the fundamentals of algebra and trigonometry.This book describes an axiomatic development of the foundations of algebra, defining complex numbers that are used to find the roots of any quadratic equation. Advanced concepts involving complex numbers are also elaborated, including the roots of polynomials, functions and function notation, and computations with logarithms. This text also discusses trigonometry from a functional standpoint. The angles, triangles, and applications involving triangles are

  11. Computational Intelligence for Engineering Systems

    CERN Document Server

    Madureira, A; Vale, Zita

    2011-01-01

    "Computational Intelligence for Engineering Systems" provides an overview and original analysis of new developments and advances in several areas of computational intelligence. Computational Intelligence have become the road-map for engineers to develop and analyze novel techniques to solve problems in basic sciences (such as physics, chemistry and biology) and engineering, environmental, life and social sciences. The contributions are written by international experts, who provide up-to-date aspects of the topics discussed and present recent, original insights into their own experien

  12. Parts of the Whole: An Algebra Lesson

    Directory of Open Access Journals (Sweden)

    Dorothy Wallace

    2011-07-01

    Full Text Available This column draws on research of Eon Harper to demonstrate how an understanding of his proposed stages of algebra acquisition would inform a systemic overhaul of algebra education. Harper's stages also explain why students may pass a series of algebra courses yet still be unable to make sense of calculus, as well as offering insight on what aspects of algebra support quantitative literacy.

  13. Finite W-algebras and intermediate statistics

    International Nuclear Information System (INIS)

    Barbarin, F.; Ragoucy, E.; Sorba, P.

    1995-01-01

    New realizations of finite W-algebras are constructed by relaxing the usual constraint conditions. Then finite W-algebras are recognized in the Heisenberg quantization recently proposed by Leinaas and Myrheim, for a system of two identical particles in d dimensions. As the anyonic parameter is directly associated to the W-algebra involved in the d=1 case, it is natural to consider that the W-algebra framework is well adapted for a possible generalization of the anyon statistics. ((orig.))

  14. Complex Algebraic Varieties

    CERN Document Server

    Peternell, Thomas; Schneider, Michael; Schreyer, Frank-Olaf

    1992-01-01

    The Bayreuth meeting on "Complex Algebraic Varieties" focussed on the classification of algebraic varieties and topics such as vector bundles, Hodge theory and hermitian differential geometry. Most of the articles in this volume are closely related to talks given at the conference: all are original, fully refereed research articles. CONTENTS: A. Beauville: Annulation du H(1) pour les fibres en droites plats.- M. Beltrametti, A.J. Sommese, J.A. Wisniewski: Results on varieties with many lines and their applications to adjunction theory.- G. Bohnhorst, H. Spindler: The stability of certain vector bundles on P(n) .- F. Catanese, F. Tovena: Vector bundles, linear systems and extensions of (1).- O. Debarre: Vers uns stratification de l'espace des modules des varietes abeliennes principalement polarisees.- J.P. Demailly: Singular hermitian metrics on positive line bundles.- T. Fujita: On adjoint bundles of ample vector bundles.- Y. Kawamata: Moderate degenerations of algebraic surfaces.- U. Persson: Genus two fibra...

  15. Applied linear algebra

    CERN Document Server

    Olver, Peter J

    2018-01-01

    This textbook develops the essential tools of linear algebra, with the goal of imparting technique alongside contextual understanding. Applications go hand-in-hand with theory, each reinforcing and explaining the other. This approach encourages students to develop not only the technical proficiency needed to go on to further study, but an appreciation for when, why, and how the tools of linear algebra can be used across modern applied mathematics. Providing an extensive treatment of essential topics such as Gaussian elimination, inner products and norms, and eigenvalues and singular values, this text can be used for an in-depth first course, or an application-driven second course in linear algebra. In this second edition, applications have been updated and expanded to include numerical methods, dynamical systems, data analysis, and signal processing, while the pedagogical flow of the core material has been improved. Throughout, the text emphasizes the conceptual connections between each application and the un...

  16. Opportunity for Realizing Ideal Computing System using Cloud Computing Model

    OpenAIRE

    Sreeramana Aithal; Vaikunth Pai T

    2017-01-01

    An ideal computing system is a computing system with ideal characteristics. The major components and their performance characteristics of such hypothetical system can be studied as a model with predicted input, output, system and environmental characteristics using the identified objectives of computing which can be used in any platform, any type of computing system, and for application automation, without making modifications in the form of structure, hardware, and software coding by an exte...

  17. Polynomial Heisenberg algebras

    International Nuclear Information System (INIS)

    Carballo, Juan M; C, David J Fernandez; Negro, Javier; Nieto, Luis M

    2004-01-01

    Polynomial deformations of the Heisenberg algebra are studied in detail. Some of their natural realizations are given by the higher order susy partners (and not only by those of first order, as is already known) of the harmonic oscillator for even-order polynomials. Here, it is shown that the susy partners of the radial oscillator play a similar role when the order of the polynomial is odd. Moreover, it will be proved that the general systems ruled by such kinds of algebras, in the quadratic and cubic cases, involve Painleve transcendents of types IV and V, respectively

  18. Elementary matrix algebra

    CERN Document Server

    Hohn, Franz E

    2012-01-01

    This complete and coherent exposition, complemented by numerous illustrative examples, offers readers a text that can teach by itself. Fully rigorous in its treatment, it offers a mathematically sound sequencing of topics. The work starts with the most basic laws of matrix algebra and progresses to the sweep-out process for obtaining the complete solution of any given system of linear equations - homogeneous or nonhomogeneous - and the role of matrix algebra in the presentation of useful geometric ideas, techniques, and terminology.Other subjects include the complete treatment of the structur

  19. Algebra & trigonometry I essentials

    CERN Document Server

    REA, Editors of

    2012-01-01

    REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Algebra & Trigonometry I includes sets and set operations, number systems and fundamental algebraic laws and operations, exponents and radicals, polynomials and rational expressions, eq

  20. Systems analysis and the computer

    Energy Technology Data Exchange (ETDEWEB)

    Douglas, A S

    1983-08-01

    The words systems analysis are used in at least two senses. Whilst the general nature of the topic is well understood in the or community, the nature of the term as used by computer scientists is less familiar. In this paper, the nature of systems analysis as it relates to computer-based systems is examined from the point of view that the computer system is an automaton embedded in a human system, and some facets of this are explored. It is concluded that or analysts and computer analysts have things to learn from each other and that this ought to be reflected in their education. The important role played by change in the design of systems is also highlighted, and it is concluded that, whilst the application of techniques developed in the artificial intelligence field have considerable relevance to constructing automata able to adapt to change in the environment, study of the human factors affecting the overall systems within which the automata are embedded has an even more important role. 19 references.

  1. Algebraic characterizations of measure algebras

    Czech Academy of Sciences Publication Activity Database

    Jech, Thomas

    2008-01-01

    Roč. 136, č. 4 (2008), s. 1285-1294 ISSN 0002-9939 R&D Projects: GA AV ČR IAA100190509 Institutional research plan: CEZ:AV0Z10190503 Keywords : Von - Neumann * sequential topology * Boolean-algebras * Souslins problem * Submeasures Subject RIV: BA - General Mathematics Impact factor: 0.584, year: 2008

  2. Quantum W-algebras and elliptic algebras

    International Nuclear Information System (INIS)

    Feigin, B.; Kyoto Univ.; Frenkel, E.

    1996-01-01

    We define a quantum W-algebra associated to sl N as an associative algebra depending on two parameters. For special values of the parameters, this algebra becomes the ordinary W-algebra of sl N , or the q-deformed classical W-algebra of sl N . We construct free field realizations of the quantum W-algebras and the screening currents. We also point out some interesting elliptic structures arising in these algebras. In particular, we show that the screening currents satisfy elliptic analogues of the Drinfeld relations in U q (n). (orig.)

  3. An algebraic approach to the scattering equations

    Energy Technology Data Exchange (ETDEWEB)

    Huang, Rijun; Rao, Junjie [Zhejiang Institute of Modern Physics, Zhejiang University,Hangzhou, 310027 (China); Feng, Bo [Zhejiang Institute of Modern Physics, Zhejiang University,Hangzhou, 310027 (China); Center of Mathematical Science, Zhejiang University,Hangzhou, 310027 (China); He, Yang-Hui [School of Physics, NanKai University,Tianjin, 300071 (China); Department of Mathematics, City University,London, EC1V 0HB (United Kingdom); Merton College, University of Oxford,Oxford, OX14JD (United Kingdom)

    2015-12-10

    We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using simple linear algebra and is amenable to an algorithmic approach. Certain identities in the amplitudes as well as rationality of the final integrand become immediate in this formalism.

  4. An algebraic approach to the scattering equations

    International Nuclear Information System (INIS)

    Huang, Rijun; Rao, Junjie; Feng, Bo; He, Yang-Hui

    2015-01-01

    We employ the so-called companion matrix method from computational algebraic geometry, tailored for zero-dimensional ideals, to study the scattering equations. The method renders the CHY-integrand of scattering amplitudes computable using simple linear algebra and is amenable to an algorithmic approach. Certain identities in the amplitudes as well as rationality of the final integrand become immediate in this formalism.

  5. On 2-Banach algebras

    International Nuclear Information System (INIS)

    Mohammad, N.; Siddiqui, A.H.

    1987-11-01

    The notion of a 2-Banach algebra is introduced and its structure is studied. After a short discussion of some fundamental properties of bivectors and tensor product, several classical results of Banach algebras are extended to the 2-Banach algebra case. A condition under which a 2-Banach algebra becomes a Banach algebra is obtained and the relation between algebra of bivectors and 2-normed algebra is discussed. 11 refs

  6. Evolution algebras generated by Gibbs measures

    International Nuclear Information System (INIS)

    Rozikov, Utkir A.; Tian, Jianjun Paul

    2009-03-01

    In this article we study algebraic structures of function spaces defined by graphs and state spaces equipped with Gibbs measures by associating evolution algebras. We give a constructive description of associating evolution algebras to the function spaces (cell spaces) defined by graphs and state spaces and Gibbs measure μ. For finite graphs we find some evolution subalgebras and other useful properties of the algebras. We obtain a structure theorem for evolution algebras when graphs are finite and connected. We prove that for a fixed finite graph, the function spaces have a unique algebraic structure since all evolution algebras are isomorphic to each other for whichever Gibbs measures are assigned. When graphs are infinite graphs then our construction allows a natural introduction of thermodynamics in studying of several systems of biology, physics and mathematics by theory of evolution algebras. (author)

  7. Function algebras on finite sets basic course on many-valued logic and clone theory

    CERN Document Server

    Lau, Dietlinde

    2006-01-01

    Gives an introduction to the theory of function algebras. This book gives the general concepts of the Universal Algebra in order to familiarize the reader from the beginning on with the algebraic side of function algebras. It is a source on function algebras for students and researchers in mathematical logic and theoretical computer science.

  8. Algebraic realization of the resonating group method for multichannel scattering problem in an eight nucleon system

    International Nuclear Information System (INIS)

    Badalov, S.A.; Filippov, G.F.

    1983-01-01

    All the basic calculation formulas of an algebraic version of the resonating-group method for a pultichannel problem of the scattering of a nucleon by 7 Li and 7 Be taking into account α+α channel are derived. The spin-orbital and the Coulomb interactions are taken into consideration. The procedure enabling an exact projection into the states with the given values of the channel quantum numbers is proposed

  9. Analytical Solutions for Systems of Singular Partial Differential-Algebraic Equations

    Directory of Open Access Journals (Sweden)

    U. Filobello-Nino

    2015-01-01

    Full Text Available This paper proposes power series method (PSM in order to find solutions for singular partial differential-algebraic equations (SPDAEs. We will solve three examples to show that PSM method can be used to search for analytical solutions of SPDAEs. What is more, we will see that, in some cases, Padé posttreatment, besides enlarging the domain of convergence, may be employed in order to get the exact solution from the truncated series solutions of PSM.

  10. Finding the radical of an algebra of linear transformations

    NARCIS (Netherlands)

    Cohen, A.M.; Ivanyos, G.; Wales, D.B.

    1997-01-01

    We present a method that reduces the problem of computing the radical of a matrix algebra over an arbitrary field to solving systems of semilinear equations. The complexity of the algorithm, measured in the number of arithmetic operations and the total number of the coefficients passed to an oracle

  11. Current algebra

    International Nuclear Information System (INIS)

    Jacob, M.

    1967-01-01

    The first three chapters of these lecture notes are devoted to generalities concerning current algebra. The weak currents are defined, and their main properties given (V-A hypothesis, conserved vector current, selection rules, partially conserved axial current,...). The SU (3) x SU (3) algebra of Gell-Mann is introduced, and the general properties of the non-leptonic weak Hamiltonian are discussed. Chapters 4 to 9 are devoted to some important applications of the algebra. First one proves the Adler- Weisberger formula, in two different ways, by either the infinite momentum frame, or the near-by singularities method. In the others chapters, the latter method is the only one used. The following topics are successively dealt with: semi leptonic decays of K mesons and hyperons, Kroll- Ruderman theorem, non leptonic decays of K mesons and hyperons ( ΔI = 1/2 rule), low energy theorems concerning processes with emission (or absorption) of a pion or a photon, super-convergence sum rules, and finally, neutrino reactions. (author) [fr

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

    Science.gov (United States)

    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…

  13. Algorithmic and experimental methods in algebra, geometry, and number theory

    CERN Document Server

    Decker, Wolfram; Malle, Gunter

    2017-01-01

    This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to create powerful new computational tools that transcend the boundaries of the individual disciplines involved.  The book covers a broad range of topics addressing the design and theoretical foundations, implementation and the successful application of algebraic algorithms in order to solve mathematical research problems. It off...

  14. A 9 x 9 Matrix Representation of Birman-Wenzl-Murakami Algebra and Berry Phase in Yang-Baxter System

    International Nuclear Information System (INIS)

    Gou Lidan; Xue Kang; Wang Gangcheng

    2011-01-01

    We present a 9 x 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 R(x, φ 1 ,φ 2 ) is generated via the Yang-Baxterization approach. Then we construct a Yang-Baxter Hamiltonian through the unitary matrix R(x, φ 1 ,φ 2 ). Berry phase of this Yang-Baxter system is investigated in detail. (general)

  15. Communication Avoiding and Overlapping for Numerical Linear Algebra

    Science.gov (United States)

    2012-05-08

    future exascale systems, communication cost must be avoided or overlapped. Communication-avoiding 2.5D algorithms improve scalability by reducing...linear algebra problems to future exascale systems, communication cost must be avoided or overlapped. Communication-avoiding 2.5D algorithms improve...will continue to grow relative to the cost of computation. With exascale computing as the long-term goal, the community needs to develop techniques

  16. Exploiting Data Sparsity In Covariance Matrix Computations on Heterogeneous Systems

    KAUST Repository

    Charara, Ali M.

    2018-05-24

    Covariance matrices are ubiquitous in computational sciences, typically describing the correlation of elements of large multivariate spatial data sets. For example, covari- ance matrices are employed in climate/weather modeling for the maximum likelihood estimation to improve prediction, as well as in computational ground-based astronomy to enhance the observed image quality by filtering out noise produced by the adap- tive optics instruments and atmospheric turbulence. The structure of these covariance matrices is dense, symmetric, positive-definite, and often data-sparse, therefore, hier- archically of low-rank. This thesis investigates the performance limit of dense matrix computations (e.g., Cholesky factorization) on covariance matrix problems as the number of unknowns grows, and in the context of the aforementioned applications. We employ recursive formulations of some of the basic linear algebra subroutines (BLAS) to accelerate the covariance matrix computation further, while reducing data traffic across the memory subsystems layers. However, dealing with large data sets (i.e., covariance matrices of billions in size) can rapidly become prohibitive in memory footprint and algorithmic complexity. Most importantly, this thesis investigates the tile low-rank data format (TLR), a new compressed data structure and layout, which is valuable in exploiting data sparsity by approximating the operator. The TLR com- pressed data structure allows approximating the original problem up to user-defined numerical accuracy. This comes at the expense of dealing with tasks with much lower arithmetic intensities than traditional dense computations. In fact, this thesis con- solidates the two trends of dense and data-sparse linear algebra for HPC. Not only does the thesis leverage recursive formulations for dense Cholesky-based matrix al- gorithms, but it also implements a novel TLR-Cholesky factorization using batched linear algebra operations to increase hardware occupancy and

  17. AMPTRACT: an algebraic model for computing pressure tube circumferential and steam temperature transients under stratified channel coolant conditions

    International Nuclear Information System (INIS)

    Gulshani, P.; So, C.B.

    1986-10-01

    In a number of postulated accident scenarios in a CANDU reactor, some of the horizontal fuel channels are predicted to experience periods of stratified channel coolant condition which can lead to a circumferential temperature gradient around the pressure tube. To study pressure tube strain and integrity under stratified flow channel conditions, it is, necessary to determine the pressure tube circumferential temperature distribution. This paper presents an algebraic model, called AMPTRACT (Algebraic Model for Pressure Tube TRAnsient Circumferential Temperature), developed to give the transient temperature distribution in a closed form. AMPTRACT models the following modes of heat transfer: radiation from the outermost elements to the pressure tube and from the pressure to calandria tube, convection between the fuel elements and the pressure tube and superheated steam, and circumferential conduction from the exposed to submerged part of the pressure tube. An iterative procedure is used to solve the mass and energy equations in closed form for axial steam and fuel-sheath transient temperature distributions. The one-dimensional conduction equation is then solved to obtain the pressure tube circumferential transient temperature distribution in a cosine series expansion. In the limit of large times and in the absence of convection and radiation to the calandria tube, the predicted pressure tube temperature distribution reduces identically to a parabolic profile. In this limit, however, radiation cannot be ignored because the temperatures are generally high. Convection and radiation tend to flatten the parabolic distribution

  18. Fibered F-Algebra

    OpenAIRE

    Kleyn, Aleks

    2007-01-01

    The concept of F-algebra and its representation can be extended to an arbitrary bundle. We define operations of fibered F-algebra in fiber. The paper presents the representation theory of of fibered F-algebra as well as a comparison of representation of F-algebra and of representation of fibered F-algebra.

  19. Synchronization of integral and fractional order chaotic systems a differential algebraic and differential geometric approach with selected applications in real-time

    CERN Document Server

    Martínez-Guerra, Rafael; Gómez-Cortés, Gian Carlo

    2015-01-01

    This book provides a general overview of several concepts of synchronization and brings together related approaches to secure communication in chaotic systems. This is achieved using a combination of analytic, algebraic, geometrical and asymptotical methods to tackle the dynamical feedback stabilization problem. In particular, differential-geometric and algebraic differential concepts reveal important structural properties of chaotic systems and serve as guide for the construction of design procedures for a wide variety of chaotic systems. The basic differential algebraic and geometric concepts are presented in the first few chapters in a novel way as design tools, together with selected experimental studies demonstrating their importance. The subsequent chapters treat recent applications. Written for graduate students in applied physical sciences, systems engineers, and applied mathematicians interested in synchronization of chaotic systems and in secure communications, this self-contained text requires only...

  20. On the classification of quantum W-algebras

    International Nuclear Information System (INIS)

    Bowcock, P.; Watts, G.T.M.

    1992-01-01

    In this paper we consider the structure of general quantum W-algebras. We introduce the notions of deformability, positive-definiteness, and reductivity of a W-algebra. We show that one can associate a reductive finite Lie algebra to each reductive W-algebra. The finite Lie algebra is also endowed with a preferred sl(2) subalgebra, which gives the conformal weights of the W-algebra. We extend this to cover W-algebras containing both bosonic and fermionic fields, and illustrate our ideas with the Poisson bracket algebras of generalised Drinfeld-Sokolov hamiltonian systems. We then discuss the possibilities of classifying deformable W-algebras which fall outside this class in the context of automorphisms of Lie algebras. In conclusion we list the cases in which the W-algebra has no weight-one fields, and further, those in which it has only one weight-two field. (orig.)

  1. Constructing canonical bases of quantized enveloping algebras

    OpenAIRE

    Graaf, W.A. de

    2001-01-01

    An algorithm for computing the elements of a given weight of the canonical basis of a quantized enveloping algebra is described. Subsequently, a similar algorithm is presented for computing the canonical basis of a finite-dimensional module.

  2. The Evaluation of Computer Systems

    Directory of Open Access Journals (Sweden)

    Cezar Octavian Mihalcescu

    2007-01-01

    Full Text Available Generally, the evaluation of the computersystems is especially interesting at present from severalpoints of view: computer-related, managerial,sociological etc. The reasons for this extended interest arerepresented by the fact that IT becomes increasinglyimportant for reaching the goals of an organization, ingeneral, and the strategic ones in particular. Evaluationmeans the estimation or determination of value, and issynonymous with measuring the value. Evaluating theeconomic value of Computer Systems should be studiedat three levels: individually, at a group level and at anorganization level.

  3. Computational system for geostatistical analysis

    Directory of Open Access Journals (Sweden)

    Vendrusculo Laurimar Gonçalves

    2004-01-01

    Full Text Available Geostatistics identifies the spatial structure of variables representing several phenomena and its use is becoming more intense in agricultural activities. This paper describes a computer program, based on Windows Interfaces (Borland Delphi, which performs spatial analyses of datasets through geostatistic tools: Classical statistical calculations, average, cross- and directional semivariograms, simple kriging estimates and jackknifing calculations. A published dataset of soil Carbon and Nitrogen was used to validate the system. The system was useful for the geostatistical analysis process, for the manipulation of the computational routines in a MS-DOS environment. The Windows development approach allowed the user to model the semivariogram graphically with a major degree of interaction, functionality rarely available in similar programs. Given its characteristic of quick prototypation and simplicity when incorporating correlated routines, the Delphi environment presents the main advantage of permitting the evolution of this system.

  4. Comments on two-loop Kac-Moody algebras

    Energy Technology Data Exchange (ETDEWEB)

    Ferreira, L A; Gomes, J F; Zimerman, A H [Instituto de Fisica Teorica (IFT), Sao Paulo, SP (Brazil); Schwimmer, A [Istituto Nazionale di Fisica Nucleare, Trieste (Italy)

    1991-10-01

    It is shown that the two-loop Kac-Moody algebra is equivalent to a two variable loop algebra and a decouple {beta}-{gamma} system. Similarly WZNW and CSW models having as algebraic structure the Kac-Moody algebra are equivalent to an infinity to versions of the corresponding ordinary models and decoupled Abelian fields. (author). 15 refs.

  5. Computer access security code system

    Science.gov (United States)

    Collins, Earl R., Jr. (Inventor)

    1990-01-01

    A security code system for controlling access to computer and computer-controlled entry situations comprises a plurality of subsets of alpha-numeric characters disposed in random order in matrices of at least two dimensions forming theoretical rectangles, cubes, etc., such that when access is desired, at least one pair of previously unused character subsets not found in the same row or column of the matrix is chosen at random and transmitted by the computer. The proper response to gain access is transmittal of subsets which complete the rectangle, and/or a parallelepiped whose opposite corners were defined by first groups of code. Once used, subsets are not used again to absolutely defeat unauthorized access by eavesdropping, and the like.

  6. Computational models of complex systems

    CERN Document Server

    Dabbaghian, Vahid

    2014-01-01

    Computational and mathematical models provide us with the opportunities to investigate the complexities of real world problems. They allow us to apply our best analytical methods to define problems in a clearly mathematical manner and exhaustively test our solutions before committing expensive resources. This is made possible by assuming parameter(s) in a bounded environment, allowing for controllable experimentation, not always possible in live scenarios. For example, simulation of computational models allows the testing of theories in a manner that is both fundamentally deductive and experimental in nature. The main ingredients for such research ideas come from multiple disciplines and the importance of interdisciplinary research is well recognized by the scientific community. This book provides a window to the novel endeavours of the research communities to present their works by highlighting the value of computational modelling as a research tool when investigating complex systems. We hope that the reader...

  7. Computer-Mediated Communication Systems

    Directory of Open Access Journals (Sweden)

    Bin Yu

    2011-10-01

    Full Text Available The essence of communication is to exchange and share information. Computers provide a new medium to human communication. CMC system, composed of human and computers, absorbs and then extends the advantages of all former formats of communication, embracing the instant interaction of oral communication, the abstract logics of printing dissemination, and the vivid images of movie and television. It also creates a series of new communication formats, such as Hyper Text, Multimedia etc. which are the information organizing methods, and cross-space message delivering patterns. Benefiting from the continuous development of technique and mechanism, the computer-mediated communication makes the dream of transmitting information cross space and time become true, which will definitely have a great impact on our social lives.

  8. System for multiprogram control of a specialized computer for geophysical investigations

    International Nuclear Information System (INIS)

    Gol'bek, G.R.; Grachev, E.M.; Kirillova, B.F.; Veksler, B.E.

    1973-01-01

    The paper describes the microprogrammed control device of a specialized computer for solving problems of the cyclical type (especially those involving a system of linear algebraic equations) in which the functions of an instruction storage unit are distributed between an address directory and an operational group switch. This made it possible to combine in a single instruction a group of elementary operations over a few numbers and eventually led to a simplification of the operational logic of the device. (author)

  9. The C*-algebra of a vector bundle and fields of Cuntz algebras

    OpenAIRE

    Vasselli, Ezio

    2004-01-01

    We study the Pimsner algebra associated with the module of continuous sections of a Hilbert bundle, and prove that it is a continuous bundle of Cuntz algebras. We discuss the role of such Pimsner algebras w.r.t. the notion of inner endomorphism. Furthermore, we study bundles of Cuntz algebras carrying a global circle action, and assign to them a class in the representable KK-group of the zero-grade bundle. We compute such class for the Pimsner algebra of a vector bundle.

  10. Guide to Geometric Algebra in Practice

    CERN Document Server

    Dorst, Leo

    2011-01-01

    This highly practical "Guide to Geometric Algebra in Practice" reviews algebraic techniques for geometrical problems in computer science and engineering, and the relationships between them. The topics covered range from powerful new theoretical developments, to successful applications, and the development of new software and hardware tools. This title: provides hands-on review exercises throughout the book, together with helpful chapter summaries; presents a concise introductory tutorial to conformal geometric algebra (CGA) in the appendices; examines the application of CGA for the d

  11. Asymptotic identity in min-plus algebra: a report on CPNS.

    Science.gov (United States)

    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.

  12. Asymptotic Identity in Min-Plus Algebra: A Report on CPNS

    Science.gov (United States)

    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

  13. Head First Algebra A Learner's Guide to Algebra I

    CERN Document Server

    Pilone, Tracey

    2008-01-01

    Having trouble understanding algebra? Do algebraic concepts, equations, and logic just make your head spin? We have great news: Head First Algebra is designed for you. Full of engaging stories and practical, real-world explanations, this book will help you learn everything from natural numbers and exponents to solving systems of equations and graphing polynomials. Along the way, you'll go beyond solving hundreds of repetitive problems, and actually use what you learn to make real-life decisions. Does it make sense to buy two years of insurance on a car that depreciates as soon as you drive i

  14. Generalized symmetry algebras

    International Nuclear Information System (INIS)

    Dragon, N.

    1979-01-01

    The possible use of trilinear algebras as symmetry algebras for para-Fermi fields is investigated. The shortcomings of the examples are argued to be a general feature of such generalized algebras. (author)

  15. A differential algebraic integration algorithm for symplectic mappings in systems with three-dimensional magnetic field

    International Nuclear Information System (INIS)

    Chang, P.; Lee, S.Y.; Yan, Y.T.

    2006-01-01

    A differential algebraic integration algorithm is developed for symplectic mapping through a three-dimensional (3-D) magnetic field. The self-consistent reference orbit in phase space is obtained by making a canonical transformation to eliminate the linear part of the Hamiltonian. Transfer maps from the entrance to the exit of any 3-D magnetic field are then obtained through slice-by-slice symplectic integration. The particle phase-space coordinates are advanced by using the integrable polynomial procedure. This algorithm is a powerful tool to attain nonlinear maps for insertion devices in synchrotron light source or complicated magnetic field in the interaction region in high energy colliders

  16. A Differential Algebraic Integration Algorithm for Symplectic Mappings in Systems with Three-Dimensional Magnetic Field

    International Nuclear Information System (INIS)

    Chang, P

    2004-01-01

    A differential algebraic integration algorithm is developed for symplectic mapping through a three-dimensional (3-D) magnetic field. The self-consistent reference orbit in phase space is obtained by making a canonical transformation to eliminate the linear part of the Hamiltonian. Transfer maps from the entrance to the exit of any 3-D magnetic field are then obtained through slice-by-slice symplectic integration. The particle phase-space coordinates are advanced by using the integrable polynomial procedure. This algorithm is a powerful tool to attain nonlinear maps for insertion devices in synchrotron light source or complicated magnetic field in the interaction region in high energy colliders

  17. Computer-aided system design

    Science.gov (United States)

    Walker, Carrie K.

    1991-01-01

    A technique has been developed for combining features of a systems architecture design and assessment tool and a software development tool. This technique reduces simulation development time and expands simulation detail. The Architecture Design and Assessment System (ADAS), developed at the Research Triangle Institute, is a set of computer-assisted engineering tools for the design and analysis of computer systems. The ADAS system is based on directed graph concepts and supports the synthesis and analysis of software algorithms mapped to candidate hardware implementations. Greater simulation detail is provided by the ADAS functional simulator. With the functional simulator, programs written in either Ada or C can be used to provide a detailed description of graph nodes. A Computer-Aided Software Engineering tool developed at the Charles Stark Draper Laboratory (CSDL CASE) automatically generates Ada or C code from engineering block diagram specifications designed with an interactive graphical interface. A technique to use the tools together has been developed, which further automates the design process.

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

    Science.gov (United States)

    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.

  19. Algebraic functions

    CERN Document Server

    Bliss, Gilbert Ames

    1933-01-01

    This book, immediately striking for its conciseness, is one of the most remarkable works ever produced on the subject of algebraic functions and their integrals. The distinguishing feature of the book is its third chapter, on rational functions, which gives an extremely brief and clear account of the theory of divisors.... A very readable account is given of the topology of Riemann surfaces and of the general properties of abelian integrals. Abel's theorem is presented, with some simple applications. The inversion problem is studied for the cases of genus zero and genus unity. The chapter on t

  20. Non-skew-symmetric classical r-matrices, algebraic Bethe ansatz, and Bardeen-Cooper-Schrieffer-type integrable systems

    International Nuclear Information System (INIS)

    Skrypnyk, T.

    2009-01-01

    We construct quantum integrable systems associated with non-skew-symmetric gl(2)-valued classical r-matrices. We find a new explicit multiparametric family of such the non-skew-symmetric classical r-matrices. We consider two classes of examples of the corresponding integrable systems, namely generalized Gaudin systems with and without an external magnetic field. In the case of arbitrary r-matrices diagonal in a standard gl(2)-basis, we calculate the spectrum of the corresponding quantum integrable systems using the algebraic Bethe ansatz. We apply these results to a construction of integrable fermionic models and obtain a wide class of integrable Bardeen-Cooper-Schrieffer (BCS)-type fermionic Hamiltonians containing the pairing and electrostatic interaction terms. We also consider special cases when the corresponding integrable Hamiltonians contain only pairing interaction term and are exact analogs of the 'reduced BCS Hamiltonian' of Richardson