Summary of research in applied mathematics, numerical analysis, and computer sciences

Science.gov (United States)

1986-01-01

The major categories of current ICASE research programs addressed include: numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; control and parameter identification problems, with emphasis on effective numerical methods; computational problems in engineering and physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and computer systems and software, especially vector and parallel computers.

Numerical methods design, analysis, and computer implementation of algorithms

CERN Document Server

Greenbaum, Anne

2012-01-01

Numerical Methods provides a clear and concise exploration of standard numerical analysis topics, as well as nontraditional ones, including mathematical modeling, Monte Carlo methods, Markov chains, and fractals. Filled with appealing examples that will motivate students, the textbook considers modern application areas, such as information retrieval and animation, and classical topics from physics and engineering. Exercises use MATLAB and promote understanding of computational results. The book gives instructors the flexibility to emphasize different aspects--design, analysis, or computer implementation--of numerical algorithms, depending on the background and interests of students. Designed for upper-division undergraduates in mathematics or computer science classes, the textbook assumes that students have prior knowledge of linear algebra and calculus, although these topics are reviewed in the text. Short discussions of the history of numerical methods are interspersed throughout the chapters. The book a...

9th and 10th Asian Symposium on Computer Mathematics

CERN Document Server

Lee, Wen-shin; Sato, Yosuke

2014-01-01

This book covers original research and the latest advances in symbolic, algebraic and geometric computation; computational methods for differential and difference equations, symbolic-numerical computation; mathematics software design and implementation; and scientific and engineering applications based on features, invited talks, special sessions and contributed papers presented at the 9th (in Fukuoka, Japan in 2009) and 10th (in Beijing China in 2012) Asian Symposium on Computer Mathematics (ASCM). Thirty selected and refereed articles in the book present the conference participants’ ideas and views on researching mathematics using computers.

Mathematical and numerical modelling of fluids at Nano-metric scales

International Nuclear Information System (INIS)

Joubaud, R.

2012-01-01

This work presents some contributions to the mathematical and numerical modelling of fluids at Nano-metric scales. We are interested in two levels of modelling. The first level consists in an atomic description. We consider the problem of computing the shear viscosity of a fluid from a microscopic description. More precisely, we study the mathematical properties of the nonequilibrium Langevin dynamics allowing to compute the shear viscosity. The second level of description is a continuous description, and we consider a class of continuous models for equilibrium electrolytes, which incorporate on the one hand a confinement by charged solid objects and on the other hand non-ideality effects stemming from electrostatic correlations and steric exclusion phenomena due to the excluded volume effects. First, we perform the mathematical analysis of the case where the free energy is a convex function (mild non-ideality). Second, we consider numerically the case where the free energy is a non convex function (strong non-ideality) leading in particular to phase separation. (author)

Numerical computation of special functions with applications to physics

CSIR Research Space (South Africa)

Motsepe, K

2008-09-01

Full Text Available Students of mathematical physics, engineering, natural and biological sciences sometimes need to use special functions that are not found in ordinary mathematical software. In this paper a simple universal numerical algorithm is developed to compute...

Computer programming in the UK undergraduate mathematics curriculum

Science.gov (United States)

Sangwin, Christopher J.; O'Toole, Claire

2017-11-01

This paper reports a study which investigated the extent to which undergraduate mathematics students in the United Kingdom are currently taught to programme a computer as a core part of their mathematics degree programme. We undertook an online survey, with significant follow-up correspondence, to gather data on current curricula and received replies from 46 (63%) of the departments who teach a BSc mathematics degree. We found that 78% of BSc degree courses in mathematics included computer programming in a compulsory module but 11% of mathematics degree programmes do not teach programming to all their undergraduate mathematics students. In 2016, programming is most commonly taught to undergraduate mathematics students through imperative languages, notably MATLAB, using numerical analysis as the underlying (or parallel) mathematical subject matter. Statistics is a very popular choice in optional courses, using the package R. Computer algebra systems appear to be significantly less popular for compulsory first-year courses than a decade ago, and there was no mention of logic programming, functional programming or automatic theorem proving software. The modal form of assessment of computing modules is entirely by coursework (i.e. no examination).

Numerical methods in matrix computations

CERN Document Server

Björck, Åke

2015-01-01

Matrix algorithms are at the core of scientific computing and are indispensable tools in most applications in engineering. This book offers a comprehensive and up-to-date treatment of modern methods in matrix computation. It uses a unified approach to direct and iterative methods for linear systems, least squares and eigenvalue problems. A thorough analysis of the stability, accuracy, and complexity of the treated methods is given. Numerical Methods in Matrix Computations is suitable for use in courses on scientific computing and applied technical areas at advanced undergraduate and graduate level. A large bibliography is provided, which includes both historical and review papers as well as recent research papers. This makes the book useful also as a reference and guide to further study and research work. Åke Björck is a professor emeritus at the Department of Mathematics, Linköping University. He is a Fellow of the Society of Industrial and Applied Mathematics.

Topics in numerical partial differential equations and scientific computing

CERN Document Server

2016-01-01

Numerical partial differential equations (PDEs) are an important part of numerical simulation, the third component of the modern methodology for science and engineering, besides the traditional theory and experiment. This volume contains papers that originated with the collaborative research of the teams that participated in the IMA Workshop for Women in Applied Mathematics: Numerical Partial Differential Equations and Scientific Computing in August 2014.

Mathematics, the Computer, and the Impact on Mathematics Education.

Science.gov (United States)

Tooke, D. James

2001-01-01

Discusses the connection between mathematics and the computer; mathematics curriculum; mathematics instruction, including teachers learning to use computers; and the impact of the computer on learning mathematics. (LRW)

Mathematics for computer graphics

CERN Document Server

Vince, John

2006-01-01

Helps you understand the mathematical ideas used in computer animation, virtual reality, CAD, and other areas of computer graphics. This work also helps you to rediscover the mathematical techniques required to solve problems and design computer programs for computer graphic applications

High-Precision Computation: Mathematical Physics and Dynamics

International Nuclear Information System (INIS)

Bailey, D.H.; Barrio, R.; Borwein, J.M.

2010-01-01

At the present time, IEEE 64-bit oating-point arithmetic is suficiently accurate for most scientic applications. However, for a rapidly growing body of important scientic computing applications, a higher level of numeric precision is required. Such calculations are facilitated by high-precision software packages that include high-level language translation modules to minimize the conversion e ort. This pa- per presents a survey of recent applications of these techniques and provides someanalysis of their numerical requirements. These applications include supernova simulations, climate modeling, planetary orbit calculations, Coulomb n-body atomic systems, studies of the one structure constant, scattering amplitudes of quarks, glu- ons and bosons, nonlinear oscillator theory, experimental mathematics, evaluation of orthogonal polynomials, numerical integration of ODEs, computation of periodic orbits, studies of the splitting of separatrices, detection of strange nonchaotic at- tractors, Ising theory, quantum held theory, and discrete dynamical systems. We conclude that high-precision arithmetic facilities are now an indispensable compo- nent of a modern large-scale scientic computing environment.

High-Precision Computation: Mathematical Physics and Dynamics

Energy Technology Data Exchange (ETDEWEB)

Bailey, D. H.; Barrio, R.; Borwein, J. M.

2010-04-01

At the present time, IEEE 64-bit oating-point arithmetic is suficiently accurate for most scientic applications. However, for a rapidly growing body of important scientic computing applications, a higher level of numeric precision is required. Such calculations are facilitated by high-precision software packages that include high-level language translation modules to minimize the conversion e ort. This pa- per presents a survey of recent applications of these techniques and provides someanalysis of their numerical requirements. These applications include supernova simulations, climate modeling, planetary orbit calculations, Coulomb n-body atomic systems, studies of the one structure constant, scattering amplitudes of quarks, glu- ons and bosons, nonlinear oscillator theory, experimental mathematics, evaluation of orthogonal polynomials, numerical integration of ODEs, computation of periodic orbits, studies of the splitting of separatrices, detection of strange nonchaotic at- tractors, Ising theory, quantum held theory, and discrete dynamical systems. We conclude that high-precision arithmetic facilities are now an indispensable compo- nent of a modern large-scale scientic computing environment.

High-Precision Computation and Mathematical Physics

International Nuclear Information System (INIS)

Bailey, David H.; Borwein, Jonathan M.

2008-01-01

At the present time, IEEE 64-bit floating-point arithmetic is sufficiently accurate for most scientific applications. However, for a rapidly growing body of important scientific computing applications, a higher level of numeric precision is required. Such calculations are facilitated by high-precision software packages that include high-level language translation modules to minimize the conversion effort. This paper presents a survey of recent applications of these techniques and provides some analysis of their numerical requirements. These applications include supernova simulations, climate modeling, planetary orbit calculations, Coulomb n-body atomic systems, scattering amplitudes of quarks, gluons and bosons, nonlinear oscillator theory, Ising theory, quantum field theory and experimental mathematics. We conclude that high-precision arithmetic facilities are now an indispensable component of a modern large-scale scientific computing environment.

Mathematical theory of compressible viscous fluids analysis and numerics

CERN Document Server

Feireisl, Eduard; Pokorný, Milan

2016-01-01

This book offers an essential introduction to the mathematical theory of compressible viscous fluids. The main goal is to present analytical methods from the perspective of their numerical applications. Accordingly, we introduce the principal theoretical tools needed to handle well-posedness of the underlying Navier-Stokes system, study the problems of sequential stability, and, lastly, construct solutions by means of an implicit numerical scheme. Offering a unique contribution – by exploring in detail the “synergy” of analytical and numerical methods – the book offers a valuable resource for graduate students in mathematics and researchers working in mathematical fluid mechanics. Mathematical fluid mechanics concerns problems that are closely connected to real-world applications and is also an important part of the theory of partial differential equations and numerical analysis in general. This book highlights the fact that numerical and mathematical analysis are not two separate fields of mathematic...

Minimal features of a computer and its basic software to executs NEPTUNIX 2 numerical step

International Nuclear Information System (INIS)

Roux, Pierre.

1982-12-01

NEPTUNIX 2 is a package which carries out the simulation of complex processes described by numerous non linear algebro-differential equations. Main features are: non linear or time dependent parameters, implicit form, stiff systems, dynamic change of equations leading to discontinuities on some variables. Thus the mathematical model is built with an equation set F(x,x',t,l) = 0, where t is the independent variable, x' the derivative of x and l an ''algebrized'' logical variable. The NEPTUNIX 2 package is divided into two successive major steps: a non numerical step and a numerical step. The non numerical step must be executed on a series 370 IBM computer or a compatible computer. This step generates a FORTRAN language model picture fitted for the computer carrying out the numerical step. The numerical step consists in building and running a mathematical model simulator. This execution step of NEPTUNIX 2 has been designed in order to be transportable on many computers. The present manual describes minimal features of such host computer used for executing the NEPTUNIX 2 numerical step [fr

Computer Aided Mathematics

DEFF Research Database (Denmark)

Sinclair, Robert

1998-01-01

Course notes of a PhD course held in 1998. The central idea is to introduce students to computational mathematics using object oriented programming in C++.......Course notes of a PhD course held in 1998. The central idea is to introduce students to computational mathematics using object oriented programming in C++....

Discrete mathematics using a computer

CERN Document Server

Hall, Cordelia

2000-01-01

Several areas of mathematics find application throughout computer science, and all students of computer science need a practical working understanding of them. These core subjects are centred on logic, sets, recursion, induction, relations and functions. The material is often called discrete mathematics, to distinguish it from the traditional topics of continuous mathematics such as integration and differential equations. The central theme of this book is the connection between computing and discrete mathematics. This connection is useful in both directions: • Mathematics is used in many branches of computer science, in applica­ tions including program specification, datastructures,design and analysis of algorithms, database systems, hardware design, reasoning about the correctness of implementations, and much more; • Computers can help to make the mathematics easier to learn and use, by making mathematical terms executable, making abstract concepts more concrete, and through the use of software tools su...

Elementary mathematical and computational tools for electrical and computer engineers using Matlab

CERN Document Server

Manassah, Jamal T

2013-01-01

Ideal for use as a short-course textbook and for self-study Elementary Mathematical and Computational Tools for Electrical and Computer Engineers Using MATLAB fills that gap. Accessible after just one semester of calculus, it introduces the many practical analytical and numerical tools that are essential to success both in future studies and in professional life. Sharply focused on the needs of the electrical and computer engineering communities, the text provides a wealth of relevant exercises and design problems. Changes in MATLAB's version 6.0 are included in a special addendum.

Mathematical structures for computer graphics

CERN Document Server

Janke, Steven J

2014-01-01

A comprehensive exploration of the mathematics behind the modeling and rendering of computer graphics scenes Mathematical Structures for Computer Graphics presents an accessible and intuitive approach to the mathematical ideas and techniques necessary for two- and three-dimensional computer graphics. Focusing on the significant mathematical results, the book establishes key algorithms used to build complex graphics scenes. Written for readers with various levels of mathematical background, the book develops a solid foundation for graphics techniques and fills in relevant grap

Computer mathematics for programmers

CERN Document Server

Abney, Darrell H; Sibrel, Donald W

1985-01-01

Computer Mathematics for Programmers presents the Mathematics that is essential to the computer programmer.The book is comprised of 10 chapters. The first chapter introduces several computer number systems. Chapter 2 shows how to perform arithmetic operations using the number systems introduced in Chapter 1. The third chapter covers the way numbers are stored in computers, how the computer performs arithmetic on real numbers and integers, and how round-off errors are generated in computer programs. Chapter 4 details the use of algorithms and flowcharting as problem-solving tools for computer p

The challenge of computer mathematics.

Science.gov (United States)

Barendregt, Henk; Wiedijk, Freek

2005-10-15

Progress in the foundations of mathematics has made it possible to formulate all thinkable mathematical concepts, algorithms and proofs in one language and in an impeccable way. This is not in spite of, but partially based on the famous results of Gödel and Turing. In this way statements are about mathematical objects and algorithms, proofs show the correctness of statements and computations, and computations are dealing with objects and proofs. Interactive computer systems for a full integration of defining, computing and proving are based on this. The human defines concepts, constructs algorithms and provides proofs, while the machine checks that the definitions are well formed and the proofs and computations are correct. Results formalized so far demonstrate the feasibility of this 'computer mathematics'. Also there are very good applications. The challenge is to make the systems more mathematician-friendly, by building libraries and tools. The eventual goal is to help humans to learn, develop, communicate, referee and apply mathematics.

A textbook of computer based numerical and statistical techniques

CERN Document Server

Jaiswal, AK

2009-01-01

About the Book: Application of Numerical Analysis has become an integral part of the life of all the modern engineers and scientists. The contents of this book covers both the introductory topics and the more advanced topics such as partial differential equations. This book is different from many other books in a number of ways. Salient Features: Mathematical derivation of each method is given to build the students understanding of numerical analysis. A variety of solved examples are given. Computer programs for almost all numerical methods discussed have been presented in `C` langu

The 6th International Conference on Computer Science and Computational Mathematics (ICCSCM 2017)

Science.gov (United States)

2017-09-01

The ICCSCM 2017 (The 6th International Conference on Computer Science and Computational Mathematics) has aimed to provide a platform to discuss computer science and mathematics related issues including Algebraic Geometry, Algebraic Topology, Approximation Theory, Calculus of Variations, Category Theory; Homological Algebra, Coding Theory, Combinatorics, Control Theory, Cryptology, Geometry, Difference and Functional Equations, Discrete Mathematics, Dynamical Systems and Ergodic Theory, Field Theory and Polynomials, Fluid Mechanics and Solid Mechanics, Fourier Analysis, Functional Analysis, Functions of a Complex Variable, Fuzzy Mathematics, Game Theory, General Algebraic Systems, Graph Theory, Group Theory and Generalizations, Image Processing, Signal Processing and Tomography, Information Fusion, Integral Equations, Lattices, Algebraic Structures, Linear and Multilinear Algebra; Matrix Theory, Mathematical Biology and Other Natural Sciences, Mathematical Economics and Financial Mathematics, Mathematical Physics, Measure Theory and Integration, Neutrosophic Mathematics, Number Theory, Numerical Analysis, Operations Research, Optimization, Operator Theory, Ordinary and Partial Differential Equations, Potential Theory, Real Functions, Rings and Algebras, Statistical Mechanics, Structure Of Matter, Topological Groups, Wavelets and Wavelet Transforms, 3G/4G Network Evolutions, Ad-Hoc, Mobile, Wireless Networks and Mobile Computing, Agent Computing & Multi-Agents Systems, All topics related Image/Signal Processing, Any topics related Computer Networks, Any topics related ISO SC-27 and SC- 17 standards, Any topics related PKI(Public Key Intrastructures), Artifial Intelligences(A.I.) & Pattern/Image Recognitions, Authentication/Authorization Issues, Biometric authentication and algorithms, CDMA/GSM Communication Protocols, Combinatorics, Graph Theory, and Analysis of Algorithms, Cryptography and Foundation of Computer Security, Data Base(D.B.) Management & Information

Integrating spatial and numerical structure in mathematical patterning

Science.gov (United States)

Ni’mah, K.; Purwanto; Irawan, E. B.; Hidayanto, E.

2018-03-01

This paper reports a study monitoring the integrating spatial and numerical structure in mathematical patterning skills of 30 students grade 7th of junior high school. The purpose of this research is to clarify the processes by which learners construct new knowledge in mathematical patterning. Findings indicate that: (1) students are unable to organize the structure of spatial and numerical, (2) students were only able to organize the spatial structure, but the numerical structure is still incorrect, (3) students were only able to organize numerical structure, but its spatial structure is still incorrect, (4) students were able to organize both of the spatial and numerical structure.

The unique and shared contributions of arithmetic operation understanding and numerical magnitude representation to children's mathematics achievement.

Science.gov (United States)

Wong, Terry Tin-Yau

2017-12-01

The current study examined the unique and shared contributions of arithmetic operation understanding and numerical magnitude representation to children's mathematics achievement. A sample of 124 fourth graders was tested on their arithmetic operation understanding (as reflected by their understanding of arithmetic principles and the knowledge about the application of arithmetic operations) and their precision of rational number magnitude representation. They were also tested on their mathematics achievement and arithmetic computation performance as well as the potential confounding factors. The findings suggested that both arithmetic operation understanding and numerical magnitude representation uniquely predicted children's mathematics achievement. The findings highlight the significance of arithmetic operation understanding in mathematics learning. Copyright © 2017 Elsevier Inc. All rights reserved.

Mathematics and Computation in Music

DEFF Research Database (Denmark)

The 5th Biennial International Conference for Mathematics and Computation in Music (MCM 2015) took place June 22–25, 2015, at Queen Mary University of London, UK, co-hosted by the School of Electronic Engineering and Computer Science (Centre for Digital Music) and the School of Mathematical...... Sciences. As the flagship conference of the Society for Mathematics and Computation in Music (SMCM), MCM 2015 provided a dedicated platform for the communication and exchange of ideas among researchers in mathematics, informatics, music theory, composition, musicology, and related disciplines. It brought...... together researchers from around the world who combine mathematics or computation with music theory, music analysis, composition, and performance. This year’s program – full details at http://mcm2015.qmul.ac.uk – featured a number of distinguished keynote speakers, including Andrée Ehresmann (who spoke...

Numerical analysis

CERN Document Server

Scott, L Ridgway

2011-01-01

Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and self-contained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software, including complete details that are missing from most textbooks. Using an inquiry-based learning approach, Numerical Analysis is written in a narrative style, provides historical background, and includes many of the proofs and technical details in exercises. Students will be able to go beyond an elementary understanding of numerical simulation and develop deep insights into the foundations of the subject. They will no longer have to accept the mathematical gaps that ex...

Analytical and empirical mathematics with computers

International Nuclear Information System (INIS)

Wolfram, S.

1986-01-01

In this presentation, some of the practical methodological and theoretical implications of computation for the mathematical sciences are discussed. Computers are becoming an increasingly significant tool for research in the mathematical sciences. This paper discusses some of the fundamental ways in which computers have and can be used to do mathematics

Advances in Reactor physics, mathematics and computation. Volume 3

Energy Technology Data Exchange (ETDEWEB)

1987-01-01

These proceedings of the international topical meeting on advances in reactor physics, mathematics and computation, volume 3, are divided into sessions bearing on: - poster sessions on benchmark and codes: 35 conferences - review of status of assembly spectrum codes: 9 conferences - Numerical methods in fluid mechanics and thermal hydraulics: 16 conferences - stochastic transport and methods: 7 conferences.

Mathematics and Computer Science | Argonne National Laboratory

Science.gov (United States)

Extreme Computing Data-Intensive Science Applied Mathematics Science & Engineering Applications Software Extreme Computing Data-Intensive Science Applied Mathematics Science & Engineering Opportunities For Employees Staff Directory Argonne National Laboratory Mathematics and Computer Science Tools

Mathematics and Computer Science: The Interplay

OpenAIRE

Madhavan, Veni CE

2005-01-01

Mathematics has been an important intellectual preoccupation of man for a long time. Computer science as a formal discipline is about seven decades young. However, one thing in common between all users and producers of mathematical thought is the almost involuntary use of computing. In this article, we bring to fore the many close connections and parallels between the two sciences of mathematics and computing. We show that, unlike in the other branches of human inquiry where mathematics is me...

The concept of stability in numerical mathematics

CERN Document Server

Hackbusch, Wolfgang

2014-01-01

In this book, the author compares the meaning of stability in different subfields of numerical mathematics.  Concept of Stability in numerical mathematics opens by examining the stability of finite algorithms. A more precise definition of stability holds for quadrature and interpolation methods, which the following chapters focus on. The discussion then progresses to the numerical treatment of ordinary differential equations (ODEs). While one-step methods for ODEs are always stable, this is not the case for hyperbolic or parabolic differential equations, which are investigated next. The final chapters discuss stability for discretisations of elliptic differential equations and integral equations. In comparison among the subfields we discuss the practical importance of stability and the possible conflict between higher consistency order and stability.  

Physics, Computer Science and Mathematics Division. Annual report, January 1-December 31, 1980

International Nuclear Information System (INIS)

Birge, R.W.

1981-12-01

Research in the physics, computer science, and mathematics division is described for the year 1980. While the division's major effort remains in high energy particle physics, there is a continually growing program in computer science and applied mathematics. Experimental programs are reported in e + e - annihilation, muon and neutrino reactions at FNAL, search for effects of a right-handed gauge boson, limits on neutrino oscillations from muon-decay neutrinos, strong interaction experiments at FNAL, strong interaction experiments at BNL, particle data center, Barrelet moment analysis of πN scattering data, astrophysics and astronomy, earth sciences, and instrument development and engineering for high energy physics. In theoretical physics research, studies included particle physics and accelerator physics. Computer science and mathematics research included analytical and numerical methods, information analysis techniques, advanced computer concepts, and environmental and epidemiological studies

Physics, Computer Science and Mathematics Division. Annual report, January 1-December 31, 1980

Energy Technology Data Exchange (ETDEWEB)

Birge, R.W.

1981-12-01

Research in the physics, computer science, and mathematics division is described for the year 1980. While the division's major effort remains in high energy particle physics, there is a continually growing program in computer science and applied mathematics. Experimental programs are reported in e/sup +/e/sup -/ annihilation, muon and neutrino reactions at FNAL, search for effects of a right-handed gauge boson, limits on neutrino oscillations from muon-decay neutrinos, strong interaction experiments at FNAL, strong interaction experiments at BNL, particle data center, Barrelet moment analysis of ..pi..N scattering data, astrophysics and astronomy, earth sciences, and instrument development and engineering for high energy physics. In theoretical physics research, studies included particle physics and accelerator physics. Computer science and mathematics research included analytical and numerical methods, information analysis techniques, advanced computer concepts, and environmental and epidemiological studies. (GHT)

International Conference on Mathematics and Computing

CERN Document Server

Giri, Debasis; Saxena, P; Srivastava, P

2014-01-01

This book discusses recent developments and contemporary research in mathematics, statistics and their applications in computing. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. The conference has emerged as a powerful forum, offering researchers a venue to discuss, interact and collaborate, and stimulating the advancement of mathematics and its applications in computer science. The book will allow aspiring researchers to update their knowledge of cryptography, algebra, frame theory, optimizations, stochastic processes, compressive sensing, functional analysis, complex variables, etc. Educating future consumers, users, producers, developers and researchers in mathematics and computing is a challenging task and essential to the development of modern society. Hence, mathematics and its applications in computer science are of vital importance to a broad range of communities, including mathematicians and computing p...

Mathematical Modeling and Computational Thinking

Science.gov (United States)

Sanford, John F.; Naidu, Jaideep T.

2017-01-01

The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…

Mathematical and numerical aspects of low mach number flows

Energy Technology Data Exchange (ETDEWEB)

Schochet, St.; Bresch, D.; Grenier, E.; Alazard, T.; Gordner, A.; Sankaran, V.; Massot, M.; Sery, R.; Pebay, P.; Lunch, O.; Mazhorova, O.; Turkel, O.E.; Faille, I.; Danchin, R.; Allain, O.; Birken, P.; Lafitte, O.; Kloczko, T.; Frick, W.; Bui, T.; Dellacherie, S.; Klein, R.; Roe, Ph.; Accary, G.; Braack, M.; Picano, F.; Cadiou, A.; Dinescu, C.; Lesage, A.C.; Wesseling, P.; Heuveline, V.; Jobelin, M.; Weisman, C.; Merkle, C.

2004-07-01

Low Mach number flows represent a significant part of the various flows encountered in geophysics, industry or every day life. Paradoxically, the mathematical analysis of the equations governing these flows is difficult and on the practical side, the research of numerical algorithms valid for all flow speeds is continuing to be a challenge. However, in the last decade, both from the theoretical and the numerical sides, significant progresses were made in the understanding and analysis of the equations governing these flows. This conference intends to provide an up-to-date inventory of recent mathematical and numerical results in the analysis of these flows by bringing together both mathematicians and numericists active in this area. In the framework of the conference, a numerical workshop is organized which proposes to compute several challenging low Mach number flows: liquid flow around non-cavitating and cavitating NACA0015 hydrofoil, natural convection with large temperature differences, free convection, free surface flow, vessel pressurization. This document brings together the descriptions of the test cases of the numerical workshop and the abstracts of the conference papers: A 3D high order finite volume method for the prediction of near-critical fluid flows (G. ACCARY, I. RASPO, P. BONTOUX, B. ZAPPOLI); low Mach number limit of the non-isentropic Navier-Stokes equations (T. ALAZARD); simulation of cavitation rolls past a forward step with a bubble model (O. ALLAIN, N. BLASKA, C. LECA); flux preconditioning methods and fire events (P. BIRKEN, A. MEISTER); an adaptive finite element solver for compressible flows: application to heat-driven cavity benchmarks in 2D and 3D (M. BRAACK); comparison of various implicit, explicit, centered and upwind schemes for the simulation of compressed flows on moving mesh (A. CADIOU, M. BUFFAT, L. Le PENVEN, C. Le RIBAULT); low Mach number limit for viscous compressible flows (R. DANCHIN); some Properties of the low Mach number

The Influence of Pre-University Students' Mathematics Test Anxiety and Numerical Anxiety on Mathematics Achievement

Science.gov (United States)

Seng, Ernest Lim Kok

2015-01-01

This study examines the relationship between mathematics test anxiety and numerical anxiety on students' mathematics achievement. 140 pre-university students who studied at one of the institutes of higher learning were being investigated. Gender issue pertaining to mathematics anxieties was being addressed besides investigating the magnitude of…

Mathematical modelling and numerical simulation of oil pollution problems

CERN Document Server

2015-01-01

Written by outstanding experts in the fields of marine engineering, atmospheric physics and chemistry, fluid dynamics and applied mathematics, the contributions in this book cover a wide range of subjects, from pure mathematics to real-world applications in the oil spill engineering business. Offering a truly interdisciplinary approach, the authors present both mathematical models and state-of-the-art numerical methods for adequately solving the partial differential equations involved, as well as highly practical experiments involving actual cases of ocean oil pollution. It is indispensable that different disciplines of mathematics, like analysis and numerics,  together with physics, biology, fluid dynamics, environmental engineering and marine science, join forces to solve today’s oil pollution problems.   The book will be of great interest to researchers and graduate students in the environmental sciences, mathematics and physics, showing the broad range of techniques needed in order to solve these poll...

Mathematics, Physics and Computer Sciences The computation of ...

African Journals Online (AJOL)

Mathematics, Physics and Computer Sciences The computation of system matrices for biquadraticsquare finite ... Global Journal of Pure and Applied Sciences ... The computation of system matrices for biquadraticsquare finite elements.

Intentional and Automatic Numerical Processing as Predictors of Mathematical Abilities in Primary School Children

Directory of Open Access Journals (Sweden)

Violeta ePina

2015-03-01

Full Text Available Previous studies have suggested that numerical processing relates to mathematical performance, but it seems that such relationship is more evident for intentional than for automatic numerical processing. In the present study we assessed the relationship between the two types of numerical processing and specific mathematical abilities in a sample of 109 children in grades 1 to 6. Participants were tested in an ample range of mathematical tests and also performed both a numerical and a size comparison task. The results showed that numerical processing related to mathematical performance only when inhibitory control was involved in the comparison tasks. Concretely, we found that intentional numerical processing, as indexed by the numerical distance effect in the numerical comparison task, was related to mathematical reasoning skills only when the task-irrelevant dimension (the physical size was incongruent; whereas automatic numerical processing, indexed by the congruency effect in the size comparison task, was related to mathematical calculation skills only when digits were separated by small distance. The observed double dissociation highlights the relevance of both intentional and automatic numerical processing in mathematical skills, but when inhibitory control is also involved.

Computational mathematics models, methods, and analysis with Matlab and MPI

CERN Document Server

White, Robert E

2004-01-01

Computational Mathematics: Models, Methods, and Analysis with MATLAB and MPI explores and illustrates this process. Each section of the first six chapters is motivated by a specific application. The author applies a model, selects a numerical method, implements computer simulations, and assesses the ensuing results. These chapters include an abundance of MATLAB code. By studying the code instead of using it as a "black box, " you take the first step toward more sophisticated numerical modeling. The last four chapters focus on multiprocessing algorithms implemented using message passing interface (MPI). These chapters include Fortran 9x codes that illustrate the basic MPI subroutines and revisit the applications of the previous chapters from a parallel implementation perspective. All of the codes are available for download from www4.ncsu.edu./~white.This book is not just about math, not just about computing, and not just about applications, but about all three--in other words, computational science. Whether us...

Will the digital computer transform classical mathematics?

Science.gov (United States)

Rotman, Brian

2003-08-15

Mathematics and machines have influenced each other for millennia. The advent of the digital computer introduced a powerfully new element that promises to transform the relation between them. This paper outlines the thesis that the effect of the digital computer on mathematics, already widespread, is likely to be radical and far-reaching. To articulate this claim, an abstract model of doing mathematics is introduced based on a triad of actors of which one, the 'agent', corresponds to the function performed by the computer. The model is used to frame two sorts of transformation. The first is pragmatic and involves the alterations and progressive colonization of the content and methods of enquiry of various mathematical fields brought about by digital methods. The second is conceptual and concerns a fundamental antagonism between the infinity enshrined in classical mathematics and physics (continuity, real numbers, asymptotic definitions) and the inherently real and material limit of processes associated with digital computation. An example which lies in the intersection of classical mathematics and computer science, the P=NP problem, is analysed in the light of this latter issue.

Applied Computational Mathematics in Social Sciences

CERN Document Server

Damaceanu, Romulus-Catalin

2010-01-01

Applied Computational Mathematics in Social Sciences adopts a modern scientific approach that combines knowledge from mathematical modeling with various aspects of social science. Special algorithms can be created to simulate an artificial society and a detailed analysis can subsequently be used to project social realities. This Ebook specifically deals with computations using the NetLogo platform, and is intended for researchers interested in advanced human geography and mathematical modeling studies.

Numerical methods of mathematical optimization with Algol and Fortran programs

CERN Document Server

Künzi, Hans P; Zehnder, C A; Rheinboldt, Werner

1971-01-01

Numerical Methods of Mathematical Optimization: With ALGOL and FORTRAN Programs reviews the theory and the practical application of the numerical methods of mathematical optimization. An ALGOL and a FORTRAN program was developed for each one of the algorithms described in the theoretical section. This should result in easy access to the application of the different optimization methods.Comprised of four chapters, this volume begins with a discussion on the theory of linear and nonlinear optimization, with the main stress on an easily understood, mathematically precise presentation. In addition

Computers as medium for mathematical writing

DEFF Research Database (Denmark)

Misfeldt, Morten

2011-01-01

The production of mathematical formalism on state of the art computers is quite different than by pen and paper.  In this paper I examine the question of how different media influence the writing of mathematical signs. The examination is based on an investigation of professional mathematicians' use...... of various media for their writing. A model for describing mathematical writing through turntakings is proposed. The model is applied to the ways mathematicians use computers for writing, and especially it is used to understand how interaction with the computer system LaTeX is different in the case...

Computer-Based Mathematics Instructions for Engineering Students

Science.gov (United States)

Khan, Mustaq A.; Wall, Curtiss E.

1996-01-01

Almost every engineering course involves mathematics in one form or another. The analytical process of developing mathematical models is very important for engineering students. However, the computational process involved in the solution of some mathematical problems may be very tedious and time consuming. There is a significant amount of mathematical software such as Mathematica, Mathcad, and Maple designed to aid in the solution of these instructional problems. The use of these packages in classroom teaching can greatly enhance understanding, and save time. Integration of computer technology in mathematics classes, without de-emphasizing the traditional analytical aspects of teaching, has proven very successful and is becoming almost essential. Sample computer laboratory modules are developed for presentation in the classroom setting. This is accomplished through the use of overhead projectors linked to graphing calculators and computers. Model problems are carefully selected from different areas.

Proceeding of 1998-workshop on MHD computations. Study on numerical methods related to plasma confinement

International Nuclear Information System (INIS)

Kako, T.; Watanabe, T.

1999-04-01

This is the proceeding of 'Study on Numerical Methods Related to Plasma Confinement' held in National Institute for Fusion Science. In this workshop, theoretical and numerical analyses of possible plasma equilibria with their stability properties are presented. These are also various talks on mathematical as well as numerical analyses related to the computational methods for fluid dynamics and plasma physics. The 14 papers are indexed individually. (J.P.N.)

Proceeding of 1998-workshop on MHD computations. Study on numerical methods related to plasma confinement

Energy Technology Data Exchange (ETDEWEB)

Kako, T.; Watanabe, T. [eds.

1999-04-01

This is the proceeding of 'Study on Numerical Methods Related to Plasma Confinement' held in National Institute for Fusion Science. In this workshop, theoretical and numerical analyses of possible plasma equilibria with their stability properties are presented. These are also various talks on mathematical as well as numerical analyses related to the computational methods for fluid dynamics and plasma physics. The 14 papers are indexed individually. (J.P.N.)

The MATH--Open Source Application for Easier Learning of Numerical Mathematics

Science.gov (United States)

Glaser-Opitz, Henrich; Budajová, Kristina

2016-01-01

The article introduces a software application (MATH) supporting an education of Applied Mathematics, with focus on Numerical Mathematics. The MATH is an easy to use tool supporting various numerical methods calculations with graphical user interface and integrated plotting tool for graphical representation written in Qt with extensive use of Qwt…

Mathematical modeling and numerical simulation of Czochralski Crystal Growth

Energy Technology Data Exchange (ETDEWEB)

Jaervinen, J.; Nieminen, R. [Center for Scientific Computing, Espoo (Finland)

1996-12-31

A detailed mathematical model and numerical simulation tools based on the SUPG Finite Element Method for the Czochralski crystal growth has been developed. In this presentation the mathematical modeling and numerical simulation of the melt flow and the temperature distribution in a rotationally symmetric crystal growth environment is investigated. The temperature distribution and the position of the free boundary between the solid and liquid phases are solved by using the Enthalpy method. Heat inside of the Czochralski furnace is transferred by radiation, conduction and convection. The melt flow is governed by the incompressible Navier-Stokes equations coupled with the enthalpy equation. The melt flow is numerically demonstrated and the temperature distribution in the whole Czochralski furnace. (author)

Mathematical modeling and numerical simulation of Czochralski Crystal Growth

Energy Technology Data Exchange (ETDEWEB)

Jaervinen, J; Nieminen, R [Center for Scientific Computing, Espoo (Finland)

1997-12-31

A detailed mathematical model and numerical simulation tools based on the SUPG Finite Element Method for the Czochralski crystal growth has been developed. In this presentation the mathematical modeling and numerical simulation of the melt flow and the temperature distribution in a rotationally symmetric crystal growth environment is investigated. The temperature distribution and the position of the free boundary between the solid and liquid phases are solved by using the Enthalpy method. Heat inside of the Czochralski furnace is transferred by radiation, conduction and convection. The melt flow is governed by the incompressible Navier-Stokes equations coupled with the enthalpy equation. The melt flow is numerically demonstrated and the temperature distribution in the whole Czochralski furnace. (author)

Mathematical and numerical models for eddy currents and magnetostatics with selected applications

CERN Document Server

Rappaz, Jacques

2013-01-01

This monograph addresses fundamental aspects of mathematical modeling and numerical solution methods of electromagnetic problems involving low frequencies, i.e. magnetostatic and eddy current problems which are rarely presented in the applied mathematics literature. In the first part, the authors introduce the mathematical models in a realistic context in view of their use for industrial applications. Several geometric configurations of electric conductors leading to different mathematical models are carefully derived and analyzed, and numerical methods for the solution of the obtained problem

International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics

CERN Document Server

DEVELOPMENTS IN RELIABLE COMPUTING

1999-01-01

The SCAN conference, the International Symposium on Scientific Com­ puting, Computer Arithmetic and Validated Numerics, takes place bian­ nually under the joint auspices of GAMM (Gesellschaft fiir Angewandte Mathematik und Mechanik) and IMACS (International Association for Mathematics and Computers in Simulation). SCAN-98 attracted more than 100 participants from 21 countries all over the world. During the four days from September 22 to 25, nine highlighted, plenary lectures and over 70 contributed talks were given. These figures indicate a large participation, which was partly caused by the attraction of the organizing country, Hungary, but also the effec­ tive support system have contributed to the success. The conference was substantially supported by the Hungarian Research Fund OTKA, GAMM, the National Technology Development Board OMFB and by the J6zsef Attila University. Due to this funding, it was possible to subsidize the participation of over 20 scientists, mainly from Eastern European countries. I...

Learning SciPy for numerical and scientific computing

CERN Document Server

Silva

2013-01-01

A step-by-step practical tutorial with plenty of examples on research-based problems from various areas of science, that prove how simple, yet effective, it is to provide solutions based on SciPy. This book is targeted at anyone with basic knowledge of Python, a somewhat advanced command of mathematics/physics, and an interest in engineering or scientific applications---this is broadly what we refer to as scientific computing.This book will be of critical importance to programmers and scientists who have basic Python knowledge and would like to be able to do scientific and numerical computatio

Representations of Numerical and Non-Numerical Magnitude Both Contribute to Mathematical Competence in Children

Science.gov (United States)

Lourenco, Stella F.; Bonny, Justin W.

2017-01-01

A growing body of evidence suggests that non-symbolic representations of number, which humans share with nonhuman animals, are functionally related to uniquely human mathematical thought. Other research suggesting that numerical and non-numerical magnitudes not only share analog format but also form part of a general magnitude system raises…

The measurement of enhancement in mathematical abilities as a result of joint cognitive trainings in numerical and visual- spatial skills: A preliminary study

International Nuclear Information System (INIS)

Agus, M; Mascia, M L; Fastame, M C; Melis, V; Pilloni, M C; Penna, M P

2015-01-01

A body of literature shows the significant role of visual-spatial skills played in the improvement of mathematical skills in the primary school. The main goal of the current study was to investigate the impact of a combined visuo-spatial and mathematical training on the improvement of mathematical skills in 146 second graders of several schools located in Italy. Participants were presented single pencil-and-paper visuo-spatial or mathematical trainings, computerised version of the above mentioned treatments, as well as a combined version of computer-assisted and pencil-and-paper visuo-spatial and mathematical trainings, respectively. Experimental groups were presented with training for 3 months, once a week. All children were treated collectively both in computer-assisted or pencil-and-paper modalities. At pre and post-test all our participants were presented with a battery of objective tests assessing numerical and visuo-spatial abilities. Our results suggest the positive effect of different types of training for the empowerment of visuo-spatial and numerical abilities. Specifically, the combination of computerised and pencil-and-paper versions of visuo-spatial and mathematical trainings are more effective than the single execution of the software or of the pencil-and-paper treatment

The measurement of enhancement in mathematical abilities as a result of joint cognitive trainings in numerical and visual- spatial skills: A preliminary study

Science.gov (United States)

Agus, M.; Mascia, M. L.; Fastame, M. C.; Melis, V.; Pilloni, M. C.; Penna, M. P.

2015-02-01

A body of literature shows the significant role of visual-spatial skills played in the improvement of mathematical skills in the primary school. The main goal of the current study was to investigate the impact of a combined visuo-spatial and mathematical training on the improvement of mathematical skills in 146 second graders of several schools located in Italy. Participants were presented single pencil-and-paper visuo-spatial or mathematical trainings, computerised version of the above mentioned treatments, as well as a combined version of computer-assisted and pencil-and-paper visuo-spatial and mathematical trainings, respectively. Experimental groups were presented with training for 3 months, once a week. All children were treated collectively both in computer-assisted or pencil-and-paper modalities. At pre and post-test all our participants were presented with a battery of objective tests assessing numerical and visuo-spatial abilities. Our results suggest the positive effect of different types of training for the empowerment of visuo-spatial and numerical abilities. Specifically, the combination of computerised and pencil-and-paper versions of visuo-spatial and mathematical trainings are more effective than the single execution of the software or of the pencil-and-paper treatment.

Numerical capacities as domain-specific predictors beyond early mathematics learning: a longitudinal study.

Science.gov (United States)

Reigosa-Crespo, Vivian; González-Alemañy, Eduardo; León, Teresa; Torres, Rosario; Mosquera, Raysil; Valdés-Sosa, Mitchell

2013-01-01

The first aim of the present study was to investigate whether numerical effects (Numerical Distance Effect, Counting Effect and Subitizing Effect) are domain-specific predictors of mathematics development at the end of elementary school by exploring whether they explain additional variance of later mathematics fluency after controlling for the effects of general cognitive skills, focused on nonnumerical aspects. The second aim was to address the same issues but applied to achievement in mathematics curriculum that requires solutions to fluency in calculation. These analyses assess whether the relationship found for fluency are generalized to mathematics content beyond fluency in calculation. As a third aim, the domain specificity of the numerical effects was examined by analyzing whether they contribute to the development of reading skills, such as decoding fluency and reading comprehension, after controlling for general cognitive skills and phonological processing. Basic numerical capacities were evaluated in children of 3(rd) and 4(th) grades (n=49). Mathematics and reading achievements were assessed in these children one year later. Results showed that the size of the Subitizing Effect was a significant domain-specific predictor of fluency in calculation and also in curricular mathematics achievement, but not in reading skills, assessed at the end of elementary school. Furthermore, the size of the Counting Effect also predicted fluency in calculation, although this association only approached significance. These findings contrast with proposals that the core numerical competencies measured by enumeration will bear little relationship to mathematics achievement. We conclude that basic numerical capacities constitute domain-specific predictors and that they are not exclusively "start-up" tools for the acquisition of Mathematics; but they continue modulating this learning at the end of elementary school.

2nd International Conference on Mathematics and Computing

CERN Document Server

Chowdhury, Dipanwita; Giri, Debasis

2015-01-01

This book discusses recent developments and contemporary research in mathematics, statistics and their applications in computing. All contributing authors are eminent academicians, scientists, researchers and scholars in their respective fields, hailing from around the world. This is the second conference on mathematics and computing organized at Haldia Institute of Technology, India. The conference has emerged as a powerful forum, offering researchers a venue to discuss, interact and collaborate, and stimulating the advancement of mathematics and its applications in computer science. The book will allow aspiring researchers to update their knowledge of cryptography, algebra, frame theory, optimizations, stochastic processes, compressive sensing, functional analysis, complex variables, etc. Educating future consumers, users, producers, developers and researchers in mathematics and computing is a challenging task and essential to the development of modern society. Hence, mathematics and its applications in com...

Mathematical and numerical analysis of PN models for photons transport problems

International Nuclear Information System (INIS)

Valentin, Xavier

2015-01-01

Computational costs for direct numerical simulations of photon transport problems are very high in terms of CPU time and memory. One way to tackle this issue is to develop reduced models that a cheaper to solve numerically. There exists number of these models: moments models, discrete ordinates models (S N ), diffusion-like models... In this thesis, we focus on P N models in which the transport operator is approached by mean of a truncated development on the spherical harmonics basis. These models are arbitrary accurate in the angular dimension and are rotationally invariants (in multiple space dimensions). The latter point is fundamental when one wants to simulate inertial confinement fusion (ICF) experiments where the spherical symmetry plays an important part in the accuracy of the numerical solutions. We study the mathematical structure of the PN models and construct a new numerical method in the special case of a one dimensional space dimension with spherical symmetry photon transport problems. We first focus on a linear transport problem in the vacuum. Even in this simple case, it appears in the P N equations geometrical source terms that are stiff in the neighborhood of r = 0 and thus hard to discretize. Existing numerical methods are not satisfactory for multiple reasons: (1) inaccuracy in the neighborhood of r = 0 ('flux-dip'), (2) do not capture steady states (well-balanced scheme), (3) no stability proof. Following recent works, we develop a new well-balanced scheme for which we show the L 2 stability. We then extend the scheme for photon transport problems within a no moving media, the linear Boltzmann equation, and interest ourselves on its behavior in the diffusion limit (asymptotic-preserving property). In a second part, we consider radiation hydrodynamics problems. Since modelization of these problems is still under discussion in the literature, we compare a set of existing models by mean of mathematical analysis and establish a hierarchy

Numerical Magnitude Representation in Children With Mathematical Difficulties With or Without Reading Difficulties.

Science.gov (United States)

Tobia, Valentina; Fasola, Anna; Lupieri, Alice; Marzocchi, Gian Marco

2016-01-01

This study aimed to explore the spatial numerical association of response codes (SNARC), the flanker, and the numerical distance effects in children with mathematical difficulties. From a sample of 720 third, fourth, and fifth graders, 60 children were selected and divided into the following three groups: typically developing children (TD; n = 29), children with mathematical difficulties only (MD only; n = 21), and children with mathematical and reading difficulties (MD+RD; n = 10). Children were tested with a numerical Eriksen task that was built to assess SNARC, numerical distance, and flanker (first and second order congruency) effects. Children with MD only showed stronger SNARC and second order congruency effects than did TD children, whereas the numerical distance effects were similar across the three groups. Finally, the first order congruency effect was associated with reading difficulties. These results showed that children with mathematical difficulties with or without reading difficulties were globally more impaired when spatial incompatibilities were presented. © Hammill Institute on Disabilities 2014.

Numerical Capacities as Domain-Specific Predictors beyond Early Mathematics Learning: A Longitudinal Study

Science.gov (United States)

Reigosa-Crespo, Vivian; González-Alemañy, Eduardo; León, Teresa; Torres, Rosario; Mosquera, Raysil; Valdés-Sosa, Mitchell

2013-01-01

The first aim of the present study was to investigate whether numerical effects (Numerical Distance Effect, Counting Effect and Subitizing Effect) are domain-specific predictors of mathematics development at the end of elementary school by exploring whether they explain additional variance of later mathematics fluency after controlling for the effects of general cognitive skills, focused on nonnumerical aspects. The second aim was to address the same issues but applied to achievement in mathematics curriculum that requires solutions to fluency in calculation. These analyses assess whether the relationship found for fluency are generalized to mathematics content beyond fluency in calculation. As a third aim, the domain specificity of the numerical effects was examined by analyzing whether they contribute to the development of reading skills, such as decoding fluency and reading comprehension, after controlling for general cognitive skills and phonological processing. Basic numerical capacities were evaluated in children of 3rd and 4th grades (n=49). Mathematics and reading achievements were assessed in these children one year later. Results showed that the size of the Subitizing Effect was a significant domain-specific predictor of fluency in calculation and also in curricular mathematics achievement, but not in reading skills, assessed at the end of elementary school. Furthermore, the size of the Counting Effect also predicted fluency in calculation, although this association only approached significance. These findings contrast with proposals that the core numerical competencies measured by enumeration will bear little relationship to mathematics achievement. We conclude that basic numerical capacities constitute domain-specific predictors and that they are not exclusively “start-up” tools for the acquisition of Mathematics; but they continue modulating this learning at the end of elementary school. PMID:24255710

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...

Review of The SIAM 100-Digit Challenge: A Study in High-Accuracy Numerical Computing

International Nuclear Information System (INIS)

Bailey, David

2005-01-01

In the January 2002 edition of SIAM News, Nick Trefethen announced the '$100, 100-Digit Challenge'. In this note he presented ten easy-to-state but hard-to-solve problems of numerical analysis, and challenged readers to find each answer to ten-digit accuracy. Trefethen closed with the enticing comment: 'Hint: They're hard. If anyone gets 50 digits in total, I will be impressed.' This challenge obviously struck a chord in hundreds of numerical mathematicians worldwide, as 94 teams from 25 nations later submitted entries. Many of these submissions exceeded the target of 50 correct digits; in fact, 20 teams achieved a perfect score of 100 correct digits. Trefethen had offered $100 for the best submission. Given the overwhelming response, a generous donor (William Browning, founder of Applied Mathematics, Inc.) provided additional funds to provide a $100 award to each of the 20 winning teams. Soon after the results were out, four participants, each from a winning team, got together and agreed to write a book about the problems and their solutions. The team is truly international: Bornemann is from Germany, Laurie is from South Africa, Wagon is from the USA, and Waldvogel is from Switzerland. This book provides some mathematical background for each problem, and then shows in detail how each of them can be solved. In fact, multiple solution techniques are mentioned in each case. The book describes how to extend these solutions to much larger problems and much higher numeric precision (hundreds or thousands of digit accuracy). The authors also show how to compute error bounds for the results, so that one can say with confidence that one's results are accurate to the level stated. Numerous numerical software tools are demonstrated in the process, including the commercial products Mathematica, Maple and Matlab. Computer programs that perform many of the algorithms mentioned in the book are provided, both in an appendix to the book and on a website. In the process, the

Proceeding of 1999-workshop on MHD computations 'study on numerical methods related to plasma confinement'

International Nuclear Information System (INIS)

Kako, T.; Watanabe, T.

2000-06-01

This is the proceeding of 'study on numerical methods related to plasma confinement' held in National Institute for Fusion Science. In this workshop, theoretical and numerical analyses of possible plasma equilibria with their stability properties are presented. There are also various lectures on mathematical as well as numerical analyses related to the computational methods for fluid dynamics and plasma physics. Separate abstracts were presented for 13 of the papers in this report. The remaining 6 were considered outside the subject scope of INIS. (J.P.N.)

CDM: Teaching Discrete Mathematics to Computer Science Majors

Science.gov (United States)

Sutner, Klaus

2005-01-01

CDM, for computational discrete mathematics, is a course that attempts to teach a number of topics in discrete mathematics to computer science majors. The course abandons the classical definition-theorem-proof model, and instead relies heavily on computation as a source of motivation and also for experimentation and illustration. The emphasis on…

Mathematical challenges from theoretical/computational chemistry

Energy Technology Data Exchange (ETDEWEB)

NONE

1995-12-31

The committee believes that this report has relevance and potentially valuable suggestions for a wide range of readers. Target audiences include: graduate departments in the mathematical and chemical sciences; federal and private agencies that fund research in the mathematical and chemical sciences; selected industrial and government research and development laboratories; developers of software and hardware for computational chemistry; and selected individual researchers. Chapter 2 of this report covers some history of computational chemistry for the nonspecialist, while Chapter 3 illustrates the fruits of some past successful cross-fertilization between mathematical scientists and computational/theoretical chemists. In Chapter 4 the committee has assembled a representative, but not exhaustive, survey of research opportunities. Most of these are descriptions of important open problems in computational/theoretical chemistry that could gain much from the efforts of innovative mathematical scientists, written so as to be accessible introductions to the nonspecialist. Chapter 5 is an assessment, necessarily subjective, of cultural differences that must be overcome if collaborative work is to be encouraged between the mathematical and the chemical communities. Finally, the report ends with a brief list of conclusions and recommendations that, if followed, could promote accelerated progress at this interface. Recognizing that bothersome language issues can inhibit prospects for collaborative research at the interface between distinctive disciplines, the committee has attempted throughout to maintain an accessible style, in part by using illustrative boxes, and has included at the end of the report a glossary of technical terms that may be familiar to only a subset of the target audiences listed above.

Computational and mathematical methods in brain atlasing.

Science.gov (United States)

Nowinski, Wieslaw L

2017-12-01

Brain atlases have a wide range of use from education to research to clinical applications. Mathematical methods as well as computational methods and tools play a major role in the process of brain atlas building and developing atlas-based applications. Computational methods and tools cover three areas: dedicated editors for brain model creation, brain navigators supporting multiple platforms, and atlas-assisted specific applications. Mathematical methods in atlas building and developing atlas-aided applications deal with problems in image segmentation, geometric body modelling, physical modelling, atlas-to-scan registration, visualisation, interaction and virtual reality. Here I overview computational and mathematical methods in atlas building and developing atlas-assisted applications, and share my contribution to and experience in this field.

Applied Mathematics, Modelling and Computational Science

CERN Document Server

Kotsireas, Ilias; Makarov, Roman; Melnik, Roderick; Shodiev, Hasan

2015-01-01

The Applied Mathematics, Modelling, and Computational Science (AMMCS) conference aims to promote interdisciplinary research and collaboration. The contributions in this volume cover the latest research in mathematical and computational sciences, modeling, and simulation as well as their applications in natural and social sciences, engineering and technology, industry, and finance. The 2013 conference, the second in a series of AMMCS meetings, was held August 26–30 and organized in cooperation with AIMS and SIAM, with support from the Fields Institute in Toronto, and Wilfrid Laurier University. There were many young scientists at AMMCS-2013, both as presenters and as organizers. This proceedings contains refereed papers contributed by the participants of the AMMCS-2013 after the conference. This volume is suitable for researchers and graduate students, mathematicians and engineers, industrialists, and anyone who would like to delve into the interdisciplinary research of applied and computational mathematics ...

Computing the Alexander Polynomial Numerically

DEFF Research Database (Denmark)

Hansen, Mikael Sonne

2006-01-01

Explains how to construct the Alexander Matrix and how this can be used to compute the Alexander polynomial numerically.......Explains how to construct the Alexander Matrix and how this can be used to compute the Alexander polynomial numerically....

Mathematical and theoretical neuroscience cell, network and data analysis

CERN Document Server

Nieus, Thierry

2017-01-01

This volume gathers contributions from theoretical, experimental and computational researchers who are working on various topics in theoretical/computational/mathematical neuroscience. The focus is on mathematical modeling, analytical and numerical topics, and statistical analysis in neuroscience with applications. The following subjects are considered: mathematical modelling in Neuroscience, analytical  and numerical topics;  statistical analysis in Neuroscience; Neural Networks; Theoretical Neuroscience. The book is addressed to researchers involved in mathematical models applied to neuroscience.

Numerical solution of ordinary differential equations

CERN Document Server

Fox, L

1987-01-01

Nearly 20 years ago we produced a treatise (of about the same length as this book) entitled Computing methods for scientists and engineers. It was stated that most computation is performed by workers whose mathematical training stopped somewhere short of the 'professional' level, and that some books are therefore needed which use quite simple mathematics but which nevertheless communicate the essence of the 'numerical sense' which is exhibited by the real computing experts and which is surely needed, at least to some extent, by all who use modern computers and modern numerical software. In that book we treated, at no great length, a variety of computational problems in which the material on ordinary differential equations occupied about 50 pages. At that time it was quite common to find books on numerical analysis, with a little on each topic ofthat field, whereas today we are more likely to see similarly-sized books on each major topic: for example on numerical linear algebra, numerical approximation, numeri...

Computational benchmark problems: a review of recent work within the American Nuclear Society Mathematics and Computation Division

International Nuclear Information System (INIS)

Dodds, H.L. Jr.

1977-01-01

An overview of the recent accomplishments of the Computational Benchmark Problems Committee of the American Nuclear Society Mathematics and Computation Division is presented. Solutions of computational benchmark problems in the following eight areas are presented and discussed: (a) high-temperature gas-cooled reactor neutronics, (b) pressurized water reactor (PWR) thermal hydraulics, (c) PWR neutronics, (d) neutron transport in a cylindrical ''black'' rod, (e) neutron transport in a boiling water reactor (BWR) rod bundle, (f) BWR transient neutronics with thermal feedback, (g) neutron depletion in a heavy water reactor, and (h) heavy water reactor transient neutronics. It is concluded that these problems and solutions are of considerable value to the nuclear industry because they have been and will continue to be useful in the development, evaluation, and verification of computer codes and numerical-solution methods

Experiences of Student Mathematics-Teachers in Computer-Based Mathematics Learning Environment

Science.gov (United States)

Karatas, Ilhan

2011-01-01

Computer technology in mathematics education enabled the students find many opportunities for investigating mathematical relationships, hypothesizing, and making generalizations. These opportunities were provided to pre-service teachers through a faculty course. At the end of the course, the teachers were assigned project tasks involving…

The Effects of Modern Mathematics Computer Games on Mathematics Achievement and Class Motivation

Science.gov (United States)

Kebritchi, Mansureh; Hirumi, Atsusi; Bai, Haiyan

2010-01-01

This study examined the effects of a computer game on students' mathematics achievement and motivation, and the role of prior mathematics knowledge, computer skill, and English language skill on their achievement and motivation as they played the game. A total of 193 students and 10 teachers participated in this study. The teachers were randomly…

Approximate numerical abilities and mathematics: Insight from correlational and experimental training studies.

Science.gov (United States)

Hyde, D C; Berteletti, I; Mou, Y

2016-01-01

Humans have the ability to nonverbally represent the approximate numerosity of sets of objects. The cognitive system that supports this ability, often referred to as the approximate number system (ANS), is present in early infancy and continues to develop in precision over the life span. It has been proposed that the ANS forms a foundation for uniquely human symbolic number and mathematics learning. Recent work has brought two types of evidence to bear on the relationship between the ANS and human mathematics: correlational studies showing individual differences in approximate numerical abilities correlate with individual differences in mathematics achievement and experimental studies showing enhancing effects of nonsymbolic approximate numerical training on exact, symbolic mathematical abilities. From this work, at least two accounts can be derived from these empirical data. It may be the case that the ANS and mathematics are related because the cognitive and brain processes responsible for representing numerical quantity in each format overlap, the Representational Overlap Hypothesis, or because of commonalities in the cognitive operations involved in mentally manipulating the representations of each format, the Operational Overlap hypothesis. The two hypotheses make distinct predictions for future work to test. © 2016 Elsevier B.V. All rights reserved.

Programming for computations Python : a gentle introduction to numerical simulations with Python

CERN Document Server

Linge, Svein

2016-01-01

This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.

Students, Computers and Mathematics the Golden Trilogy in the Teaching-Learning Process

Science.gov (United States)

García-Santillán, Arturo; Escalera-Chávez, Milka Elena; López-Morales, José Satsumi; Córdova Rangel, Arturo

2014-01-01

In this paper we examine the relationships between students' attitudes towards mathematics and technology, therefore, we take a Galbraith and Hines' scale (1998, 2000) about mathematics confidence, computer confidence, computer and mathematics interaction, mathematics motivation, computer motivation, and mathematics engagement. 164 questionnaires…

MATHEMATICS AND COMPUTERS IN SPORT - OVERVIEW

Directory of Open Access Journals (Sweden)

John Hammond

2006-12-01

Full Text Available MATHEMATICS AND COMPUTERS IN SPORT - OVERVIEW The first 17 papers in this (December issue of the Journal of Sports Science and Medicine are selected papers from the Eighth Australasian Conference on Mathematics and Computers in Sport, held in Queensland in July 2006. Of the first seven conferences, five were held at Bond University in Queensland, one at the University of Technology in Sydney during the year of the Sydney Olympics, and the last one was in New Zealand at Massey University. The emerging discipline of mathematics and computers in sport has developed under the auspices of the Australian and New Zealand Industrial and Applied Mathematics (ANZIAM Division of the Australian Mathematics Society through an interest group known as MathSport, bringing together sports scientists who are interested inmathematical and statistical modelling in sport, the use of computers in sport, the application of these to improve coaching and individual performance, and teaching that combines mathematics, computers and sport. This eighth conference in the series returned to Queensland but not at Bond University, because campus accommodation for conference participants was no longer available at that venue. Instead delegates gathered at the Greenmount Beach Resort, which has been used during the past decade for a number of Applied Mathematics Conferences. There were 33 papers presented during the 3 days, across topics that covered a variety of individual and team sports. Participants attended from the United Kingdom, France, Germany, India, New Zealand and Australia. These participants were drawn from those working in mainstream mathematics, statistics, computers science, sports science support, coaching and education.Professor Steve Clarke and Emeritus Professor Neville de Mestre have been to all eight conferences and this year delivered papers on Australian rules football and golf putting respectively. Tony Lewis, of the Duckworth-Lewis formula for

Equity and Computers for Mathematics Learning: Access and Attitudes

Science.gov (United States)

Forgasz, Helen J.

2004-01-01

Equity and computer use for secondary mathematics learning was the focus of a three year study. In 2003, a survey was administered to a large sample of grade 7-10 students. Some of the survey items were aimed at determining home access to and ownership of computers, and students' attitudes to mathematics, computers, and computer use for…

Symbolic mathematical computing: orbital dynamics and application to accelerators

International Nuclear Information System (INIS)

Fateman, R.

1986-01-01

Computer-assisted symbolic mathematical computation has become increasingly useful in applied mathematics. A brief introduction to such capabilitites and some examples related to orbital dynamics and accelerator physics are presented. (author)

Numerical magnitude processing in abacus-trained children with superior mathematical ability: an EEG study.

Science.gov (United States)

Huang, Jian; Du, Feng-lei; Yao, Yuan; Wan, Qun; Wang, Xiao-Song; Chen, Fei-Yan

2015-08-01

Distance effect has been regarded as the best established marker of basic numerical magnitude processes and is related to individual mathematical abilities. A larger behavioral distance effect is suggested to be concomitant with lower mathematical achievement in children. However, the relationship between distance effect and superior mathematical abilities is unclear. One could get superior mathematical abilities by acquiring the skill of abacus-based mental calculation (AMC), which can be used to solve calculation problems with exceptional speed and high accuracy. In the current study, we explore the relationship between distance effect and superior mathematical abilities by examining whether and how the AMC training modifies numerical magnitude processing. Thus, mathematical competencies were tested in 18 abacus-trained children (who accepted the AMC training) and 18 non-trained children. Electroencephalography (EEG) waveforms were recorded when these children executed numerical comparison tasks in both Arabic digit and dot array forms. We found that: (a) the abacus-trained group had superior mathematical abilities than their peers; (b) distance effects were found both in behavioral results and on EEG waveforms; (c) the distance effect size of the average amplitude on the late negative-going component was different between groups in the digit task, with a larger effect size for abacus-trained children; (d) both the behavioral and EEG distance effects were modulated by the notation. These results revealed that the neural substrates of magnitude processing were modified by AMC training, and suggested that the mechanism of the representation of numerical magnitude for children with superior mathematical abilities was different from their peers. In addition, the results provide evidence for a view of non-abstract numerical representation.

Courant Mathematics and Computing Laboratory, New York University. Progress report No. 54, October 1, 1977--September 30, 1978

International Nuclear Information System (INIS)

1978-01-01

Work is reported in the following areas: applied mathematics (computational fluid dynamics, numerical analysis), computational magnetohydrodynamics, computational physics and chemistry (materials science, quantum many-body systems, chemistry), computer science (CIMS PL/I, Version II; distributed systems and resource sharing, computer design - PUMA; SETL; algorithmic combinatorics), systems programing and user services. The relationship to other projects, list of seminars, and list of publications are also included. The research descriptions are administrative in nature, usually less than a page in length

Fourth SIAM conference on mathematical and computational issues in the geosciences: Final program and abstracts

Energy Technology Data Exchange (ETDEWEB)

NONE

1997-12-31

The conference focused on computational and modeling issues in the geosciences. Of the geosciences, problems associated with phenomena occurring in the earth`s subsurface were best represented. Topics in this area included petroleum recovery, ground water contamination and remediation, seismic imaging, parameter estimation, upscaling, geostatistical heterogeneity, reservoir and aquifer characterization, optimal well placement and pumping strategies, and geochemistry. Additional sessions were devoted to the atmosphere, surface water and oceans. The central mathematical themes included computational algorithms and numerical analysis, parallel computing, mathematical analysis of partial differential equations, statistical and stochastic methods, optimization, inversion, homogenization and renormalization. The problem areas discussed at this conference are of considerable national importance, with the increasing importance of environmental issues, global change, remediation of waste sites, declining domestic energy sources and an increasing reliance on producing the most out of established oil reservoirs.

Computer-Game-Based Tutoring of Mathematics

Science.gov (United States)

Ke, Fengfeng

2013-01-01

This in-situ, descriptive case study examined the potential of implementing computer mathematics games as an anchor for tutoring of mathematics. Data were collected from middle school students at a rural pueblo school and an urban Hispanic-serving school, through in-field observation, content analysis of game-based tutoring-learning interactions,…

Secondary School Mathematics Teachers’ and Students’ Views on Computer Assisted Mathematics Instruction in Turkey: Mathematica Example

OpenAIRE

Mehmet Alper Ardıç; Tevfik İşleyen

2017-01-01

This study aimed at determining the secondary school mathematics teachers’ and students’ views on computer-assisted mathematics instruction (CAMI) conducted via Mathematica. Accordingly, three mathematics teachers in Adıyaman and nine 10th-grade students participated in the research. Firstly, the researchers trained the mathematics teachers in the Mathematica program, a computer algebra system (CAS) and CAMI. Then, they provided a suitable environment for teachers to practice CAMI with their ...

Handbook of numerical analysis

CERN Document Server

Ciarlet, Philippe G

Mathematical finance is a prolific scientific domain in which there exists a particular characteristic of developing both advanced theories and practical techniques simultaneously. Mathematical Modelling and Numerical Methods in Finance addresses the three most important aspects in the field: mathematical models, computational methods, and applications, and provides a solid overview of major new ideas and results in the three domains. Coverage of all aspects of quantitative finance including models, computational methods and applications Provides an overview of new ideas an

Mathematical, numerical and experimental analysis of the swirling flow at a Kaplan runner outlet

International Nuclear Information System (INIS)

Muntean, S; Ciocan, T; Susan-Resiga, R F; Cervantes, M; Nilsson, H

2012-01-01

The paper presents a novel mathematical model for a-priori computation of the swirling flow at Kaplan runners outlet. The model is an extension of the initial version developed by Susan-Resiga et al [1], to include the contributions of non-negligible radial velocity and of the variable rothalpy. Simple analytical expressions are derived for these additional data from three-dimensional numerical simulations of the Kaplan turbine. The final results, i.e. velocity components profiles, are validated against experimental data at two operating points, with the same Kaplan runner blades opening, but variable discharge.

Mathematical, numerical and experimental analysis of the swirling flow at a Kaplan runner outlet

Science.gov (United States)

Muntean, S.; Ciocan, T.; Susan-Resiga, R. F.; Cervantes, M.; Nilsson, H.

2012-11-01

The paper presents a novel mathematical model for a-priori computation of the swirling flow at Kaplan runners outlet. The model is an extension of the initial version developed by Susan-Resiga et al [1], to include the contributions of non-negligible radial velocity and of the variable rothalpy. Simple analytical expressions are derived for these additional data from three-dimensional numerical simulations of the Kaplan turbine. The final results, i.e. velocity components profiles, are validated against experimental data at two operating points, with the same Kaplan runner blades opening, but variable discharge.

Brain stimulation, mathematical, and numerical training: Contribution of core and noncore skills.

Science.gov (United States)

Looi, C Y; Cohen Kadosh, R

2016-01-01

Mathematical abilities that are correlated with various life outcomes vary across individuals. One approach to improve mathematical abilities is by understanding the underlying cognitive functions. Theoretical and experimental evidence suggest that mathematical abilities are subserved by "core" and "noncore" skills. Core skills are commonly regarded as the "innate" capacity to attend to and process numerical information, while noncore skills are those that are important for mathematical cognition, but are not exclusive to the mathematical domain such as executive functions, spatial skills, and attention. In recent years, mathematical training has been combined with the application of noninvasive brain stimulation to further enhance training outcomes. However, the development of more strategic training paradigms is hindered by the lack of understanding on the contributory nature of core and noncore skills and their neural underpinnings. In the current review, we will examine the effects of brain stimulation with focus on transcranial electrical stimulation on core and noncore skills, and its impact on mathematical and numerical training. We will conclude with a discussion on the theoretical and experimental implications of these studies and directions for further research. © 2016 Elsevier B.V. All rights reserved.

Numerical approximation abilities correlate with and predict informal but not formal mathematics abilities.

Science.gov (United States)

Libertus, Melissa E; Feigenson, Lisa; Halberda, Justin

2013-12-01

Previous research has found a relationship between individual differences in children's precision when nonverbally approximating quantities and their school mathematics performance. School mathematics performance emerges from both informal (e.g., counting) and formal (e.g., knowledge of mathematics facts) abilities. It remains unknown whether approximation precision relates to both of these types of mathematics abilities. In the current study, we assessed the precision of numerical approximation in 85 3- to 7-year-old children four times over a span of 2years. In addition, at the final time point, we tested children's informal and formal mathematics abilities using the Test of Early Mathematics Ability (TEMA-3). We found that children's numerical approximation precision correlated with and predicted their informal, but not formal, mathematics abilities when controlling for age and IQ. These results add to our growing understanding of the relationship between an unlearned nonsymbolic system of quantity representation and the system of mathematics reasoning that children come to master through instruction. Copyright © 2013 Elsevier Inc. All rights reserved.

Analytical calculations by computer in physics and mathematics

International Nuclear Information System (INIS)

Gerdt, V.P.; Tarasov, O.V.; Shirokov, D.V.

1978-01-01

The review of present status of analytical calculations by computer is given. Some programming systems for analytical computations are considered. Such systems as SCHOONSCHIP, CLAM, REDUCE-2, SYMBAL, CAMAL, AVTO-ANALITIK which are implemented or will be implemented in JINR, and MACSYMA - one of the most developed systems - are discussed. It is shown on the basis of mathematical operations, realized in these systems, that they are appropriated for different problems of theoretical physics and mathematics, for example, for problems of quantum field theory, celestial mechanics, general relativity and so on. Some problems solved in JINR by programming systems for analytical computations are described. The review is intended for specialists in different fields of theoretical physics and mathematics

Practical scientific computing

CERN Document Server

Muhammad, A

2011-01-01

Scientific computing is about developing mathematical models, numerical methods and computer implementations to study and solve real problems in science, engineering, business and even social sciences. Mathematical modelling requires deep understanding of classical numerical methods. This essential guide provides the reader with sufficient foundations in these areas to venture into more advanced texts. The first section of the book presents numEclipse, an open source tool for numerical computing based on the notion of MATLAB®. numEclipse is implemented as a plug-in for Eclipse, a leading integ

Approximation and Computation

CERN Document Server

Gautschi, Walter; Rassias, Themistocles M

2011-01-01

Approximation theory and numerical analysis are central to the creation of accurate computer simulations and mathematical models. Research in these areas can influence the computational techniques used in a variety of mathematical and computational sciences. This collection of contributed chapters, dedicated to renowned mathematician Gradimir V. Milovanovia, represent the recent work of experts in the fields of approximation theory and numerical analysis. These invited contributions describe new trends in these important areas of research including theoretic developments, new computational alg

Proceedings of the 2013 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering - M and C 2013

International Nuclear Information System (INIS)

2013-01-01

The Mathematics and Computation Division of the American Nuclear (ANS) and the Idaho Section of the ANS hosted the 2013 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M and C 2013). This proceedings contains over 250 full papers with topics ranging from reactor physics; radiation transport; materials science; nuclear fuels; core performance and optimization; reactor systems and safety; fluid dynamics; medical applications; analytical and numerical methods; algorithms for advanced architectures; and validation verification, and uncertainty quantification

Proceedings of the 2013 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering - M and C 2013

Energy Technology Data Exchange (ETDEWEB)

NONE

2013-07-01

The Mathematics and Computation Division of the American Nuclear (ANS) and the Idaho Section of the ANS hosted the 2013 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M and C 2013). This proceedings contains over 250 full papers with topics ranging from reactor physics; radiation transport; materials science; nuclear fuels; core performance and optimization; reactor systems and safety; fluid dynamics; medical applications; analytical and numerical methods; algorithms for advanced architectures; and validation verification, and uncertainty quantification.

Interpolation Environment of Tensor Mathematics at the Corpuscular Stage of Computational Experiments in Hydromechanics

Science.gov (United States)

Bogdanov, Alexander; Degtyarev, Alexander; Khramushin, Vasily; Shichkina, Yulia

2018-02-01

Stages of direct computational experiments in hydromechanics based on tensor mathematics tools are represented by conditionally independent mathematical models for calculations separation in accordance with physical processes. Continual stage of numerical modeling is constructed on a small time interval in a stationary grid space. Here coordination of continuity conditions and energy conservation is carried out. Then, at the subsequent corpuscular stage of the computational experiment, kinematic parameters of mass centers and surface stresses at the boundaries of the grid cells are used in modeling of free unsteady motions of volume cells that are considered as independent particles. These particles can be subject to vortex and discontinuous interactions, when restructuring of free boundaries and internal rheological states has place. Transition from one stage to another is provided by interpolation operations of tensor mathematics. Such interpolation environment formalizes the use of physical laws for mechanics of continuous media modeling, provides control of rheological state and conditions for existence of discontinuous solutions: rigid and free boundaries, vortex layers, their turbulent or empirical generalizations.

Coherent structures in granular crystals from experiment and modelling to computation and mathematical analysis

CERN Document Server

Chong, Christopher

2018-01-01

This book summarizes a number of fundamental developments at the interface of granular crystals and the mathematical and computational analysis of some of their key localized nonlinear wave solutions. The subject presents a blend of the appeal of granular crystals as a prototypical engineering tested for a variety of diverse applications, the novelty in the nonlinear physics of its coherent structures, and the tractability of a series of mathematical and computational techniques to analyse them. While the focus is on principal one-dimensional solutions such as shock waves, traveling waves, and discrete breathers, numerous extensions of the discussed patterns, e.g., in two dimensions, chains with defects, heterogeneous settings, and other recent developments are discussed. The book appeals to researchers in the field, as well as for graduate and advanced undergraduate students. It will be of interest to mathematicians, physicists and engineers alike.

An approach to first principles electronic structure calculation by symbolic-numeric computation

Directory of Open Access Journals (Sweden)

Akihito Kikuchi

2013-04-01

Full Text Available There is a wide variety of electronic structure calculation cooperating with symbolic computation. The main purpose of the latter is to play an auxiliary role (but not without importance to the former. In the field of quantum physics [1-9], researchers sometimes have to handle complicated mathematical expressions, whose derivation seems almost beyond human power. Thus one resorts to the intensive use of computers, namely, symbolic computation [10-16]. Examples of this can be seen in various topics: atomic energy levels, molecular dynamics, molecular energy and spectra, collision and scattering, lattice spin models and so on [16]. How to obtain molecular integrals analytically or how to manipulate complex formulas in many body interactions, is one such problem. In the former, when one uses special atomic basis for a specific purpose, to express the integrals by the combination of already known analytic functions, may sometimes be very difficult. In the latter, one must rearrange a number of creation and annihilation operators in a suitable order and calculate the analytical expectation value. It is usual that a quantitative and massive computation follows a symbolic one; for the convenience of the numerical computation, it is necessary to reduce a complicated analytic expression into a tractable and computable form. This is the main motive for the introduction of the symbolic computation as a forerunner of the numerical one and their collaboration has won considerable successes. The present work should be classified as one such trial. Meanwhile, the use of symbolic computation in the present work is not limited to indirect and auxiliary part to the numerical computation. The present work can be applicable to a direct and quantitative estimation of the electronic structure, skipping conventional computational methods.

Proceeding of 1999-workshop on MHD computations 'study on numerical methods related to plasma confinement'

Energy Technology Data Exchange (ETDEWEB)

Kako, T.; Watanabe, T. [eds.

2000-06-01

This is the proceeding of 'study on numerical methods related to plasma confinement' held in National Institute for Fusion Science. In this workshop, theoretical and numerical analyses of possible plasma equilibria with their stability properties are presented. There are also various lectures on mathematical as well as numerical analyses related to the computational methods for fluid dynamics and plasma physics. Separate abstracts were presented for 13 of the papers in this report. The remaining 6 were considered outside the subject scope of INIS. (J.P.N.)

The Use of Computers in Mathematics Education: A Paradigm Shift from "Computer Assisted Instruction" towards "Student Programming"

Science.gov (United States)

Aydin, Emin

2005-01-01

The purpose of this study is to review the changes that computers have on mathematics itself and on mathematics curriculum. The study aims at investigating different applications of computers in education in general, and mathematics education in particular and their applications on mathematics curriculum and on teaching and learning of…

Numerical linear algebra with applications using Matlab

CERN Document Server

Ford, William

2014-01-01

Designed for those who want to gain a practical knowledge of modern computational techniques for the numerical solution of linear algebra problems, Numerical Linear Algebra with Applications contains all the material necessary for a first year graduate or advanced undergraduate course on numerical linear algebra with numerous applications to engineering and science. With a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions, this book is ideal for solving real-world problems. It provides necessary mathematical background information for

Numerical analysis of bifurcations

International Nuclear Information System (INIS)

Guckenheimer, J.

1996-01-01

This paper is a brief survey of numerical methods for computing bifurcations of generic families of dynamical systems. Emphasis is placed upon algorithms that reflect the structure of the underlying mathematical theory while retaining numerical efficiency. Significant improvements in the computational analysis of dynamical systems are to be expected from more reliance of geometric insight coming from dynamical systems theory. copyright 1996 American Institute of Physics

Mathematics for engineering, technology and computing science

CERN Document Server

Martin, Hedley G

1970-01-01

Mathematics for Engineering, Technology and Computing Science is a text on mathematics for courses in engineering, technology, and computing science. It covers linear algebra, ordinary differential equations, and vector analysis, together with line and multiple integrals. This book consists of eight chapters and begins with a discussion on determinants and linear equations, with emphasis on how the value of a determinant is defined and how it may be obtained. Solution of linear equations and the dependence between linear equations are also considered. The next chapter introduces the reader to

Ferrofluids: Modeling, numerical analysis, and scientific computation

Science.gov (United States)

Tomas, Ignacio

simplified version of this model and the corresponding numerical scheme we prove (in addition to stability) convergence and existence of solutions as by-product . Throughout this dissertation, we will provide numerical experiments, not only to validate mathematical results, but also to help the reader gain a qualitative understanding of the PDE models analyzed in this dissertation (the MNSE, the Rosenweig's model, and the Two-phase model). In addition, we also provide computational experiments to illustrate the potential of these simple models and their ability to capture basic phenomenological features of ferrofluids, such as the Rosensweig instability for the case of the two-phase model. In this respect, we highlight the incisive numerical experiments with the two-phase model illustrating the critical role of the demagnetizing field to reproduce physically realistic behavior of ferrofluids.

Theorema 2.0: Computer-Assisted Natural-Style Mathematics

Directory of Open Access Journals (Sweden)

Bruno Buchberger

2016-01-01

Full Text Available The Theorema project aims at the development of a computer assistant for the working mathematician. Support should be given throughout all phases of mathematical activity, from introducing new mathematical concepts by definitions or axioms, through first (computational experiments, the formulation of theorems, their justification by an exact proof, the application of a theorem as an algorithm, until to the dissemination of the results in form of a mathematical publication, the build up of bigger libraries of certified mathematical content and the like. This ambitious project is exactly along the lines of the QED manifesto issued in 1994 (see e.g. http://www.cs.ru.nl/~freek/qed/qed.html and it was initiated in the mid-1990s by Bruno Buchberger. The Theorema system is a computer implementation of the ideas behind the Theorema project. One focus lies on the natural style of system input (in form of definitions, theorems, algorithms, etc., system output (mainly in form of mathematical proofs and user interaction. Another focus is theory exploration, i.e. the development of large consistent mathematical theories in a formal frame, in contrast to just proving single isolated theorems. When using the Theorema system, a user should not have to follow a certain style of mathematics enforced by the system (e.g. basing all of mathematics on set theory or certain variants of type theory, rather should the system support the user in her preferred flavour of doing math. The new implementation of the system, which we refer to as Theorema 2.0, is open-source and available through GitHub.

Numerical methods in software and analysis

CERN Document Server

Rice, John R

1992-01-01

Numerical Methods, Software, and Analysis, Second Edition introduces science and engineering students to the methods, tools, and ideas of numerical computation. Introductory courses in numerical methods face a fundamental problem-there is too little time to learn too much. This text solves that problem by using high-quality mathematical software. In fact, the objective of the text is to present scientific problem solving using standard mathematical software. This book discusses numerous programs and software packages focusing on the IMSL library (including the PROTRAN system) and ACM Algorithm

Effects of finger counting on numerical development – the opposing views of neurocognition and mathematics education

Directory of Open Access Journals (Sweden)

Korbinian eMoeller

2011-11-01

Full Text Available Usually children learn the basic principles of number and arithmetic by the help of finger-based representations. However, whether the reliance on finger-based representations is only beneficial or whether it may even become detrimental is the subject of an ongoing debate between neuro-cognitive and mathematics education researchers. From the neuro-cognitive perspective finger counting provides multi-sensory input conveying both cardinal and ordinal aspects of numbers. Recent data indicate that children with good finger-based numerical representations show better arithmetic skills and that training finger gnosis enhances mathematical skills. From this neuro-cognitive researchers conclude that elaborate finger-based numerical representations are beneficial for later numerical development.However, mathematics education research recommends fostering mental numerical representations so as to induce children to abandon finger-counting. More precisely mathematics education recommends moving from finger counting to concrete structured representations and then, finally, to mental representations of numbers.Taken together, there is obviously an important debate between the neuro-cognitve and mathematics education research concerning the benefits or detriments of finger-based strategies for numerical development. In the present review, the rationale of both lines of evidence will be presented and discussed.

Secondary School Mathematics Teachers' and Students' Views on Computer Assisted Mathematics Instruction in Turkey: Mathematica Example

Science.gov (United States)

Ardiç, Mehmet Alper; Isleyen, Tevfik

2017-01-01

This study aimed at determining the secondary school mathematics teachers' and students' views on computer-assisted mathematics instruction (CAMI) conducted via Mathematica. Accordingly, three mathematics teachers in Adiyaman and nine 10th-grade students participated in the research. Firstly, the researchers trained the mathematics teachers in the…

Mathematical and numerical study of nonlinear hyperbolic equations: model coupling and nonclassical shocks

International Nuclear Information System (INIS)

Boutin, B.

2009-11-01

This thesis concerns the mathematical and numerical study of nonlinear hyperbolic partial differential equations. A first part deals with an emergent problematic: the coupling of hyperbolic equations. The pursued applications are linked with the mathematical coupling of computing platforms, dedicated to an adaptative simulation of multi-scale phenomena. We propose and analyze a new coupling formalism based on extended PDE systems avoiding the geometric treatment of the interfaces. In addition, it allows to formulate the problem in a multidimensional setting, with possible covering of the coupled models. This formalism allows in particular to equip the coupling procedure with viscous regularization mechanisms, useful in the selection of natural discontinuous solutions. We analyze existence and uniqueness in the framework of a parabolic regularization a la Dafermos. Existence of a solution holds true under very general conditions but failure of uniqueness may naturally arise as soon as resonance occurs at the interfaces. Next, we highlight that our extended PDE framework gives rise to another regularization strategy based on thick interfaces. In this setting, we prove existence and uniqueness of the solutions of the Cauchy problem for initial data in L ∞ . The main tool consists in the derivation of a flexible and robust finite volume method for general triangulation which is analyzed in the setting of entropy measure-valued solutions by DiPerna. The second part is devoted to the definition of a finite volume scheme for the computing of nonclassical solutions of a scalar conservation law based on a kinetic relation. This scheme offers the feature to be stricto sensu conservative, in opposition to a Glimm approach that is only statistically conservative. The validity of our approach is illustrated through numerical examples. (author)

Programming for computations MATLAB/Octave : a gentle introduction to numerical simulations with MATLAB/Octave

CERN Document Server

Linge, Svein

2016-01-01

This book presents computer programming as a key method for solving mathematical problems. There are two versions of the book, one for MATLAB and one for Python. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows the students to write simple programs for solving common mathematical problems with numerical methods in engineering and science courses. The emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.

Changing Pre-Service Mathematics Teachers' Beliefs about Using Computers for Teaching and Learning Mathematics: The Effect of Three Different Models

Science.gov (United States)

Karatas, Ilhan

2014-01-01

This study examines the effect of three different computer integration models on pre-service mathematics teachers' beliefs about using computers in mathematics education. Participants included 104 pre-service mathematics teachers (36 second-year students in the Computer Oriented Model group, 35 fourth-year students in the Integrated Model (IM)…

Contributions to mathematical analysis and to numerical approximation in plasma physics

International Nuclear Information System (INIS)

Besse, N.

2009-01-01

The author's scientific works deal with numerical analysis and the simulation of the partial differential equations that intervene in the transport of charged particles and in plasma physics. In the chapters 2 and 3, a reduction of the Vlasov equation is presented, this method is based on the Liouville geometric invariants and it leads to a mathematical model named water-bag model that can be coupled with various equations of the electromagnetic field: the Poisson equation, the quasi-neutral equation or Maxwell equations. In the chapter 3 this reduction method is applied to the Vlasov gyro-kinetic equation to form the gyro-water-bag model. The mathematical analysis of this model produces interesting analytical results such as: threshold instabilities, instability growth rate, transport coefficient and non-linear turbulence mechanisms. Simulations have been performed to study turbulence in magnetized plasmas. In these plasmas occurred numerous instabilities due to the presence of high density and temperature gradients. These instabilities generate turbulence that deteriorates plasma confinement conditions required for thermonuclear fusion. The numerical calculation of turbulent thermal diffusivities is important since confinement time is determined by these transport coefficients. The chapter 4 gathers mathematical analysis issues like convergence or prior knowledge of errors concerning several high-order numerical methods used to solve Vlasov-Poisson or Vlasov-Einstein equation systems as well as the induction equation of an idealistic MHD system. The chapter 5 presents original numerical methods to solve several non-linear Vlasov equations such as Vlasov-Poisswell, Vlasov-Darwin, Vlasov-Maxwell and Vlasov-gyrokinetic that are involved either in inertial fusion or in magnetic confinement fusion

Numerical discrepancy between serial and MPI parallel computations

Directory of Open Access Journals (Sweden)

Sang Bong Lee

2016-09-01

Full Text Available Numerical simulations of 1D Burgers equation and 2D sloshing problem were carried out to study numerical discrepancy between serial and parallel computations. The numerical domain was decomposed into 2 and 4 subdomains for parallel computations with message passing interface. The numerical solution of Burgers equation disclosed that fully explicit boundary conditions used on subdomains of parallel computation was responsible for the numerical discrepancy of transient solution between serial and parallel computations. Two dimensional sloshing problems in a rectangular domain were solved using OpenFOAM. After a lapse of initial transient time sloshing patterns of water were significantly different in serial and parallel computations although the same numerical conditions were given. Based on the histograms of pressure measured at two points near the wall the statistical characteristics of numerical solution was not affected by the number of subdomains as much as the transient solution was dependent on the number of subdomains.

Mathematical optics classical, quantum, and computational methods

CERN Document Server

Lakshminarayanan, Vasudevan

2012-01-01

Going beyond standard introductory texts, Mathematical Optics: Classical, Quantum, and Computational Methods brings together many new mathematical techniques from optical science and engineering research. Profusely illustrated, the book makes the material accessible to students and newcomers to the field. Divided into six parts, the text presents state-of-the-art mathematical methods and applications in classical optics, quantum optics, and image processing. Part I describes the use of phase space concepts to characterize optical beams and the application of dynamic programming in optical wave

Mathematical and numerical analysis of hyper-elastic systems and introduction of plasticity

International Nuclear Information System (INIS)

Kluth, G.

2008-12-01

The goal is to model mathematically and numerically the dynamic phenomenons for solids in finite plasticity. We suggest a model that we call hyper-elasto-plastic based on hyper-elastic systems of conservation laws and on the use of an equation of state that we have constructed so as to achieve the plastic yield criterion of Von Mises. This model gives exact (analytic) solutions with shock split to flyer-plate experiments. The mathematical analysis of this model is done (hyperbolicity, characteristic fields, involutions and entropy). In the numerical part, we give 1D and 2D Lagrangian schemes which satisfy an entropy criterion. Moreover, thanks to a special discretization of the equations on deformation gradient, we satisfy some discrete involutions. In this work, the degeneracy of the solid model into hydrodynamic models is studied at the continuous level, and achieved at the numerical one. On different problems, we show the validity of our model and our numerical schemes. (author)

Introduction to precise numerical methods

CERN Document Server

Aberth, Oliver

2007-01-01

Precise numerical analysis may be defined as the study of computer methods for solving mathematical problems either exactly or to prescribed accuracy. This book explains how precise numerical analysis is constructed. The book also provides exercises which illustrate points from the text and references for the methods presented. All disc-based content for this title is now available on the Web. · Clearer, simpler descriptions and explanations ofthe various numerical methods· Two new types of numerical problems; accurately solving partial differential equations with the included software and computing line integrals in the complex plane.

Mathematical and Computational Modeling for Tumor Virotherapy with Mediated Immunity.

Science.gov (United States)

Timalsina, Asim; Tian, Jianjun Paul; Wang, Jin

2017-08-01

We propose a new mathematical modeling framework based on partial differential equations to study tumor virotherapy with mediated immunity. The model incorporates both innate and adaptive immune responses and represents the complex interaction among tumor cells, oncolytic viruses, and immune systems on a domain with a moving boundary. Using carefully designed computational methods, we conduct extensive numerical simulation to the model. The results allow us to examine tumor development under a wide range of settings and provide insight into several important aspects of the virotherapy, including the dependence of the efficacy on a few key parameters and the delay in the adaptive immunity. Our findings also suggest possible ways to improve the virotherapy for tumor treatment.

Mathematics and Computer Science: Exploring a Symbiotic Relationship

Science.gov (United States)

Bravaco, Ralph; Simonson, Shai

2004-01-01

This paper describes a "learning community" designed for sophomore computer science majors who are simultaneously studying discrete mathematics. The learning community consists of three courses: Discrete Mathematics, Data Structures and an Integrative Seminar/Lab. The seminar functions as a link that integrates the two disciplines. Participation…

Computational geometry lectures at the morningside center of mathematics

CERN Document Server

Wang, Ren-Hong

2003-01-01

Computational geometry is a borderline subject related to pure and applied mathematics, computer science, and engineering. The book contains articles on various topics in computational geometry, which are based on invited lectures and some contributed papers presented by researchers working during the program on Computational Geometry at the Morningside Center of Mathematics of the Chinese Academy of Science. The opening article by R.-H. Wang gives a nice survey of various aspects of computational geometry, many of which are discussed in more detail in other papers in the volume. The topics include problems of optimal triangulation, splines, data interpolation, problems of curve and surface design, problems of shape control, quantum teleportation, and others.

Large quantum systems: a mathematical and numerical perspective

International Nuclear Information System (INIS)

Lewin, M.

2009-06-01

This thesis is devoted to the mathematical study of variational models for large quantum systems. The mathematical methods are that of nonlinear analysis, calculus of variations, partial differential equations, spectral theory, and numerical analysis. The first part contains some results on finite systems. We study several approximations of the N-body Schroedinger equation for electrons in an atom or a molecule, and then the so-called Hartree-Fock- Bogoliubov model for a system of fermions interacting via the gravitational force. In a second part, we propose a new method allowing to prove the existence of the thermodynamic limit of Coulomb quantum systems. Then, we construct two Hartree-Fock-type models for infinite systems. The first is a relativistic theory deduced from Quantum Electrodynamics, allowing to describe the behavior of electrons, coupled to that of Dirac's vacuum which can become polarized. The second model describes a nonrelativistic quantum crystal in the presence of a charged defect. A new numerical method is also proposed. The last part of the thesis is devoted to spectral pollution, a phenomenon which is observed when trying to approximate eigenvalues in a gap of the essential spectrum of a self-adjoint operator, for instance for periodic Schroedinger operators or Dirac operators. (author)

Cognitive correlates of performance in advanced mathematics.

Science.gov (United States)

Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin

2012-03-01

Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic). To promote mathematical knowledge among college students, it is necessary to understand what factors (including cognitive factors) are important for acquiring advanced mathematics. We recruited 80 undergraduates from four universities in Beijing. The current study investigated the associations between students' performance on a test of advanced mathematics and a battery of 17 cognitive tasks on basic numerical processing, complex numerical processing, spatial abilities, language abilities, and general cognitive processing. The results showed that spatial abilities were significantly correlated with performance in advanced mathematics after controlling for other factors. In addition, certain language abilities (i.e., comprehension of words and sentences) also made unique contributions. In contrast, basic numerical processing and computation were generally not correlated with performance in advanced mathematics. Results suggest that spatial abilities and language comprehension, but not basic numerical processing, may play an important role in advanced mathematics. These results are discussed in terms of their theoretical significance and practical implications. ©2011 The British Psychological Society.

Progress report No. 53, October 1, 1976--September 30, 1977. [Courant Mathematics and Computing Laboratory, New York University

Energy Technology Data Exchange (ETDEWEB)

None

1977-12-01

Work in the following areas is considered in this annual report: applied mathematics (partial differential equations) in computational fluid dynamics, numerical analysis, etc.; computational physics and chemistry (partial differential equations); programing languages and compilers and other applications of computer science; and network access methods and applications of the ARPA network. Also discussed is the relation of work done at the Courant Institute to other projects, systems programing and user services, seminars, and publications. Individual reports are a paragraph or so in length. Completed work is reported in the appropriate publications. (RWR)

Computational Literacy and "The Big Picture" Concerning Computers in Mathematics Education

Science.gov (United States)

diSessa, Andrea A.

2018-01-01

This article develops some ideas concerning the "big picture" of how using computers might fundamentally change learning, with an emphasis on mathematics (and, more generally, STEM education). I develop the big-picture model of "computation as a new literacy" in some detail and with concrete examples of sixth grade students…

Computational error and complexity in science and engineering computational error and complexity

CERN Document Server

Lakshmikantham, Vangipuram; Chui, Charles K; Chui, Charles K

2005-01-01

The book "Computational Error and Complexity in Science and Engineering” pervades all the science and engineering disciplines where computation occurs. Scientific and engineering computation happens to be the interface between the mathematical model/problem and the real world application. One needs to obtain good quality numerical values for any real-world implementation. Just mathematical quantities symbols are of no use to engineers/technologists. Computational complexity of the numerical method to solve the mathematical model, also computed along with the solution, on the other hand, will tell us how much computation/computational effort has been spent to achieve that quality of result. Anyone who wants the specified physical problem to be solved has every right to know the quality of the solution as well as the resources spent for the solution. The computed error as well as the complexity provide the scientific convincing answer to these questions. Specifically some of the disciplines in which the book w...

Fluid Dynamics Theory, Computation, and Numerical Simulation

CERN Document Server

Pozrikidis, Constantine

2009-01-01

Fluid Dynamics: Theory, Computation, and Numerical Simulation is the only available book that extends the classical field of fluid dynamics into the realm of scientific computing in a way that is both comprehensive and accessible to the beginner. The theory of fluid dynamics, and the implementation of solution procedures into numerical algorithms, are discussed hand-in-hand and with reference to computer programming. This book is an accessible introduction to theoretical and computational fluid dynamics (CFD), written from a modern perspective that unifies theory and numerical practice. There are several additions and subject expansions in the Second Edition of Fluid Dynamics, including new Matlab and FORTRAN codes. Two distinguishing features of the discourse are: solution procedures and algorithms are developed immediately after problem formulations are presented, and numerical methods are introduced on a need-to-know basis and in increasing order of difficulty. Matlab codes are presented and discussed for ...

Prospective Turkish Primary Teachers' Views about the Use of Computers in Mathematics Education

Science.gov (United States)

Dogan, Mustafa

2012-01-01

The use of computers and technology in mathematics education affects students' learning, achievements, and affective dimensions. This study explores prospective Turkish primary mathematics teachers' views about the use of computers in mathematics education. The sample comprised of 129 fourth-year prospective primary mathematics teachers from two…

Theoretical numerical analysis a functional analysis framework

CERN Document Server

Atkinson, Kendall

2005-01-01

This textbook prepares graduate students for research in numerical analysis/computational mathematics by giving to them a mathematical framework embedded in functional analysis and focused on numerical analysis. This helps the student to move rapidly into a research program. The text covers basic results of functional analysis, approximation theory, Fourier analysis and wavelets, iteration methods for nonlinear equations, finite difference methods, Sobolev spaces and weak formulations of boundary value problems, finite element methods, elliptic variational inequalities and their numerical solu

Physics, Computer Science and Mathematics Division. Annual report, 1 January--31 December 1977

International Nuclear Information System (INIS)

Lepore, J.V.

1977-01-01

This annual report of the Physics, Computer Science and Mathematics Division describes the scientific research and other work carried out within the Division during 1977. The Division is concerned with work in experimental and theoretical physics, with computer science and applied mathematics, and with the operation of a computer center. The major physics research activity is in high-energy physics, although there is a relatively small program of medium-energy research. The High Energy Physics research program in the Physics Division is concerned with fundamental research which will enable man to comprehend the nature of the physical world. The major effort is now directed toward experiments with positron-electron colliding beam at PEP. The Medium Energy Physics program is concerned with research using mesons and nucleons to probe the properties of matter. This research is concerned with the study of nuclear structure, nuclear reactions, and the interactions between nuclei and electromagnetic radiation and mesons. The Computer Science and Applied Mathematics Department engages in research in a variety of computer science and mathematics disciplines. Work in computer science and applied mathematics includes construction of data bases, computer graphics, computational physics and data analysis, mathematical modeling, and mathematical analysis of differential and integral equations resulting from physical problems. The Computer Center provides large-scale computational support to LBL's scientific programs. Descriptions of the various activities are quite short; references to published results are given. 24 figures

A mathematical and numerical analysis of the Maxwell-Stefan diffusion equations

OpenAIRE

Boudin , Laurent; Grec , Bérénice; Salvarani , Francesco

2012-01-01

International audience; We consider the Maxwell-Stefan model of diffusion in a multicomponent gaseous mixture. After focusing on the main differences with the Fickian diffusion model, we study the equations governing a three-component gas mixture. We provide a qualitative and quantitative mathematical analysis of the model. The main properties of the standard explicit numerical scheme are also analyzed. We eventually include some numerical simulations pointing out the uphill diffusion phenome...

Mathematical modeling and computational prediction of cancer drug resistance.

Science.gov (United States)

Sun, Xiaoqiang; Hu, Bin

2017-06-23

Diverse forms of resistance to anticancer drugs can lead to the failure of chemotherapy. Drug resistance is one of the most intractable issues for successfully treating cancer in current clinical practice. Effective clinical approaches that could counter drug resistance by restoring the sensitivity of tumors to the targeted agents are urgently needed. As numerous experimental results on resistance mechanisms have been obtained and a mass of high-throughput data has been accumulated, mathematical modeling and computational predictions using systematic and quantitative approaches have become increasingly important, as they can potentially provide deeper insights into resistance mechanisms, generate novel hypotheses or suggest promising treatment strategies for future testing. In this review, we first briefly summarize the current progress of experimentally revealed resistance mechanisms of targeted therapy, including genetic mechanisms, epigenetic mechanisms, posttranslational mechanisms, cellular mechanisms, microenvironmental mechanisms and pharmacokinetic mechanisms. Subsequently, we list several currently available databases and Web-based tools related to drug sensitivity and resistance. Then, we focus primarily on introducing some state-of-the-art computational methods used in drug resistance studies, including mechanism-based mathematical modeling approaches (e.g. molecular dynamics simulation, kinetic model of molecular networks, ordinary differential equation model of cellular dynamics, stochastic model, partial differential equation model, agent-based model, pharmacokinetic-pharmacodynamic model, etc.) and data-driven prediction methods (e.g. omics data-based conventional screening approach for node biomarkers, static network approach for edge biomarkers and module biomarkers, dynamic network approach for dynamic network biomarkers and dynamic module network biomarkers, etc.). Finally, we discuss several further questions and future directions for the use of

Creators of mathematical and computational sciences

CERN Document Server

Agarwal, Ravi P

2014-01-01

The book records the essential discoveries of mathematical and computational scientists in chronological order, following the birth of ideas on the basis of prior ideas ad infinitum. The authors document the winding path of mathematical scholarship throughout history, and most importantly, the thought process of each individual that resulted in the mastery of their subject. The book implicitly addresses the nature and character of every scientist as one tries to understand their visible actions in both adverse and congenial environments. The authors hope that this will enable the reader to understand their mode of thinking, and perhaps even to emulate their virtues in life. … presents a picture of mathematics as a creation of the human imagination. … brings the history of mathematics to life by describing the contributions of the world’s greatest mathematicians. —Rex F. Gandy, Provost and Vice President for Academic Affairs, TAMUK   It starts with the explanation and history of numbers, arithmetic, ...

Computer Programming in the UK Undergraduate Mathematics Curriculum

Science.gov (United States)

Sangwin, Christopher J.; O'Toole, Claire

2017-01-01

This paper reports a study which investigated the extent to which undergraduate mathematics students in the United Kingdom are currently taught to programme a computer as a core part of their mathematics degree programme. We undertook an online survey, with significant follow-up correspondence, to gather data on current curricula and received…

Teachers, Equity, and Computers for Secondary Mathematics Learning

Science.gov (United States)

Forgasz, Helen

2006-01-01

The findings presented in this article were derived from a 3-year study aimed at examining issues associated with the use of computers for secondary mathematics learning in Victorian (Australia) schools. Gender and other equity factors were of particular interest. In this article, the focus is on the participating mathematics teachers. Data on…

The Effects of Computer Games on the Achievement of Basic Mathematical Skills

Science.gov (United States)

Sayan, Hamiyet

2015-01-01

This study aims to analyze the relationship between playing computer games and learning basic mathematics skills. It shows the role computer games play in the learning and achievement of basic mathematical skills by students. Nowadays it is clear that individuals, especially young persons are very fond of computer and computer games. Since…

Attitudes towards Computer and Computer Self-Efficacy as Predictors of Preservice Mathematics Teachers' Computer Anxiety

Science.gov (United States)

Awofala, Adeneye O. A.; Akinoso, Sabainah O.; Fatade, Alfred O.

2017-01-01

The study investigated attitudes towards computer and computer self-efficacy as predictors of computer anxiety among 310 preservice mathematics teachers from five higher institutions of learning in Lagos and Ogun States of Nigeria using the quantitative research method within the blueprint of the descriptive survey design. Data collected were…

Fluid dynamics theory, computation, and numerical simulation

CERN Document Server

Pozrikidis, C

2001-01-01

Fluid Dynamics Theory, Computation, and Numerical Simulation is the only available book that extends the classical field of fluid dynamics into the realm of scientific computing in a way that is both comprehensive and accessible to the beginner The theory of fluid dynamics, and the implementation of solution procedures into numerical algorithms, are discussed hand-in-hand and with reference to computer programming This book is an accessible introduction to theoretical and computational fluid dynamics (CFD), written from a modern perspective that unifies theory and numerical practice There are several additions and subject expansions in the Second Edition of Fluid Dynamics, including new Matlab and FORTRAN codes Two distinguishing features of the discourse are solution procedures and algorithms are developed immediately after problem formulations are presented, and numerical methods are introduced on a need-to-know basis and in increasing order of difficulty Matlab codes are presented and discussed for a broad...

Advances in Numerical Methods

CERN Document Server

Mastorakis, Nikos E

2009-01-01

Features contributions that are focused on significant aspects of current numerical methods and computational mathematics. This book carries chapters that advanced methods and various variations on known techniques that can solve difficult scientific problems efficiently.

Probabilistic numerics and uncertainty in computations.

Science.gov (United States)

Hennig, Philipp; Osborne, Michael A; Girolami, Mark

2015-07-08

We deliver a call to arms for probabilistic numerical methods : algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation with limited time or hardware, are important for much contemporary science and industry. Within applications such as climate science and astrophysics, the need to make decisions on the basis of computations with large and complex data have led to a renewed focus on the management of numerical uncertainty. We describe how several seminal classic numerical methods can be interpreted naturally as probabilistic inference. We then show that the probabilistic view suggests new algorithms that can flexibly be adapted to suit application specifics, while delivering improved empirical performance. We provide concrete illustrations of the benefits of probabilistic numeric algorithms on real scientific problems from astrometry and astronomical imaging, while highlighting open problems with these new algorithms. Finally, we describe how probabilistic numerical methods provide a coherent framework for identifying the uncertainty in calculations performed with a combination of numerical algorithms (e.g. both numerical optimizers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations.

COMPUTER MATHEMATICS SYSTEMS IN STUDENTS’ LEARNING OF "INFORMATIСS"

Directory of Open Access Journals (Sweden)

Taras P. Kobylnyk

2014-04-01

Full Text Available The article describes the general characteristics of the most popular computer mathematics systems such as commercial (Maple, Mathematica, Matlab and open source (Scilab, Maxima, GRAN, Sage, as well as the conditions of use of these systems as means of fundamentalization of the educational process of bachelor of informatics. It is considered the role of CMS in bachelor of informatics training. It is identified the approaches of CMS pedagogical use while learning information and physics and mathematics disciplines. There are presented some tasks, in which we must carefully use the «responses» have been received using CMS. It is identified the promising directions of development of computer mathematics systems in high-tech environment.

Physics, Computer Science and Mathematics Division annual report, 1 January-31 December 1983

Energy Technology Data Exchange (ETDEWEB)

Jackson, J.D.

1984-08-01

This report summarizes the research performed in the Physics, Computer Science and Mathematics Division of the Lawrence Berkeley Laboratory during calendar year 1983. The major activity of the Division is research in high-energy physics, both experimental and theoretical, and research and development in associated technologies. A smaller, but still significant, program is in computer science and applied mathematics. During 1983 there were approximately 160 people in the Division active in or supporting high-energy physics research, including about 40 graduate students. In computer science and mathematics, the total staff, including students and faculty, was roughly 50. Because of the creation in late 1983 of a Computing Division at LBL and the transfer of the Computer Science activities to the new Division, this annual report is the last from the Physics, Computer Science and Mathematics Division. In December 1983 the Division reverted to its historic name, the Physics Division. Its future annual reports will document high energy physics activities and also those of its Mathematics Department.

Physics, Computer Science and Mathematics Division annual report, 1 January-31 December 1983

International Nuclear Information System (INIS)

Jackson, J.D.

1984-08-01

This report summarizes the research performed in the Physics, Computer Science and Mathematics Division of the Lawrence Berkeley Laboratory during calendar year 1983. The major activity of the Division is research in high-energy physics, both experimental and theoretical, and research and development in associated technologies. A smaller, but still significant, program is in computer science and applied mathematics. During 1983 there were approximately 160 people in the Division active in or supporting high-energy physics research, including about 40 graduate students. In computer science and mathematics, the total staff, including students and faculty, was roughly 50. Because of the creation in late 1983 of a Computing Division at LBL and the transfer of the Computer Science activities to the new Division, this annual report is the last from the Physics, Computer Science and Mathematics Division. In December 1983 the Division reverted to its historic name, the Physics Division. Its future annual reports will document high energy physics activities and also those of its Mathematics Department

Logic, mathematics, and computer science modern foundations with practical applications

CERN Document Server

Nievergelt, Yves

2015-01-01

This text for the first or second year undergraduate in mathematics, logic, computer science, or social sciences, introduces the reader to logic, proofs, sets, and number theory. It also serves as an excellent independent study reference and resource for instructors. Adapted from Foundations of Logic and Mathematics: Applications to Science and Cryptography © 2002 Birkhӓuser, this second edition provides a modern introduction to the foundations of logic, mathematics, and computers science, developing the theory that demonstrates construction of all mathematics and theoretical computer science from logic and set theory.  The focus is on foundations, with specific statements of all the associated axioms and rules of logic and set theory, and  provides complete details and derivations of formal proofs. Copious references to literature that document historical development is also provided. Answers are found to many questions that usually remain unanswered: Why is the truth table for logical implication so uni...

Essential numerical computer methods

CERN Document Server

Johnson, Michael L

2010-01-01

The use of computers and computational methods has become ubiquitous in biological and biomedical research. During the last 2 decades most basic algorithms have not changed, but what has is the huge increase in computer speed and ease of use, along with the corresponding orders of magnitude decrease in cost. A general perception exists that the only applications of computers and computer methods in biological and biomedical research are either basic statistical analysis or the searching of DNA sequence data bases. While these are important applications they only scratch the surface of the current and potential applications of computers and computer methods in biomedical research. The various chapters within this volume include a wide variety of applications that extend far beyond this limited perception. As part of the Reliable Lab Solutions series, Essential Numerical Computer Methods brings together chapters from volumes 210, 240, 321, 383, 384, 454, and 467 of Methods in Enzymology. These chapters provide ...

Mathematical and numerical modeling of early atherosclerotic lesions***

Directory of Open Access Journals (Sweden)

Raoult Annie

2010-12-01

Full Text Available This article is devoted to the construction of a mathematical model describing the early formation of atherosclerotic lesions. The early stage of atherosclerosis is an inflammatory process that starts with the penetration of low density lipoproteins in the intima and with their oxidation. This phenomenon is closely linked to the local blood flow dynamics. Extending a previous work [5] that was mainly restricted to a one-dimensional setting, we couple a simple lesion growth model relying on the biomolecular process that takes place in the intima with blood flow dynamics and mass transfer. We perform numerical simulations on a two-dimensional geometry taken from [6,7] that mimicks a carotid artery deformed by a perivascular cast and we compare the numerical results with experimental data.

Parallel computing: numerics, applications, and trends

National Research Council Canada - National Science Library

Trobec, Roman; Vajteršic, Marián; Zinterhof, Peter

2009-01-01

... and/or distributed systems. The contributions to this book are focused on topics most concerned in the trends of today's parallel computing. These range from parallel algorithmics, programming, tools, network computing to future parallel computing. Particular attention is paid to parallel numerics: linear algebra, differential equations, numerica...

Three views of logic mathematics, philosophy, and computer science

CERN Document Server

Loveland, Donald W; Sterrett, S G

2014-01-01

Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional logic and first-orde

An Improved Mathematical Model for Computing Power Output of Solar Photovoltaic Modules

Directory of Open Access Journals (Sweden)

Abdul Qayoom Jakhrani

2014-01-01

Full Text Available It is difficult to determine the input parameters values for equivalent circuit models of photovoltaic modules through analytical methods. Thus, the previous researchers preferred to use numerical methods. Since, the numerical methods are time consuming and need long term time series data which is not available in most developing countries, an improved mathematical model was formulated by combination of analytical and numerical methods to overcome the limitations of existing methods. The values of required model input parameters were computed analytically. The expression for output current of photovoltaic module was determined explicitly by Lambert W function and voltage was determined numerically by Newton-Raphson method. Moreover, the algebraic equations were derived for the shape factor which involves the ideality factor and the series resistance of a single diode photovoltaic module power output model. The formulated model results were validated with rated power output of a photovoltaic module provided by manufacturers using local meteorological data, which gave ±2% error. It was found that the proposed model is more practical in terms of precise estimations of photovoltaic module power output for any required location and number of variables used.

Mathematics for Nonlinear Phenomena : Analysis and Computation : International Conference in honor of Professor Yoshikazu Giga on his 60th birthday

CERN Document Server

Jimbo, Shuichi

2017-01-01

This volume covers some of the most seminal research in the areas of mathematical analysis and numerical computation for nonlinear phenomena. Collected from the international conference held in honor of Professor Yoshikazu Giga’s 60th birthday, the featured research papers and survey articles discuss partial differential equations related to fluid mechanics,　electromagnetism, surface diffusion, and evolving interfaces. Specific focus is placed on topics such as the solvability of the Navier-Stokes equations and the regularity, stability, and symmetry of their solutions, analysis of a living fluid, stochastic effects and numerics for Maxwell’s equations, nonlinear heat equations in critical spaces, viscosity solutions describing various kinds of interfaces, numerics for evolving interfaces, and a hyperbolic obstacle problem. Also included in this volume are an introduction of Yoshikazu Giga’s extensive academic career and a long list of his published work. Students and researchers in mathematical analy...

The ANS mathematics and computation software standards

Energy Technology Data Exchange (ETDEWEB)

Smetana, A. O. [Savannah River National Laboratory, Washington Savannah River Company, Aiken, SC 29808 (United States)

2006-07-01

The Mathematics and Computations Div. of the American Nuclear Society sponsors the ANS-10 Standards Subcommittee. This subcommittee, which is part of the ANS Standards Committee, currently maintains three ANSI/ANS software standards. These standards are: Portability of Scientific and Engineering Software, ANS-10.2; Guidelines for the Verification and Validation of Scientific and Engineering Computer Programs for the Nuclear Industry, ANS-10.4; and Accommodating User Needs in Scientific and Engineering Computer Software Development, ANS-10.5. A fourth Standard, Documentation of Computer Software, ANS-10.3, is available as a historical Standard. (authors)

The ANS mathematics and computation software standards

International Nuclear Information System (INIS)

Smetana, A. O.

2006-01-01

The Mathematics and Computations Div. of the American Nuclear Society sponsors the ANS-10 Standards Subcommittee. This subcommittee, which is part of the ANS Standards Committee, currently maintains three ANSI/ANS software standards. These standards are: Portability of Scientific and Engineering Software, ANS-10.2; Guidelines for the Verification and Validation of Scientific and Engineering Computer Programs for the Nuclear Industry, ANS-10.4; and Accommodating User Needs in Scientific and Engineering Computer Software Development, ANS-10.5. A fourth Standard, Documentation of Computer Software, ANS-10.3, is available as a historical Standard. (authors)

Multi-band effective mass approximations advanced mathematical models and numerical techniques

CERN Document Server

Koprucki, Thomas

2014-01-01

This book addresses several mathematical models from the most relevant class of kp-Schrödinger systems. Both mathematical models and state-of-the-art numerical methods for adequately solving the arising systems of differential equations are presented. The operational principle of modern semiconductor nano structures, such as quantum wells, quantum wires or quantum dots, relies on quantum mechanical effects. The goal of numerical simulations using quantum mechanical models in the development of semiconductor nano structures is threefold: First they are needed for a deeper understanding of experimental data and of the operational principle. Secondly, they allow us to predict and optimize in advance the qualitative and quantitative properties of new devices in order to minimize the number of prototypes needed. Semiconductor nano structures are embedded as an active region in semiconductor devices. Thirdly and finally, the results of quantum mechanical simulations of semiconductor nano structures can be used wit...

Mathematical modelling in solid mechanics

CERN Document Server

Sofonea, Mircea; Steigmann, David

2017-01-01

This book presents new research results in multidisciplinary fields of mathematical and numerical modelling in mechanics. The chapters treat the topics: mathematical modelling in solid, fluid and contact mechanics nonconvex variational analysis with emphasis to nonlinear solid and structural mechanics numerical modelling of problems with non-smooth constitutive laws, approximation of variational and hemivariational inequalities, numerical analysis of discrete schemes, numerical methods and the corresponding algorithms, applications to mechanical engineering numerical aspects of non-smooth mechanics, with emphasis on developing accurate and reliable computational tools mechanics of fibre-reinforced materials behaviour of elasto-plastic materials accounting for the microstructural defects definition of structural defects based on the differential geometry concepts or on the atomistic basis interaction between phase transformation and dislocations at nano-scale energetic arguments bifurcation and post-buckling a...

Physics, Computer Science and Mathematics Division annual report, 1 January--31 December 1975

International Nuclear Information System (INIS)

Lepore, J.L.

1975-01-01

This annual report describes the scientific research and other work carried out during the calendar year 1975. The report is nontechnical in nature, with almost no data. A 17-page bibliography lists the technical papers which detail the work. The contents of the report include the following: experimental physics (high-energy physics--SPEAR, PEP, SLAC, FNAL, BNL, Bevatron; particle data group; medium-energy physics; astrophysics, astronomy, and cosmic rays; instrumentation development), theoretical physics (particle theory and accelerator theory and design), computer science and applied mathematics (data management systems, socio-economic environment demographic information system, computer graphics, computer networks, management information systems, computational physics and data analysis, mathematical modeling, programing languages, applied mathematics research), real-time systems (ModComp and PDP networks), and computer center activities (systems programing, user services, hardware development, computer operations). A glossary of computer science and mathematics terms is also included. 32 figures

Modelling and Optimizing Mathematics Learning in Children

Science.gov (United States)

Käser, Tanja; Busetto, Alberto Giovanni; Solenthaler, Barbara; Baschera, Gian-Marco; Kohn, Juliane; Kucian, Karin; von Aster, Michael; Gross, Markus

2013-01-01

This study introduces a student model and control algorithm, optimizing mathematics learning in children. The adaptive system is integrated into a computer-based training system for enhancing numerical cognition aimed at children with developmental dyscalculia or difficulties in learning mathematics. The student model consists of a dynamic…

Research in Applied Mathematics, Fluid Mechanics and Computer Science

Science.gov (United States)

1999-01-01

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period October 1, 1998 through March 31, 1999.

COMPUTER TOOLS OF DYNAMIC MATHEMATIC SOFTWARE AND METHODICAL PROBLEMS OF THEIR USE

Directory of Open Access Journals (Sweden)

Olena V. Semenikhina

2014-08-01

Full Text Available The article presents results of analyses of standard computer tools of dynamic mathematic software which are used in solving tasks, and tools on which the teacher can support in the teaching of mathematics. Possibility of the organization of experimental investigating of mathematical objects on the basis of these tools and the wording of new tasks on the basis of the limited number of tools, fast automated check are specified. Some methodological comments on application of computer tools and methodological features of the use of interactive mathematical environments are presented. Problems, which are arising from the use of computer tools, among which rethinking forms and methods of training by teacher, the search for creative problems, the problem of rational choice of environment, check the e-solutions, common mistakes in the use of computer tools are selected.

Physics, Computer Science and Mathematics Division annual report, January 1--December 31, 1976

International Nuclear Information System (INIS)

Lepore, J.V.

1977-01-01

This annual report of the Physics, Computer Science and Mathematics Division describes the scientific research and other work carried out within the Division during the calendar year 1976. The Division is concerned with work in experimental and theoretical physics, with computer science and applied mathematics, and with the operation of a computer center. The major physics research activity is in high-energy physics; a vigorous program is maintained in this pioneering field. The high-energy physics research program in the Division now focuses on experiments with e + e - colliding beams using advanced techniques and developments initiated and perfected at the Laboratory. The Division continues its work in medium energy physics, with experimental work carried out at the Bevatron and at the Los Alamos Pi-Meson Facility. Work in computer science and applied mathematics includes construction of data bases, computer graphics, computational physics and data analysis, mathematical modeling, and mathematical analysis of differential and integral equations resulting from physical problems. The computer center serves the Laboratory by constantly upgrading its facility and by providing day-to-day service. This report is descriptive in nature; references to detailed publications are given

Physics, Computer Science and Mathematics Division annual report, January 1--December 31, 1976

Energy Technology Data Exchange (ETDEWEB)

Lepore, J.V. (ed.)

1977-01-01

This annual report of the Physics, Computer Science and Mathematics Division describes the scientific research and other work carried out within the Division during the calendar year 1976. The Division is concerned with work in experimental and theoretical physics, with computer science and applied mathematics, and with the operation of a computer center. The major physics research activity is in high-energy physics; a vigorous program is maintained in this pioneering field. The high-energy physics research program in the Division now focuses on experiments with e/sup +/e/sup -/ colliding beams using advanced techniques and developments initiated and perfected at the Laboratory. The Division continues its work in medium energy physics, with experimental work carried out at the Bevatron and at the Los Alamos Pi-Meson Facility. Work in computer science and applied mathematics includes construction of data bases, computer graphics, computational physics and data analysis, mathematical modeling, and mathematical analysis of differential and integral equations resulting from physical problems. The computer center serves the Laboratory by constantly upgrading its facility and by providing day-to-day service. This report is descriptive in nature; references to detailed publications are given. (RWR)

Numerical analysis

CERN Document Server

Brezinski, C

2012-01-01

Numerical analysis has witnessed many significant developments in the 20th century. This book brings together 16 papers dealing with historical developments, survey papers and papers on recent trends in selected areas of numerical analysis, such as: approximation and interpolation, solution of linear systems and eigenvalue problems, iterative methods, quadrature rules, solution of ordinary-, partial- and integral equations. The papers are reprinted from the 7-volume project of the Journal of Computational and Applied Mathematics on '/homepage/sac/cam/na2000/index.html<

A History of Computer Numerical Control.

Science.gov (United States)

Haggen, Gilbert L.

Computer numerical control (CNC) has evolved from the first significant counting method--the abacus. Babbage had perhaps the greatest impact on the development of modern day computers with his analytical engine. Hollerith's functioning machine with punched cards was used in tabulating the 1890 U.S. Census. In order for computers to become a…

Effects of Attitudes and Behaviours on Learning Mathematics with Computer Tools

Science.gov (United States)

Reed, Helen C.; Drijvers, Paul; Kirschner, Paul A.

2010-01-01

This mixed-methods study investigates the effects of student attitudes and behaviours on the outcomes of learning mathematics with computer tools. A computer tool was used to help students develop the mathematical concept of function. In the whole sample (N = 521), student attitudes could account for a 3.4 point difference in test scores between…

The semantic system is involved in mathematical problem solving.

Science.gov (United States)

Zhou, Xinlin; Li, Mengyi; Li, Leinian; Zhang, Yiyun; Cui, Jiaxin; Liu, Jie; Chen, Chuansheng

2018-02-01

Numerous studies have shown that the brain regions around bilateral intraparietal cortex are critical for number processing and arithmetical computation. However, the neural circuits for more advanced mathematics such as mathematical problem solving (with little routine arithmetical computation) remain unclear. Using functional magnetic resonance imaging (fMRI), this study (N = 24 undergraduate students) compared neural bases of mathematical problem solving (i.e., number series completion, mathematical word problem solving, and geometric problem solving) and arithmetical computation. Direct subject- and item-wise comparisons revealed that mathematical problem solving typically had greater activation than arithmetical computation in all 7 regions of the semantic system (which was based on a meta-analysis of 120 functional neuroimaging studies on semantic processing). Arithmetical computation typically had greater activation in the supplementary motor area and left precentral gyrus. The results suggest that the semantic system in the brain supports mathematical problem solving. Copyright © 2017 Elsevier Inc. All rights reserved.

Mathematical, physical and numerical principles essential for models of turbulent mixing

Energy Technology Data Exchange (ETDEWEB)

Sharp, David Howland [Los Alamos National Laboratory; Lim, Hyunkyung [STONY BROOK UNIV; Yu, Yan [STONY BROOK UNIV; Glimm, James G [STONY BROOK UNIV

2009-01-01

We propose mathematical, physical and numerical principles which are important for the modeling of turbulent mixing, especially the classical and well studied Rayleigh-Taylor and Richtmyer-Meshkov instabilities which involve acceleration driven mixing of a fluid discontinuity layer, by a steady accerleration or an impulsive force.

Some unsolved problems in discrete mathematics and mathematical cybernetics

Science.gov (United States)

Korshunov, Aleksei D.

2009-10-01

There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.

Some unsolved problems in discrete mathematics and mathematical cybernetics

International Nuclear Information System (INIS)

Korshunov, Aleksei D

2009-01-01

There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.

Optimization and mathematical modeling in computer architecture

CERN Document Server

Sankaralingam, Karu; Nowatzki, Tony

2013-01-01

In this book we give an overview of modeling techniques used to describe computer systems to mathematical optimization tools. We give a brief introduction to various classes of mathematical optimization frameworks with special focus on mixed integer linear programming which provides a good balance between solver time and expressiveness. We present four detailed case studies -- instruction set customization, data center resource management, spatial architecture scheduling, and resource allocation in tiled architectures -- showing how MILP can be used and quantifying by how much it outperforms t

Mathematical models in medicine: Diseases and epidemics

International Nuclear Information System (INIS)

Witten, M.

1987-01-01

This volume presents the numerous applications of mathematics in the life sciences and medicine, and demonstrates how mathematics and computers have taken root in these fields. The work covers a variety of techniques and applications including mathematical and modelling methodology, modelling/simulation technology, and philosophical issues in model formulation, leading to speciality medical modelling, artificial intelligence, psychiatric models, medical decision making, and molecular modelling

Computing the zeros of analytic functions

CERN Document Server

Kravanja, Peter

2000-01-01

Computing all the zeros of an analytic function and their respective multiplicities, locating clusters of zeros and analytic fuctions, computing zeros and poles of meromorphic functions, and solving systems of analytic equations are problems in computational complex analysis that lead to a rich blend of mathematics and numerical analysis. This book treats these four problems in a unified way. It contains not only theoretical results (based on formal orthogonal polynomials or rational interpolation) but also numerical analysis and algorithmic aspects, implementation heuristics, and polished software (the package ZEAL) that is available via the CPC Program Library. Graduate studets and researchers in numerical mathematics will find this book very readable.

Novel methods in computational finance

CERN Document Server

Günther, Michael; Maten, E

2017-01-01

This book discusses the state-of-the-art and open problems in computational finance. It presents a collection of research outcomes and reviews of the work from the STRIKE project, an FP7 Marie Curie Initial Training Network (ITN) project in which academic partners trained early-stage researchers in close cooperation with a broader range of associated partners, including from the private sector. The aim of the project was to arrive at a deeper understanding of complex (mostly nonlinear) financial models and to develop effective and robust numerical schemes for solving linear and nonlinear problems arising from the mathematical theory of pricing financial derivatives and related financial products. This was accomplished by means of financial modelling, mathematical analysis and numerical simulations, optimal control techniques and validation of models. In recent years the computational complexity of mathematical models employed in financial mathematics has witnessed tremendous growth. Advanced numerical techni...

Secondary School Mathematics Teachers’ and Students’ Views on Computer Assisted Mathematics Instruction in Turkey: Mathematica Example

Directory of Open Access Journals (Sweden)

Mehmet Alper Ardıç

2017-01-01

Full Text Available This study aimed at determining the secondary school mathematics teachers’ and students’ views on computer-assisted mathematics instruction (CAMI conducted via Mathematica. Accordingly, three mathematics teachers in Adıyaman and nine 10th-grade students participated in the research. Firstly, the researchers trained the mathematics teachers in the Mathematica program, a computer algebra system (CAS and CAMI. Then, they provided a suitable environment for teachers to practice CAMI with their students to teach quadratic functions (parabola. Case study, a qualitative research design, was utilized in the study. Semi-structured interview forms were used as data collection tools. The interview data were analyzed using descriptive and content analysis, and the codes and themes related to the topic were obtained. The findings revealed that all the teachers found CAMI implementations interesting as supported by students’ views. While all mathematics teachers wanted to benefit from CAMI in mathematics and geometry courses, most of the students asked that CAMI be used in different courses. It was found that students did not have any problems with the Mathematica used with CAMI activities. However, it was also revealed by one student and one teacher that involving CAMI constantly in the courses would hinder preparations for the university entrance exam.

Dynamic transition between fixed- and mobile-bed: mathematical and numerical aspects

Science.gov (United States)

Zugliani, Daniel; Pasqualini, Matteo; Rosatti, Giorgio

2017-04-01

Free-surface flows with high sediment transport (as debris flow or hyper-concentrated flow) are composed by a mixture of fluid and solid phase, usually water and sediment. When these flows propagate over loose beds, particles constituting the mixture of water and sediments strongly interact with the ones forming the bed, leading to erosion or deposition. However, there are lots of other situations when the mixture flows over rigid bedrocks or over artificially paved transects, so there is no mass exchange between bed and mixture. The two situations are usually referred to as, respectively, mobile- and fixed-bed conditions. From a mathematical point of view, the systems of Partial Differential Equations (PDEs) that describe these flows derive from mass and momentum balance of both phases, but, the two resulting PDEs systems are different. The main difference concerns the concentration: in the mobile-bed condition, the concentration is linked to the local flow conditions by means of a suitable rheological relation, while in the fixed-bed case, the concentration is an unknown of the problem. It is quite common that a free surface flow with high sediment transport, in its path, encounters both conditions. In the recent work of Rosatti & Zugliani 2015, the mathematical and numerical description of the transition between fixed- and mobile-bed was successfully resolved, for the case of low sediment transport phenomena, by the introduction of a suitable erodibility variable and satisfactory results were obtained. The main disadvantage of the approach is related to the erodibility variable, that changes in space, based on bed characteristics, but remains constant in time. However, the nature of the bed can change dynamically as result of deposition over fixed bed or high erosion over mobile bed. With this work, we extend the applicability of the mentioned approach to the more complex PDEs describing the hyper-concentrated flow. Moreover, we introduce a strategy that allows

PENGEMBANGAN MODEL COMPUTER-BASED E-LEARNING UNTUK MENINGKATKAN KEMAMPUAN HIGH ORDER MATHEMATICAL THINKING SISWA SMA

OpenAIRE

Jarnawi Afgani Dahlan; Yaya Sukjaya Kusumah; Mr Heri Sutarno

2011-01-01

The focus of this research is on the development of mathematics teaching and learning activity which is based on the application of computer software. The aim of research is as follows : 1) to identify some mathematics topics which feasible to be presented by computer-based e-learning, 2) design, develop, and implement computer-based e-learning on mathematics, and 3) analyze the impact of computer-based e-learning in the enhancement of SMA students’ high order mathematical thinking. All activ...

Applied mathematics and condensed matter; Mathematiques appliquees et matiere condensee

Energy Technology Data Exchange (ETDEWEB)

Bouche, D.; Jollet, F. [CEA Bruyeres-le-Chatel, 91 (France)

2011-01-15

Applied mathematics have always been a key tool in computing the structure of condensed matter. In this paper, we present the most widely used methods, and show the importance of mathematics in their genesis and evolution. After a brief survey of quantum Monte Carlo methods, which try to compute the N electrons wave function, the paper describes the theoretical foundations of N independent particle approximations. We mainly focus on density functional theory (DFT). This theory associated with advanced numerical methods, and high performance computing, has produced significant achievements in the field. This paper presents the foundations of the theory, as well as different numerical methods used to solve DFT equations. (authors)

A MATLAB-Aided Method for Teaching Calculus-Based Business Mathematics

Science.gov (United States)

Liang, Jiajuan; Pan, William S. Y.

2009-01-01

MATLAB is a powerful package for numerical computation. MATLAB contains a rich pool of mathematical functions and provides flexible plotting functions for illustrating mathematical solutions. The course of calculus-based business mathematics consists of two major topics: 1) derivative and its applications in business; and 2) integration and its…

The numerical parallel computing of photon transport

International Nuclear Information System (INIS)

Huang Qingnan; Liang Xiaoguang; Zhang Lifa

1998-12-01

The parallel computing of photon transport is investigated, the parallel algorithm and the parallelization of programs on parallel computers both with shared memory and with distributed memory are discussed. By analyzing the inherent law of the mathematics and physics model of photon transport according to the structure feature of parallel computers, using the strategy of 'to divide and conquer', adjusting the algorithm structure of the program, dissolving the data relationship, finding parallel liable ingredients and creating large grain parallel subtasks, the sequential computing of photon transport into is efficiently transformed into parallel and vector computing. The program was run on various HP parallel computers such as the HY-1 (PVP), the Challenge (SMP) and the YH-3 (MPP) and very good parallel speedup has been gotten

Intentional and automatic processing of numerical information in mathematical anxiety: testing the influence of emotional priming.

Science.gov (United States)

Ashkenazi, Sarit

2018-02-05

Current theoretical approaches suggest that mathematical anxiety (MA) manifests itself as a weakness in quantity manipulations. This study is the first to examine automatic versus intentional processing of numerical information using the numerical Stroop paradigm in participants with high MA. To manipulate anxiety levels, we combined the numerical Stroop task with an affective priming paradigm. We took a group of college students with high MA and compared their performance to a group of participants with low MA. Under low anxiety conditions (neutral priming), participants with high MA showed relatively intact number processing abilities. However, under high anxiety conditions (mathematical priming), participants with high MA showed (1) higher processing of the non-numerical irrelevant information, which aligns with the theoretical view regarding deficits in selective attention in anxiety and (2) an abnormal numerical distance effect. These results demonstrate that abnormal, basic numerical processing in MA is context related.

Mathematical and computational modeling with applications in natural and social sciences, engineering, and the arts

CERN Document Server

Melnik, Roderick

2015-01-01

Illustrates the application of mathematical and computational modeling in a variety of disciplines With an emphasis on the interdisciplinary nature of mathematical and computational modeling, Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts features chapters written by well-known, international experts in these fields and presents readers with a host of state-of-the-art achievements in the development of mathematical modeling and computational experiment methodology. The book is a valuable guide to the methods, ideas,

The Computer Student Worksheet Based Mathematical Literacy for Statistics

Science.gov (United States)

Manoy, J. T.; Indarasati, N. A.

2018-01-01

The student worksheet is one of media teaching which is able to improve teaching an activity in the classroom. Indicators in mathematical literacy were included in a student worksheet is able to help the students for applying the concept in daily life. Then, the use of computers in learning can create learning with environment-friendly. This research used developmental research which was Thiagarajan (Four-D) development design. There are 4 stages in the Four-D, define, design, develop, and disseminate. However, this research was finish until the third stage, develop stage. The computer student worksheet based mathematical literacy for statistics executed good quality. This student worksheet is achieving the criteria if able to achieve three aspects, validity, practicality, and effectiveness. The subject in this research was the students at The 1st State Senior High School of Driyorejo, Gresik, grade eleven of The 5th Mathematics and Natural Sciences. The computer student worksheet products based mathematical literacy for statistics executed good quality, while it achieved the aspects for validity, practical, and effectiveness. This student worksheet achieved the validity aspects with an average of 3.79 (94.72%), and practical aspects with an average of 2.85 (71.43%). Besides, it achieved the effectiveness aspects with a percentage of the classical complete students of 94.74% and a percentage of the student positive response of 75%.

Physics, Computer Science and Mathematics Division annual report, 1 January--31 December 1975. [LBL

Energy Technology Data Exchange (ETDEWEB)

Lepore, J.L. (ed.)

1975-01-01

This annual report describes the scientific research and other work carried out during the calendar year 1975. The report is nontechnical in nature, with almost no data. A 17-page bibliography lists the technical papers which detail the work. The contents of the report include the following: experimental physics (high-energy physics--SPEAR, PEP, SLAC, FNAL, BNL, Bevatron; particle data group; medium-energy physics; astrophysics, astronomy, and cosmic rays; instrumentation development), theoretical physics (particle theory and accelerator theory and design), computer science and applied mathematics (data management systems, socio-economic environment demographic information system, computer graphics, computer networks, management information systems, computational physics and data analysis, mathematical modeling, programing languages, applied mathematics research), real-time systems (ModComp and PDP networks), and computer center activities (systems programing, user services, hardware development, computer operations). A glossary of computer science and mathematics terms is also included. 32 figures. (RWR)

Associations of non-symbolic and symbolic numerical magnitude processing with mathematical competence: a meta-analysis.

Science.gov (United States)

Schneider, Michael; Beeres, Kassandra; Coban, Leyla; Merz, Simon; Susan Schmidt, S; Stricker, Johannes; De Smedt, Bert

2017-05-01

Many studies have investigated the association between numerical magnitude processing skills, as assessed by the numerical magnitude comparison task, and broader mathematical competence, e.g. counting, arithmetic, or algebra. Most correlations were positive but varied considerably in their strengths. It remains unclear whether and to what extent the strength of these associations differs systematically between non-symbolic and symbolic magnitude comparison tasks and whether age, magnitude comparison measures or mathematical competence measures are additional moderators. We investigated these questions by means of a meta-analysis. The literature search yielded 45 articles reporting 284 effect sizes found with 17,201 participants. Effect sizes were combined by means of a two-level random-effects regression model. The effect size was significantly higher for the symbolic (r = .302, 95% CI [.243, .361]) than for the non-symbolic (r = .241, 95% CI [.198, .284]) magnitude comparison task and decreased very slightly with age. The correlation was higher for solution rates and Weber fractions than for alternative measures of comparison proficiency. It was higher for mathematical competencies that rely more heavily on the processing of magnitudes (i.e. mental arithmetic and early mathematical abilities) than for others. The results support the view that magnitude processing is reliably associated with mathematical competence over the lifespan in a wide range of tasks, measures and mathematical subdomains. The association is stronger for symbolic than for non-symbolic numerical magnitude processing. So symbolic magnitude processing might be a more eligible candidate to be targeted by diagnostic screening instruments and interventions for school-aged children and for adults. © 2016 John Wiley & Sons Ltd.

Physics, Computer Science and Mathematics Division. Annual report, 1 January--31 December 1977. [LBL, 1977

Energy Technology Data Exchange (ETDEWEB)

Lepore, J.V. (ed.)

1977-01-01

This annual report of the Physics, Computer Science and Mathematics Division describes the scientific research and other work carried out within the Division during 1977. The Division is concerned with work in experimental and theoretical physics, with computer science and applied mathematics, and with the operation of a computer center. The major physics research activity is in high-energy physics, although there is a relatively small program of medium-energy research. The High Energy Physics research program in the Physics Division is concerned with fundamental research which will enable man to comprehend the nature of the physical world. The major effort is now directed toward experiments with positron-electron colliding beam at PEP. The Medium Energy Physics program is concerned with research using mesons and nucleons to probe the properties of matter. This research is concerned with the study of nuclear structure, nuclear reactions, and the interactions between nuclei and electromagnetic radiation and mesons. The Computer Science and Applied Mathematics Department engages in research in a variety of computer science and mathematics disciplines. Work in computer science and applied mathematics includes construction of data bases, computer graphics, computational physics and data analysis, mathematical modeling, and mathematical analysis of differential and integral equations resulting from physical problems. The Computer Center provides large-scale computational support to LBL's scientific programs. Descriptions of the various activities are quite short; references to published results are given. 24 figures. (RWR)

COMPUTER TOOLS OF DYNAMIC MATHEMATIC SOFTWARE AND METHODICAL PROBLEMS OF THEIR USE

OpenAIRE

Olena V. Semenikhina; Maryna H. Drushliak

2014-01-01

The article presents results of analyses of standard computer tools of dynamic mathematic software which are used in solving tasks, and tools on which the teacher can support in the teaching of mathematics. Possibility of the organization of experimental investigating of mathematical objects on the basis of these tools and the wording of new tasks on the basis of the limited number of tools, fast automated check are specified. Some methodological comments on application of computer tools and ...

Some unsolved problems in discrete mathematics and mathematical cybernetics

Energy Technology Data Exchange (ETDEWEB)

Korshunov, Aleksei D [S.L. Sobolev Institute for Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk (Russian Federation)

2009-10-31

There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.

Numerical Computation of Detonation Stability

KAUST Repository

Kabanov, Dmitry

2018-06-03

Detonation is a supersonic mode of combustion that is modeled by a system of conservation laws of compressible fluid mechanics coupled with the equations describing thermodynamic and chemical properties of the fluid. Mathematically, these governing equations admit steady-state travelling-wave solutions consisting of a leading shock wave followed by a reaction zone. However, such solutions are often unstable to perturbations and rarely observed in laboratory experiments. The goal of this work is to study the stability of travelling-wave solutions of detonation models by the following novel approach. We linearize the governing equations about a base travelling-wave solution and solve the resultant linearized problem using high-order numerical methods. The results of these computations are postprocessed using dynamic mode decomposition to extract growth rates and frequencies of the perturbations and predict stability of travelling-wave solutions to infinitesimal perturbations. We apply this approach to two models based on the reactive Euler equations for perfect gases. For the first model with a one-step reaction mechanism, we find agreement of our results with the results of normal-mode analysis. For the second model with a two-step mechanism, we find that both types of admissible travelling-wave solutions exhibit the same stability spectra. Then we investigate the Fickett’s detonation analogue coupled with a particular reaction-rate expression. In addition to the linear stability analysis of this model, we demonstrate that it exhibits rich nonlinear dynamics with multiple bifurcations and chaotic behavior.

Mathematical modeling and optimization of complex structures

CERN Document Server

Repin, Sergey; Tuovinen, Tero

2016-01-01

This volume contains selected papers in three closely related areas: mathematical modeling in mechanics, numerical analysis, and optimization methods. The papers are based upon talks presented  on the International Conference for Mathematical Modeling and Optimization in Mechanics, held in Jyväskylä, Finland, March 6-7, 2014 dedicated to Prof. N. Banichuk on the occasion of his 70th birthday. The articles are written by well-known scientists working in computational mechanics and in optimization of complicated technical models. Also, the volume contains papers discussing the historical development, the state of the art, new ideas, and open problems arising in  modern continuum mechanics and applied optimization problems. Several papers are concerned with mathematical problems in numerical analysis, which are also closely related to important mechanical models. The main topics treated include:  * Computer simulation methods in mechanics, physics, and biology;  * Variational problems and methods; minimiz...

Classical and modern numerical analysis theory, methods and practice

CERN Document Server

Ackleh, Azmy S; Kearfott, R Baker; Seshaiyer, Padmanabhan

2009-01-01

Mathematical Review and Computer Arithmetic Mathematical Review Computer Arithmetic Interval ComputationsNumerical Solution of Nonlinear Equations of One Variable Introduction Bisection Method The Fixed Point Method Newton's Method (Newton-Raphson Method) The Univariate Interval Newton MethodSecant Method and Müller's Method Aitken Acceleration and Steffensen's Method Roots of Polynomials Additional Notes and SummaryNumerical Linear Algebra Basic Results from Linear Algebra Normed Linear Spaces Direct Methods for Solving Linear SystemsIterative Methods for Solving Linear SystemsThe Singular Value DecompositionApproximation TheoryIntroduction Norms, Projections, Inner Product Spaces, and Orthogonalization in Function SpacesPolynomial ApproximationPiecewise Polynomial ApproximationTrigonometric ApproximationRational ApproximationWavelet BasesLeast Squares Approximation on a Finite Point SetEigenvalue-Eigenvector Computation Basic Results from Linear Algebra The Power Method The Inverse Power Method Deflation T...

Relations of Different Types of Numerical Magnitude Representations to Each Other and to Mathematics Achievement

Science.gov (United States)

Fazio, Lisa K.; Bailey, Drew H.; Thompson, Clarissa A.; Siegler, Robert S.

2014-01-01

We examined relations between symbolic and non-symbolic numerical magnitude representations, between whole number and fraction representations, and between these representations and overall mathematics achievement in fifth graders. Fraction and whole number symbolic and non-symbolic numerical magnitude understandings were measured using both…

NATO Advanced Research Workshop on Exploiting Mental Imagery with Computers in Mathematics Education

CERN Document Server

Mason, John

1995-01-01

The advent of fast and sophisticated computer graphics has brought dynamic and interactive images under the control of professional mathematicians and mathematics teachers. This volume in the NATO Special Programme on Advanced Educational Technology takes a comprehensive and critical look at how the computer can support the use of visual images in mathematical problem solving. The contributions are written by researchers and teachers from a variety of disciplines including computer science, mathematics, mathematics education, psychology, and design. Some focus on the use of external visual images and others on the development of individual mental imagery. The book is the first collected volume in a research area that is developing rapidly, and the authors pose some challenging new questions.

Correlation Educational Model in Primary Education Curriculum of Mathematics and Computer Science

Science.gov (United States)

Macinko Kovac, Maja; Eret, Lidija

2012-01-01

This article gives insight into methodical correlation model of teaching mathematics and computer science. The model shows the way in which the related areas of computer science and mathematics can be supplemented, if it transforms the way of teaching and creates a "joint" lessons. Various didactic materials are designed, in which all…

The Incorporation of Micro-Computer Technology into School Mathematics: Some Suggestions for Middle and Senior Mathematics Courses.

Science.gov (United States)

Newton, Bill

1987-01-01

Argues that the use of computer technologies in secondary schools should change the nature of mathematics education. Urges the rethinking of the uses of traditional paper-and-pencil computations. Suggests some computer applications for elementary algebra and for problem solving in arithmetic and calculus. (TW)

[Research activities in applied mathematics, fluid mechanics, and computer science

Science.gov (United States)

1995-01-01

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period April 1, 1995 through September 30, 1995.

Optimisation of gas-cooled reactors with the aid of mathematical computers

Energy Technology Data Exchange (ETDEWEB)

Margen, P H

1959-04-15

Reactor optimisation is the task of finding the combination of values of the independent variables in a reactor design producing the lowest cost of electricity. In a gas-cooled reactor the number of independent variables is particularly large and the optimisation process is, therefore, laborious. The present note describes a procedure for performing the entire optimisation procedure with the aid of a mathematical computer in a single operation, thus saving time for the design staff. Detailed equations and numerical constants are proposed for the thermal and cost relations involved. The reactor physics equations, on the other hand are merely stated as general functions of the relevant variables. The task of expressing these functions as detailed equations will be covered by separate documents prepared by the reactor physics department.

Optimisation of gas-cooled reactors with the aid of mathematical computers

International Nuclear Information System (INIS)

Margen, P.H.

1959-04-01

Reactor optimisation is the task of finding the combination of values of the independent variables in a reactor design producing the lowest cost of electricity. In a gas-cooled reactor the number of independent variables is particularly large and the optimisation process is, therefore, laborious. The present note describes a procedure for performing the entire optimisation procedure with the aid of a mathematical computer in a single operation, thus saving time for the design staff. Detailed equations and numerical constants are proposed for the thermal and cost relations involved. The reactor physics equations, on the other hand are merely stated as general functions of the relevant variables. The task of expressing these functions as detailed equations will be covered by separate documents prepared by the reactor physics department

Numerical simulation in plasma physics

International Nuclear Information System (INIS)

Samarskii, A.A.

1980-01-01

Plasma physics is not only a field for development of physical theories and mathematical models but also an object of application of the computational experiment comprising analytical and numerical methods adapted for computers. The author considers only MHD plasma physics problems. Examples treated are dissipative structures in plasma; MHD model of solar dynamo; supernova explosion simulation; and plasma compression by a liner. (Auth.)

Mathematics in computed tomography and related techniques

International Nuclear Information System (INIS)

Sawicka, B.

1992-01-01

The mathematical basis of computed tomography (CT) was formulated in 1917 by Radon. His theorem states that the 2-D function f(x,y) can be determined at all points from a complete set of its line integrals. Modern methods of image reconstruction include three approaches: algebraic reconstruction techniques with simultaneous iterative reconstruction or simultaneous algebraic reconstruction; convolution back projection; and the Fourier transform method. There is no one best approach. Because the experimental data do not strictly satisfy theoretical models, a number of effects have to be taken into account; in particular, the problems of beam geometry, finite beam dimensions and distribution, beam scattering, and the radiation source spectrum. Tomography with truncated data is of interest, employing mathematical approximations to compensate for the unmeasured projection data. Mathematical techniques in image processing and data analysis are also extensively used. 13 refs

International Conference on Applied Mathematics, Modeling and Computational Science & Annual meeting of the Canadian Applied and Industrial Mathematics

CERN Document Server

Bélair, Jacques; Kunze, Herb; Makarov, Roman; Melnik, Roderick; Spiteri, Raymond J

2016-01-01

Focusing on five main groups of interdisciplinary problems, this book covers a wide range of topics in mathematical modeling, computational science and applied mathematics. It presents a wealth of new results in the development of modeling theories and methods, advancing diverse areas of applications and promoting interdisciplinary interactions between mathematicians, scientists, engineers and representatives from other disciplines. The book offers a valuable source of methods, ideas, and tools developed for a variety of disciplines, including the natural and social sciences, medicine, engineering, and technology. Original results are presented on both the fundamental and applied level, accompanied by an ample number of real-world problems and examples emphasizing the interdisciplinary nature and universality of mathematical modeling, and providing an excellent outline of today’s challenges. Mathematical modeling, with applied and computational methods and tools, plays a fundamental role in modern science a...

Recent progress and modern challenges in applied mathematics, modeling and computational science

CERN Document Server

Makarov, Roman; Belair, Jacques

2017-01-01

This volume is an excellent resource for professionals in various areas of applications of mathematics, modeling, and computational science. It focuses on recent progress and modern challenges in these areas. The volume provides a balance between fundamental theoretical and applied developments, emphasizing the interdisciplinary nature of modern trends and detailing state-of-the-art achievements in Applied Mathematics, Modeling, and Computational Science.  The chapters have been authored by international experts in their respective fields, making this book ideal for researchers in academia, practitioners, and graduate students. It can also serve as a reference in the diverse selected areas of applied mathematics, modelling, and computational sciences, and is ideal for interdisciplinary collaborations.

Improving Mathematics Learning of Kindergarten Students through Computer-Assisted Instruction

Science.gov (United States)

Foster, Matthew E.; Anthony, Jason L.; Clements, Doug H.; Sarama, Julie; Williams, Jeffrey M.

2016-01-01

This study evaluated the effects of a mathematics software program, the Building Blocks software suite, on young children's mathematics performance. Participants included 247 Kindergartners from 37 classrooms in 9 schools located in low-income communities. Children within classrooms were randomly assigned to receive 21 weeks of computer-assisted…

Application of computer mathematical modeling in nuclear well-logging industry

International Nuclear Information System (INIS)

Cai Shaohui

1994-01-01

Nuclear well logging techniques have made rapid progress since the first well log calibration facility (the API pits) was dedicated in 1959. Then came the first computer mathematical model in the late 70's. Mathematical modeling can now minimize design and experiment time, as well as provide new information and idea on tool design, environmental effects and result interpretation. The author gives a brief review on the achievements of mathematical modeling on nuclear logging problems

Foundations of children's numerical and mathematical skills: the roles of symbolic and nonsymbolic representations of numerical magnitude.

Science.gov (United States)

Lyons, Ian M; Ansari, Daniel

2015-01-01

Numerical and mathematical skills are critical predictors of academic success. The last three decades have seen a substantial growth in our understanding of how the human mind and brain represent and process numbers. In particular, research has shown that we share with animals the ability to represent numerical magnitude (the total number of items in a set) and that preverbal infants can process numerical magnitude. Further research has shown that similar processing signatures characterize numerical magnitude processing across species and developmental time. These findings suggest that an approximate system for nonsymbolic (e.g., dot arrays) numerical magnitude representation serves as the basis for the acquisition of cultural, symbolic (e.g., Arabic numerals) representations of numerical magnitude. This chapter explores this hypothesis by reviewing studies that have examined the relation between individual differences in nonsymbolic numerical magnitude processing and symbolic math abilities (e.g., arithmetic). Furthermore, we examine the extent to which the available literature provides strong evidence for a link between symbolic and nonsymbolic representations of numerical magnitude at the behavioral and neural levels of analysis. We conclude that claims that symbolic number abilities are grounded in the approximate system for the nonsymbolic representation of numerical magnitude are not strongly supported by the available evidence. Alternative models and future research directions are discussed. © 2015 Elsevier Inc. All rights reserved.

Computational problems in engineering

CERN Document Server

Mladenov, Valeri

2014-01-01

This book provides readers with modern computational techniques for solving variety of problems from electrical, mechanical, civil and chemical engineering. Mathematical methods are presented in a unified manner, so they can be applied consistently to problems in applied electromagnetics, strength of materials, fluid mechanics, heat and mass transfer, environmental engineering, biomedical engineering, signal processing, automatic control and more.   • Features contributions from distinguished researchers on significant aspects of current numerical methods and computational mathematics; • Presents actual results and innovative methods that provide numerical solutions, while minimizing computing times; • Includes new and advanced methods and modern variations of known techniques that can solve difficult scientific problems efficiently.  

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

Numerical methods in finance and economics a MATLAB-based introduction

CERN Document Server

Brandimarte, Paolo

2006-01-01

A state-of-the-art introduction to the powerful mathematical and statistical tools used in the field of financeThe use of mathematical models and numerical techniques is a practice employed by a growing number of applied mathematicians working on applications in finance. Reflecting this development, Numerical Methods in Finance and Economics: A MATLAB?-Based Introduction, Second Edition bridges the gap between financial theory and computational practice while showing readers how to utilize MATLAB?--the powerful numerical computing environment--for financial applications.The author provides an essential foundation in finance and numerical analysis in addition to background material for students from both engineering and economics perspectives. A wide range of topics is covered, including standard numerical analysis methods, Monte Carlo methods to simulate systems affected by significant uncertainty, and optimization methods to find an optimal set of decisions.Among this book''s most outstanding features is the...

Problem-Based Instructional Strategy and Numerical Ability as Determinants of Senior Secondary Achievement in Mathematics

Science.gov (United States)

Badru, Ademola K.

2016-01-01

The study investigated Problem-based Instructional Strategy and Numerical ability as determinants of Senior Secondary Achievement in Mathematics. This study used 4 x 2 x 2 non-randomised control group Pretest-Posttest Quasi-experimental Factorial design. It consisted of two independent variables (treatment and Numerical ability) and one moderating…

Methodological Potential of Computer Experiment in Teaching Mathematics at University

Science.gov (United States)

Lin, Kequan; Sokolova, Anna Nikolaevna; Vlasova, Vera K.

2017-01-01

The study is relevant due to the opportunity of increasing efficiency of teaching mathematics at university through integration of students of computer experiment conducted with the use of IT in this process. The problem of there search is defined by a contradiction between great potential opportunities of mathematics experiment for motivating and…

Physics, Computer Science and Mathematics Division. Annual report, 1 January-31 December 1979

International Nuclear Information System (INIS)

Lepore, J.V.

1980-09-01

This annual report describes the research work carried out by the Physics, Computer Science and Mathematics Division during 1979. The major research effort of the Division remained High Energy Particle Physics with emphasis on preparing for experiments to be carried out at PEP. The largest effort in this field was for development and construction of the Time Projection Chamber, a powerful new particle detector. This work took a large fraction of the effort of the physics staff of the Division together with the equivalent of more than a hundred staff members in the Engineering Departments and shops. Research in the Computer Science and Mathematics Department of the Division (CSAM) has been rapidly expanding during the last few years. Cross fertilization of ideas and talents resulting from the diversity of effort in the Physics, Computer Science and Mathematics Division contributed to the software design for the Time Projection Chamber, made by the Computer Science and Applied Mathematics Department

Integrating numerical computation into the undergraduate education physics curriculum using spreadsheet excel

Science.gov (United States)

Fauzi, Ahmad

2017-11-01

Numerical computation has many pedagogical advantages: it develops analytical skills and problem-solving skills, helps to learn through visualization, and enhances physics education. Unfortunately, numerical computation is not taught to undergraduate education physics students in Indonesia. Incorporate numerical computation into the undergraduate education physics curriculum presents many challenges. The main challenges are the dense curriculum that makes difficult to put new numerical computation course and most students have no programming experience. In this research, we used case study to review how to integrate numerical computation into undergraduate education physics curriculum. The participants of this research were 54 students of the fourth semester of physics education department. As a result, we concluded that numerical computation could be integrated into undergraduate education physics curriculum using spreadsheet excel combined with another course. The results of this research become complements of the study on how to integrate numerical computation in learning physics using spreadsheet excel.

Numerical computation of linear instability of detonations

Science.gov (United States)

Kabanov, Dmitry; Kasimov, Aslan

2017-11-01

We propose a method to study linear stability of detonations by direct numerical computation. The linearized governing equations together with the shock-evolution equation are solved in the shock-attached frame using a high-resolution numerical algorithm. The computed results are processed by the Dynamic Mode Decomposition technique to generate dispersion relations. The method is applied to the reactive Euler equations with simple-depletion chemistry as well as more complex multistep chemistry. The results are compared with those known from normal-mode analysis. We acknowledge financial support from King Abdullah University of Science and Technology.

Implementing a Flipped Classroom Approach in a University Numerical Methods Mathematics Course

Science.gov (United States)

Johnston, Barbara M.

2017-01-01

This paper describes and analyses the implementation of a "flipped classroom" approach, in an undergraduate mathematics course on numerical methods. The approach replaced all the lecture contents by instructor-made videos and was implemented in the consecutive years 2014 and 2015. The sequential case study presented here begins with an…

Artificial Intelligence, Computational Thinking, and Mathematics Education

Science.gov (United States)

Gadanidis, George

2017-01-01

Purpose: The purpose of this paper is to examine the intersection of artificial intelligence (AI), computational thinking (CT), and mathematics education (ME) for young students (K-8). Specifically, it focuses on three key elements that are common to AI, CT and ME: agency, modeling of phenomena and abstracting concepts beyond specific instances.…

War of ontology worlds: mathematics, computer code, or Esperanto?

Science.gov (United States)

Rzhetsky, Andrey; Evans, James A

2011-09-01

The use of structured knowledge representations-ontologies and terminologies-has become standard in biomedicine. Definitions of ontologies vary widely, as do the values and philosophies that underlie them. In seeking to make these views explicit, we conducted and summarized interviews with a dozen leading ontologists. Their views clustered into three broad perspectives that we summarize as mathematics, computer code, and Esperanto. Ontology as mathematics puts the ultimate premium on rigor and logic, symmetry and consistency of representation across scientific subfields, and the inclusion of only established, non-contradictory knowledge. Ontology as computer code focuses on utility and cultivates diversity, fitting ontologies to their purpose. Like computer languages C++, Prolog, and HTML, the code perspective holds that diverse applications warrant custom designed ontologies. Ontology as Esperanto focuses on facilitating cross-disciplinary communication, knowledge cross-referencing, and computation across datasets from diverse communities. We show how these views align with classical divides in science and suggest how a synthesis of their concerns could strengthen the next generation of biomedical ontologies.

Mathematical foundations of computed tomography

International Nuclear Information System (INIS)

Smith, K.T.; Keinert, F.

1985-01-01

Along with a review of some of the mathematical foundations of computed tomography, the article contains new results on derivation of reconstruction formulas in a general setting encompassing all standard formulas; discussion and examples of the role of the point spread function with recipes for producing suitable ones; formulas for, and examples of, the reconstruction of certain functions of the attenuation coefficient, e.g., sharpened versions of it, some of them with the property that reconstruction at a point requires only the attenuation along rays meeting a small neighborhood of the point

The Contributions of Domain-General and Numerical Factors to Third-Grade Arithmetic Skills and Mathematical Learning Disability

Science.gov (United States)

Cowan, Richard; Powell, Daisy

2014-01-01

Explanations of the marked individual differences in elementary school mathematical achievement and mathematical learning disability (MLD or dyscalculia) have involved domain-general factors (working memory, reasoning, processing speed, and oral language) and numerical factors that include single-digit processing efficiency and multidigit skills…

The presence of mathematics and computer anxiety in nursing students and their effects on medication dosage calculations.

Science.gov (United States)

Glaister, Karen

2007-05-01

To determine if the presence of mathematical and computer anxiety in nursing students affects learning of dosage calculations. The quasi-experimental study compared learning outcomes at differing levels of mathematical and computer anxiety when integrative and computer based learning approaches were used. Participants involved a cohort of second year nursing students (n=97). Mathematical anxiety exists in 20% (n=19) of the student nurse population, and 14% (n=13) experienced mathematical testing anxiety. Those students more anxious about mathematics and the testing of mathematics benefited from integrative learning to develop conditional knowledge (F(4,66)=2.52 at pComputer anxiety was present in 12% (n=11) of participants, with those reporting medium and high levels of computer anxiety performing less well than those with low levels (F(1,81)=3.98 at pmathematical and computer anxiety when planning an educational program to develop competency in dosage calculations.

Mathematics of shape description a morphological approach to image processing and computer graphics

CERN Document Server

Ghosh, Pijush K

2009-01-01

Image processing problems are often not well defined because real images are contaminated with noise and other uncertain factors. In Mathematics of Shape Description, the authors take a mathematical approach to address these problems using the morphological and set-theoretic approach to image processing and computer graphics by presenting a simple shape model using two basic shape operators called Minkowski addition and decomposition. This book is ideal for professional researchers and engineers in Information Processing, Image Measurement, Shape Description, Shape Representation and Computer Graphics. Post-graduate and advanced undergraduate students in pure and applied mathematics, computer sciences, robotics and engineering will also benefit from this book.  Key FeaturesExplains the fundamental and advanced relationships between algebraic system and shape description through the set-theoretic approachPromotes interaction of image processing geochronology and mathematics in the field of algebraic geometryP...

Computers in Science and Mathematics Education in the ASEAN Region.

Science.gov (United States)

Talisayon, Vivien M.

1989-01-01

Compares policies and programs on computers in science and mathematics education in the six ASEAN countries: Brunei, Indonesia; Malaysia, Philippines, Singapore, and Thailand. Limits discussion to the computer as a teaching aid and object of study, attendant problems, and regional cooperation. (MVL)

Numerical mathematics

National Research Council Canada - National Science Library

Quarteroni, Alfio; Sacco, Riccardo; Saleri, Fausto

2000-01-01

... for their qualitative and quantitative analysis. This role is also emphasized by the continual development of computers and algorithms, which make it possible nowadays, using scientific computing, to tackle problems of such a large size that real-life phenomena can be simulated providing accurate responses at affordable computational cost. The corresp...

Uncertainty and variability in computational and mathematical models of cardiac physiology.

Science.gov (United States)

Mirams, Gary R; Pathmanathan, Pras; Gray, Richard A; Challenor, Peter; Clayton, Richard H

2016-12-01

Mathematical and computational models of cardiac physiology have been an integral component of cardiac electrophysiology since its inception, and are collectively known as the Cardiac Physiome. We identify and classify the numerous sources of variability and uncertainty in model formulation, parameters and other inputs that arise from both natural variation in experimental data and lack of knowledge. The impact of uncertainty on the outputs of Cardiac Physiome models is not well understood, and this limits their utility as clinical tools. We argue that incorporating variability and uncertainty should be a high priority for the future of the Cardiac Physiome. We suggest investigating the adoption of approaches developed in other areas of science and engineering while recognising unique challenges for the Cardiac Physiome; it is likely that novel methods will be necessary that require engagement with the mathematics and statistics community. The Cardiac Physiome effort is one of the most mature and successful applications of mathematical and computational modelling for describing and advancing the understanding of physiology. After five decades of development, physiological cardiac models are poised to realise the promise of translational research via clinical applications such as drug development and patient-specific approaches as well as ablation, cardiac resynchronisation and contractility modulation therapies. For models to be included as a vital component of the decision process in safety-critical applications, rigorous assessment of model credibility will be required. This White Paper describes one aspect of this process by identifying and classifying sources of variability and uncertainty in models as well as their implications for the application and development of cardiac models. We stress the need to understand and quantify the sources of variability and uncertainty in model inputs, and the impact of model structure and complexity and their consequences for

Mathematics anxiety reduces default mode network deactivation in response to numerical tasks

Directory of Open Access Journals (Sweden)

Belinda ePletzer

2015-04-01

Full Text Available Mathematics anxiety is negatively related to mathematics performance, thereby threatening the professional success. Preoccupation with the emotional content of the stimuli may consume working memory resources, which may be reflected in decreased deactivation of areas associated with the default mode network (DMN activated during self-referential and emotional processing. The common problem is that math anxiety is usually associated with poor math performance, so that any group differences are difficult to interpret.Here we compared the BOLD-response of 18 participants with high (HMAs and 18 participants with low mathematics anxiety (LMAs matched for their mathematical performance to two numerical tasks (number comparison, number bisection. During both tasks, we found stronger deactivation within the DMN in LMAs compared to HMAs, while BOLD-response in task-related activation areas did not differ between HMAs and LMAs. The difference in DMN deactivation between the HMA and LMA group was more pronounced in stimuli with additional requirement on inhibitory functions, but did not differ between number magnitude processing and arithmetic fact retrieval.

Mathematics anxiety reduces default mode network deactivation in response to numerical tasks.

Science.gov (United States)

Pletzer, Belinda; Kronbichler, Martin; Nuerk, Hans-Christoph; Kerschbaum, Hubert H

2015-01-01

Mathematics anxiety is negatively related to mathematics performance, thereby threatening the professional success. Preoccupation with the emotional content of the stimuli may consume working memory resources, which may be reflected in decreased deactivation of areas associated with the default mode network (DMN) activated during self-referential and emotional processing. The common problem is that math anxiety is usually associated with poor math performance, so that any group differences are difficult to interpret. Here we compared the BOLD-response of 18 participants with high (HMAs) and 18 participants with low mathematics anxiety (LMAs) matched for their mathematical performance to two numerical tasks (number comparison, number bisection). During both tasks, we found stronger deactivation within the DMN in LMAs compared to HMAs, while BOLD-response in task-related activation areas did not differ between HMAs and LMAs. The difference in DMN deactivation between the HMA and LMA group was more pronounced in stimuli with additional requirement on inhibitory functions, but did not differ between number magnitude processing and arithmetic fact retrieval.

Mathematics++ selected topics beyond the basic courses

CERN Document Server

Kantor, Ida; Šámal, Robert

2015-01-01

Mathematics++ is a concise introduction to six selected areas of 20th century mathematics providing numerous modern mathematical tools used in contemporary research in computer science, engineering, and other fields. The areas are: measure theory, high-dimensional geometry, Fourier analysis, representations of groups, multivariate polynomials, and topology. For each of the areas, the authors introduce basic notions, examples, and results. The presentation is clear and accessible, stressing intuitive understanding, and it includes carefully selected exercises as an integral part. Theory is comp

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.

Numerical computation of MHD equilibria

International Nuclear Information System (INIS)

Atanasiu, C.V.

1982-10-01

A numerical code for a two-dimensional MHD equilibrium computation has been carried out. The code solves the Grad-Shafranov equation in its integral form, for both formulations: the free-boundary problem and the fixed boundary one. Examples of the application of the code to tokamak design are given. (author)

Parallel Processing and Applied Mathematics. 10th International Conference, PPAM 2013. Revised Selected Papers

DEFF Research Database (Denmark)

The following topics are dealt with: parallel scientific computing; numerical algorithms; parallel nonnumerical algorithms; cloud computing; evolutionary computing; metaheuristics; applied mathematics; GPU computing; multicore systems; hybrid architectures; hierarchical parallelism; HPC systems......; power monitoring; energy monitoring; and distributed computing....

Developing Teaching Material Software Assisted for Numerical Methods

Science.gov (United States)

Handayani, A. D.; Herman, T.; Fatimah, S.

2017-09-01

The NCTM vision shows the importance of two things in school mathematics, which is knowing the mathematics of the 21st century and the need to continue to improve mathematics education to answer the challenges of a changing world. One of the competencies associated with the great challenges of the 21st century is the use of help and tools (including IT), such as: knowing the existence of various tools for mathematical activity. One of the significant challenges in mathematical learning is how to teach students about abstract concepts. In this case, technology in the form of mathematics learning software can be used more widely to embed the abstract concept in mathematics. In mathematics learning, the use of mathematical software can make high level math activity become easier accepted by student. Technology can strengthen student learning by delivering numerical, graphic, and symbolic content without spending the time to calculate complex computing problems manually. The purpose of this research is to design and develop teaching materials software assisted for numerical method. The process of developing the teaching material starts from the defining step, the process of designing the learning material developed based on information obtained from the step of early analysis, learners, materials, tasks that support then done the design step or design, then the last step is the development step. The development of teaching materials software assisted for numerical methods is valid in content. While validator assessment for teaching material in numerical methods is good and can be used with little revision.

The normative structure of mathematization in systematic biology.

Science.gov (United States)

Sterner, Beckett; Lidgard, Scott

2014-06-01

We argue that the mathematization of science should be understood as a normative activity of advocating for a particular methodology with its own criteria for evaluating good research. As a case study, we examine the mathematization of taxonomic classification in systematic biology. We show how mathematization is a normative activity by contrasting its distinctive features in numerical taxonomy in the 1960s with an earlier reform advocated by Ernst Mayr starting in the 1940s. Both Mayr and the numerical taxonomists sought to formalize the work of classification, but Mayr introduced a qualitative formalism based on human judgment for determining the taxonomic rank of populations, while the numerical taxonomists introduced a quantitative formalism based on automated procedures for computing classifications. The key contrast between Mayr and the numerical taxonomists is how they conceptualized the temporal structure of the workflow of classification, specifically where they allowed meta-level discourse about difficulties in producing the classification. Copyright © 2014. Published by Elsevier Ltd.

Increasing Mathematical Computation Skills for Students with Physical and Health Disabilities

Science.gov (United States)

Webb, Paula

2017-01-01

Students with physical and health disabilities struggle with basic mathematical concepts. The purpose of this research study was to increase the students' mathematical computation skills through implementing new strategies and/or methods. The strategies implemented with the students was utilizing the ten-frame tiles and technology with the purpose…

Mathematica with a Numerical Methods Course

Science.gov (United States)

Varley, Rodney

2003-04-01

An interdisciplinary "Numerical Methods" course has been shared between physics, mathematics and computer science since 1992 at Hunter C. Recently, the lectures and workshops for this course have become formalized and placed on the internet at http://www.ph.hunter.cuny.edu (follow the links "Course Listings and Websites" >> "PHYS385 (Numerical Methods)". Mathematica notebooks for the lectures are available for automatic download (by "double clicking" the lecture icon) for student use in the classroom or at home. AOL (or Netscape/Explorer) can be used provided Mathematica (or the "free" MathReader) has been made a "helper application". Using Mathematica has the virtue that mathematical equations (no LaTex required) can easily be included with the text and Mathematica's graphing is easy to use. Computational cells can be included within the notebook and students may easily modify the calculation to see the result of "what if..." questions. Homework is sent as Mathematica notebooks to the instructor via the internet and the corrected workshops are returned in the same manner. Most exam questions require computational solutions.

Numerical methods for solution of some nonlinear problems of mathematical physics

International Nuclear Information System (INIS)

Zhidkov, E.P.

1981-01-01

The continuous analog of the Newton method and its application to some nonlinear problems of mathematical physics using a computer is considered. It is shown that the application of this method in JINR to the wide range of nonlinear problems has shown its universality and high efficiency [ru

3rd International Conference on Computer Science, Applied Mathematics and Applications

CERN Document Server

Nguyen, Ngoc; Do, Tien

2015-01-01

This volume contains the extended versions of papers presented at the 3rd International Conference on Computer Science, Applied Mathematics and Applications (ICCSAMA 2015) held on 11-13 May, 2015 in Metz, France. The book contains 5 parts: 1. Mathematical programming and optimization: theory, methods and software, Operational research and decision making, Machine learning, data security, and bioinformatics, Knowledge information system, Software engineering. All chapters in the book discuss theoretical and algorithmic as well as practical issues connected with computation methods & optimization methods for knowledge engineering and machine learning techniques.  

Remote access to mathematical software

International Nuclear Information System (INIS)

Dolan, E.; Hovland, P.; More, J.; Norris, B.; Smith, B.

2001-01-01

The network-oriented application services paradigm is becoming increasingly common for scientific computing. The popularity of this approach can be attributed to the numerous advantages to both user and developer provided by network-enabled mathematical software. The burden of installing and maintaining complex systems is lifted from the user, while enabling developers to provide frequent updates without disrupting service. Access to software with similar functionality can be unified under the same interface. Remote servers can utilize potentially more powerful computing resources than may be available locally. We discuss some of the application services developed by the Mathematics and Computer Science Division at Argonne National Laboratory, including the Network Enabled Optimization System (NEOS) Server and the Automatic Differentiation of C (ADIC) Server, as well as preliminary work on Web access to the Portable Extensible Toolkit for Scientific Computing (PETSc). We also provide a brief survey of related work

Computing the stability of steady-state solutions of mathematical models of the electrical activity in the heart.

Science.gov (United States)

Tveito, Aslak; Skavhaug, Ola; Lines, Glenn T; Artebrant, Robert

2011-08-01

Instabilities in the electro-chemical resting state of the heart can generate ectopic waves that in turn can initiate arrhythmias. We derive methods for computing the resting state for mathematical models of the electro-chemical process underpinning a heartbeat, and we estimate the stability of the resting state by invoking the largest real part of the eigenvalues of a linearized model. The implementation of the methods is described and a number of numerical experiments illustrate the feasibility of the methods. In particular, we test the methods for problems where we can compare the solutions with analytical results, and problems where we have solutions computed by independent software. The software is also tested for a fairly realistic 3D model. Copyright © 2011 Elsevier Ltd. All rights reserved.

The Gap between Expectations and Reality: Integrating Computers into Mathematics Classrooms

Science.gov (United States)

Guven, Bulent; Cakiroglu, Unal; Akkan, Yasar

2009-01-01

As a result of dramatic changes in mathematics education around the world, in Turkey both elementary and secondary school mathematics curriculums have changed in the light of new demands since 2005. In order to perform the expected change in newly developed curriculum, computer should be integrated into learning and teaching process. Teachers'…

BOOK REVIEW: Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming

Science.gov (United States)

Katsaounis, T. D.

2005-02-01

equations in Diffpack can be used to derive fully implicit solvers for systems. The proposed techniques are illustrated in terms of two applications, namely a system of PDEs modelling pipeflow and a two-phase porous media flow. Stochastic PDEs is the topic of chapter 7. The first part of the chapter is a simple introduction to stochastic PDEs; basic analytical properties are presented for simple models like transport phenomena and viscous drag forces. The second part considers the numerical solution of stochastic PDEs. Two basic techniques are presented, namely Monte Carlo and perturbation methods. The last part explains how to implement and incorporate these solvers into Diffpack. Chapter 8 describes how to operate Diffpack from Python scripts. The main goal here is to provide all the programming and technical details in order to glue the programming environment of Diffpack with visualization packages through Python and in general take advantage of the Python interfaces. Chapter 9 attempts to show how to use numerical experiments to measure the performance of various PDE solvers. The authors gathered a rather impressive list, a total of 14 PDE solvers. Solvers for problems like Poisson, Navier--Stokes, elasticity, two-phase flows and methods such as finite difference, finite element, multigrid, and gradient type methods are presented. The authors provide a series of numerical results combining various solvers with various methods in order to gain insight into their computational performance and efficiency. In Chapter 10 the authors consider a computationally challenging problem, namely the computation of the electrical activity of the human heart. After a brief introduction on the biology of the problem the authors present the mathematical models involved and a numerical method for solving them within the framework of Diffpack. Chapter 11 and 12 are closely related; actually they could have been combined in a single chapter. Chapter 11 introduces several mathematical

Structural Equation Model to Validate: Mathematics-Computer Interaction, Computer Confidence, Mathematics Commitment, Mathematics Motivation and Mathematics Confidence

Science.gov (United States)

Garcia-Santillán, Arturo; Moreno-Garcia, Elena; Escalera-Chávez, Milka E.; Rojas-Kramer, Carlos A.; Pozos-Texon, Felipe

2016-01-01

Most mathematics students show a definite tendency toward an attitudinal deficiency, which can be primarily understood as intolerance to the matter, affecting their scholar performance adversely. In addition, information and communication technologies have been gradually included within the process of teaching mathematics. Such adoption of…

Effectiveness of Computer-Assisted Mathematics Education (CAME) over Academic Achievement: A Meta-Analysis Study

Science.gov (United States)

Demir, Seda; Basol, Gülsah

2014-01-01

The aim of the current study is to determine the overall effects of Computer-Assisted Mathematics Education (CAME) on academic achievement. After an extensive review of the literature, studies using Turkish samples and observing the effects of Computer-Assisted Education (CAE) on mathematics achievement were examined. As a result of this…

Mathematical analysis, approximation theory and their applications

CERN Document Server

Gupta, Vijay

2016-01-01

Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.

Advances in Reactor Physics, Mathematics and Computation. Volume 1

Energy Technology Data Exchange (ETDEWEB)

1987-01-01

These proceedings of the international topical meeting on advances in reactor physics, mathematics and computation, volume one, are divided into 6 sessions bearing on: - session 1: Advances in computational methods including utilization of parallel processing and vectorization (7 conferences) - session 2: Fast, epithermal, reactor physics, calculation, versus measurements (9 conferences) - session 3: New fast and thermal reactor designs (9 conferences) - session 4: Thermal radiation and charged particles transport (7 conferences) - session 5: Super computers (7 conferences) - session 6: Thermal reactor design, validation and operating experience (8 conferences).

Progress in Computational Physics (PiCP) Volume 1 Wave Propagation in Periodic Media

CERN Document Server

Ehrhardt, Matthias

2010-01-01

Progress in Computational Physics is a new e-book series devoted to recent research trends in computational physics. It contains chapters contributed by outstanding experts of modeling of physical problems. The series focuses on interdisciplinary computational perspectives of current physical challenges, new numerical techniques for the solution of mathematical wave equations and describes certain real-world applications. With the help of powerful computers and sophisticated methods of numerical mathematics it is possible to simulate many ultramodern devices, e.g. photonic crystals structures,

Examining Student Opinions on Computer Use Based on the Learning Styles in Mathematics Education

Science.gov (United States)

Ozgen, Kemal; Bindak, Recep

2012-01-01

The purpose of this study is to identify the opinions of high school students, who have different learning styles, related to computer use in mathematics education. High school students' opinions on computer use in mathematics education were collected with both qualitative and quantitative approaches in the study conducted with a survey model. For…

Description of mathematical models and computer programs

International Nuclear Information System (INIS)

1977-01-01

The paper gives a description of mathematical models and computer programs for analysing possible strategies for spent fuel management, with emphasis on economic analysis. The computer programs developed, describe the material flows, facility construction schedules, capital investment schedules and operating costs for the facilities used in managing the spent fuel. The computer programs use a combination of simulation and optimization procedures for the economic analyses. Many of the fuel cycle steps (such as spent fuel discharges, storage at the reactor, and transport to the RFCC) are described in physical and economic terms through simulation modeling, while others (such as reprocessing plant size and commissioning schedules, interim storage facility commissioning schedules etc.) are subjected to economic optimization procedures to determine the approximate lowest-cost plans from among the available feasible alternatives

Formal languages, automata and numeration systems introduction to combinatorics on words

CERN Document Server

Rigo, Michel

2014-01-01

Formal Languages, Automaton and Numeration Systems presents readers with a review of research related to formal language theory, combinatorics on words or numeration systems, such as Words, DLT (Developments in Language Theory), ICALP, MFCS (Mathematical Foundation of Computer Science), Mons Theoretical Computer Science Days, Numeration, CANT (Combinatorics, Automata and Number Theory). Combinatorics on words deals with problems that can be stated in a non-commutative monoid, such as subword complexity of finite or infinite words, construction and properties of infinite words, unavoidabl

6th World Conference on 21st Century Mathematics

CERN Document Server

Choudary, ADR; Waldschmidt, Michel

2015-01-01

Numerous well-presented and important papers from the conference are gathered in the proceedings for the purpose of pointing directions for useful future research in diverse areas of mathematics including algebraic geometry, analysis, commutative algebra, complex analysis, discrete mathematics, dynamical systems, number theory and topology. Several papers on computational and applied mathematics such as wavelet analysis, quantum mechanics, piecewise linear modeling, cosmological models of super symmetry, fluid dynamics, interpolation theory, optimization, ergodic theory and games theory are also presented.

Improving science and mathematics education with computational modelling in interactive engagement environments

Science.gov (United States)

Neves, Rui Gomes; Teodoro, Vítor Duarte

2012-09-01

A teaching approach aiming at an epistemologically balanced integration of computational modelling in science and mathematics education is presented. The approach is based on interactive engagement learning activities built around computational modelling experiments that span the range of different kinds of modelling from explorative to expressive modelling. The activities are designed to make a progressive introduction to scientific computation without requiring prior development of a working knowledge of programming, generate and foster the resolution of cognitive conflicts in the understanding of scientific and mathematical concepts and promote performative competency in the manipulation of different and complementary representations of mathematical models. The activities are supported by interactive PDF documents which explain the fundamental concepts, methods and reasoning processes using text, images and embedded movies, and include free space for multimedia enriched student modelling reports and teacher feedback. To illustrate, an example from physics implemented in the Modellus environment and tested in undergraduate university general physics and biophysics courses is discussed.

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

Students' Mathematics Word Problem-Solving Achievement in a Computer-Based Story

Science.gov (United States)

Gunbas, N.

2015-01-01

The purpose of this study was to investigate the effect of a computer-based story, which was designed in anchored instruction framework, on sixth-grade students' mathematics word problem-solving achievement. Problems were embedded in a story presented on a computer as computer story, and then compared with the paper-based version of the same story…

Mathematical model of accelerator output characteristics and their calculation on a computer

International Nuclear Information System (INIS)

Mishulina, O.A.; Ul'yanina, M.N.; Kornilova, T.V.

1975-01-01

A mathematical model is described of output characteristics of a linear accelerator. The model is a system of differential equations. Presence of phase limitations is a specific feature of setting the problem which makes it possible to ensure higher simulation accuracy and determine a capture coefficient. An algorithm is elaborated of computing output characteristics based upon the mathematical model suggested. A capture coefficient, coordinate expectation characterizing an average phase value of the beam particles, coordinate expectation characterizing an average value of the reverse relative velocity of the beam particles as well as dispersion of these coordinates are output characteristics of the accelerator. Calculation methods of the accelerator output characteristics are described in detail. The computations have been performed on the BESM-6 computer, the characteristics computing time being 2 min 20 sec. Relative error of parameter computation averages 10 -2

Numerical study of a mathematical model of internal erosion of soil

Science.gov (United States)

Sibin, A.

2017-10-01

The process of internal erosion in a three-phase saturated soil is studied. A mathematical model describing the process consists of the equations of mass conservation, Darcy’s law and equation for capillary pressure. The original system of equations is reduced to a system of three equations for porosity, pressure and water saturation. Obtained equation for the water saturation is degenerate. The degenerate problem in an one-dimensional domain is solved numerically using the finite-difference method.

Mathematical and numerical methods for partial differential equations applications for engineering sciences

CERN Document Server

Chaskalovic, Joël

2014-01-01

This self-tutorial offers a concise yet thorough introduction into the mathematical analysis of approximation methods for partial differential equation. A particular emphasis is put on finite element methods. The unique approach first summarizes and outlines the finite-element mathematics in general and then, in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverse exercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite- element methods instead of passively absorbing the material, as in most standard textbooks. This English edition is based on the Finite Element Methods for Engineering Sciences by Joel Chaskalovic

Research in mathematics and computer science, March 1, 1991--September 30, 1992

Energy Technology Data Exchange (ETDEWEB)

Pieper, G.W.

1992-10-01

This report discusses the following topics in mathematics and computer science at Argonne National Laboratory: Harnessing the Power; Modeling Piezoelectric Crystals; A Two-Way Street; The Challenge Is On; A True Molecular Engineering Capability; CHAMMPions Attack Climate Issues; Studying Vortex Dynamics; Studying Vortex Structure; Providing Reliable and Fast Derivatives; Automating Reasoning for Scientific Problem Solving; Optimization and Mathematical Programming; Scalable Algorithms for Linear Algebra; Reliable Core Software; Computing Phylogenetic Trees; Managing Life-Critical Systems; Interacting with Data through Visualization; New Tools for New Technologies.

Mathematics for multimedia

CERN Document Server

Wickerhauser, Mladen Victor

2003-01-01

Mathematics and Multimedia focuses on the mathematics behind multimedia applications. This timely and thoroughly modern text is a rigorous survey of selected results from algebra and analysis, requiring only undergraduate math skills.The topics are `gems' chosen for their usefulness in understanding and creating application software for multimedia signal processing and communication.The book is aimed at a wide audience, including computer science and mathematics majors and those interested in employing mathematics in multimedia design and implementation. For the instructor, the material is divided into six chapters that may be presented in six lecture hours each. Thus, the entire text may be covered in one semester, with time left for examinations and student projects. For the student,there are more than 100 exercises with complete solutions, and numerous example programs in Standard C. Each chapter ends with suggestions for further reading. A companion website provides more insight for both instructors and s...

The pressure equation arising in reservoir simulation. Mathematical properties, numerical methods and upscaling

Energy Technology Data Exchange (ETDEWEB)

Nielsen, Bjoern Fredrik

1997-12-31

The main purpose of this thesis has been to analyse self-adjoint second order elliptic partial differential equations arising in reservoir simulation. It studies several mathematical and numerical problems for the pressure equation arising in models of fluid flow in porous media. The theoretical results obtained have been illustrated by a series of numerical experiments. The influence of large variations in the mobility tensor upon the solution of the pressure equation is analysed. The performance of numerical methods applied to such problems have been studied. A new upscaling technique for one-phase flow in heterogeneous reservoirs is developed. The stability of the solution of the pressure equation with respect to small perturbations of the mobility tensor is studied. The results are used to develop a new numerical method for a model of fully nonlinear water waves. 158 refs, 39 figs., 12 tabs.

The pressure equation arising in reservoir simulation. Mathematical properties, numerical methods and upscaling

Energy Technology Data Exchange (ETDEWEB)

Nielsen, Bjoern Fredrik

1998-12-31

The main purpose of this thesis has been to analyse self-adjoint second order elliptic partial differential equations arising in reservoir simulation. It studies several mathematical and numerical problems for the pressure equation arising in models of fluid flow in porous media. The theoretical results obtained have been illustrated by a series of numerical experiments. The influence of large variations in the mobility tensor upon the solution of the pressure equation is analysed. The performance of numerical methods applied to such problems have been studied. A new upscaling technique for one-phase flow in heterogeneous reservoirs is developed. The stability of the solution of the pressure equation with respect to small perturbations of the mobility tensor is studied. The results are used to develop a new numerical method for a model of fully nonlinear water waves. 158 refs, 39 figs., 12 tabs.

Computational engineering

CERN Document Server

2014-01-01

The book presents state-of-the-art works in computational engineering. Focus is on mathematical modeling, numerical simulation, experimental validation and visualization in engineering sciences. In particular, the following topics are presented: constitutive models and their implementation into finite element codes, numerical models in nonlinear elasto-dynamics including seismic excitations, multiphase models in structural engineering and multiscale models of materials systems, sensitivity and reliability analysis of engineering structures, the application of scientific computing in urban water management and hydraulic engineering, and the application of genetic algorithms for the registration of laser scanner point clouds.

Analysis and computation of microstructure in finite plasticity

CERN Document Server

Hackl, Klaus

2015-01-01

This book addresses the need for a fundamental understanding of the physical origin, the mathematical behavior, and the numerical treatment of models which include microstructure. Leading scientists present their efforts involving mathematical analysis, numerical analysis, computational mechanics, material modelling and experiment. The mathematical analyses are based on methods from the calculus of variations, while in the numerical implementation global optimization algorithms play a central role. The modeling covers all length scales, from the atomic structure up to macroscopic samples. The development of the models ware guided by experiments on single and polycrystals, and results will be checked against experimental data.

Numerical analysis of electromagnetic fields

CERN Document Server

Zhou Pei Bai

1993-01-01

Numerical methods for solving boundary value problems have developed rapidly. Knowledge of these methods is important both for engineers and scientists. There are many books published that deal with various approximate methods such as the finite element method, the boundary element method and so on. However, there is no textbook that includes all of these methods. This book is intended to fill this gap. The book is designed to be suitable for graduate students in engineering science, for senior undergraduate students as well as for scientists and engineers who are interested in electromagnetic fields. Objective Numerical calculation is the combination of mathematical methods and field theory. A great number of mathematical concepts, principles and techniques are discussed and many computational techniques are considered in dealing with practical problems. The purpose of this book is to provide students with a solid background in numerical analysis of the field problems. The book emphasizes the basic theories ...

Computational Methods in Plasma Physics

CERN Document Server

Jardin, Stephen

2010-01-01

Assuming no prior knowledge of plasma physics or numerical methods, Computational Methods in Plasma Physics covers the computational mathematics and techniques needed to simulate magnetically confined plasmas in modern magnetic fusion experiments and future magnetic fusion reactors. Largely self-contained, the text presents the basic concepts necessary for the numerical solution of partial differential equations. Along with discussing numerical stability and accuracy, the author explores many of the algorithms used today in enough depth so that readers can analyze their stability, efficiency,

Applications of a Sequence of Points in Teaching Linear Algebra, Numerical Methods and Discrete Mathematics

Science.gov (United States)

Shi, Yixun

2009-01-01

Based on a sequence of points and a particular linear transformation generalized from this sequence, two recent papers (E. Mauch and Y. Shi, "Using a sequence of number pairs as an example in teaching mathematics". Math. Comput. Educ., 39 (2005), pp. 198-205; Y. Shi, "Case study projects for college mathematics courses based on a particular…

Variables that Affect Math Teacher Candidates' Intentions to Integrate Computer-Assisted Mathematics Education (CAME)

Science.gov (United States)

Erdogan, Ahmet

2010-01-01

Based on Social Cognitive Carier Theory (SCCT) (Lent, Brown, & Hackett, 1994, 2002), this study tested the effects of mathematics teacher candidates' self-efficacy in, outcome expectations from, and interest in CAME on their intentions to integrate Computer-Assisted Mathematics Education (CAME). While mathematics teacher candidates' outcome…

Mathematics for informatics and computer science

CERN Document Server

Audibert, Pierre

2013-01-01

How many ways do exist to mix different ingredients, how many chances to win a gambling game, how many possible paths going from one place to another in a network ? To this kind of questions Mathematics applied to computer gives a stimulating and exhaustive answer. This text, presented in three parts (Combinatorics, Probability, Graphs) addresses all those who wish to acquire basic or advanced knowledge in combinatorial theories. It is actually also used as a textbook. Basic and advanced theoretical elements are presented through simple applications like the Sudoku game, search engine al

Effect of Numerical Error on Gravity Field Estimation for GRACE and Future Gravity Missions

Science.gov (United States)

McCullough, Christopher; Bettadpur, Srinivas

2015-04-01

In recent decades, gravity field determination from low Earth orbiting satellites, such as the Gravity Recovery and Climate Experiment (GRACE), has become increasingly more effective due to the incorporation of high accuracy measurement devices. Since instrumentation quality will only increase in the near future and the gravity field determination process is computationally and numerically intensive, numerical error from the use of double precision arithmetic will eventually become a prominent error source. While using double-extended or quadruple precision arithmetic will reduce these errors, the numerical limitations of current orbit determination algorithms and processes must be accurately identified and quantified in order to adequately inform the science data processing techniques of future gravity missions. The most obvious numerical limitation in the orbit determination process is evident in the comparison of measured observables with computed values, derived from mathematical models relating the satellites' numerically integrated state to the observable. Significant error in the computed trajectory will corrupt this comparison and induce error in the least squares solution of the gravitational field. In addition, errors in the numerically computed trajectory propagate into the evaluation of the mathematical measurement model's partial derivatives. These errors amalgamate in turn with numerical error from the computation of the state transition matrix, computed using the variational equations of motion, in the least squares mapping matrix. Finally, the solution of the linearized least squares system, computed using a QR factorization, is also susceptible to numerical error. Certain interesting combinations of each of these numerical errors are examined in the framework of GRACE gravity field determination to analyze and quantify their effects on gravity field recovery.

Numerical simulation of plasmas

International Nuclear Information System (INIS)

Dnestrovskii, Y.N.; Kostomarov, D.P.

1986-01-01

This book contains a modern consistent and systematic presentation of numerical computer simulation of plasmas in controlled thermonuclear fusion. The authors focus on the Soviet research in mathematical modelling of Tokamak plasmas, and present kinetic hydrodynamic and transport models with special emphasis on the more recent hybrid models. Compared with the first edition (in Russian) this book has been greatly revised and updated. (orig./WL)

IPython interactive computing and visualization cookbook

CERN Document Server

Rossant, Cyrille

2014-01-01

Intended to anyone interested in numerical computing and data science: students, researchers, teachers, engineers, analysts, hobbyists... Basic knowledge of Python/NumPy is recommended. Some skills in mathematics will help you understand the theory behind the computational methods.

Computer-Assisted Mathematics Instruction for Students with Specific Learning Disability: A Review of the Literature

Science.gov (United States)

Stultz, Sherry L.

2017-01-01

This review was conducted to evaluate the current body of scholarly research regarding the use of computer-assisted instruction (CAI) to teach mathematics to students with specific learning disability (SLD). For many years, computers are utilized for educational purposes. However, the effectiveness of CAI for teaching mathematics to this specific…

XVI 'Jacques-Louis Lions' Spanish-French School on Numerical Simulation in Physics and Engineering

CERN Document Server

Roldán, Teo; Torrens, Juan

2016-01-01

This book presents lecture notes from the XVI ‘Jacques-Louis Lions’ Spanish-French School on Numerical Simulation in Physics and Engineering, held in Pamplona (Navarra, Spain) in September 2014. The subjects covered include: numerical analysis of isogeometric methods, convolution quadrature for wave simulations, mathematical methods in image processing and computer vision, modeling and optimization techniques in food processes, bio-processes and bio-systems, and GPU computing for numerical simulation. The book is highly recommended to graduate students in Engineering or Science who want to focus on numerical simulation, either as a research topic or in the field of industrial applications. It can also benefit senior researchers and technicians working in industry who are interested in the use of state-of-the-art numerical techniques in the fields addressed here. Moreover, the book can be used as a textbook for master courses in Mathematics, Physics, or Engineering.

Secondary School Students' Attitudes towards Mathematics Computer--Assisted Instruction Environment in Kenya

Science.gov (United States)

Mwei, Philip K.; Wando, Dave; Too, Jackson K.

2012-01-01

This paper reports the results of research conducted in six classes (Form IV) with 205 students with a sample of 94 respondents. Data represent students' statements that describe (a) the role of Mathematics teachers in a computer-assisted instruction (CAI) environment and (b) effectiveness of CAI in Mathematics instruction. The results indicated…

Recent developments and applications in mathematics and computer science

International Nuclear Information System (INIS)

Churchhouse, R.F.; Tahir Shah, K.; Zanella, P.

1991-01-01

The book contains 8 invited lectures and 4 short seminars presented at the College on Recent Developments and Applications in Mathematics and Computer Science held in Trieste from 7 May to 1 June 1990. A separate abstract was prepared for each paper. Refs, figs and tabs

Using the Tower of Hanoi Puzzle to Infuse Your Mathematics Classroom with Computer Science Concepts

Science.gov (United States)

Marzocchi, Alison S.

2016-01-01

This article suggests that logic puzzles, such as the well-known Tower of Hanoi puzzle, can be used to introduce computer science concepts to mathematics students of all ages. Mathematics teachers introduce their students to computer science concepts that are enacted spontaneously and subconsciously throughout the solution to the Tower of Hanoi…

Computer-Aided Numerical Inversion of Laplace Transform

Directory of Open Access Journals (Sweden)

Umesh Kumar

2000-01-01

Full Text Available This paper explores the technique for the computer aided numerical inversion of Laplace transform. The inversion technique is based on the properties of a family of three parameter exponential probability density functions. The only limitation in the technique is the word length of the computer being used. The Laplace transform has been used extensively in the frequency domain solution of linear, lumped time invariant networks but its application to the time domain has been limited, mainly because of the difficulty in finding the necessary poles and residues. The numerical inversion technique mentioned above does away with the poles and residues but uses precomputed numbers to find the time response. This technique is applicable to the solution of partially differentiable equations and certain classes of linear systems with time varying components.

Computer-based image studies on tumor nests mathematical features of breast cancer and their clinical prognostic value.

Science.gov (United States)

Wang, Lin-Wei; Qu, Ai-Ping; Yuan, Jing-Ping; Chen, Chuang; Sun, Sheng-Rong; Hu, Ming-Bai; Liu, Juan; Li, Yan

2013-01-01

The expending and invasive features of tumor nests could reflect the malignant biological behaviors of breast invasive ductal carcinoma. Useful information on cancer invasiveness hidden within tumor nests could be extracted and analyzed by computer image processing and big data analysis. Tissue microarrays from invasive ductal carcinoma (n = 202) were first stained with cytokeratin by immunohistochemical method to clearly demarcate the tumor nests. Then an expert-aided computer analysis system was developed to study the mathematical and geometrical features of the tumor nests. Computer recognition system and imaging analysis software extracted tumor nests information, and mathematical features of tumor nests were calculated. The relationship between tumor nests mathematical parameters and patients' 5-year disease free survival was studied. There were 8 mathematical parameters extracted by expert-aided computer analysis system. Three mathematical parameters (number, circularity and total perimeter) with area under curve >0.5 and 4 mathematical parameters (average area, average perimeter, total area/total perimeter, average (area/perimeter)) with area under curve nests could be a useful parameter to predict the prognosis of early stage breast invasive ductal carcinoma.

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.…

An electrophysiological investigation of non-symbolic magnitude processing: numerical distance effects in children with and without mathematical learning disabilities.

Science.gov (United States)

Heine, Angela; Wissmann, Jacqueline; Tamm, Sascha; De Smedt, Bert; Schneider, Michael; Stern, Elsbeth; Verschaffel, Lieven; Jacobs, Arthur M

2013-09-01

The aim of the present study was to probe electrophysiological effects of non-symbolic numerical processing in 20 children with mathematical learning disabilities (mean age = 99.2 months) compared to a group of 20 typically developing matched controls (mean age = 98.4 months). EEG data were obtained while children were tested with a standard non-symbolic numerical comparison paradigm that allowed us to investigate the effects of numerical distance manipulations for different set sizes, i.e., the classical subitizing, counting and estimation ranges. Effects of numerical distance manipulations on event-related potential (ERP) amplitudes as well as activation patterns of underlying current sources were analyzed. In typically developing children, the amplitudes of a late parietal positive-going ERP component showed systematic numerical distance effects that did not depend on set size. For the group of children with mathematical learning disabilities, ERP distance effects were found only for stimuli within the subitizing range. Current source density analysis of distance-related group effects suggested that areas in right inferior parietal regions are involved in the generation of the parietal ERP amplitude differences. Our results suggest that right inferior parietal regions are recruited differentially by controls compared to children with mathematical learning disabilities in response to non-symbolic numerical magnitude processing tasks, but only for stimuli with set sizes that exceed the subitizing range. Copyright © 2012 Elsevier Ltd. All rights reserved.

Getting from x to y without Crashing: Computer Syntax in Mathematics Education

Science.gov (United States)

Jeffrey, David J.

2010-01-01

When we use technology to teach mathematics, we hope to focus on the mathematics, restricting the computer software systems to providing support for our pedagogy. It is a matter of common experience, however, that students can become distracted or frustrated by the quirks of the particular software system being used. Here, experience using the…

Mathematical and computational analyses of cracking formation fracture morphology and its evolution in engineering materials and structures

CERN Document Server

Sumi, Yoichi

2014-01-01

This book is about the pattern formation and the evolution of crack propagation in engineering materials and structures, bridging mathematical analyses of cracks based on singular integral equations, to computational simulation of engineering design. The first two parts of this book focus on elasticity and fracture and provide the basis for discussions on fracture morphology and its numerical simulation, which may lead to a simulation-based fracture control in engineering structures. Several design concepts are discussed for the prevention of fatigue and fracture in engineering structures, including safe-life design, fail-safe design, damage tolerant design. After starting with basic elasticity and fracture theories in parts one and two, this book focuses on the fracture morphology that develops due to the propagation of brittle cracks or fatigue cracks.   In part three, the mathematical analysis of a curved crack is precisely described, based on the perturbation method. The stability theory of interactive ...

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…

Las Matematicas: Lenguaje Universal. Nivel 1: Numeros y Numeracion (Mathematics: A Universal Language. Level 1: Numbers and Numeration).

Science.gov (United States)

Dissemination and Assessment Center for Bilingual Education, Austin, TX.

This is one of a series of student booklets designed for use in a bilingual mathematics program in grades 6-8. The general format is to present each page in both Spanish and English. The mathematical topics in this booklet include graphing on a number line, place value, using exponents, flow charts, and Roman numerals. (MK)

[Geometry, analysis, and computation in mathematics and applied science]. Progress report

Energy Technology Data Exchange (ETDEWEB)

Hoffman, D.

1994-02-01

The principal investigators` work on a variety of pure and applied problems in Differential Geometry, Calculus of Variations and Mathematical Physics has been done in a computational laboratory and been based on interactive scientific computer graphics and high speed computation created by the principal investigators to study geometric interface problems in the physical sciences. We have developed software to simulate various physical phenomena from constrained plasma flow to the electron microscope imaging of the microstructure of compound materials, techniques for the visualization of geometric structures that has been used to make significant breakthroughs in the global theory of minimal surfaces, and graphics tools to study evolution processes, such as flow by mean curvature, while simultaneously developing the mathematical foundation of the subject. An increasingly important activity of the laboratory is to extend this environment in order to support and enhance scientific collaboration with researchers at other locations. Toward this end, the Center developed the GANGVideo distributed video software system and software methods for running lab-developed programs simultaneously on remote and local machines. Further, the Center operates a broadcast video network, running in parallel with the Center`s data networks, over which researchers can access stored video materials or view ongoing computations. The graphical front-end to GANGVideo can be used to make ``multi-media mail`` from both ``live`` computing sessions and stored materials without video editing. Currently, videotape is used as the delivery medium, but GANGVideo is compatible with future ``all-digital`` distribution systems. Thus as a byproduct of mathematical research, we are developing methods for scientific communication. But, most important, our research focuses on important scientific problems; the parallel development of computational and graphical tools is driven by scientific needs.

Numerical computation of molecular integrals via optimized (vectorized) FORTRAN code

International Nuclear Information System (INIS)

Scott, T.C.; Grant, I.P.; Saunders, V.R.

1997-01-01

The calculation of molecular properties based on quantum mechanics is an area of fundamental research whose horizons have always been determined by the power of state-of-the-art computers. A computational bottleneck is the numerical calculation of the required molecular integrals to sufficient precision. Herein, we present a method for the rapid numerical evaluation of molecular integrals using optimized FORTRAN code generated by Maple. The method is based on the exploitation of common intermediates and the optimization can be adjusted to both serial and vectorized computations. (orig.)

Scientific computing an introduction using Maple and Matlab

CERN Document Server

Gander, Walter; Kwok, Felix

2014-01-01

Scientific computing is the study of how to use computers effectively to solve problems that arise from the mathematical modeling of phenomena in science and engineering. It is based on mathematics, numerical and symbolic/algebraic computations and visualization. This book serves as an introduction to both the theory and practice of scientific computing, with each chapter presenting the basic algorithms that serve as the workhorses of many scientific codes; we explain both the theory behind these algorithms and how they must be implemented in order to work reliably in finite-precision arithmetic. The book includes many programs written in Matlab and Maple – Maple is often used to derive numerical algorithms, whereas Matlab is used to implement them. The theory is developed in such a way that students can learn by themselves as they work through the text. Each chapter contains numerous examples and problems to help readers understand the material “hands-on”.

Probability and statistics for computer science

CERN Document Server

Johnson, James L

2011-01-01

Comprehensive and thorough development of both probability and statistics for serious computer scientists; goal-oriented: ""to present the mathematical analysis underlying probability results"" Special emphases on simulation and discrete decision theory Mathematically-rich, but self-contained text, at a gentle pace Review of calculus and linear algebra in an appendix Mathematical interludes (in each chapter) which examine mathematical techniques in the context of probabilistic or statistical importance Numerous section exercises, summaries, historical notes, and Further Readings for reinforcem

Mathematical modelling and numerical resolution of multi-phase compressible fluid flows problems

International Nuclear Information System (INIS)

Lagoutiere, Frederic

2000-01-01

This work deals with Eulerian compressible multi-species fluid dynamics, the species being either mixed or separated (with interfaces). The document is composed of three parts. The first parts devoted to the numerical resolution of model problems: advection equation, Burgers equation, and Euler equations, in dimensions one and two. The goal is to find a precise method, especially for discontinuous initial conditions, and we develop non dissipative algorithms. They are based on a downwind finite-volume discretization under some stability constraints. The second part treats of the mathematical modelling of fluids mixtures. We construct and analyse a set of multi-temperature and multi-pressure models that are entropy, symmetrizable, hyperbolic, not ever conservative. In the third part, we apply the ideas developed in the first part (downwind discretization) to the numerical resolution of the partial differential problems we have constructed for fluids mixtures in the second part. We present some numerical results in dimensions one and two. (author) [fr

Applied and numerical partial differential equations scientific computing in simulation, optimization and control in a multidisciplinary context

CERN Document Server

Glowinski, R; Kuznetsov, Y A; Periaux, Jacques; Neittaanmaki, Pekka; Pironneau, Olivier

2010-01-01

Standing at the intersection of mathematics and scientific computing, this collection of state-of-the-art papers in nonlinear PDEs examines their applications to subjects as diverse as dynamical systems, computational mechanics, and the mathematics of finance.

Numerical methods and modelling for engineering

CERN Document Server

Khoury, Richard

2016-01-01

This textbook provides a step-by-step approach to numerical methods in engineering modelling. The authors provide a consistent treatment of the topic, from the ground up, to reinforce for students that numerical methods are a set of mathematical modelling tools which allow engineers to represent real-world systems and compute features of these systems with a predictable error rate. Each method presented addresses a specific type of problem, namely root-finding, optimization, integral, derivative, initial value problem, or boundary value problem, and each one encompasses a set of algorithms to solve the problem given some information and to a known error bound. The authors demonstrate that after developing a proper model and understanding of the engineering situation they are working on, engineers can break down a model into a set of specific mathematical problems, and then implement the appropriate numerical methods to solve these problems. Uses a “building-block” approach, starting with simpler mathemati...

Numerical methods in multibody dynamics

CERN Document Server

Eich-Soellner, Edda

1998-01-01

Today computers play an important role in the development of complex mechanical systems, such as cars, railway vehicles or machines. Efficient simulation of these systems is only possible when based on methods that explore the strong link between numerics and computational mechanics. This book gives insight into modern techniques of numerical mathematics in the light of an interesting field of applications: multibody dynamics. The important interaction between modeling and solution techniques is demonstrated by using a simplified multibody model of a truck. Different versions of this mechanical model illustrate all key concepts in static and dynamic analysis as well as in parameter identification. The book focuses in particular on constrained mechanical systems. Their formulation in terms of differential-algebraic equations is the backbone of nearly all chapters. The book is written for students and teachers in numerical analysis and mechanical engineering as well as for engineers in industrial research labor...

Digital image processing mathematical and computational methods

CERN Document Server

Blackledge, J M

2005-01-01

This authoritative text (the second part of a complete MSc course) provides mathematical methods required to describe images, image formation and different imaging systems, coupled with the principle techniques used for processing digital images. It is based on a course for postgraduates reading physics, electronic engineering, telecommunications engineering, information technology and computer science. This book relates the methods of processing and interpreting digital images to the 'physics' of imaging systems. Case studies reinforce the methods discussed, with examples of current research

Using Computational and Mechanical Models to Study Animal Locomotion

Science.gov (United States)

Miller, Laura A.; Goldman, Daniel I.; Hedrick, Tyson L.; Tytell, Eric D.; Wang, Z. Jane; Yen, Jeannette; Alben, Silas

2012-01-01

Recent advances in computational methods have made realistic large-scale simulations of animal locomotion possible. This has resulted in numerous mathematical and computational studies of animal movement through fluids and over substrates with the purpose of better understanding organisms’ performance and improving the design of vehicles moving through air and water and on land. This work has also motivated the development of improved numerical methods and modeling techniques for animal locomotion that is characterized by the interactions of fluids, substrates, and structures. Despite the large body of recent work in this area, the application of mathematical and numerical methods to improve our understanding of organisms in the context of their environment and physiology has remained relatively unexplored. Nature has evolved a wide variety of fascinating mechanisms of locomotion that exploit the properties of complex materials and fluids, but only recently are the mathematical, computational, and robotic tools available to rigorously compare the relative advantages and disadvantages of different methods of locomotion in variable environments. Similarly, advances in computational physiology have only recently allowed investigators to explore how changes at the molecular, cellular, and tissue levels might lead to changes in performance at the organismal level. In this article, we highlight recent examples of how computational, mathematical, and experimental tools can be combined to ultimately answer the questions posed in one of the grand challenges in organismal biology: “Integrating living and physical systems.” PMID:22988026

Numerical Methods for Stochastic Computations A Spectral Method Approach

CERN Document Server

Xiu, Dongbin

2010-01-01

The first graduate-level textbook to focus on fundamental aspects of numerical methods for stochastic computations, this book describes the class of numerical methods based on generalized polynomial chaos (gPC). These fast, efficient, and accurate methods are an extension of the classical spectral methods of high-dimensional random spaces. Designed to simulate complex systems subject to random inputs, these methods are widely used in many areas of computer science and engineering. The book introduces polynomial approximation theory and probability theory; describes the basic theory of gPC meth

On the non-uniqueness of the nodal mathematical adjoint

International Nuclear Information System (INIS)

Müller, Erwin

2014-01-01

Highlights: • We evaluate three CMFD schemes for computing the nodal mathematical adjoint. • The nodal mathematical adjoint is not unique and can be non-positive (nonphysical). • Adjoint and forward eigenmodes are compatible if produced by the same CMFD method. • In nodal applications the excited eigenmodes are purely mathematical entities. - Abstract: Computation of the neutron adjoint flux within the framework of modern nodal diffusion methods is often facilitated by reducing the nodal equation system for the forward flux into a simpler coarse-mesh finite-difference form and then transposing the resultant matrix equations. The solution to the transposed problem is known as the nodal mathematical adjoint. Since the coarse-mesh finite-difference reduction of a given nodal formulation can be obtained in a number of ways, different nodal mathematical adjoint solutions can be computed. This non-uniqueness of the nodal mathematical adjoint challenges the credibility of the reduction strategy and demands a verdict as to its suitability in practical applications. This is the matter under consideration in this paper. A selected number of coarse-mesh finite-difference reduction schemes are described and compared. Numerical calculations are utilised to illustrate the differences in the adjoint solutions as well as to appraise the impact on such common applications as the computation of core point kinetics parameters. Recommendations are made for the proper application of the coarse-mesh finite-difference reduction approach to the nodal mathematical adjoint problem

Learning Mathematics by Designing, Programming, and Investigating with Interactive, Dynamic Computer-Based Objects

Science.gov (United States)

Marshall, Neil; Buteau, Chantal

2014-01-01

As part of their undergraduate mathematics curriculum, students at Brock University learn to create and use computer-based tools with dynamic, visual interfaces, called Exploratory Objects, developed for the purpose of conducting pure or applied mathematical investigations. A student's Development Process Model of creating and using an Exploratory…

Concentrator optical characterization using computer mathematical modelling and point source testing

Science.gov (United States)

Dennison, E. W.; John, S. L.; Trentelman, G. F.

1984-01-01

The optical characteristics of a paraboloidal solar concentrator are analyzed using the intercept factor curve (a format for image data) to describe the results of a mathematical model and to represent reduced data from experimental testing. This procedure makes it possible not only to test an assembled concentrator, but also to evaluate single optical panels or to conduct non-solar tests of an assembled concentrator. The use of three-dimensional ray tracing computer programs to calculate the mathematical model is described. These ray tracing programs can include any type of optical configuration from simple paraboloids to array of spherical facets and can be adapted to microcomputers or larger computers, which can graphically display real-time comparison of calculated and measured data.

Structure problems in the analog computation

International Nuclear Information System (INIS)

Braffort, P.L.

1957-01-01

The recent mathematical development showed the importance of elementary structures (algebraic, topological, etc.) in abeyance under the great domains of classical analysis. Such structures in analog computation are put in evidence and possible development of applied mathematics are discussed. It also studied the topological structures of the standard representation of analog schemes such as additional triangles, integrators, phase inverters and functions generators. The analog method gives only the function of the variable: time, as results of its computations. But the course of computation, for systems including reactive circuits, introduces order structures which are called 'chronological'. Finally, it showed that the approximation methods of ordinary numerical and digital computation present the same structure as these analog computation. The structure analysis permits fruitful comparisons between the several domains of applied mathematics and suggests new important domains of application for analog method. (M.P.)

Singular problems in shell theory. Computing and asymptotics

Energy Technology Data Exchange (ETDEWEB)

Sanchez-Palencia, Evariste [Institut Jean Le Rond d' Alembert, Paris (France); Millet, Olivier [La Rochelle Univ. (France). LEPTIAB; Bechet, Fabien [Metz Univ. (France). LPMM

2010-07-01

It is known that deformations of thin shells exhibit peculiarities such as propagation of singularities, edge and internal layers, piecewise quasi inextensional deformations, sensitive problems and others, leading in most cases to numerical locking phenomena under several forms, and very poor quality of computations for small relative thickness. Most of these phenomena have a local and often anisotropic character (elongated in some directions), so that efficient numerical schemes should take them in consideration. This book deals with various topics in this context: general geometric formalism, analysis of singularities, numerical computing of thin shell problems, estimates for finite element approximation (including non-uniform and anisotropic meshes), mathematical considerations on boundary value problems in connection with sensitive problems encountered for very thin shells; and others. Most of numerical computations presented here use an adaptive anisotropic mesh procedure which allows a good computation of the physical peculiarities on one hand, and the possibility to perform automatic computations (without a previous mathematical description of the singularities) on the other. The book is recommended for PhD students, postgraduates and researchers who want to improve their knowledge in shell theory and in particular in the areas addressed (analysis of singularities, numerical computing of thin and very thin shell problems, sensitive problems). The lecture of the book may not be continuous and the reader may refer directly to the chapters concerned. (orig.)

Teaching Mathematical Modelling for Earth Sciences via Case Studies

Science.gov (United States)

Yang, Xin-She

2010-05-01

Mathematical modelling is becoming crucially important for earth sciences because the modelling of complex systems such as geological, geophysical and environmental processes requires mathematical analysis, numerical methods and computer programming. However, a substantial fraction of earth science undergraduates and graduates may not have sufficient skills in mathematical modelling, which is due to either limited mathematical training or lack of appropriate mathematical textbooks for self-study. In this paper, we described a detailed case-study-based approach for teaching mathematical modelling. We illustrate how essential mathematical skills can be developed for students with limited training in secondary mathematics so that they are confident in dealing with real-world mathematical modelling at university level. We have chosen various topics such as Airy isostasy, greenhouse effect, sedimentation and Stokes' flow,free-air and Bouguer gravity, Brownian motion, rain-drop dynamics, impact cratering, heat conduction and cooling of the lithosphere as case studies; and we use these step-by-step case studies to teach exponentials, logarithms, spherical geometry, basic calculus, complex numbers, Fourier transforms, ordinary differential equations, vectors and matrix algebra, partial differential equations, geostatistics and basic numeric methods. Implications for teaching university mathematics for earth scientists for tomorrow's classroom will also be discussed. Refereces 1) D. L. Turcotte and G. Schubert, Geodynamics, 2nd Edition, Cambridge University Press, (2002). 2) X. S. Yang, Introductory Mathematics for Earth Scientists, Dunedin Academic Press, (2009).

Mathematical Model and Computational Analysis of Selected Transient States of Cylindrical Linear Induction Motor Fed via Frequency Converter

Directory of Open Access Journals (Sweden)

Andrzej Rusek

2008-01-01

Full Text Available The mathematical model of cylindrical linear induction motor (C-LIM fed via frequency converter is presented in the paper. The model was developed in order to analyze numerically the transient states. Problems concerning dynamics of ac-machines especially linear induction motor are presented in [1 – 7]. Development of C-LIM mathematical model is based on circuit method and analogy to rotary induction motor. The analogy between both: (a stator and rotor windings of rotary induction motor and (b winding of primary part of C-LIM (inductor and closed current circuits in external secondary part of C-LIM (race is taken into consideration. The equations of C-LIM mathematical model are presented as matrix together with equations expressing each vector separately. A computational analysis of selected transient states of C-LIM fed via frequency converter is presented in the paper. Two typical examples of C-LIM operation are considered for the analysis: (a starting the motor at various static loads and various synchronous velocities and (b reverse of the motor at the same operation conditions. Results of simulation are presented as transient responses including transient electromagnetic force, transient linear velocity and transient phase current.

Mathematical tools for physicists

International Nuclear Information System (INIS)

Trigg, G.L.

2005-01-01

Mathematical Tools for Physisists is a unique collection of 18 review articles, each one written by a renowned expert of its field. Their professional style will be beneficial for advanced students as well as for the scientist at work. The first may find a comprehensive introduction while the latter use it as a quick reference. Great attention was paid to ensuring fast access to the information, and each carefully reviewed article includes a glossary of terms and a guide to further reading. The contributions range from fundamental methods right up to the latest applications, including: - Algebraic Methods - Analytic Methods - Fourier and Other Mathematical Transforms - Fractal Geometry - Geometrical Methods - Green's Functions - Group Theory - Mathematical Modeling - Monte Carlo Methods - Numerical Methods - Perturbation Methods - Quantum Computation - Quantum Logic - Special Functions - Stochastic Processes - Symmetries and Conservation Laws - Topology - Variational Methods. (orig.)

special algorithm for the numerical solution of system of initial value ...

African Journals Online (AJOL)

Nwokem et al.

Science World Journal Vol 12(No 4) 2017 ... Over the years, several researchers have considered the collocation method as a way of generating numerical solutions to ... study problems in mathematics, engineering, computer science and.

Industrial numerical analysis

International Nuclear Information System (INIS)

McKee, S.; Elliott, C.M.

1986-01-01

The applications of mathematics to industrial problems involves the formulation of problems which are amenable to mathematical investigation, mathematical modelling, the solution of the mathematical problem and the inter-pretation of the results. There are 12 chapters describing industrial problems where mathematics and numerical analysis can be applied. These range from the numerical assessment of the flatness of engineering surfaces and plates, the design of chain links, control problems in tidal power generation and low thrust satellite trajectory optimization to mathematical models in welding. One chapter, on the ageing of stainless steels, is indexed separately. (UK)

Institute for Computer Applications in Science and Engineering (ICASE)

Science.gov (United States)

1984-01-01

Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis and computer science during the period April 1, 1983 through September 30, 1983 is summarized.

Advances in Reactor Physics, Mathematics and Computation. Volume 2

Energy Technology Data Exchange (ETDEWEB)

1987-01-01

These proceedings of the international topical meeting on advances in reactor physics, mathematics and computation, Volume 2, are divided into 7 sessions bearing on: - session 7: Deterministic transport methods 1 (7 conferences), - session 8: Interpretation and analysis of reactor instrumentation (6 conferences), - session 9: High speed computing applied to reactor operations (5 conferences), - session 10: Diffusion theory and kinetics (7 conferences), - session 11: Fast reactor design, validation and operating experience (8 conferences), - session 12: Deterministic transport methods 2 (7 conferences), - session 13: Application of expert systems to physical aspects of reactor design and operation.

Generic Mathematical Programming Formulation and Solution for Computer-Aided Molecular Design

DEFF Research Database (Denmark)

Zhang, Lei; Cignitti, Stefano; Gani, Rafiqul

2015-01-01

This short communication presents a generic mathematical programming formulation for Computer-Aided Molecular Design (CAMD). A given CAMD problem, based on target properties, is formulated as a Mixed Integer Linear/Non-Linear Program (MILP/MINLP). The mathematical programming model presented here......, which is formulated as an MILP/MINLP problem, considers first-order and second-order molecular groups for molecular structure representation and property estimation. It is shown that various CAMD problems can be formulated and solved through this model....

Numerical and symbolic scientific computing

CERN Document Server

Langer, Ulrich

2011-01-01

The book presents the state of the art and results and also includes articles pointing to future developments. Most of the articles center around the theme of linear partial differential equations. Major aspects are fast solvers in elastoplasticity, symbolic analysis for boundary problems, symbolic treatment of operators, computer algebra, and finite element methods, a symbolic approach to finite difference schemes, cylindrical algebraic decomposition and local Fourier analysis, and white noise analysis for stochastic partial differential equations. Further numerical-symbolic topics range from

Tensor Arithmetic, Geometric and Mathematic Principles of Fluid Mechanics in Implementation of Direct Computational Experiments

Directory of Open Access Journals (Sweden)

Bogdanov Alexander

2016-01-01

Full Text Available The architecture of a digital computing system determines the technical foundation of a unified mathematical language for exact arithmetic-logical description of phenomena and laws of continuum mechanics for applications in fluid mechanics and theoretical physics. The deep parallelization of the computing processes results in functional programming at a new technological level, providing traceability of the computing processes with automatic application of multiscale hybrid circuits and adaptive mathematical models for the true reproduction of the fundamental laws of physics and continuum mechanics.

Cognitive Skills Used to Solve Mathematical Word Problems and Numerical Operations: A Study of 6- to 7-Year-Old Children

Science.gov (United States)

Bjork, Isabel Maria; Bowyer-Crane, Claudine

2013-01-01

This study investigates the relationship between skills that underpin mathematical word problems and those that underpin numerical operations, such as addition, subtraction, division and multiplication. Sixty children aged 6-7 years were tested on measures of mathematical ability, reading accuracy, reading comprehension, verbal intelligence and…

A summary of numerical computation for special functions

International Nuclear Information System (INIS)

Zhang Shanjie

1992-01-01

In the paper, special functions frequently encountered in science and engineering calculations are introduced. The computation of the values of Bessel function and elliptic integrals are taken as the examples, and some common algorithms for computing most special functions, such as series expansion for small argument, asymptotic approximations for large argument, polynomial approximations, recurrence formulas and iteration method, are discussed. In addition, the determination of zeros of some special functions, and the other questions related to numerical computation are also discussed

Research in progress and other activities of the Institute for Computer Applications in Science and Engineering

Science.gov (United States)

1993-01-01

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics and computer science during the period April 1, 1993 through September 30, 1993. The major categories of the current ICASE research program are: (1) applied and numerical mathematics, including numerical analysis and algorithm development; (2) theoretical and computational research in fluid mechanics in selected areas of interest to LaRC, including acoustic and combustion; (3) experimental research in transition and turbulence and aerodynamics involving LaRC facilities and scientists; and (4) computer science.

Computer Facilitated Mathematical Methods in Chemical Engineering--Similarity Solution

Science.gov (United States)

Subramanian, Venkat R.

2006-01-01

High-performance computers coupled with highly efficient numerical schemes and user-friendly software packages have helped instructors to teach numerical solutions and analysis of various nonlinear models more efficiently in the classroom. One of the main objectives of a model is to provide insight about the system of interest. Analytical…

3rd International Conference on Applied Mathematics and Approximation Theory

CERN Document Server

Duman, Oktay

2016-01-01

This special volume is a collection of outstanding theoretical articles presented at the conference AMAT 2015, held in Ankara, Turkey from May 28-31, 2015, at TOBB University of Economics and Technology. The collection is suitable for a range of applications: from researchers and practitioners of applied and computational mathematics, to students in graduate-level seminars. Furthermore it will be a useful resource for all science libraries. This book includes 27 self-contained and expertly-refereed chapters that provide numerous insights into the latest developments at the intersection of applied and computational mathematics, engineering, and statistics.

Improving the reliability of nuclear reprocessing by application of computers and mathematical modelling

International Nuclear Information System (INIS)

Gabowitsch, E.; Trauboth, H.

1982-01-01

After a brief survey of the present and expected future state of nuclear energy utilization, which should demonstrate the significance of nuclear reprocessing, safety and reliability aspects of nuclear reprocessing plants (NRP) are considered. Then, the principal possibilities of modern computer technology including computer systems architecture and application-oriented software for improving the reliability and availability are outlined. In this context, two information systems being developed at the Nuclear Research Center Karlsruhe (KfK) are briefly described. For design evaluation of certain areas of a large NRP mathematical methods and computer-aided tools developed, used or being designed by KfK are discussed. In conclusion, future research to be pursued in information processing and applied mathematics in support of reliable operation of NRP's is proposed. (Auth.)

Univolatility curves in ternary mixtures: geometry and numerical computation

DEFF Research Database (Denmark)

Shcherbakova, Nataliya; Rodriguez-Donis, Ivonne; Abildskov, Jens

2017-01-01

We propose a new non-iterative numerical algorithm allowing computation of all univolatility curves in homogeneous ternary mixtures independently of the presence of the azeotropes. The key point is the concept of generalized univolatility curves in the 3D state space, which allows the main comput...

Using Mental Imagery Processes for Teaching and Research in Mathematics and Computer Science

Science.gov (United States)

Arnoux, Pierre; Finkel, Alain

2010-01-01

The role of mental representations in mathematics and computer science (for teaching or research) is often downplayed or even completely ignored. Using an ongoing work on the subject, we argue for a more systematic study and use of mental representations, to get an intuition of mathematical concepts, and also to understand and build proofs. We…

Gulf International Conference on Applied Mathematics 2013

CERN Document Server

Advances in Applied Mathematics

2014-01-01

This volume contains contributions from the Gulf International Conference in Applied Mathematics, held at the Gulf University for Science & Technology. The proceedings reflects the three major themes of the conference. The first of these was mathematical biology, including a keynote address by Professor Philip Maini. The second theme was computational science/numerical analysis, including a keynote address by Professor Grigorii Shishkin. The conference also addressed more general applications topics, with papers in business applications, fluid mechanics, optimization, scheduling problems, and engineering applications, as well as a keynote by Professor Ali Nayfeh.

Quasi-optical converters for high-power gyrotrons: a brief review of physical models, numerical methods and computer codes

International Nuclear Information System (INIS)

Sabchevski, S; Zhelyazkov, I; Benova, E; Atanassov, V; Dankov, P; Thumm, M; Arnold, A; Jin, J; Rzesnicki, T

2006-01-01

Quasi-optical (QO) mode converters are used to transform electromagnetic waves of complex structure and polarization generated in gyrotron cavities into a linearly polarized, Gaussian-like beam suitable for transmission. The efficiency of this conversion as well as the maintenance of low level of diffraction losses are crucial for the implementation of powerful gyrotrons as radiation sources for electron-cyclotron-resonance heating of fusion plasmas. The use of adequate physical models, efficient numerical schemes and up-to-date computer codes may provide the high accuracy necessary for the design and analysis of these devices. In this review, we briefly sketch the most commonly used QO converters, the mathematical base they have been treated on and the basic features of the numerical schemes used. Further on, we discuss the applicability of several commercially available and free software packages, their advantages and drawbacks, for solving QO related problems

Internalization of Malaysian mathematical and computer science journals

OpenAIRE

Zainab, A. N.

2008-01-01

The internationalization characteristics of two Malaysian journals, Bulletin of the Malaysian Mathematical Sciences Society ( indexed by ISI) and the Malaysian Journal of Computer Science ( indexed by Inspec and Scopus) is observed. All issues for the years 2000 to 2007 were looked at to obtain the following information, (i) total articles published between 2000 and 2007; (ii) the distribution of foreign and Malaysian authors publishing in the journals; (iii) the distribution of articles by c...

9th Annual Conference of the North East Polytechnics Mathematical Modelling & Computer Simulation Group

CERN Document Server

Bradley, R

1987-01-01

In recent years, mathematical modelling allied to computer simulation has emerged as en effective and invaluable design tool for industry and a discipline in its own right. This has been reflected in the popularity of the growing number of courses and conferences devoted to the area. The North East Polytechnics Mathematical Modelling and Computer Simulation Group has a balanced representation of academics and industrialists and, as a Group, has the objective of promoting a continuing partnership between the Polytechnics in the North East and local industry. Prior to the present conference the Group has organised eight conferences with a variety of themes related to mathematical modelling and computer simulation. The theme chosen for the Polymodel 9 Conference held in Newcastle upon Tyne in May 1986 was Industrial Vibration Modelling, which is particularly approp riate for 'Industry Year' and is an area which continues to present industry and academics with new and challenging problems. The aim of the Conferen...

Stratified flows with variable density: mathematical modelling and numerical challenges.

Science.gov (United States)

Murillo, Javier; Navas-Montilla, Adrian

2017-04-01

Stratified flows appear in a wide variety of fundamental problems in hydrological and geophysical sciences. They may involve from hyperconcentrated floods carrying sediment causing collapse, landslides and debris flows, to suspended material in turbidity currents where turbulence is a key process. Also, in stratified flows variable horizontal density is present. Depending on the case, density varies according to the volumetric concentration of different components or species that can represent transported or suspended materials or soluble substances. Multilayer approaches based on the shallow water equations provide suitable models but are not free from difficulties when moving to the numerical resolution of the governing equations. Considering the variety of temporal and spatial scales, transfer of mass and energy among layers may strongly differ from one case to another. As a consequence, in order to provide accurate solutions, very high order methods of proved quality are demanded. Under these complex scenarios it is necessary to observe that the numerical solution provides the expected order of accuracy but also converges to the physically based solution, which is not an easy task. To this purpose, this work will focus in the use of Energy balanced augmented solvers, in particular, the Augmented Roe Flux ADER scheme. References: J. Murillo , P. García-Navarro, Wave Riemann description of friction terms in unsteady shallow flows: Application to water and mud/debris floods. J. Comput. Phys. 231 (2012) 1963-2001. J. Murillo B. Latorre, P. García-Navarro. A Riemann solver for unsteady computation of 2D shallow flows with variable density. J. Comput. Phys.231 (2012) 4775-4807. A. Navas-Montilla, J. Murillo, Energy balanced numerical schemes with very high order. The Augmented Roe Flux ADER scheme. Application to the shallow water equations, J. Comput. Phys. 290 (2015) 188-218. A. Navas-Montilla, J. Murillo, Asymptotically and exactly energy balanced augmented flux

Mathematical and computational modeling and simulation fundamentals and case studies

CERN Document Server

Moeller, Dietmar P F

2004-01-01

Mathematical and Computational Modeling and Simulation - a highly multi-disciplinary field with ubiquitous applications in science and engineering - is one of the key enabling technologies of the 21st century. This book introduces to the use of Mathematical and Computational Modeling and Simulation in order to develop an understanding of the solution characteristics of a broad class of real-world problems. The relevant basic and advanced methodologies are explained in detail, with special emphasis on ill-defined problems. Some 15 simulation systems are presented on the language and the logical level. Moreover, the reader can accumulate experience by studying a wide variety of case studies. The latter are briefly described within the book but their full versions as well as some simulation software demos are available on the Web. The book can be used for University courses of different level as well as for self-study. Advanced sections are marked and can be skipped in a first reading or in undergraduate courses...

The effects of computer-assisted instruction on the mathematics performance and classroom behavior of children with ADHD.

Science.gov (United States)

Mautone, Jennifer A; DuPaul, George J; Jitendra, Asha K

2005-08-01

The present study examines the effects of computer-assisted instruction (CAI) on the mathematics performance and classroom behavior of three second-through fourth-grade students with ADHD. A controlled case study is used to evaluate the effects of the computer software on participants' mathematics performance and on-task behavior. Participants' mathematics achievement improve and their on-task behavior increase during the CAI sessions relative to independent seatwork conditions. In addition, students and teachers consider CAI to be an acceptable intervention for some students with ADHD who are having difficulty with mathematics. Implications of these results for practice and research are discussed.

Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming

International Nuclear Information System (INIS)

Katsaounis, T D

2005-01-01

The scope of this book is to present well known simple and advanced numerical methods for solving partial differential equations (PDEs) and how to implement these methods using the programming environment of the software package Diffpack. A basic background in PDEs and numerical methods is required by the potential reader. Further, a basic knowledge of the finite element method and its implementation in one and two space dimensions is required. The authors claim that no prior knowledge of the package Diffpack is required, which is true, but the reader should be at least familiar with an object oriented programming language like C++ in order to better comprehend the programming environment of Diffpack. Certainly, a prior knowledge or usage of Diffpack would be a great advantage to the reader. The book consists of 15 chapters, each one written by one or more authors. Each chapter is basically divided into two parts: the first part is about mathematical models described by PDEs and numerical methods to solve these models and the second part describes how to implement the numerical methods using the programming environment of Diffpack. Each chapter closes with a list of references on its subject. The first nine chapters cover well known numerical methods for solving the basic types of PDEs. Further, programming techniques on the serial as well as on the parallel implementation of numerical methods are also included in these chapters. The last five chapters are dedicated to applications, modelled by PDEs, in a variety of fields. In summary, the book focuses on the computational and implementational issues involved in solving partial differential equations. The potential reader should have a basic knowledge of PDEs and the finite difference and finite element methods. The examples presented are solved within the programming framework of Diffpack and the reader should have prior experience with the particular software in order to take full advantage of the book. Overall

Fluid dynamics theory, computation, and numerical simulation

CERN Document Server

Pozrikidis, C

2017-01-01

This book provides an accessible introduction to the basic theory of fluid mechanics and computational fluid dynamics (CFD) from a modern perspective that unifies theory and numerical computation. Methods of scientific computing are introduced alongside with theoretical analysis and MATLAB® codes are presented and discussed for a broad range of topics: from interfacial shapes in hydrostatics, to vortex dynamics, to viscous flow, to turbulent flow, to panel methods for flow past airfoils. The third edition includes new topics, additional examples, solved and unsolved problems, and revised images. It adds more computational algorithms and MATLAB programs. It also incorporates discussion of the latest version of the fluid dynamics software library FDLIB, which is freely available online. FDLIB offers an extensive range of computer codes that demonstrate the implementation of elementary and advanced algorithms and provide an invaluable resource for research, teaching, classroom instruction, and self-study. This ...

Design and evaluation of the computer-based training program Calcularis for enhancing numerical cognition

Directory of Open Access Journals (Sweden)

Tanja eKäser

2013-08-01

Full Text Available This article presents the design and a first pilot evaluation of the computer-based training program Calcularis for children with developmental dyscalculia (DD or difficulties in learning mathematics. The program has been designed according to insights on the typical and atypical development of mathematical abilities. The learning process is supported through multimodal cues, which encode different properties of numbers. To offer optimal learning conditions, a user model completes the program and allows flexible adaptation to a child’s individual learning and knowledge profile. 32 children with difficulties in learning mathematics completed the 6 to 12-weeks computer training. The children played the game for 20 minutes per day for 5 days a week. The training effects were evaluated using neuropsychological tests. Generally, children benefited significantly from the training regarding number representation and arithmetic operations. Furthermore, children liked to play with the program and reported that the training improved their mathematical abilities.

Mathematical and numerical analysis of a few hydrodynamic and kinetic models of plasma physics

International Nuclear Information System (INIS)

Buet, C.

2005-01-01

My research work deals mainly with the mathematical modelling and the numerical simulation of plasma physics. This document is divided into 3 parts. The first one is a summary of the works done for the numerical solving of collision operators. The common thread of this part is obtaining numerical schemes preserving operators' properties namely physical invariants like mass, momentum and energy, equilibrium states and entropy decrease. These properties are generally checked formally for continuous operators, may give rise to some difficulties for discrete operators. In the second part I present a summary of the works regarding moments methods applied to radiative transfer and the numerical issues dealing with their discretization. The common thread of this part is how to get numerical schemes preserving asymptotic scattering and invariant domains for Lorentz models and also for non-linear telegraph-type equations involved in radiative transfer or electronic plasma. In the third part I present 2 themes linked to collision operators: multi-fluid ionization and the non-existence of linear monotone schemes for some linear parabolic equations

The Impact of Specialist School Status: A Case Study of Two Contrasting Mathematics and Computing Colleges

Science.gov (United States)

Sinkinson, Anne J.

2006-01-01

The research examines the range of effects of obtaining Specialist School status in two contrasting mathematics and computing colleges, concentrating on the mathematics department. The positive impact of a wider range of technology was evident in both schools although the inherent pedagogical perspectives within each mathematics department…

Overview of the ANS [American Nuclear Society] mathematics and computation software standards

International Nuclear Information System (INIS)

Smetana, A.O.

1991-01-01

The Mathematics and Computations Division of the American Nuclear Society sponsors the ANS-10 Standards Subcommittee. This subcommittee, which is part of the ANS Standards Committee, currently maintains four ANSI/ANS software standards. These standards are: Recommended Programming Practices to Facilitate the Portability of Scientific Computer Programs, ANS-10.2; Guidelines for the Documentation of Computer Software, ANS-10.3; Guidelines for the Verification and Validation of Scientific and Engineering Computer Programs for the Nuclear Industry, ANS-10.4; and Guidelines for Accommodating User Needs in Computer Program Development, ANS-10.5. 5 refs

A numerical library in Java for scientists and engineers

CERN Document Server

Lau, Hang T

2003-01-01

At last researchers have an inexpensive library of Java-based numeric procedures for use in scientific computation. The first and only book of its kind, A Numeric Library in Java for Scientists and Engineers is a translation into Java of the library NUMAL (NUMerical procedures in ALgol 60). This groundbreaking text presents procedural descriptions for linear algebra, ordinary and partial differential equations, optimization, parameter estimation, mathematical physics, and other tools that are indispensable to any dynamic research group. The book offers test programs that allow researchers to execute the examples provided; users are free to construct their own tests and apply the numeric procedures to them in order to observe a successful computation or simulate failure. The entry for each procedure is logically presented, with name, usage parameters, and Java code included. This handbook serves as a powerful research tool, enabling the performance of critical computations in Java. It stands as a cost-effi...

The Application of Visual Basic Computer Programming Language to Simulate Numerical Iterations

Directory of Open Access Journals (Sweden)

Abdulkadir Baba HASSAN

2006-06-01

Full Text Available This paper examines the application of Visual Basic Computer Programming Language to Simulate Numerical Iterations, the merit of Visual Basic as a Programming Language and the difficulties faced when solving numerical iterations analytically, this research paper encourage the uses of Computer Programming methods for the execution of numerical iterations and finally fashion out and develop a reliable solution using Visual Basic package to write a program for some selected iteration problems.

Mathematical paradigms of climate science

CERN Document Server

Cannarsa, Piermarco; Jones, Christopher; Portaluri, Alessandro

2016-01-01

This book, featuring a truly interdisciplinary approach, provides an overview of cutting-edge mathematical theories and techniques that promise to play a central role in climate science. It brings together some of the most interesting overview lectures given by the invited speakers at an important workshop held in Rome in 2013 as a part of MPE2013 (“Mathematics of Planet Earth 2013”). The aim of the workshop was to foster the interaction between climate scientists and mathematicians active in various fields linked to climate sciences, such as dynamical systems, partial differential equations, control theory, stochastic systems, and numerical analysis. Mathematics and statistics already play a central role in this area. Likewise, computer science must have a say in the efforts to simulate the Earth’s environment on the unprecedented scale of petabytes. In the context of such complexity, new mathematical tools are needed to organize and simplify the approach. The growing importance of data assimilation te...

The history of theoretical, material and computational mechanics mathematics meets mechanics and engineering

CERN Document Server

2014-01-01

This collection of 23 articles is the output of lectures in special sessions on “The History of Theoretical, Material and Computational Mechanics” within the yearly conferences of the GAMM in the years 2010 in Karlsruhe, Germany, 2011 in Graz, Austria, and in 2012 in Darmstadt, Germany; GAMM is the “Association for Applied Mathematics and Mechanics”, founded in 1922 by Ludwig Prandtl and Richard von Mises. The contributions in this volume discuss different aspects of mechanics. They are related to solid and fluid mechanics in general and to specific problems in these areas including the development of numerical solution techniques. In the first part the origins and developments of conservation principles in mechanics and related variational methods are treated together with challenging applications from the 17th to the 20th century. Part II treats general and more specific aspects of material theories of deforming solid continua and porous soils. and Part III presents important theoretical and enginee...

Can Digital Computers Support Ancient Mathematical Consciousness?

Directory of Open Access Journals (Sweden)

Aaron Sloman

2018-05-01

Full Text Available This paper poses, discusses, but does not definitively answer, the following questions: What sorts of reasoning machinery could the ancient mathematicians, and other intelligent animals, be using for spatial reasoning, before the discovery of modern logical mechanisms? “Diagrams in minds” perhaps? How and why did natural selection produce such machinery? Is there a single package of biological abilities for spatial reasoning, or did different sorts of mathematical competence evolve at different times, forming a “layered” system? Do the layers develop in individuals at different stages? Which components are shared with other intelligent species? Does some or all of the machinery exist at or before birth in humans and if not how and when does it develop, and what is the role of experience in its development? How do brains implement such machinery? Could similar machines be implemented as virtual machines on digital computers, and if not what sorts of non-digital “Super Turing” mechanisms could replicate the required functionality, including discovery of impossibility and necessity? How are impossibility and necessity represented in brains? Are chemical mechanisms required? How could such mechanisms be specified in a genome? Are some not specified in the genome but products of interaction between genome and environment? Does Turing’s work on chemical morphogenesis published shortly before he died indicate that he was interested in this problem? Will the answers to these questions vindicate Immanuel Kant’s claims about the nature of mathematical knowledge, including his claim that mathematical truths are non-empirical, synthetic and necessary? Perhaps it’s time for discussions of consciousness to return to the nature of ancient mathematical consciousness, and related aspects of everyday human and non-human intelligence, usually ignored by consciousness theorists.

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…

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...

Does Computer Use Promote the Mathematical Proficiency of ELL Students?

Science.gov (United States)

Kim, Sunha; Chang, Mido

2010-01-01

The study explored the effects of computer use on the mathematical performance of students with special attention to ELL students. To achieve a high generalizability of findings, the study used a U.S. nationally representative database, the Early Childhood Longitudinal Survey Kindergarten Cohort (ECLS-K), and adopted proper weights. The study…

Children’s Mapping between Non-Symbolic and Symbolic Numerical Magnitudes and Its Association with Timed and Untimed Tests of Mathematics Achievement

Science.gov (United States)

Brankaer, Carmen; Ghesquière, Pol; De Smedt, Bert

2014-01-01

The ability to map between non-symbolic numerical magnitudes and Arabic numerals has been put forward as a key factor in children’s mathematical development. This mapping ability has been mainly examined indirectly by looking at children’s performance on a symbolic magnitude comparison task. The present study investigated mapping in a more direct way by using a task in which children had to choose which of two choice quantities (Arabic digits or dot arrays) matched the target quantity (dot array or Arabic digit), thereby focusing on small quantities ranging from 1 to 9. We aimed to determine the development of mapping over time and its relation to mathematics achievement. Participants were 36 first graders (M = 6 years 8 months) and 46 third graders (M = 8 years 8 months) who all completed mapping tasks, symbolic and non-symbolic magnitude comparison tasks and standardized timed and untimed tests of mathematics achievement. Findings revealed that children are able to map between non-symbolic and symbolic representations and that this mapping ability develops over time. Moreover, we found that children’s mapping ability is related to timed and untimed measures of mathematics achievement, over and above the variance accounted for by their numerical magnitude comparison skills. PMID:24699664

Traditional vs. Innovative Uses of Computers among Mathematics Pre-Service Teachers in Serbia

Science.gov (United States)

Teo, Timothy; Milutinovic, Verica; Zhou, Mingming; Bankovic, Dragic

2017-01-01

This study examined pre-service teachers' intentions to use computers in traditional and innovative teaching practices in primary mathematics classrooms. It extended the technology acceptance model (TAM) by adding as external variables pre-service teachers' experience with computers and their technological pedagogical content knowledge (TPCK).…

18th European Conference on Mathematics for Industry

CERN Document Server

Capasso, Vincenzo; Nicosia, Giuseppe; Romano, Vittorio

2016-01-01

This book presents a collection of papers emphasizing applications of mathematical models and methods to real-world problems of relevance for industry, life science, environment, finance, and so on. The biannual Conference of ECMI (the European Consortium of Mathematics in Industry) held in 2014 focused on various aspects of industrial and applied mathematics. The five main topics addressed at the conference were mathematical models in life science, material science and semiconductors, mathematical methods in the environment, design automation and industrial applications, and computational finance. Several other topics have been treated, such as, among others, optimization and inverse problems, education, numerical methods for stiff pdes, model reduction, imaging processing, multi physics simulation, mathematical models in textile industry. The conference, which brought together applied mathematicians and experts from industry, provided a unique opportunity to exchange ideas, problems and methodologies...

Instrumentation for Scientific Computing in Neural Networks, Information Science, Artificial Intelligence, and Applied Mathematics.

Science.gov (United States)

1987-10-01

include Security Classification) Instrumentation for scientific computing in neural networks, information science, artificial intelligence, and...instrumentation grant to purchase equipment for support of research in neural networks, information science, artificail intellignece , and applied mathematics...in Neural Networks, Information Science, Artificial Intelligence, and Applied Mathematics Contract AFOSR 86-0282 Principal Investigator: Stephen

Scientific computing in electrical engineering SCEE 2010

Energy Technology Data Exchange (ETDEWEB)

Michielsen, Bastiaan [Office National d' Etudes et de Recherches Aerospatiales (ONERA), 31 - Toulouse (France); Poirier, Jean-Rene (eds.) [LAPLACE-ENSEEIHT, Toulouse (France)

2012-07-01

Selected from papers presented at the 8th Scientific Computation in Electrical Engineering conference in Toulouse in 2010, the contributions to this volume cover every angle of numerically modelling electronic and electrical systems, including computational electromagnetics, circuit theory and simulation and device modelling. On computational electromagnetics, the chapters examine cutting-edge material ranging from low-frequency electrical machine modelling problems to issues in high-frequency scattering. Regarding circuit theory and simulation, the book details the most advanced techniques for modelling networks with many thousands of components. Modelling devices at microscopic levels is covered by a number of fundamental mathematical physics papers, while numerous papers on model order reduction help engineers and systems designers to bring their modelling of industrial-scale systems within the reach of present-day computational power. Complementing these more specific papers, the volume also contains a selection of mathematical methods which can be used in any application domain. (orig.)

Steel heat treating: mathematical modelling and numerical simulation of a problem arising in the automotive industry

Directory of Open Access Journals (Sweden)

Jose Manuel Diaz Moreno

2017-12-01

Full Text Available We describe a mathematical model for the industrial heating and cooling processes of a steel workpiece representing the steering rack of an automobile. The goal of steel heat treating is to provide a hardened surface on critical parts of the workpiece while keeping the rest soft and ductile in order to reduce fatigue. The high hardness is due to the phase transformation of steel accompanying the rapid cooling. This work takes into account both heating-cooling stage and viscoplastic model. Once the general mathematical formulation is derived, we can perform some numerical simulations.

Early numerical foundations of young children's mathematical development.

Science.gov (United States)

Chu, Felicia W; vanMarle, Kristy; Geary, David C

2015-04-01

This study focused on the relative contributions of the acuity of the approximate number system (ANS) and knowledge of quantitative symbols to young children's early mathematical learning. At the beginning of preschool, 191 children (Mage=46 months) were administered tasks that assessed ANS acuity and explicit knowledge of the cardinal values represented by number words, and their mathematics achievement was assessed at the end of the school year. Children's executive functions, intelligence, and preliteracy skills and their parents' educational levels were also assessed and served as covariates. Both the ANS and cardinality tasks were significant predictors of end-of-year mathematics achievement with and without control of the covariates. As simultaneous predictors and with control of the covariates, cardinality remained significantly related to mathematics achievement, but ANS acuity did not. Mediation analyses revealed that the relation between ANS acuity and mathematics achievement was fully mediated by cardinality, suggesting that the ANS may facilitate children's explicit understanding of cardinal value and in this way may indirectly influence early mathematical learning. Copyright © 2015 Elsevier Inc. All rights reserved.

Activities of the Institute for Computer Applications in Science and Engineering

Science.gov (United States)

1985-01-01

Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period April 1, 1985 through October 2, 1985 is summarized.

Formative questioning in computer learning environments: a course for pre-service mathematics teachers

Science.gov (United States)

Akkoç, Hatice

2015-11-01

This paper focuses on a specific aspect of formative assessment, namely questioning. Given that computers have gained widespread use in learning and teaching, specific attention should be made when organizing formative assessment in computer learning environments (CLEs). A course including various workshops was designed to develop knowledge and skills of questioning in CLEs. This study investigates how pre-service mathematics teachers used formative questioning with technological tools such as Geogebra and Graphic Calculus software. Participants are 35 pre-service mathematics teachers. To analyse formative questioning, two types of questions are investigated: mathematical questions and technical questions. Data were collected through lesson plans, teaching notes, interviews and observations. Descriptive statistics of the number of questions in the lesson plans before and after the workshops are presented. Examples of two types of questions are discussed using the theoretical framework. One pre-service teacher was selected and a deeper analysis of the way he used questioning during his three lessons was also investigated. The findings indicated an improvement in using technical questions for formative purposes and that the course provided a guideline in planning and using mathematical and technical questions in CLEs.

Effective Computer-Aided Assessment of Mathematics; Principles, Practice and Results

Science.gov (United States)

Greenhow, Martin

2015-01-01

This article outlines some key issues for writing effective computer-aided assessment (CAA) questions in subjects with substantial mathematical or statistical content, especially the importance of control of random parameters and the encoding of wrong methods of solution (mal-rules) commonly used by students. The pros and cons of using CAA and…

A virtual component method in numerical computation of cascades for isotope separation

International Nuclear Information System (INIS)

Zeng Shi; Cheng Lu

2014-01-01

The analysis, optimization, design and operation of cascades for isotope separation involve computations of cascades. In analytical analysis of cascades, using virtual components is a very useful analysis method. For complicated cases of cascades, numerical analysis has to be employed. However, bound up to the conventional idea that the concentration of a virtual component should be vanishingly small, virtual component is not yet applied to numerical computations. Here a method of introducing the method of using virtual components to numerical computations is elucidated, and its application to a few types of cascades is explained and tested by means of numerical experiments. The results show that the concentration of a virtual component is not restrained at all by the 'vanishingly small' idea. For the same requirements on cascades, the cascades obtained do not depend on the concentrations of virtual components. (authors)

Introduction to computation and modeling for differential equations

CERN Document Server

Edsberg, Lennart

2008-01-01

An introduction to scientific computing for differential equationsIntroduction to Computation and Modeling for Differential Equations provides a unified and integrated view of numerical analysis, mathematical modeling in applications, and programming to solve differential equations, which is essential in problem-solving across many disciplines, such as engineering, physics, and economics. This book successfully introduces readers to the subject through a unique ""Five-M"" approach: Modeling, Mathematics, Methods, MATLAB, and Multiphysics. This approach facilitates a thorough understanding of h

Mathematical modeling of the heat frozen earth in OpenFOAM

International Nuclear Information System (INIS)

Kudryashov, N.A.; Chmykhov, M.A.; Kartashev, A.P.

2015-01-01

A mathematical model of heating permafrost has been presented with allowance for the Stefan condition at the boundary melting. A numerical algorithm has been proposed for analyzing this process. A computation module has been developed on an open architecture with the use of object-oriented programming language OpenFOAM. The computation module has been verified on the known exact solutions of simplified problems [ru

Mathematical and numerical analysis of systems of compressible hydrodynamics and photonics with polar coordinates

International Nuclear Information System (INIS)

Meltz, Bertrand

2015-01-01

This thesis deals with the mathematical and numerical analysis of the systems of compressible hydrodynamics and radiative transfer. More precisely, we study the derivation of numerical methods with 2D polar coordinates (one for the radius, one for the angle) where equations are discretized on regular polar grids. On one hand, these methods are well-suited for the simulation of flows with polar symmetries since they preserve these symmetries by construction. On the other hand, such coordinates systems introduce geometrical singularities as well as geometrical source terms which must be carefully treated. The first part of this document is devoted to the study of hydrodynamics equations, or Euler equations. We propose a new class of arbitrary high-order numerical schemes in both space and time and rely on directional splitting methods for the resolution of 2D equations. Each sub-system is solved using a Lagrange+Remap solver. We study the influence of the r=0 geometrical singularities of the cylindrical and spherical coordinates systems on the precision of the 2D numerical solutions. The second part of this document is devoted to the study of radiative transfer equations. In these equations, the unknowns depend on a large number of variables and a stiff source term is involved. The main difficulty consists in capturing the correct asymptotic behavior on coarse grids. We first construct a class of models where the radiative intensity is projected on a truncated spherical harmonics basis in order to lower the number of mathematical dimensions. Then we propose an Asymptotic Preserving scheme built in polar coordinates and we show that the scheme capture the correct diffusion limit in the radial direction as well as in the polar direction. (author) [fr

Personalized Computer-Assisted Mathematics Problem-Solving Program and Its Impact on Taiwanese Students

Science.gov (United States)

Chen, Chiu-Jung; Liu, Pei-Lin

2007-01-01

This study evaluated the effects of a personalized computer-assisted mathematics problem-solving program on the performance and attitude of Taiwanese fourth grade students. The purpose of this study was to determine whether the personalized computer-assisted program improved student performance and attitude over the nonpersonalized program.…

Numerical problems with the Pascal triangle in moment computation

Czech Academy of Sciences Publication Activity Database

Kautsky, J.; Flusser, Jan

2016-01-01

Roč. 306, č. 1 (2016), s. 53-68 ISSN 0377-0427 R&D Projects: GA ČR GA15-16928S Institutional support: RVO:67985556 Keywords : moment computation * Pascal triangle * appropriate polynomial basis * numerical problems Subject RIV: JD - Computer Applications, Robotics Impact factor: 1.357, year: 2016 http://library.utia.cas.cz/separaty/2016/ZOI/flusser-0459096.pdf

Computing the demagnetizing tensor for finite difference micromagnetic simulations via numerical integration

International Nuclear Information System (INIS)

Chernyshenko, Dmitri; Fangohr, Hans

2015-01-01

In the finite difference method which is commonly used in computational micromagnetics, the demagnetizing field is usually computed as a convolution of the magnetization vector field with the demagnetizing tensor that describes the magnetostatic field of a cuboidal cell with constant magnetization. An analytical expression for the demagnetizing tensor is available, however at distances far from the cuboidal cell, the numerical evaluation of the analytical expression can be very inaccurate. Due to this large-distance inaccuracy numerical packages such as OOMMF compute the demagnetizing tensor using the explicit formula at distances close to the originating cell, but at distances far from the originating cell a formula based on an asymptotic expansion has to be used. In this work, we describe a method to calculate the demagnetizing field by numerical evaluation of the multidimensional integral in the demagnetizing tensor terms using a sparse grid integration scheme. This method improves the accuracy of computation at intermediate distances from the origin. We compute and report the accuracy of (i) the numerical evaluation of the exact tensor expression which is best for short distances, (ii) the asymptotic expansion best suited for large distances, and (iii) the new method based on numerical integration, which is superior to methods (i) and (ii) for intermediate distances. For all three methods, we show the measurements of accuracy and execution time as a function of distance, for calculations using single precision (4-byte) and double precision (8-byte) floating point arithmetic. We make recommendations for the choice of scheme order and integrating coefficients for the numerical integration method (iii). - Highlights: • We study the accuracy of demagnetization in finite difference micromagnetics. • We introduce a new sparse integration method to compute the tensor more accurately. • Newell, sparse integration and asymptotic method are compared for all ranges

Assessing numerical methods used in nuclear aerosol transport models

International Nuclear Information System (INIS)

McDonald, B.H.

1987-01-01

Several computer codes are in use for predicting the behaviour of nuclear aerosols released into containment during postulated accidents in water-cooled reactors. Each of these codes uses numerical methods to discretize and integrate the equations that govern the aerosol transport process. Computers perform only algebraic operations and generate only numbers. It is in the numerical methods that sense can be made of these numbers and where they can be related to the actual solution of the equations. In this report, the numerical methods most commonly used in the aerosol transport codes are examined as special cases of a general solution procedure, the Method of Weighted Residuals. It would appear that the numerical methods used in the codes are all capable of producing reasonable answers to the mathematical problem when used with skill and care. 27 refs

5th International Conference on High Performance Scientific Computing

CERN Document Server

Hoang, Xuan; Rannacher, Rolf; Schlöder, Johannes

2014-01-01

This proceedings volume gathers a selection of papers presented at the Fifth International Conference on High Performance Scientific Computing, which took place in Hanoi on March 5-9, 2012. The conference was organized by the Institute of Mathematics of the Vietnam Academy of Science and Technology (VAST), the Interdisciplinary Center for Scientific Computing (IWR) of Heidelberg University, Ho Chi Minh City University of Technology, and the Vietnam Institute for Advanced Study in Mathematics. The contributions cover the broad interdisciplinary spectrum of scientific computing and present recent advances in theory, development of methods, and practical applications. Subjects covered include mathematical modeling; numerical simulation; methods for optimization and control; parallel computing; software development; and applications of scientific computing in physics, mechanics and biomechanics, material science, hydrology, chemistry, biology, biotechnology, medicine, sports, psychology, transport, logistics, com...

3rd International Conference on High Performance Scientific Computing

CERN Document Server

Kostina, Ekaterina; Phu, Hoang; Rannacher, Rolf

2008-01-01

This proceedings volume contains a selection of papers presented at the Third International Conference on High Performance Scientific Computing held at the Hanoi Institute of Mathematics, Vietnamese Academy of Science and Technology (VAST), March 6-10, 2006. The conference has been organized by the Hanoi Institute of Mathematics, Interdisciplinary Center for Scientific Computing (IWR), Heidelberg, and its International PhD Program ``Complex Processes: Modeling, Simulation and Optimization'', and Ho Chi Minh City University of Technology. The contributions cover the broad interdisciplinary spectrum of scientific computing and present recent advances in theory, development of methods, and applications in practice. Subjects covered are mathematical modelling, numerical simulation, methods for optimization and control, parallel computing, software development, applications of scientific computing in physics, chemistry, biology and mechanics, environmental and hydrology problems, transport, logistics and site loca...

Numerical simulation of the fluid flow between blades and around the turbine blade

International Nuclear Information System (INIS)

Donevski, Bozin; Antoska, Vesna; Chodkiewicz, Ryszard

2006-01-01

In this paper are presented the results of investigations of the flow in turbine cascade giving a contribution to development of both numerical method and upgrading the mathematical model describing the physics of the flow in the turbine cascade. The objective is to classified the influenced factors which affects the efficiency of the work of the turbine stage at defined thermodynamics properties of the flow. The numerical computation is conducted on the turbine model of two stage using CFD commercial computer code CF-TascFlow, based on solving of Navier-Stokes equation with applying a standard ?-? SST (Short-Stress Transport) turbulence model. Results of the numerical computation are discussed in the paper.

Numerical simulation of the fluid flow between blades and around the turbine blade

Energy Technology Data Exchange (ETDEWEB)

Donevski, Bozin; Antoska, Vesna [Faculty of Technical Science, University St. Kliment Ohridski, Bitola (Macedonia, The Former Yugoslav Republic of); Chodkiewicz, Ryszard [Institute of Turbomachinery, Technical University of Lodz (Poland)

2006-07-01

In this paper are presented the results of investigations of the flow in turbine cascade giving a contribution to development of both numerical method and upgrading the mathematical model describing the physics of the flow in the turbine cascade. The objective is to classified the influenced factors which affects the efficiency of the work of the turbine stage at defined thermodynamics properties of the flow. The numerical computation is conducted on the turbine model of two stage using CFD commercial computer code CF-TascFlow, based on solving of Navier-Stokes equation with applying a standard ?-? SST (Short-Stress Transport) turbulence model. Results of the numerical computation are discussed in the paper.

Mathematical Footprints Discovering Mathematics Everywhere

CERN Document Server

Pappas, Theoni

1999-01-01

MATHEMATICAL FOOTPRINTS takes a creative look at the role mathematics has played since prehistoric times, and will play in the future, and uncovers mathematics where you least expect to find it from its many uses in medicine, the sciences, and its appearance in art to its patterns in nature and its central role in the development of computers. Pappas presents mathematical ideas in a readable non-threatening manner. MATHEMATICAL FOOTPRINTS is another gem by the creator of THE MATHEMATICS CALENDAR and author of THE JOY OF MATHEMATICS. "Pappas's books have been gold mines of mathematical ent

Mathematical problems in meteorological modelling

CERN Document Server

Csomós, Petra; Faragó, István; Horányi, András; Szépszó, Gabriella

2016-01-01

This book deals with mathematical problems arising in the context of meteorological modelling. It gathers and presents some of the most interesting and important issues from the interaction of mathematics and meteorology. It is unique in that it features contributions on topics like data assimilation, ensemble prediction, numerical methods, and transport modelling, from both mathematical and meteorological perspectives. The derivation and solution of all kinds of numerical prediction models require the application of results from various mathematical fields. The present volume is divided into three parts, moving from mathematical and numerical problems through air quality modelling, to advanced applications in data assimilation and probabilistic forecasting. The book arose from the workshop “Mathematical Problems in Meteorological Modelling” held in Budapest in May 2014 and organized by the ECMI Special Interest Group on Numerical Weather Prediction. Its main objective is to highlight the beauty of the de...

Mathematical and computational methods for semiclassical Schrödinger equations

KAUST Repository

Jin, Shi

2011-04-28

We consider time-dependent (linear and nonlinear) Schrödinger equations in a semiclassical scaling. These equations form a canonical class of (nonlinear) dispersive models whose solutions exhibit high-frequency oscillations. The design of efficient numerical methods which produce an accurate approximation of the solutions, or at least of the associated physical observables, is a formidable mathematical challenge. In this article we shall review the basic analytical methods for dealing with such equations, including WKB asymptotics, Wigner measure techniques and Gaussian beams. Moreover, we shall give an overview of the current state of the art of numerical methods (most of which are based on the described analytical techniques) for the Schrödinger equation in the semiclassical regime. © 2011 Cambridge University Press.

Addressing current challenges in cancer immunotherapy with mathematical and computational modelling.

Science.gov (United States)

Konstorum, Anna; Vella, Anthony T; Adler, Adam J; Laubenbacher, Reinhard C

2017-06-01

The goal of cancer immunotherapy is to boost a patient's immune response to a tumour. Yet, the design of an effective immunotherapy is complicated by various factors, including a potentially immunosuppressive tumour microenvironment, immune-modulating effects of conventional treatments and therapy-related toxicities. These complexities can be incorporated into mathematical and computational models of cancer immunotherapy that can then be used to aid in rational therapy design. In this review, we survey modelling approaches under the umbrella of the major challenges facing immunotherapy development, which encompass tumour classification, optimal treatment scheduling and combination therapy design. Although overlapping, each challenge has presented unique opportunities for modellers to make contributions using analytical and numerical analysis of model outcomes, as well as optimization algorithms. We discuss several examples of models that have grown in complexity as more biological information has become available, showcasing how model development is a dynamic process interlinked with the rapid advances in tumour-immune biology. We conclude the review with recommendations for modellers both with respect to methodology and biological direction that might help keep modellers at the forefront of cancer immunotherapy development. © 2017 The Author(s).

Numerical computation of gravitational field for general axisymmetric objects

Science.gov (United States)

Fukushima, Toshio

2016-10-01

We developed a numerical method to compute the gravitational field of a general axisymmetric object. The method (I) numerically evaluates a double integral of the ring potential by the split quadrature method using the double exponential rules, and (II) derives the acceleration vector by numerically differentiating the numerically integrated potential by Ridder's algorithm. Numerical comparison with the analytical solutions for a finite uniform spheroid and an infinitely extended object of the Miyamoto-Nagai density distribution confirmed the 13- and 11-digit accuracy of the potential and the acceleration vector computed by the method, respectively. By using the method, we present the gravitational potential contour map and/or the rotation curve of various axisymmetric objects: (I) finite uniform objects covering rhombic spindles and circular toroids, (II) infinitely extended spheroids including Sérsic and Navarro-Frenk-White spheroids, and (III) other axisymmetric objects such as an X/peanut-shaped object like NGC 128, a power-law disc with a central hole like the protoplanetary disc of TW Hya, and a tear-drop-shaped toroid like an axisymmetric equilibrium solution of plasma charge distribution in an International Thermonuclear Experimental Reactor-like tokamak. The method is directly applicable to the electrostatic field and will be easily extended for the magnetostatic field. The FORTRAN 90 programs of the new method and some test results are electronically available.

Finger-Based Numerical Skills Link Fine Motor Skills to Numerical Development in Preschoolers.

Science.gov (United States)

Suggate, Sebastian; Stoeger, Heidrun; Fischer, Ursula

2017-12-01

Previous studies investigating the association between fine-motor skills (FMS) and mathematical skills have lacked specificity. In this study, we test whether an FMS link to numerical skills is due to the involvement of finger representations in early mathematics. We gave 81 pre-schoolers (mean age of 4 years, 9 months) a set of FMS measures and numerical tasks with and without a specific finger focus. Additionally, we used receptive vocabulary and chronological age as control measures. FMS linked more closely to finger-based than to nonfinger-based numerical skills even after accounting for the control variables. Moreover, the relationship between FMS and numerical skill was entirely mediated by finger-based numerical skills. We concluded that FMS are closely related to early numerical skill development through finger-based numerical counting that aids the acquisition of mathematical mental representations.

Proceedings of the Third International Workshop on Mathematical Foundations of Computational Anatomy

DEFF Research Database (Denmark)

the mathematical community around shapes and the MICCAI community in view of computational anatomy applications. It targets more particularly researchers investigating the combination of statistical and geometrical aspects in the modeling of the variability of biological shapes. The workshop is a forum...... of the workshop: statistics on manifolds and diff eomorphisms for surface or longitudinal registration. One session gathers papers exploring new mathematical structures beyond Riemannian geometry while the last oral session deals with the emerging theme of statistics on graphs and trees. Finally, a poster session......Computational anatomy is an emerging discipline at the interface of geometry, statistics and image analysis which aims at modeling and analyzing the biological shape of tissues and organs. The goal is to estimate representative organ anatomies across diseases, populations, species or ages, to model...

Mathematical models and numerical simulation in electromagnetism

CERN Document Server

Bermúdez, Alfredo; Salgado, Pilar

2014-01-01

The book represents a basic support for a master course in electromagnetism oriented to numerical simulation. The main goal of the book is that the reader knows the boundary-value problems of partial differential equations that should be solved in order to perform computer simulation of electromagnetic processes. Moreover it includes a part devoted to electric circuit theory  based on ordinary differential equations. The book is mainly oriented to electric engineering applications, going from the general to the specific, namely, from the full Maxwell’s equations to the particular cases of electrostatics, direct current, magnetostatics and eddy currents models. Apart from standard exercises related to analytical calculus, the book includes some others oriented to real-life applications solved with MaxFEM free simulation software.

Annual report 1 January - 31 December 1978 computer installation

International Nuclear Information System (INIS)

1979-05-01

The computer installation of Risoe National Laboratory functions as an internal service bureau. The staff is concentrated around operating the computer and providing expertise in the fields of numerical mathematics, statistics, operation research, systems software, and software engineering. Selected parts of the activities at the Computer Installation are described. (B.P.)

Mathematics of Computed Tomography

Science.gov (United States)

Hawkins, William Grant

A review of the applications of the Radon transform is presented, with emphasis on emission computed tomography and transmission computed tomography. The theory of the 2D and 3D Radon transforms, and the effects of attenuation for emission computed tomography are presented. The algebraic iterative methods, their importance and limitations are reviewed. Analytic solutions of the 2D problem the convolution and frequency filtering methods based on linear shift invariant theory, and the solution of the circular harmonic decomposition by integral transform theory--are reviewed. The relation between the invisible kernels, the inverse circular harmonic transform, and the consistency conditions are demonstrated. The discussion and review are extended to the 3D problem-convolution, frequency filtering, spherical harmonic transform solutions, and consistency conditions. The Cormack algorithm based on reconstruction with Zernike polynomials is reviewed. An analogous algorithm and set of reconstruction polynomials is developed for the spherical harmonic transform. The relations between the consistency conditions, boundary conditions and orthogonal basis functions for the 2D projection harmonics are delineated and extended to the 3D case. The equivalence of the inverse circular harmonic transform, the inverse Radon transform, and the inverse Cormack transform is presented. The use of the number of nodes of a projection harmonic as a filter is discussed. Numerical methods for the efficient implementation of angular harmonic algorithms based on orthogonal functions and stable recursion are presented. The derivation of a lower bound for the signal-to-noise ratio of the Cormack algorithm is derived.

M and c'99 : Mathematics and computation, reactor physics and environmental analysis in nuclear applications, Madrid, September 27-30, 1999

International Nuclear Information System (INIS)

Aragones, J. M.; Ahnert, C.; Cabellos, O.

1999-01-01

The international conference on mathematics and computation, reactor physics and environmental analysis in nuclear applications in the biennial topical meeting of the mathematics and computation division of the American Nuclear Society. (Author)

Numerical analysis using Sage

CERN Document Server

Anastassiou, George A

2015-01-01

This is the first numerical analysis text to use Sage for the implementation of algorithms and can be used in a one-semester course for undergraduates in mathematics, math education, computer science/information technology, engineering, and physical sciences. The primary aim of this text is to simplify understanding of the theories and ideas from a numerical analysis/numerical methods course via a modern programming language like Sage. Aside from the presentation of fundamental theoretical notions of numerical analysis throughout the text, each chapter concludes with several exercises that are oriented to real-world application.  Answers may be verified using Sage.  The presented code, written in core components of Sage, are backward compatible, i.e., easily applicable to other software systems such as Mathematica®.  Sage is  open source software and uses Python-like syntax. Previous Python programming experience is not a requirement for the reader, though familiarity with any programming language is a p...

A Handbook of Essential Mathematical Formulae

CERN Document Server

Davies, Alan

2005-01-01

Intended for students of mathematics as well as of engineering, physical science, economics, business studies, and computer science, this handbook contains vital information and formulas for algebra, geometry, calculus, numerical methods, and statistics. Comprehensive tables of standard derivatives and integrals, together with the tables of Laplace, Fourier, and Z transforms are included. A spiral binding that allows the handbook to lay flat for easy reference enhances the user-friendly design.

Activities of the Institute for Computer Applications in Science and Engineering (ICASE)

Science.gov (United States)

1988-01-01

This report summarizes research conducted at the Institute for Computer Applications Science and Engineering in applied mathematics, numerical analysis, and computer science during the period October 2, 1987 through March 31, 1988.

METRIC CHARACTERISTICS OF VARIOUS METHODS FOR NUMERICAL DENSITY ESTIMATION IN TRANSMISSION LIGHT MICROSCOPY – A COMPUTER SIMULATION

Directory of Open Access Journals (Sweden)

Miroslav Kališnik

2011-05-01

Full Text Available In the introduction the evolution of methods for numerical density estimation of particles is presented shortly. Three pairs of methods have been analysed and compared: (1 classical methods for particles counting in thin and thick sections, (2 original and modified differential counting methods and (3 physical and optical disector methods. Metric characteristics such as accuracy, efficiency, robustness, and feasibility of methods have been estimated and compared. Logical, geometrical and mathematical analysis as well as computer simulations have been applied. In computer simulations a model of randomly distributed equal spheres with maximal contrast against surroundings has been used. According to our computer simulation all methods give accurate results provided that the sample is representative and sufficiently large. However, there are differences in their efficiency, robustness and feasibility. Efficiency and robustness increase with increasing slice thickness in all three pairs of methods. Robustness is superior in both differential and both disector methods compared to both classical methods. Feasibility can be judged according to the additional equipment as well as to the histotechnical and counting procedures necessary for performing individual counting methods. However, it is evident that not all practical problems can efficiently be solved with models.

Numerical methods and computers used in elastohydrodynamic lubrication

Science.gov (United States)

Hamrock, B. J.; Tripp, J. H.

1982-01-01

Some of the methods of obtaining approximate numerical solutions to boundary value problems that arise in elastohydrodynamic lubrication are reviewed. The highlights of four general approaches (direct, inverse, quasi-inverse, and Newton-Raphson) are sketched. Advantages and disadvantages of these approaches are presented along with a flow chart showing some of the details of each. The basic question of numerical stability of the elastohydrodynamic lubrication solutions, especially in the pressure spike region, is considered. Computers used to solve this important class of lubrication problems are briefly described, with emphasis on supercomputers.

Using Computational and Mechanical Models to Study Animal Locomotion

OpenAIRE

Miller, Laura A.; Goldman, Daniel I.; Hedrick, Tyson L.; Tytell, Eric D.; Wang, Z. Jane; Yen, Jeannette; Alben, Silas

2012-01-01

Recent advances in computational methods have made realistic large-scale simulations of animal locomotion possible. This has resulted in numerous mathematical and computational studies of animal movement through fluids and over substrates with the purpose of better understanding organisms’ performance and improving the design of vehicles moving through air and water and on land. This work has also motivated the development of improved numerical methods and modeling techniques for animal locom...

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…

Effects of Computer Graphics Types and Epistemological Beliefs on Students' Learning of Mathematical Concepts.

Science.gov (United States)

Lin, Chi-Hui

2002-01-01

Describes a study that determined the implications of computer graphics types and epistemological beliefs with regard to the design of computer-based mathematical concept learning with elementary school students in Taiwan. Discusses the factor structure of the epistemological belief questionnaire, student performance, and students' attitudes…

Principles of computational fluid dynamics

CERN Document Server

Wesseling, Pieter

2001-01-01

The book is aimed at graduate students, researchers, engineers and physicists involved in flow computations. An up-to-date account is given of the present state-of-the-art of numerical methods employed in computational fluid dynamics. The underlying numerical principles are treated with a fair amount of detail, using elementary mathematical analysis. Attention is given to difficulties arising from geometric complexity of the flow domain and of nonuniform structured boundary-fitted grids. Uniform accuracy and efficiency for singular perturbation problems is studied, pointing the way to accurate computation of flows at high Reynolds number. Much attention is given to stability analysis, and useful stability conditions are provided, some of them new, for many numerical schemes used in practice. Unified methods for compressible and incompressible flows are discussed. Numerical analysis of the shallow-water equations is included. The theory of hyperbolic conservation laws is treated. Godunov's order barrier and ho...

Contributions to the uncertainty management in numerical modelization: wave propagation in random media and analysis of computer experiments

International Nuclear Information System (INIS)

Iooss, B.

2009-01-01

The present document constitutes my Habilitation thesis report. It recalls my scientific activity of the twelve last years, since my PhD thesis until the works completed as a research engineer at CEA Cadarache. The two main chapters of this document correspond to two different research fields both referring to the uncertainty treatment in engineering problems. The first chapter establishes a synthesis of my work on high frequency wave propagation in random medium. It more specifically relates to the study of the statistical fluctuations of acoustic wave travel-times in random and/or turbulent media. The new results mainly concern the introduction of the velocity field statistical anisotropy in the analytical expressions of the travel-time statistical moments according to those of the velocity field. This work was primarily carried by requirements in geophysics (oil exploration and seismology). The second chapter is concerned by the probabilistic techniques to study the effect of input variables uncertainties in numerical models. My main applications in this chapter relate to the nuclear engineering domain which offers a large variety of uncertainty problems to be treated. First of all, a complete synthesis is carried out on the statistical methods of sensitivity analysis and global exploration of numerical models. The construction and the use of a meta-model (inexpensive mathematical function replacing an expensive computer code) are then illustrated by my work on the Gaussian process model (kriging). Two additional topics are finally approached: the high quantile estimation of a computer code output and the analysis of stochastic computer codes. We conclude this memory with some perspectives about the numerical simulation and the use of predictive models in industry. This context is extremely positive for future researches and application developments. (author)

Mathematical and numerical analysis of the resistive magnetohydrodynamics system with self-generated magnetic field terms

International Nuclear Information System (INIS)

Wolff, Marc

2011-01-01

This work is devoted to the construction of numerical methods that allow the accurate simulation of inertial confinement fusion (ICF) implosion processes by taking self-generated magnetic field terms into account. In the sequel, we first derive a two-temperature resistive magnetohydrodynamics model and describe the considered closure relations. The resulting system of equations is then split in several subsystems according to the nature of the underlying mathematical operator. Adequate numerical methods are then proposed for each of these subsystems. Particular attention is paid to the development of finite volume schemes for the hyperbolic operator which actually is the hydrodynamics or ideal magnetohydrodynamics system depending on whether magnetic fields are considered or not. More precisely, a new class of high-order accurate dimensionally split schemes for structured meshes is proposed using the Lagrange re-map formalism. One of these schemes' most innovative features is that they have been designed in order to take advantage of modern massively parallel computer architectures. This property can for example be illustrated by the dimensionally split approach or the use of artificial viscosity techniques and is practically highlighted by sequential performance and parallel efficiency figures. Hyperbolic schemes are then combined with finite volume methods for dealing with the thermal and resistive conduction operators and taking magnetic field generation into account. In order to study the characteristics and effects of self-generated magnetic field terms, simulation results are finally proposed with the complete two-temperature resistive magnetohydrodynamics model on a test problem that represents the state of an ICF capsule at the beginning of the deceleration phase. (author)

Computational physics and applied mathematics capability review June 8-10, 2010

Energy Technology Data Exchange (ETDEWEB)

Lee, Stephen R [Los Alamos National Laboratory

2010-01-01

Los Alamos National Laboratory will review its Computational Physics and Applied Mathematics (CPAM) capabilities in 2010. The goals of capability reviews are to assess the quality of science, technology, and engineering (STE) performed by the capability, evaluate the integration of this capability across the Laboratory and within the scientific community, examine the relevance of this capability to the Laboratory's programs, and provide advice on the current and future directions of this capability. This is the first such review for CPAM, which has a long and unique history at the Laboratory, starting from the inception of the Laboratory in 1943. The CPAM capability covers an extremely broad technical area at Los Alamos, encompassing a wide array of disciplines, research topics, and organizations. A vast array of technical disciplines and activities are included in this capability, from general numerical modeling, to coupled multi-physics simulations, to detailed domain science activities in mathematics, methods, and algorithms. The CPAM capability involves over 12 different technical divisions and a majority of our programmatic and scientific activities. To make this large scope tractable, the CPAM capability is broken into the following six technical 'themes.' These themes represent technical slices through the CPAM capability and collect critical core competencies of the Laboratory, each of which contributes to the capability (and each of which is divided into multiple additional elements in the detailed descriptions of the themes in subsequent sections), as follows. Theme 1: Computational Fluid Dynamics - This theme speaks to the vast array of scientific capabilities for the simulation of fluids under shocks, low-speed flow, and turbulent conditions - which are key, historical, and fundamental strengths of the Laboratory. Theme 2: Partial Differential Equations - The technical scope of this theme is the applied mathematics and numerical solution

Mathematical model for solid fuel combustion in fluidized bed

International Nuclear Information System (INIS)

Kostikj, Zvonimir; Noshpal, Aleksandar

1994-01-01

A mathematical model for computation of the combustion process of solid fuel in fluidized bed is presented in this work. Only the combustor part of the plant (the fluidized bed and the free board) is treated with this model. In that manner, all principal, physical presumption and improvements (upon which this model is based) are given. Finally, the results of the numerical realisation of the mathematical model for combustion of minced straw as well as the results of the experimental investigation of a concrete physical model are presented. (author)

Scilab software as an alternative low-cost computing in solving the linear equations problem

Science.gov (United States)

Agus, Fahrul; Haviluddin

2017-02-01

Numerical computation packages are widely used both in teaching and research. These packages consist of license (proprietary) and open source software (non-proprietary). One of the reasons to use the package is a complexity of mathematics function (i.e., linear problems). Also, number of variables in a linear or non-linear function has been increased. The aim of this paper was to reflect on key aspects related to the method, didactics and creative praxis in the teaching of linear equations in higher education. If implemented, it could be contribute to a better learning in mathematics area (i.e., solving simultaneous linear equations) that essential for future engineers. The focus of this study was to introduce an additional numerical computation package of Scilab as an alternative low-cost computing programming. In this paper, Scilab software was proposed some activities that related to the mathematical models. In this experiment, four numerical methods such as Gaussian Elimination, Gauss-Jordan, Inverse Matrix, and Lower-Upper Decomposition (LU) have been implemented. The results of this study showed that a routine or procedure in numerical methods have been created and explored by using Scilab procedures. Then, the routine of numerical method that could be as a teaching material course has exploited.

Mathematical modelling and numerical solution of swelling of cartilaginous tissues. Part II: Mixed hybrid finite element solution

NARCIS (Netherlands)

Malakpoor, K.; Kaasschieter, E.F.; Huyghe, J.M.R.J.

2007-01-01

The swelling and shrinkage of biological tissues are modelled by a four-component mixture theory [J.M. Huyghe and J.D. Janssen, Int. J. Engng. Sci. 35 (1997) 793-802; K. Malakpoor, E.F. Kaasschieter and J.M. Huyghe, Mathematical modelling and numerical solution of swelling of cartilaginous tissues.

Domain-Specific and Domain-General Training to Improve Kindergarten Children’s Mathematics

Directory of Open Access Journals (Sweden)

Geetha B. Ramani

2017-12-01

Full Text Available Ensuring that kindergarten children have a solid foundation in early numerical knowledge is of critical importance for later mathematical achievement. In this study, we targeted improving the numerical knowledge of kindergarteners (n = 81 from primarily low-income backgrounds using two approaches: one targeting their conceptual knowledge, specifically, their understanding of numerical magnitudes; and the other targeting their underlying cognitive system, specifically, their working memory. Both interventions involved playing game-like activities on tablet computers over the course of several sessions. As predicted, both interventions improved children’s numerical magnitude knowledge as compared to a no-contact control group, suggesting that both domain-specific and domain-general interventions facilitate mathematical learning. Individual differences in effort during the working memory game, but not the number knowledge training game predicted children’s improvements in number line estimation. The results demonstrate the potential of using a rapidly growing technology in early childhood classrooms to promote young children’s numerical knowledge.

Numerical modeling of batch formation in waste incineration plants

Directory of Open Access Journals (Sweden)

Obroučka Karel

2015-03-01

Full Text Available The aim of this paper is a mathematical description of algorithm for controlled assembly of incinerated batch of waste. The basis for formation of batch is selected parameters of incinerated waste as its calorific value or content of pollutants or the combination of both. The numerical model will allow, based on selected criteria, to compile batch of wastes which continuously follows the previous batch, which is a prerequisite for optimized operation of incinerator. The model was prepared as for waste storage in containers, as well as for waste storage in continuously refilled boxes. The mathematical model was developed into the computer program and its functionality was verified either by practical measurements or by numerical simulations. The proposed model can be used in incinerators for hazardous and municipal waste.

The influence of early computer use on educational achievement in mathematics

Directory of Open Access Journals (Sweden)

Andrés Fernández Aráuz

2014-11-01

Full Text Available Does early access to computer use improve student achievement? Empirical evidence from experimental designs shows little or no relationship between the use of ICT and academic performance. Using the data collected in PISA it can be analyzed this association some years after that the student had access to a computer for the first time. Performing an exploratory data analysis of Costa Rican students in PISA 2012 mathematics assessment and by estimating a linear regression model even controlling for factors with high explanatory power on academic performance, it’s shown that age at access to a computer is a determinant of educational performance.

Mathematical modeling and signal processing in speech and hearing sciences

CERN Document Server

Xin, Jack

2014-01-01

The aim of the book is to give an accessible introduction of mathematical models and signal processing methods in speech and hearing sciences for senior undergraduate and beginning graduate students with basic knowledge of linear algebra, differential equations, numerical analysis, and probability. Speech and hearing sciences are fundamental to numerous technological advances of the digital world in the past decade, from music compression in MP3 to digital hearing aids, from network based voice enabled services to speech interaction with mobile phones. Mathematics and computation are intimately related to these leaps and bounds. On the other hand, speech and hearing are strongly interdisciplinary areas where dissimilar scientific and engineering publications and approaches often coexist and make it difficult for newcomers to enter.

Pulse cleaning flow models and numerical computation of candle ceramic filters.

Science.gov (United States)

Tian, Gui-shan; Ma, Zhen-ji; Zhang, Xin-yi; Xu, Ting-xiang

2002-04-01

Analytical and numerical computed models are developed for reverse pulse cleaning system of candle ceramic filters. A standard turbulent model is demonstrated suitably to the designing computation of reverse pulse cleaning system from the experimental and one-dimensional computational result. The computed results can be used to guide the designing of reverse pulse cleaning system, which is optimum Venturi geometry. From the computed results, the general conclusions and the designing methods are obtained.

NEPTUNIX 2: Operating on computers network - Catalogued procedures

International Nuclear Information System (INIS)

Roux, Pierre.

1982-06-01

NEPTUNIX 2 is a package which carries out the simulation of complex processes described by numerous non linear algebro-differential equations. Main features are: non linear or time dependent parameters, implicit form, stiff systems, dynamic change of equations leading to discontinuities on some variables. Thus the mathematical model is built with an equations set F(x,x',1,t), where t is the independent variable, x' the derivative of x and 1 an ''algebrized'' logical variable. The NEPTUNIX 2 package is divided into two successive major steps: a non numerical step and a numerical step. The numerical step, using results from a picture of the model translated in FORTRAN language, in a form fitted for the executive computer, carries out the simulmations; in this way, NEPTUNIX 2 numerical step is portable. On the opposite, the non numerical step must be executed on a series 370 IBM computer or on a compatible computer. The present manual describes NEPTUNIX 2 operating procedures when the two steps are executed on the same computer and also when the numerical step is executed on an other computer connected or not on the same computing network [fr

The Effectiveness of Computer-Assisted Instruction for Teaching Mathematics to Students with Specific Learning Disability

Science.gov (United States)

Stultz, Sherry L.

2013-01-01

Using computers to teach students is not a new idea. Computers have been utilized for educational purposes for over 80 years. However, the effectiveness of these programs for teaching mathematics to students with specific learning disability is unclear. This study was undertaken to determine if computer-assisted instruction was as effective as…

Research in progress at the Institute for Computer Applications in Science and Engineering

Science.gov (United States)

1987-01-01

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period April 1, 1987 through October 1, 1987.

M and c'99 : Mathematics and computation, reactor physics and environmental analysis in nuclear applications, Madrid, September 27-30, 1999

Energy Technology Data Exchange (ETDEWEB)

Aragones, J. M.; Ahnert, C.; Cabellos, O.

1999-07-01

The international conference on mathematics and computation, reactor physics and environmental analysis in nuclear applications in the biennial topical meeting of the mathematics and computation division of the American Nuclear Society. (Author)

Mathematical foundation of computer science

CERN Document Server

Singh, YN

2005-01-01

The interesting feature of this book is its organization and structure. That consists of systematizing of the definitions, methods, and results that something resembling a theory. Simplicity, clarity, and precision of mathematical language makes theoretical topics more appealing to the readers who are of mathematical or non-mathematical background. For quick references and immediate attentions¾concepts and definitions, methods and theorems, and key notes are presented through highlighted points from beginning to end. Whenever, necessary and probable a visual approach of presentation is used. The amalgamation of text and figures make mathematical rigors easier to understand. Each chapter begins with the detailed contents, which are discussed inside the chapter and conclude with a summary of the material covered in the chapter. Summary provides a brief overview of all the topics covered in the chapter. To demonstrate the principles better, the applicability of the concepts discussed in each topic are illustrat...

ECMOR III: Third European Conference on the Mathematics of Oil Recovery

Energy Technology Data Exchange (ETDEWEB)

Christie, M.A.; Da Silva, F.V.; Farmer, C.L.; Guillon, O.; Heinemann, Z.E.; Lemonnier, P.; Regtien, J.M.M.; Van Spronsen, E. [eds.

1992-12-31

35 papers are presented in four groups: reservoir characterization (11), analytical methods (6), numerical methods (11), and reservoir simulation (7). With 11 papers the mathematical aspects of reservoir characterization are getting the attention they deserve. The geological and reservoir engineering concepts must be supplied by other disciplines, but no progress would be possible without mathematical modelling of these concepts. Analytical methods can be very helpful in deepening our insight. However, in this computer age they have a hard time competing with numerical methods. Fortunately this section is well presented with some very interesting papers. The numerical section covers a number of techniques aimed at improved reservoir simulation. Some are dealing with special applications: permeability prediction, steam injection, fractured reservoirs, hydrocarbons migration. In the reservoir simulation section the emphasis is on simulation of relatively small-scale features: fractures, fingering and wells

Partnership in Being a Specialist Mathematics and Computing College--Who Gains What, How and Why?

Science.gov (United States)

Sinkinson, Anne J.

2007-01-01

The research took place in a mathematics and computing specialist school. The article reports on part of a case study of the mathematics department's experience of being a major contributor to the requirements of being a specialist school. This article aims to explore and describe one model of partnership within the "community" remit of…

Introductory discrete mathematics

CERN Document Server

Balakrishnan, V K

2010-01-01

This concise text offers an introduction to discrete mathematics for undergraduate students in computer science and mathematics. Mathematics educators consider it vital that their students be exposed to a course in discrete methods that introduces them to combinatorial mathematics and to algebraic and logical structures focusing on the interplay between computer science and mathematics. The present volume emphasizes combinatorics, graph theory with applications to some stand network optimization problems, and algorithms to solve these problems.Chapters 0-3 cover fundamental operations involv

Scientific Computing in Electrical Engineering

CERN Document Server

Amrhein, Wolfgang; Zulehner, Walter

2018-01-01

This collection of selected papers presented at the 11th International Conference on Scientific Computing in Electrical Engineering (SCEE), held in St. Wolfgang, Austria, in 2016, showcases the state of the art in SCEE. The aim of the SCEE 2016 conference was to bring together scientists from academia and industry, mathematicians, electrical engineers, computer scientists, and physicists, and to promote intensive discussions on industrially relevant mathematical problems, with an emphasis on the modeling and numerical simulation of electronic circuits and devices, electromagnetic fields, and coupled problems. The focus in methodology was on model order reduction and uncertainty quantification. This extensive reference work is divided into six parts: Computational Electromagnetics, Circuit and Device Modeling and Simulation, Coupled Problems and Multi‐Scale Approaches in Space and Time, Mathematical and Computational Methods Including Uncertainty Quantification, Model Order Reduction, and Industrial Applicat...

Mathematical cardiac electrophysiology

CERN Document Server

Colli Franzone, Piero; Scacchi, Simone

2014-01-01

This book covers the main mathematical and numerical models in computational electrocardiology, ranging from microscopic membrane models of cardiac ionic channels to macroscopic bidomain, monodomain, eikonal models and cardiac source representations. These advanced multiscale and nonlinear models describe the cardiac bioelectrical activity from the cell level to the body surface and are employed in both the direct and inverse problems of electrocardiology. The book also covers advanced numerical techniques needed to efficiently carry out large-scale cardiac simulations, including time and space discretizations, decoupling and operator splitting techniques, parallel finite element solvers. These techniques are employed in 3D cardiac simulations illustrating the excitation mechanisms, the anisotropic effects on excitation and repolarization wavefronts, the morphology of electrograms in normal and pathological tissue and some reentry phenomena. The overall aim of the book is to present rigorously the mathematica...

Mathematical models for therapeutic approaches to control HIV disease transmission

CERN Document Server

Roy, Priti Kumar

2015-01-01

The book discusses different therapeutic approaches based on different mathematical models to control the HIV/AIDS disease transmission. It uses clinical data, collected from different cited sources, to formulate the deterministic as well as stochastic mathematical models of HIV/AIDS. It provides complementary approaches, from deterministic and stochastic points of view, to optimal control strategy with perfect drug adherence and also tries to seek viewpoints of the same issue from different angles with various mathematical models to computer simulations. The book presents essential methods and techniques for students who are interested in designing epidemiological models on HIV/AIDS. It also guides research scientists, working in the periphery of mathematical modeling, and helps them to explore a hypothetical method by examining its consequences in the form of a mathematical modelling and making some scientific predictions. The model equations, mathematical analysis and several numerical simulations that are...

Numerical models for differential problems

CERN Document Server

Quarteroni, Alfio

2017-01-01

In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, an...

Mathematical Sciences Institute Workshop

CERN Document Server

Scott, Philip

1990-01-01

A so-called "effective" algorithm may require arbitrarily large finite amounts of time and space resources, and hence may not be practical in the real world. A "feasible" algorithm is one which only requires a limited amount of space and/or time for execution; the general idea is that a feasible algorithm is one which may be practical on today's or at least tomorrow's computers. There is no definitive analogue of Church's thesis giving a mathematical definition of feasibility; however, the most widely studied mathematical model of feasible computability is polynomial-time computability. Feasible Mathematics includes both the study of feasible computation from a mathematical and logical point of view and the reworking of traditional mathematics from the point of view of feasible computation. The diversity of Feasible Mathematics is illustrated by the. contents of this volume which includes papers on weak fragments of arithmetic, on higher type functionals, on bounded linear logic, on sub recursive definitions ...

Computational Physics Simulation of Classical and Quantum Systems

CERN Document Server

Scherer, Philipp O. J

2010-01-01

This book encapsulates the coverage for a two-semester course in computational physics. The first part introduces the basic numerical methods while omitting mathematical proofs but demonstrating the algorithms by way of numerous computer experiments. The second part specializes in simulation of classical and quantum systems with instructive examples spanning many fields in physics, from a classical rotor to a quantum bit. All program examples are realized as Java applets ready to run in your browser and do not require any programming skills.