Applied geometry and discrete mathematics
Sturm; Gritzmann, Peter; Sturmfels, Bernd
1991-01-01
This volume, published jointly with the Association for Computing Machinery, comprises a collection of research articles celebrating the occasion of Victor Klee's sixty-fifth birthday in September 1990. During his long career, Klee has made contributions to a wide variety of areas, such as discrete and computational geometry, convexity, combinatorics, graph theory, functional analysis, mathematical programming and optimization, and theoretical computer science. In addition, Klee made important contributions to mathematics education, mathematical methods in economics and the decision sciences, applications of discrete mathematics in the biological and social sciences, and the transfer of knowledge from applied mathematics to industry. In honor of Klee's achievements, this volume presents more than forty papers on topics related to Klee's research. While the majority of the papers are research articles, a number of survey articles are also included. Mirroring the breadth of Klee's mathematical contributions, th...
Sørensen, John Aasted
2011-01-01
The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...
Sørensen, John Aasted
2011-01-01
; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics...... to new problems. Relations and functions: Define a product set; define and apply equivalence relations; construct and apply functions. Apply these concepts to new problems. Natural numbers and induction: Define the natural numbers; apply the principle of induction to verify a selection of properties...
Sørensen, John Aasted
2010-01-01
The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Spring 2010 Ectent: 5 ects Class size: 18...
Sørensen, John Aasted
2010-01-01
The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15......The introduction of the mathematics needed for analysis, design and verification of discrete systems, including applications within programming languages for computer systems. Course sessions and project work. Semester: Autumn 2010 Ectent: 5 ects Class size: 15...
Nedelec, J.C.
1988-01-01
The 1988 progress report of the Applied Mathematics center (Polytechnic School, France), is presented. The research fields of the Center are the scientific calculus, the probabilities and statistics and the video image synthesis. The research topics developed are: the analysis of numerical methods, the mathematical analysis of the physics and mechanics fundamental models, the numerical solution of complex models related to the industrial problems, the stochastic calculus and the brownian movement, the stochastic partial differential equations, the identification of the adaptive filtering parameters, the discrete element systems, statistics, the stochastic control and the development, the image synthesis techniques for education and research programs. The published papers, the congress communications and the thesis are listed [fr
Discrete Mathematics Re "Tooled."
Grassl, Richard M.; Mingus, Tabitha T. Y.
1999-01-01
Indicates the importance of teaching discrete mathematics. Describes how the use of technology can enhance the teaching and learning of discrete mathematics. Explorations using Excel, Derive, and the TI-92 proved how preservice and inservice teachers experienced a new dimension in problem solving and discovery. (ASK)
Introductory discrete mathematics
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
Sharp, Karen Tobey
This paper cites information received from a number of sources, e.g., mathematics teachers in two-year colleges, publishers, and convention speakers, about the nature of discrete mathematics and about what topics a course in this subject should contain. Note is taken of the book edited by Ralston and Young which discusses the future of college…
DISCRETE MATHEMATICS/NUMBER THEORY
Mrs. Manju Devi*
2017-01-01
Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics such as integers, graphs, and statements do not vary smoothly in this way, but have distinct, separated values. Discrete mathematics therefore excludes topics in "continuous mathematics" such as calculus and analysis. Discrete objects can often be enumerated by ...
Logan, J David
2013-01-01
Praise for the Third Edition"Future mathematicians, scientists, and engineers should find the book to be an excellent introductory text for coursework or self-study as well as worth its shelf space for reference." -MAA Reviews Applied Mathematics, Fourth Edition is a thoroughly updated and revised edition on the applications of modeling and analyzing natural, social, and technological processes. The book covers a wide range of key topics in mathematical methods and modeling and highlights the connections between mathematics and the applied and nat
Discrete Mathematics and Curriculum Reform.
Kenney, Margaret J.
1996-01-01
Defines discrete mathematics as the mathematics necessary to effect reasoned decision making in finite situations and explains how its use supports the current view of mathematics education. Discrete mathematics can be used by curriculum developers to improve the curriculum for students of all ages and abilities. (SLD)
Discrete mathematics with applications
Koshy, Thomas
2003-01-01
This approachable text studies discrete objects and the relationsips that bind them. It helps students understand and apply the power of discrete math to digital computer systems and other modern applications. It provides excellent preparation for courses in linear algebra, number theory, and modern/abstract algebra and for computer science courses in data structures, algorithms, programming languages, compilers, databases, and computation.* Covers all recommended topics in a self-contained, comprehensive, and understandable format for students and new professionals * Emphasizes problem-solving techniques, pattern recognition, conjecturing, induction, applications of varying nature, proof techniques, algorithm development and correctness, and numeric computations* Weaves numerous applications into the text* Helps students learn by doing with a wealth of examples and exercises: - 560 examples worked out in detail - More than 3,700 exercises - More than 150 computer assignments - More than 600 writing projects*...
Discrete Mathematics and Its Applications
Oxley, Alan
2010-01-01
The article gives ideas that lecturers of undergraduate Discrete Mathematics courses can use in order to make the subject more interesting for students and encourage them to undertake further studies in the subject. It is possible to teach Discrete Mathematics with little or no reference to computing. However, students are more likely to be…
Discrete Mathematics and the Secondary Mathematics Curriculum.
Dossey, John
Discrete mathematics, the mathematics of decision making for finite settings, is a topic of great interest in mathematics education at all levels. Attention is being focused on resolving the diversity of opinion concerning the exact nature of the subject, what content the curriculum should contain, who should study that material, and how that…
Discrete mathematics using a computer
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...
Discrete algorithmic mathematics
Maurer, Stephen B
2005-01-01
The exposition is self-contained, complemented by diverse exercises and also accompanied by an introduction to mathematical reasoning … this book is an excellent textbook for a one-semester undergraduate course and it includes a lot of additional material to choose from.-EMS, March 2006In a textbook, it is necessary to select carefully the statements and difficulty of the problems … in this textbook, this is fully achieved … This review considers this book an excellent one.-The Mathematical Gazette, March 2006
Journal of applied mathematics
2001-01-01
"[The] Journal of Applied Mathematics is a refereed journal devoted to the publication of original research papers and review articles in all areas of applied, computational, and industrial mathematics...
Finite Mathematics and Discrete Mathematics: Is There a Difference?
Johnson, Marvin L.
Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…
Inevitable randomness in discrete mathematics
Beck, Jozsef
2009-01-01
Mathematics has been called the science of order. The subject is remarkably good for generalizing specific cases to create abstract theories. However, mathematics has little to say when faced with highly complex systems, where disorder reigns. This disorder can be found in pure mathematical arenas, such as the distribution of primes, the 3n+1 conjecture, and class field theory. The purpose of this book is to provide examples--and rigorous proofs--of the complexity law: (1) discrete systems are either simple or they exhibit advanced pseudorandomness; (2) a priori probabilities often exist even when there is no intrinsic symmetry. Part of the difficulty in achieving this purpose is in trying to clarify these vague statements. The examples turn out to be fascinating instances of deep or mysterious results in number theory and combinatorics. This book considers randomness and complexity. The traditional approach to complexity--computational complexity theory--is to study very general complexity classes, such as P...
Alfa, Attahiru S
2016-01-01
This book introduces the theoretical fundamentals for modeling queues in discrete-time, and the basic procedures for developing queuing models in discrete-time. There is a focus on applications in modern telecommunication systems. It presents how most queueing models in discrete-time can be set up as discrete-time Markov chains. Techniques such as matrix-analytic methods (MAM) that can used to analyze the resulting Markov chains are included. This book covers single node systems, tandem system and queueing networks. It shows how queues with time-varying parameters can be analyzed, and illustrates numerical issues associated with computations for the discrete-time queueing systems. Optimal control of queues is also covered. Applied Discrete-Time Queues targets researchers, advanced-level students and analysts in the field of telecommunication networks. It is suitable as a reference book and can also be used as a secondary text book in computer engineering and computer science. Examples and exercises are includ...
Theoretical Basics of Teaching Discrete Mathematics
Y. A. Perminov
2012-01-01
Full Text Available The paper deals with the research findings concerning the process of mastering the theoretical basics of discrete mathematics by the students of vocational pedagogic profile. The methodological analysis is based on the subject and functions of the modern discrete mathematics and its role in mathematical modeling and computing. The modern discrete mathematics (i.e. mathematics of the finite type structures plays the important role in modernization of vocational training. It is especially rele- vant to training students for vocational pedagogic qualifications, as in the future they will be responsible for training the middle and the senior level specialists in engineer- ing and technical spheres. Nowadays in different industries, there arise the problems which require for their solving both continual – based on the classical mathematical methods – and discrete modeling. The teaching course of discrete mathematics for the future vocational teachers should be relevant to the target qualification and aimed at mastering the mathematical modeling, systems of computer mathematics and computer technologies. The author emphasizes the fundamental role of mastering the language of algebraic and serial structures, as well as the logical, algorithmic, combinatory schemes dominating in dis- crete mathematics. The guidelines for selecting the content of the course in discrete mathematics are specified. The theoretical findings of the research can be put into practice whilst developing curricula and working programs for bachelors and masters’ training.
Discrete mathematics in the high school curriculum
Anderson, I.; Asch, van A.G.; van Lint, J.H.
2004-01-01
In this paper we present some topics from the field of discrete mathematics which might be suitable for the high school curriculum. These topics yield both easy to understand challenging problems and important applications of discrete mathematics. We choose elements from number theory and various
Applied Mathematics Seminar 1982
1983-01-01
This report contains the abstracts of the lectures delivered at 1982 Applied Mathematics Seminar of the DPD/LCC/CNPq and Colloquy on Applied Mathematics of LCC/CNPq. The Seminar comprised 36 conferences. Among these, 30 were presented by researchers associated to brazilian institutions, 9 of them to the LCC/CNPq, and the other 6 were given by visiting lecturers according to the following distribution: 4 from the USA, 1 from England and 1 from Venezuela. The 1981 Applied Mathematics Seminar was organized by Leon R. Sinay and Nelson do Valle Silva. The Colloquy on Applied Mathematics was held from october 1982 on, being organized by Ricardo S. Kubrusly and Leon R. Sinay. (Author) [pt
Applied impulsive mathematical models
Stamova, Ivanka
2016-01-01
Using the theory of impulsive differential equations, this book focuses on mathematical models which reflect current research in biology, population dynamics, neural networks and economics. The authors provide the basic background from the fundamental theory and give a systematic exposition of recent results related to the qualitative analysis of impulsive mathematical models. Consisting of six chapters, the book presents many applicable techniques, making them available in a single source easily accessible to researchers interested in mathematical models and their applications. Serving as a valuable reference, this text is addressed to a wide audience of professionals, including mathematicians, applied researchers and practitioners.
Applied mathematics made simple
Murphy, Patrick
1982-01-01
Applied Mathematics: Made Simple provides an elementary study of the three main branches of classical applied mathematics: statics, hydrostatics, and dynamics. The book begins with discussion of the concepts of mechanics, parallel forces and rigid bodies, kinematics, motion with uniform acceleration in a straight line, and Newton's law of motion. Separate chapters cover vector algebra and coplanar motion, relative motion, projectiles, friction, and rigid bodies in equilibrium under the action of coplanar forces. The final chapters deal with machines and hydrostatics. The standard and conte
A Note on Discrete Mathematics and Calculus.
O'Reilly, Thomas J.
1987-01-01
Much of the current literature on the topic of discrete mathematics and calculus during the first two years of an undergraduate mathematics curriculum is cited. A relationship between the recursive integration formulas and recursively defined polynomials is described. A Pascal program is included. (Author/RH)
Discrete Mathematics Course Supported by CAS MATHEMATICA
Ivanov, O. A.; Ivanova, V. V.; Saltan, A. A.
2017-01-01
In this paper, we discuss examples of assignments for a course in discrete mathematics for undergraduate students majoring in business informatics. We consider several problems with computer-based solutions and discuss general strategies for using computers in teaching mathematics and its applications. In order to evaluate the effectiveness of our…
Web-Based Implementation of Discrete Mathematics
Love, Tanzy; Keinert, Fritz; Shelley, Mack
2006-01-01
The Department of Mathematics at Iowa State University teaches a freshman-level Discrete Mathematics course with total enrollment of about 1,800 students per year. The traditional format includes large lectures, with about 150 students each, taught by faculty and temporary instructors in two class sessions per week and recitation sections, with…
Methods of applied mathematics
Hildebrand, Francis B
1992-01-01
This invaluable book offers engineers and physicists working knowledge of a number of mathematical facts and techniques not commonly treated in courses in advanced calculus, but nevertheless extremely useful when applied to typical problems in many different fields. It deals principally with linear algebraic equations, quadratic and Hermitian forms, operations with vectors and matrices, the calculus of variations, and the formulations and theory of linear integral equations. Annotated problems and exercises accompany each chapter.
Rosenstein, Joseph G., Ed.; Franzblau, Deborah S., Ed.; Roberts, Fred S., Ed.
This book is a collection of articles by experienced educators and explains why and how discrete mathematics should be taught in K-12 classrooms. It includes evidence for "why" and practical guidance for "how" and also discusses how discrete mathematics can be used as a vehicle for achieving the broader goals of the major…
Application of multivariate splines to discrete mathematics
Xu, Zhiqiang
2005-01-01
Using methods developed in multivariate splines, we present an explicit formula for discrete truncated powers, which are defined as the number of non-negative integer solutions of linear Diophantine equations. We further use the formula to study some classical problems in discrete mathematics as follows. First, we extend the partition function of integers in number theory. Second, we exploit the relation between the relative volume of convex polytopes and multivariate truncated powers and giv...
Logic and discrete mathematics a concise introduction
Conradie, Willem
2015-01-01
A concise yet rigorous introduction to logic and discrete mathematics. This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that has been tested and refined by the authors in university courses taught over more than a decade. The chapters on logic - propositional and first-order - provide a robust toolkit for logical reasoning, emphasizing the conceptual understanding of the language and the semantics of classical logic as well as practical applications through the easy
Discrete mathematics course supported by CAS MATHEMATICA
Ivanov, O. A.; Ivanova, V. V.; Saltan, A. A.
2017-08-01
In this paper, we discuss examples of assignments for a course in discrete mathematics for undergraduate students majoring in business informatics. We consider several problems with computer-based solutions and discuss general strategies for using computers in teaching mathematics and its applications. In order to evaluate the effectiveness of our approach, we conducted an anonymous survey. The results of the survey provide evidence that our approach contributes to high outcomes and aligns with the course aims and objectives.
Some unsolved problems in discrete mathematics and mathematical cybernetics
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.
Some unsolved problems in discrete mathematics and mathematical cybernetics
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
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.
A short course in discrete mathematics
Bender, Edward A
2004-01-01
What sort of mathematics do I need for computer science? In response to this frequently asked question, a pair of professors at the University of California at San Diego created this text. Its sources are two of the university's most basic courses: Discrete Mathematics, and Mathematics for Algorithm and System Analysis. Intended for use by sophomores in the first of a two-quarter sequence, the text assumes some familiarity with calculus. Topics include Boolean functions and computer arithmetic; logic; number theory and cryptography; sets and functions; equivalence and order; and induction, seq
A discrete transition to advanced mathematics
Richmond, Bettina
2009-01-01
As the title indicates, this book is intended for courses aimed at bridging the gap between lower-level mathematics and advanced mathematics. The text provides a careful introduction to techniques for writing proofs and a logical development of topics based on intuitive understanding of concepts. The authors utilize a clear writing style and a wealth of examples to develop an understanding of discrete mathematics and critical thinking skills. While including many traditional topics, the text offers innovative material throughout. Surprising results are used to motivate the reader. The last thr
Is Discrete Mathematics the New Math of the Eighties?
Hart, Eric W.
1985-01-01
Considered are what discrete mathematics includes, some parallels and differences between new math and discrete mathematics (listed in a table), and lessons to be learned. A list of references is included. (MNS)
Discrete mathematics in deaf education: a survey of teachers' knowledge and use.
Pagliaro, Claudia M; Kritzer, Karen L
The study documents what deaf education teachers know about discrete mathematics topics and determines if these topics are present in the mathematics curriculum. Survey data were collected from 290 mathematics teachers at center and public school programs serving a minimum of 120 students with hearing loss, grades K-8 or K-12, in the United States. Findings indicate that deaf education teachers are familiar with many discrete mathematics topics but do not include them in instruction because they consider the concepts too complicated for their students. Also, regardless of familiarity level, deaf education teachers are not familiar with discrete mathematics terminology; nor is their mathematics teaching structured to provide opportunities to apply the real-world-oriented activities used in discrete mathematics instruction. Findings emphasize the need for higher expectations of students with hearing loss, and for reform in mathematics curriculum and instruction within deaf education.
How Bob Barker Would (Probably) Teach Discrete Mathematics
Urness, Timothy
2010-01-01
This article proposes a discrete mathematics course in which games from "The Price Is Right" are used to engage students in a deeper, practical study of discrete mathematics. The games themselves are not the focus of the course; rather, the mathematical principles of the games give motivation for the concepts being taught. The game examples are…
Applied Mathematical Problems in Engineering
Carlos Llopis-Albert
2016-10-01
Full Text Available There is a close relationship between engineering and mathematics, which has led to the development of new techniques in recent years. Likewise the developments in technology and computers have led to new ways of teaching mathematics for engineering students and the use of modern techniques and methods. This research aims to provide insight on how to deal with mathematical problems for engineering students. This is performed by means of a fuzzy set/Qualitative Comparative Analysis applied to conflict resolution of Public Participation Projects in support to the EU Water Framework Directive.
Applied Behavior Analysis: Beyond Discrete Trial Teaching
Steege, Mark W.; Mace, F. Charles; Perry, Lora; Longenecker, Harold
2007-01-01
We discuss the problem of autism-specific special education programs representing themselves as Applied Behavior Analysis (ABA) programs when the only ABA intervention employed is Discrete Trial Teaching (DTT), and often for limited portions of the school day. Although DTT has many advantages to recommend its use, it is not well suited to teach…
CDM: Teaching Discrete Mathematics to Computer Science Majors
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…
Lectures on financial mathematics discrete asset pricing
Anderson, Greg
2010-01-01
This is a short book on the fundamental concepts of the no-arbitrage theory of pricing financial derivatives. Its scope is limited to the general discrete setting of models for which the set of possible states is finite and so is the set of possible trading times--this includes the popular binomial tree model. This setting has the advantage of being fairly general while not requiring a sophisticated understanding of analysis at the graduate level. Topics include understanding the several variants of "arbitrage", the fundamental theorems of asset pricing in terms of martingale measures, and applications to forwards and futures. The authors' motivation is to present the material in a way that clarifies as much as possible why the often confusing basic facts are true. Therefore the ideas are organized from a mathematical point of view with the emphasis on understanding exactly what is under the hood and how it works. Every effort is made to include complete explanations and proofs, and the reader is encouraged t...
Implementing the Standards. Teaching Discrete Mathematics in Grades 7-12.
Hart, Eric W.; And Others
1990-01-01
Discrete mathematics are defined briefly. A course in discrete mathematics for high school students and teaching discrete mathematics in grades 7 and 8 including finite differences, recursion, and graph theory are discussed. (CW)
D. Shchedrolosev
2010-01-01
Fundamental mathematical background is an important part of training future engineers and programmers. The paper considers existing approaches to teaching the fundamentals of discrete mathematics specialist IT profile, a comparative analysis of modern textbooks on discrete mathematics for IT professionals was conducted
D. Shchedrolosev
2010-04-01
Full Text Available Fundamental mathematical background is an important part of training future engineers and programmers. The paper considers existing approaches to teaching the fundamentals of discrete mathematics specialist IT profile, a comparative analysis of modern textbooks on discrete mathematics for IT professionals was conducted
Applied Mathematics Should Be Taught Mixed.
Brown, Gary I.
1994-01-01
Discusses the differences between applied and pure mathematics and provides extensive history of mixed mathematics. Argues that applied mathematics should be taught allowing for speculative mathematics, which involves breaking down a given problem into simpler parts until one arrives at first principles. (ASK)
Mathematical biology modules based on modern molecular biology and modern discrete mathematics.
Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander
2010-01-01
We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network.
Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics
Davies, Robin; Hodge, Terrell; Enyedi, Alexander
2010-01-01
We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network. PMID:20810955
Mathematical aspects of the discrete space-time hypothesis
Sardanashvili, G.A.
1979-01-01
A hypothesis of a microcosm space discreteness is considered from the theoretical-mathematical point of view. The type of topological spaces, which formalizes representations on the discrete space-time, is determined. It is explained, how these spaces arise in physical models. The physical task, in which the discrete space could arise as a version of its solution, is considered. It is shown that the discrete structure of space can arise with a certain interaction type in the system, for example, with its considerable self-shielding, which can take place, in particular, in the particles or in the cosmological and astrophysical singularities
Current problems in applied mathematics and mathematical physics
Samarskii, A. A.
Papers are presented on such topics as mathematical models in immunology, mathematical problems of medical computer tomography, classical orthogonal polynomials depending on a discrete variable, and boundary layer methods for singular perturbation problems in partial derivatives. Consideration is also given to the computer simulation of supernova explosion, nonstationary internal waves in a stratified fluid, the description of turbulent flows by unsteady solutions of the Navier-Stokes equations, and the reduced Galerkin method for external diffraction problems using the spline approximation of fields.
A RUTCOR Project on Discrete Applied Mathematics
1989-01-30
the more important results of this work is the possibility that Groebner basis methods of computational commutative algebra might lead to effective...Billera, L.J., " Groebner Basis Methods for Multivariate Splines," prepared for the Proceedings of the Oslo Conference on Computer-aided Geometric Design
A RUTCOR Project in Discrete Applied Mathematics
1990-02-20
representations of smooth piecewise polynomial functions over triangulated regions have led in particular to the conclusion that Groebner basis methods of...Reversing Number of a Digraph," in preparation. 4. Billera, L.J., and Rose, L.L., " Groebner Basis Methods for Multivariate Splines," RRR 1-89, January
Logic and discrete mathematics a concise introduction : solutions manual
Conradie, Willem; Robinson, Claudette
2015-01-01
Solutions manual to accompany Logic and Discrete Mathematics: A Concise Introduction This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that has been tested and refined by the authors in university courses taught over more than a decade. Written in a clear and reader-friendly style, each section ends with an extensive set of exercises, most of them provided with complete solutions which are available in this accompanying solutions manual.
Teaching Discrete Mathematics Entirely from Primary Historical Sources
Barnett, Janet Heine; Bezhanishvili, Guram; Lodder, Jerry; Pengelley, David
2016-01-01
We describe teaching an introductory discrete mathematics course entirely from student projects based on primary historical sources. We present case studies of four projects that cover the content of a one-semester course, and mention various other courses that we have taught with primary source projects.
An Application of Discrete Mathematics to Coding Theory.
Donohoe, L. Joyce
1992-01-01
Presents a public-key cryptosystem application to introduce students to several topics in discrete mathematics. A computer algorithms using recursive methods is presented to solve a problem in which one person wants to send a coded message to a second person while keeping the message secret from a third person. (MDH)
System for Automatic Generation of Examination Papers in Discrete Mathematics
Fridenfalk, Mikael
2013-01-01
A system was developed for automatic generation of problems and solutions for examinations in a university distance course in discrete mathematics and tested in a pilot experiment involving 200 students. Considering the success of such systems in the past, particularly including automatic assessment, it should not take long before such systems are…
Constructing Contracts: Making Discrete Mathematics Relevant to Beginning Programmers
Gegg-Harrison, Timothy S.
2005-01-01
Although computer scientists understand the importance of discrete mathematics to the foundations of their field, computer science (CS) students do not always see the relevance. Thus, it is important to find a way to show students its relevance. The concept of program correctness is generally taught as an activity independent of the programming…
Lecture Note on Discrete Mathematics: Predicates and Quantifiers
Nordbjerg, Finn Ebertsen
2016-01-01
This lecture note supplements the treatment of predicates and quantifiers given in standard textbooks on Discrete Mathematics (e.g.: [1]) and introduces the notation used in this course. We will present central concepts that are important, when predicate logic is used for specification...
Using a Card Trick to Teach Discrete Mathematics
Simonson, Shai; Holm, Tara S.
2003-01-01
We present a card trick that can be used to review or teach a variety of topics in discrete mathematics. We address many subjects, including permutations, combinations, functions, graphs, depth first search, the pigeonhole principle, greedy algorithms, and concepts from number theory. Moreover, the trick motivates the use of computers in…
Applied algebra codes, ciphers and discrete algorithms
Hardy, Darel W; Walker, Carol L
2009-01-01
This book attempts to show the power of algebra in a relatively simple setting.-Mathematical Reviews, 2010… The book supports learning by doing. In each section we can find many examples which clarify the mathematics introduced in the section and each section is followed by a series of exercises of which approximately half are solved in the end of the book. Additional the book comes with a CD-ROM containing an interactive version of the book powered by the computer algebra system Scientific Notebook. … the mathematics in the book are developed as needed and the focus of the book lies clearly o
Activities report 1977--78. Applied mathematics department 5640
1979-03-01
This report is a compilation of independent articles highlighting some of the work done in the Applied Mathematics Department during the years 1977 and 1978. It is neither an exhaustive report on all activities in the department during this period nor a list of the most substantial mathematical contributions. Instead, it is a selection of topics which are thought to be of greatest interest because of their importance to Sandia. The report is divided into four principal sections which reflect the department's major areas of interest: Mathematical Physics, Computational Mathematics, Probability and Statistics, and Discrete Mathematics. To provide a smoother narrative, references are omitted from the text. However, a complete department bibliography of corporate and open publications as well as technical presentations for the period October 1977 through December 1978 is appended. 4 figures, 3 tables
Paterson, Judy; Sneddon, Jamie
2011-01-01
This article reports on the learning conversations between a mathematician and a mathematics educator as they worked together to change the delivery model of a third year discrete mathematics course from a traditional lecture mode to team-based learning (TBL). This change prompted the mathematician to create team tasks which increasingly focused…
A First Course in Applied Mathematics
Rebaza, Jorge
2012-01-01
Explore real-world applications of selected mathematical theory, concepts, and methods Exploring related methods that can be utilized in various fields of practice from science and engineering to business, A First Course in Applied Mathematics details how applied mathematics involves predictions, interpretations, analysis, and mathematical modeling to solve real-world problems. Written at a level that is accessible to readers from a wide range of scientific and engineering fields, the book masterfully blends standard topics with modern areas of application and provides the needed foundation
a Discrete Mathematical Model to Simulate Malware Spreading
Del Rey, A. Martin; Sánchez, G. Rodriguez
2012-10-01
With the advent and worldwide development of Internet, the study and control of malware spreading has become very important. In this sense, some mathematical models to simulate malware propagation have been proposed in the scientific literature, and usually they are based on differential equations exploiting the similarities with mathematical epidemiology. The great majority of these models study the behavior of a particular type of malware called computer worms; indeed, to the best of our knowledge, no model has been proposed to simulate the spreading of a computer virus (the traditional type of malware which differs from computer worms in several aspects). In this sense, the purpose of this work is to introduce a new mathematical model not based on continuous mathematics tools but on discrete ones, to analyze and study the epidemic behavior of computer virus. Specifically, cellular automata are used in order to design such model.
Mathematics applied to nuclear geophysics
Pereira, E.B.; Nordemann, D.J.R.
1987-01-01
One of the powerful auxiliary to nuclear geophysics is the obtention and interpretation of the alpha and gamma radiation spectra. This work discuss, qualitative and quantitative, the lost information problem, motivated by the noise in the process of information codification. The decodification process must be suppield by the appropriate mathematical model on the measure system to recovery the information from nuclear source. (C.D.G.) [pt
The 1989 progress report: Applied Mathematics
Nedelec, J.C.
1989-01-01
The 1989 progress report of the laboratory of Applied Mathematics of the Polytechnic School (France) is presented. The investigations reported were performed in the following fields: mathematical and numerical aspects of wave propagation, nonlinear hyperbolic fluid mechanics, numerical simulations and mathematical aspects of semiconductors and electron beams, mechanics of solids, plasticity, viscoelasticity, stochastic, automatic and statistic calculations, synthesis and image processing. The published papers, the conferences and the Laboratory staff are listed [fr
Applied Computational Mathematics in Social Sciences
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.
Proceedings of the workshop on applied mathematics
Lee, H.C.; Couture, M.; Douglas, S.; Leivo, H.P.
1992-10-01
The Workshop on Applied Mathematics was held at the Cockcroft Centre, Deep River, Ontario, 1992 February 7-8. The purpose of the workshop was to provide a forum for applied mathematicians to survey the use and to discuss the future of applied mathematics at AECL Research. There were 57 participants at the workshop A total of eight 30-minute and 25 15-minute talks were presented describing mathematical techniques used in the whole range of activities at AECL Research, from numerical simulation of fluid flow through eddy current testing to quantum algebra and accelerator physics
Proceedings of the workshop on applied mathematics
Lee, H C; Couture, M; Douglas, S; Leivo, H P
1992-10-01
The Workshop on Applied Mathematics was held at the Cockcroft Centre, Deep River, Ontario, 1992 February 7-8. The purpose of the workshop was to provide a forum for applied mathematicians to survey the use and to discuss the future of applied mathematics at AECL Research. There were 57 participants at the workshop A total of eight 30-minute and 25 15-minute talks were presented describing mathematical techniques used in the whole range of activities at AECL Research, from numerical simulation of fluid flow through eddy current testing to quantum algebra and accelerator physics.
International Conference on Advances in Applied Mathematics
Hammami, Mohamed; Masmoudi, Afif
2015-01-01
This contributed volume presents some recent theoretical advances in mathematics and its applications in various areas of science and technology. Written by internationally recognized scientists and researchers, the chapters in this book are based on talks given at the International Conference on Advances in Applied Mathematics (ICAAM), which took place December 16-19, 2013, in Hammamet, Tunisia. Topics discussed at the conference included spectral theory, operator theory, optimization, numerical analysis, ordinary and partial differential equations, dynamical systems, control theory, probability, and statistics. These proceedings aim to foster and develop further growth in all areas of applied mathematics.
Applied mathematics for science and engineering
Glasgow, Larry A
2014-01-01
Prepare students for success in using applied mathematics for engineering practice and post-graduate studies moves from one mathematical method to the next sustaining reader interest and easing the application of the techniques Uses different examples from chemical, civil, mechanical and various other engineering fields Based on a decade's worth of the authors lecture notes detailing the topic of applied mathematics for scientists and engineers Concisely writing with numerous examples provided including historical perspectives as well as a solutions manual for academic adopters
Intelligent mathematics II applied mathematics and approximation theory
Duman, Oktay
2016-01-01
This special volume is a collection of outstanding more applied articles presented in AMAT 2015 held in Ankara, May 28-31, 2015, at TOBB Economics and Technology University. The collection is suitable for Applied and Computational Mathematics and Engineering practitioners, also for related graduate students and researchers. Furthermore it will be a useful resource for all science and engineering libraries. This book includes 29 self-contained and well-edited chapters that can be among others useful for seminars in applied and computational mathematics, as well as in engineering.
Mathematical physics applied mathematics for scientists and engineers
Kusse, Bruce R
2006-01-01
What sets this volume apart from other mathematics texts is its emphasis on mathematical tools commonly used by scientists and engineers to solve real-world problems. Using a unique approach, it covers intermediate and advanced material in a manner appropriate for undergraduate students. Based on author Bruce Kusse's course at the Department of Applied and Engineering Physics at Cornell University, Mathematical Physics begins with essentials such as vector and tensor algebra, curvilinear coordinate systems, complex variables, Fourier series, Fourier and Laplace transforms, differential and integral equations, and solutions to Laplace's equations
Methods of applied mathematics with a software overview
Davis, Jon H
2016-01-01
This textbook, now in its second edition, provides students with a firm grasp of the fundamental notions and techniques of applied mathematics as well as the software skills to implement them. The text emphasizes the computational aspects of problem solving as well as the limitations and implicit assumptions inherent in the formal methods. Readers are also given a sense of the wide variety of problems in which the presented techniques are useful. Broadly organized around the theme of applied Fourier analysis, the treatment covers classical applications in partial differential equations and boundary value problems, and a substantial number of topics associated with Laplace, Fourier, and discrete transform theories. Some advanced topics are explored in the final chapters such as short-time Fourier analysis and geometrically based transforms applicable to boundary value problems. The topics covered are useful in a variety of applied fields such as continuum mechanics, mathematical physics, control theory, and si...
Expander graphs in pure and applied mathematics
Lubotzky, Alexander
2012-01-01
Expander graphs are highly connected sparse finite graphs. They play an important role in computer science as basic building blocks for network constructions, error correcting codes, algorithms and more. In recent years they have started to play an increasing role also in pure mathematics: number theory, group theory, geometry and more. This expository article describes their constructions and various applications in pure and applied mathematics.
Applied mathematics for engineers and physicists
Pipes, Louis A
2014-01-01
One of the most widely used reference books on applied mathematics for a generation, distributed in multiple languages throughout the world, this text is geared toward use with a one-year advanced course in applied mathematics for engineering students. The treatment assumes a solid background in the theory of complex variables and a familiarity with complex numbers, but it includes a brief review. Chapters are as self-contained as possible, offering instructors flexibility in designing their own courses. The first eight chapters explore the analysis of lumped parameter systems. Succeeding topi
Applied Mathematics, Modelling and Computational Science
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 ...
Gulf International Conference on Applied Mathematics 2013
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.
Study guide for applied finite mathematics
Macri, Nicholas A
1982-01-01
Study Guide for Applied Finite Mathematics, Third Edition is a study guide that introduces beginners to the fundamentals of finite mathematics and its various realistic and relevant applications. Some applications of probability, game theory, and Markov chains are given. Each chapter includes exercises, and each set begins with basic computational ""drill"" problems and then progresses to problems with more substance.Comprised of 10 chapters, this book begins with exercises related to set theory and concepts such as the union and intersection of sets. Exercises on Cartesian coordinate
The Applied Mathematics for Power Systems (AMPS)
Chertkov, Michael [Los Alamos National Laboratory
2012-07-24
Increased deployment of new technologies, e.g., renewable generation and electric vehicles, is rapidly transforming electrical power networks by crossing previously distinct spatiotemporal scales and invalidating many traditional approaches for designing, analyzing, and operating power grids. This trend is expected to accelerate over the coming years, bringing the disruptive challenge of complexity, but also opportunities to deliver unprecedented efficiency and reliability. Our Applied Mathematics for Power Systems (AMPS) Center will discover, enable, and solve emerging mathematics challenges arising in power systems and, more generally, in complex engineered networks. We will develop foundational applied mathematics resulting in rigorous algorithms and simulation toolboxes for modern and future engineered networks. The AMPS Center deconstruction/reconstruction approach 'deconstructs' complex networks into sub-problems within non-separable spatiotemporal scales, a missing step in 20th century modeling of engineered networks. These sub-problems are addressed within the appropriate AMPS foundational pillar - complex systems, control theory, and optimization theory - and merged or 'reconstructed' at their boundaries into more general mathematical descriptions of complex engineered networks where important new questions are formulated and attacked. These two steps, iterated multiple times, will bridge the growing chasm between the legacy power grid and its future as a complex engineered network.
Global Conference on Applied Physics and Mathematics
2016-01-01
The Global Conference on Applied Physics and Mathematics is organized by academics and researchers belonging to different scientific areas of the C3i/Polytechnic Institute of Portalegre (Portugal) and the University of Extremadura (Spain) with the technical support of ScienceKnow Conferences. The event has the objective of creating an international forum for academics, researchers and scientists from worldwide to discuss worldwide results and proposals regarding to the soundest issues related to Applied Physics and Mathematics. This event will include the participation of renowned keynote speakers, oral presentations, posters sessions and technical conferences related to the topics dealt with in the Scientific Program as well as an attractive social and cultural program. The papers will be published in the Proceedings e-books. The proceedings of the conference will be sent to possible indexing on Thomson Reuters (selective by Thomson Reuters, not all-inclusive) and Google Scholar. Those communications con...
A Study of the Use of a Handheld Computer Algebra System in Discrete Mathematics
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…
Applied mathematical methods in nuclear thermal hydraulics
Ransom, V.H.; Trapp, J.A.
1983-01-01
Applied mathematical methods are used extensively in modeling of nuclear reactor thermal-hydraulic behavior. This application has required significant extension to the state-of-the-art. The problems encountered in modeling of two-phase fluid transients and the development of associated numerical solution methods are reviewed and quantified using results from a numerical study of an analogous linear system of differential equations. In particular, some possible approaches for formulating a well-posed numerical problem for an ill-posed differential model are investigated and discussed. The need for closer attention to numerical fidelity is indicated
Ludwig Kohaupt
2015-12-01
Full Text Available The discrete Fourier series is a valuable tool developed and used by mathematicians and engineers alike. One of the most prominent applications is signal processing. Usually, it is important that the signals be transmitted fast, for example, when transmitting images over large distances such as between the moon and the earth or when generating images in computer tomography. In order to achieve this, appropriate algorithms are necessary. In this context, the fast Fourier transform (FFT plays a key role which is an algorithm for calculating the discrete Fourier transform (DFT; this, in turn, is tightly connected with the discrete Fourier series. The last one itself is the discrete analog of the common (continuous-time Fourier series and is usually learned by mathematics students from a theoretical point of view. The aim of this expository/pedagogical paper is to give an introduction to the discrete Fourier series for both mathematics and engineering students. It is intended to expand the purely mathematical view; the engineering aspect is taken into account by applying the FFT to an example from signal processing that is small enough to be used in class-room teaching and elementary enough to be understood also by mathematics students. The MATLAB program is employed to do the computations.
van Rosmalen, Joost; Toy, Mehlika; O'Mahony, James F
2013-08-01
Markov models are a simple and powerful tool for analyzing the health and economic effects of health care interventions. These models are usually evaluated in discrete time using cohort analysis. The use of discrete time assumes that changes in health states occur only at the end of a cycle period. Discrete-time Markov models only approximate the process of disease progression, as clinical events typically occur in continuous time. The approximation can yield biased cost-effectiveness estimates for Markov models with long cycle periods and if no half-cycle correction is made. The purpose of this article is to present an overview of methods for evaluating Markov models in continuous time. These methods use mathematical results from stochastic process theory and control theory. The methods are illustrated using an applied example on the cost-effectiveness of antiviral therapy for chronic hepatitis B. The main result is a mathematical solution for the expected time spent in each state in a continuous-time Markov model. It is shown how this solution can account for age-dependent transition rates and discounting of costs and health effects, and how the concept of tunnel states can be used to account for transition rates that depend on the time spent in a state. The applied example shows that the continuous-time model yields more accurate results than the discrete-time model but does not require much computation time and is easily implemented. In conclusion, continuous-time Markov models are a feasible alternative to cohort analysis and can offer several theoretical and practical advantages.
Discrete Mathematics in Deaf Education: A Survey of Teachers' Knowledge and Use
Pagliaro, C.; Kritzer, K. L.
2005-01-01
The study documents what deaf education teachers know about discrete mathematics topics and determines if these topics are present in the mathematics curriculum. Survey data were collected from 290 mathematics teachers at center and public school programs serving a minimum of 120 students with hearing loss, grades K-8 or K-12, in the United…
An excursion through elementary mathematics, volume iii discrete mathematics and polynomial algebra
Caminha Muniz Neto, Antonio
2018-01-01
This book provides a comprehensive, in-depth overview of elementary mathematics as explored in Mathematical Olympiads around the world. It expands on topics usually encountered in high school and could even be used as preparation for a first-semester undergraduate course. This third and last volume covers Counting, Generating Functions, Graph Theory, Number Theory, Complex Numbers, Polynomials, and much more. As part of a collection, the book differs from other publications in this field by not being a mere selection of questions or a set of tips and tricks that applies to specific problems. It starts from the most basic theoretical principles, without being either too general or too axiomatic. Examples and problems are discussed only if they are helpful as applications of the theory. Propositions are proved in detail and subsequently applied to Olympic problems or to other problems at the Olympic level. The book also explores some of the hardest problems presented at National and International Mathematics Ol...
Interval Mathematics Applied to Critical Point Transitions
Benito A. Stradi
2012-03-01
Full Text Available The determination of critical points of mixtures is important for both practical and theoretical reasons in the modeling of phase behavior, especially at high pressure. The equations that describe the behavior of complex mixtures near critical points are highly nonlinear and with multiplicity of solutions to the critical point equations. Interval arithmetic can be used to reliably locate all the critical points of a given mixture. The method also verifies the nonexistence of a critical point if a mixture of a given composition does not have one. This study uses an interval Newton/Generalized Bisection algorithm that provides a mathematical and computational guarantee that all mixture critical points are located. The technique is illustrated using several example problems. These problems involve cubic equation of state models; however, the technique is general purpose and can be applied in connection with other nonlinear problems.
Particulate morphology mathematics applied to particle assemblies
Gotoh, Keishi
2012-01-01
Encompassing over fifty years of research, Professor Gotoh addresses the correlation function of spatial structures and the statistical geometry of random particle assemblies. In this book morphological study is formed into random particle assemblies to which various mathematics are applied such as correlation function, radial distribution function and statistical geometry. This leads to the general comparison between the thermodynamic state such as gases and liquids and the random particle assemblies. Although structures of molecular configurations change at every moment due to thermal vibration, liquids can be regarded as random packing of particles. Similarly, gaseous states correspond to particle dispersion. If physical and chemical properties are taken away from the subject, the remainder is the structure itself. Hence, the structural study is ubiquitous and of fundamental importance. This book will prove useful to chemical engineers working on powder technology as well as mathematicians interested in le...
Application of methods of discrete mathematics at modular synthesis of mechatronic devices
Nikiforov, S.; Nikiforov, B.; Mandarov, E.; Rabdanova, N.
2010-01-01
The article is devoted to application of methods of discrete mathematics (the theory of counts, the method of matrix code and others) and synthesis of executive mechanisms of mechatronic handling devices
Solving applied mathematical problems with Matlab
Xue, Dingyu
2008-01-01
Computer Mathematics Language-An Overview. Fundamentals of MATLAB Programming. Calculus Problems. MATLAB Computations of Linear Algebra Problems. Integral Transforms and Complex Variable Functions. Solutions to Nonlinear Equations and Optimization Problems. MATLAB Solutions to Differential Equation Problems. Solving Interpolations and Approximations Problems. Solving Probability and Mathematical Statistics Problems. Nontraditional Solution Methods for Mathematical Problems.
Differential-discrete mathematical model of two phase flow heat exchanger
Debeljkovic, D.Lj.; Zitek, Pavel; Simeunovic, G.; Inard, Christian
2007-01-01
A dynamic thermal-hydraulic mathematical model of evaporator dynamics of a once - through sub critical steam generator is derived and presented. This model allows the investigation of evaporator dynamics including its transients responses. The evaporator was considered as a part of three-section (economizer, evaporator and super-heater) model with time varying phase boundaries and is described by a set of linearized discrete - difference equations which, with some other algebraic equations, constitutes a closed system of equations possible for exact computer solution. This model has been derived upon the fundamental equations of mass, energy and momentum balance. For the first time, a discrete differential approach has been applied in order to investigate such complex, two phase processes. Namely, this approach allows one to escape from the model of this process usually described by a set of partial differential equations and enables one, using this method, to simulate evaporators dynamics in an extraordinarily simple way. In current literature this approach is sometimes called physical discretization. (author)
TURČÁNI, Milan
2013-03-01
Full Text Available Nowadays, quality Mathematical basis - Informatics is an inherent part of study. Mathematical basis is provided by Discrete Mathematics that is taught as a compulsory subject in stated study program in the Department of Mathematics. Authors clarify significance and importance of simple thematic units of subject Discrete Mathematics in teaching technical-system subjects in study programme Applied Informatics. Mentioned subject is being taught in first year of University study and knowledge that students acquire during the study of this course are the "cornerstone" for their further development in technical-system study. Justness and importance of individual topics were analysed based on the evaluation of questionnaires, in which pedagogues teaching professional IT subjects alloted weighted coefficients to individual thematic units. Weighted coefficients were alloted based on the significance of the given topic of the subject Discrete Math, with regard to the IT subject they are teaching. Upon designing the e-course, experience with the creation of linear and branch teaching software were used. For the simulation of the transition of students through individual lessons as well as the whole course, authors employed the method of the teaching process simulation using Petri nets.
Winkel, Brian
2012-01-01
We give an example of cross coursing in which a subject or approach in one course in undergraduate mathematics is used in a completely different course. This situation crosses falling body modelling in an upper level differential equations course into a modest discrete dynamical systems unit of a first-year mathematics course. (Contains 1 figure.)
Discrete thoughts essays on mathematics, science, and philosophy
Kac, Mark; Schwartz, Jacob T
1992-01-01
This is a volume of essays and reviews that delightfully explore mathematics in all its moods — from the light and the witty, and humorous to serious, rational, and cerebral. Topics include: logic, combinatorics, statistics, economics, artificial intelligence, computer science, and applications of mathematics broadly. You will also find history and philosophy covered, including discussion of the work of Ulam, Kant, Heidegger among others. "...these papers reflect on mathematics and its influence on human society. They can help the specialist to notice what is going on around him, and they may lead educated people from other domains to a better understanding of mathematics. Many of these papers can advise educators how to form a modern mathematics education, which develops approved ideas and institutions...I admire the stimulating perspectives of the authors."---American Mathematical Society "‘Mathematicians, like Proust and everyone else, are at their best when writing about their first love’ … They a...
International Conference on Applied Mathematics and Informatics
Vasilieva, Olga
2015-01-01
This book highlights recent compelling research results and trends in various aspects of contemporary mathematics, emphasizing applications to real-world situations. The chapters present exciting new findings and developments in situations where mathematical rigor is combined with common sense. A multi-disciplinary approach, both within each chapter and in the volume as a whole, leads to practical insights that may result in a more synthetic understanding of specific global issues—as well as their possible solutions. The volume will be of interest not only to experts in mathematics, but also to graduate students, scientists, and practitioners from other fields including physics, biology, geology, management, and medicine.
Applied Mathematical Methods in Theoretical Physics
Masujima, Michio
2005-04-01
All there is to know about functional analysis, integral equations and calculus of variations in a single volume. This advanced textbook is divided into two parts: The first on integral equations and the second on the calculus of variations. It begins with a short introduction to functional analysis, including a short review of complex analysis, before continuing a systematic discussion of different types of equations, such as Volterra integral equations, singular integral equations of Cauchy type, integral equations of the Fredholm type, with a special emphasis on Wiener-Hopf integral equations and Wiener-Hopf sum equations. After a few remarks on the historical development, the second part starts with an introduction to the calculus of variations and the relationship between integral equations and applications of the calculus of variations. It further covers applications of the calculus of variations developed in the second half of the 20th century in the fields of quantum mechanics, quantum statistical mechanics and quantum field theory. Throughout the book, the author presents over 150 problems and exercises -- many from such branches of physics as quantum mechanics, quantum statistical mechanics, and quantum field theory -- together with outlines of the solutions in each case. Detailed solutions are given, supplementing the materials discussed in the main text, allowing problems to be solved making direct use of the method illustrated. The original references are given for difficult problems. The result is complete coverage of the mathematical tools and techniques used by physicists and applied mathematicians Intended for senior undergraduates and first-year graduates in science and engineering, this is equally useful as a reference and self-study guide.
Discrete Event Supervisory Control Applied to Propulsion Systems
Litt, Jonathan S.; Shah, Neerav
2005-01-01
The theory of discrete event supervisory (DES) control was applied to the optimal control of a twin-engine aircraft propulsion system and demonstrated in a simulation. The supervisory control, which is implemented as a finite-state automaton, oversees the behavior of a system and manages it in such a way that it maximizes a performance criterion, similar to a traditional optimal control problem. DES controllers can be nested such that a high-level controller supervises multiple lower level controllers. This structure can be expanded to control huge, complex systems, providing optimal performance and increasing autonomy with each additional level. The DES control strategy for propulsion systems was validated using a distributed testbed consisting of multiple computers--each representing a module of the overall propulsion system--to simulate real-time hardware-in-the-loop testing. In the first experiment, DES control was applied to the operation of a nonlinear simulation of a turbofan engine (running in closed loop using its own feedback controller) to minimize engine structural damage caused by a combination of thermal and structural loads. This enables increased on-wing time for the engine through better management of the engine-component life usage. Thus, the engine-level DES acts as a life-extending controller through its interaction with and manipulation of the engine s operation.
How to solve applied mathematics problems
Moiseiwitsch, B L
2011-01-01
This workbook bridges the gap between lectures and practical applications, offering students of mathematics, engineering, and physics the chance to practice solving problems from a wide variety of fields. 2011 edition.
Mathematical Modeling Applied to Maritime Security
Center for Homeland Defense and Security
2010-01-01
Center for Homeland Defense and Security, OUT OF THE CLASSROOM Download the paper: Layered Defense: Modeling Terrorist Transfer Threat Networks and Optimizing Network Risk Reduction” Students in Ted Lewis’ Critical Infrastructure Protection course are taught how mathematic modeling can provide...
Quantum mechanics as applied mathematical statistics
Skala, L.; Cizek, J.; Kapsa, V.
2011-01-01
Basic mathematical apparatus of quantum mechanics like the wave function, probability density, probability density current, coordinate and momentum operators, corresponding commutation relation, Schroedinger equation, kinetic energy, uncertainty relations and continuity equation is discussed from the point of view of mathematical statistics. It is shown that the basic structure of quantum mechanics can be understood as generalization of classical mechanics in which the statistical character of results of measurement of the coordinate and momentum is taken into account and the most important general properties of statistical theories are correctly respected.
Applying Multivariate Discrete Distributions to Genetically Informative Count Data.
Kirkpatrick, Robert M; Neale, Michael C
2016-03-01
We present a novel method of conducting biometric analysis of twin data when the phenotypes are integer-valued counts, which often show an L-shaped distribution. Monte Carlo simulation is used to compare five likelihood-based approaches to modeling: our multivariate discrete method, when its distributional assumptions are correct, when they are incorrect, and three other methods in common use. With data simulated from a skewed discrete distribution, recovery of twin correlations and proportions of additive genetic and common environment variance was generally poor for the Normal, Lognormal and Ordinal models, but good for the two discrete models. Sex-separate applications to substance-use data from twins in the Minnesota Twin Family Study showed superior performance of two discrete models. The new methods are implemented using R and OpenMx and are freely available.
Discrete calculus applied analysis on graphs for computational science
Grady, Leo J
2010-01-01
This unique text brings together into a single framework current research in the three areas of discrete calculus, complex networks, and algorithmic content extraction. Many example applications from several fields of computational science are provided.
Ching, J.; Oblow, E.M.; Goldstein, H.
1976-01-01
An algebraic equivalence between the point-energy and multigroup forms of the Boltzmann transport equation is demonstrated that allows the development of a discrete energy, discrete ordinates method for the solution of radiation transport problems. In the discrete energy method, the group averaging required in the cross-section processing for multigroup calculations is replaced by a faster numerical quadrature scheme capable of generating transfer cross sections describing all the physical processes of interest on a fine point-energy grid. Test calculations in which the discrete energy method is compared with the multigroup method show that, for the same energy grid, the discrete energy method is much faster, although somewhat less accurate, than the multigroup method. However, the accuracy of the discrete energy method increases rapidly as the spacing between energy grid points is decreased, approaching that of multigroup calculations. For problems requiring great detail in the energy spectrum, the discrete energy method is therefore expected to be far more economical than the multigroup technique for equivalent accuracy solutions. This advantage of the point method is demonstrated by application to the study of neutron transport in a thick iron slab
Functional analysis in modern applied mathematics
Curtain, Ruth F
1977-01-01
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat
Teaching Proofs and Algorithms in Discrete Mathematics with Online Visual Logic Puzzles
Cigas, John; Hsin, Wen-Jung
2005-01-01
Visual logic puzzles provide a fertile environment for teaching multiple topics in discrete mathematics. Many puzzles can be solved by the repeated application of a small, finite set of strategies. Explicitly reasoning from a strategy to a new puzzle state illustrates theorems, proofs, and logic principles. These provide valuable, concrete…
Discrete mathematics, formal methods, the Z schema and the software life cycle
Bown, Rodney L.
1991-01-01
The proper role and scope for the use of discrete mathematics and formal methods in support of engineering the security and integrity of components within deployed computer systems are discussed. It is proposed that the Z schema can be used as the specification language to capture the precise definition of system and component interfaces. This can be accomplished with an object oriented development paradigm.
Research in Applied Mathematics, Fluid Mechanics and Computer Science
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.
[Research activities in applied mathematics, fluid mechanics, and computer science
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.
On the uncertainty inequality as applied to discrete signals
Y. V. Venkatesh
2006-01-01
Full Text Available Given a continuous-time bandlimited signal, the Shannon sampling theorem provides an interpolation scheme for exactly reconstructing it from its discrete samples. We analyze the relationship between concentration (or compactness in the temporal/spectral domains of the (i continuous-time and (ii discrete-time signals. The former is governed by the Heisenberg uncertainty inequality which prescribes a lower bound on the product of effective temporal and spectral spreads of the signal. On the other hand, the discrete-time counterpart seems to exhibit some strange properties, and this provides motivation for the present paper. We consider the following problem: for a bandlimited signal, can the uncertainty inequality be expressed in terms of the samples, using thestandard definitions of the temporal and spectral spreads of the signal? In contrast with the results of the literature, we present a new approach to solve this problem. We also present a comparison of the results obtained using the proposed definitions with those available in the literature.
Ellington, Roni; Wachira, James; Nkwanta, Asamoah
2010-01-01
The focus of this Research Experience for Undergraduates (REU) project was on RNA secondary structure prediction by using a lattice walk approach. The lattice walk approach is a combinatorial and computational biology method used to enumerate possible secondary structures and predict RNA secondary structure from RNA sequences. The method uses discrete mathematical techniques and identifies specified base pairs as parameters. The goal of the REU was to introduce upper-level undergraduate students to the principles and challenges of interdisciplinary research in molecular biology and discrete mathematics. At the beginning of the project, students from the biology and mathematics departments of a mid-sized university received instruction on the role of secondary structure in the function of eukaryotic RNAs and RNA viruses, RNA related to combinatorics, and the National Center for Biotechnology Information resources. The student research projects focused on RNA secondary structure prediction on a regulatory region of the yellow fever virus RNA genome and on an untranslated region of an mRNA of a gene associated with the neurological disorder epilepsy. At the end of the project, the REU students gave poster and oral presentations, and they submitted written final project reports to the program director. The outcome of the REU was that the students gained transferable knowledge and skills in bioinformatics and an awareness of the applications of discrete mathematics to biological research problems.
Ellington, Roni; Wachira, James
2010-01-01
The focus of this Research Experience for Undergraduates (REU) project was on RNA secondary structure prediction by using a lattice walk approach. The lattice walk approach is a combinatorial and computational biology method used to enumerate possible secondary structures and predict RNA secondary structure from RNA sequences. The method uses discrete mathematical techniques and identifies specified base pairs as parameters. The goal of the REU was to introduce upper-level undergraduate students to the principles and challenges of interdisciplinary research in molecular biology and discrete mathematics. At the beginning of the project, students from the biology and mathematics departments of a mid-sized university received instruction on the role of secondary structure in the function of eukaryotic RNAs and RNA viruses, RNA related to combinatorics, and the National Center for Biotechnology Information resources. The student research projects focused on RNA secondary structure prediction on a regulatory region of the yellow fever virus RNA genome and on an untranslated region of an mRNA of a gene associated with the neurological disorder epilepsy. At the end of the project, the REU students gave poster and oral presentations, and they submitted written final project reports to the program director. The outcome of the REU was that the students gained transferable knowledge and skills in bioinformatics and an awareness of the applications of discrete mathematics to biological research problems. PMID:20810968
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...
Fischer, Roland
1992-01-01
Discusses the impact that the relationship between people and mathematics could have on the development of pure and applied mathematics. Argues for (1) a growing interest in philosophy, history and sociology of science; (2) new models in educational and psychological research; and (3) a growing awareness of the human factor in technology,…
3rd International Conference on Applied Mathematics and Approximation Theory
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.
Workshop on Women of Applied Mathematics: Research and Leadership
Dianne P. O' Leary; Tamara G. Kolda
2004-09-28
We held a two and a half day workshop on Women of Applied Mathematics: Research and Leadership at the University of Maryland in College Park, Maryland, October 8--10, 2003. The workshop provided a technical and professional forum for eleven senior women and twenty-four early-career women in applied mathematics. Each participant committed to an outreach activity and publication of a report on the workshop's web site. The final session of the workshop produced recommendations for future action.
Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics
Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander
2010-01-01
We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to…
System for corrosion monitoring in pipeline applying fuzzy logic mathematics
Kuzyakov, O. N.; Kolosova, A. L.; Andreeva, M. A.
2018-05-01
A list of factors influencing corrosion rate on the external side of underground pipeline is determined. Principles of constructing a corrosion monitoring system are described; the system performance algorithm and program are elaborated. A comparative analysis of methods for calculating corrosion rate is undertaken. Fuzzy logic mathematics is applied to reduce calculations while considering a wider range of corrosion factors.
Mathematical Modeling of Contact Problems of Elasticity Theory with Unilateral Discrete Contact
I. V. Stankevich
2015-01-01
Full Text Available Development and operation of modern machinery and latest technology require reliable estimates of the strength characteristics of the critical elements of structures and technological equipment under the impact of high-intensity thermomechanical loading, accompanied, as a rule, by complex contact interaction. Mathematical modeling of stress-strain state of such parts and components in the contact area, based on adequate mathematical models, modern numerical methods and efficient algorithms that implement the direct determination of displacement fields, strains and stresses, is the main tool that allows fast acquisition of data required for the calculations of strength and durability. The paper considers an algorithm for constructing the numerical solution of the contact problem of elasticity theory in relation to the body, which has an obvious one-sided discrete contact interaction with an elastic half-space. The proposed algorithm is specially designed to have a correction of the tangential forces at discrete contact points, allowing us to achieve sufficiently accurate implementation of the adopted law of friction. The algorithm is embedded in a general finite element technology, with which the application code is generated. Numerical study of discrete unilateral contact interaction of an elastic plate and a rigid half-space showed a high efficiency of the developed algorithm and the application code that implements it.
Applied mathematics and condensed matter; Mathematiques appliquees et matiere condensee
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)
Molecular modeling: An open invitation for applied mathematics
Mezey, Paul G.
2013-10-01
Molecular modeling methods provide a very wide range of challenges for innovative mathematical and computational techniques, where often high dimensionality, large sets of data, and complicated interrelations imply a multitude of iterative approximations. The physical and chemical basis of these methodologies involves quantum mechanics with several non-intuitive aspects, where classical interpretation and classical analogies are often misleading or outright wrong. Hence, instead of the everyday, common sense approaches which work so well in engineering, in molecular modeling one often needs to rely on rather abstract mathematical constraints and conditions, again emphasizing the high level of reliance on applied mathematics. Yet, the interdisciplinary aspects of the field of molecular modeling also generates some inertia and perhaps too conservative reliance on tried and tested methodologies, that is at least partially caused by the less than up-to-date involvement in the newest developments in applied mathematics. It is expected that as more applied mathematicians take up the challenge of employing the latest advances of their field in molecular modeling, important breakthroughs may follow. In this presentation some of the current challenges of molecular modeling are discussed.
Johannes Kepler and his contribution to Applied Mathematics
Pichler, Franz
The worldwide renown of Johannes Kepler is based above all on his contribution to astronomy. The 3 Kepler's Laws relating to the planets are well known and will ensure that his name is remembered by future generations. Besides his astronomical work, Kepler also made important contributions in the fields of theology, physics, phylosophy and mathematics. The actual paper discusses the advances by Kepler in the application of mathematics to the solution of "real life problems". The author made a concise account of some of the disciples by Kepler: Klug, Wieleitner, Caspar, Hammer, paying particular attention to works published by Kepler while he was living in Linz (1612-1628). The Kepler's contribution to applied mathematics is an example supremely worthy of emulation, the author concludes.
Derivation and computation of discrete-delay and continuous-delay SDEs in mathematical biology.
Allen, Edward J
2014-06-01
Stochastic versions of several discrete-delay and continuous-delay differential equations, useful in mathematical biology, are derived from basic principles carefully taking into account the demographic, environmental, or physiological randomness in the dynamic processes. In particular, stochastic delay differential equation (SDDE) models are derived and studied for Nicholson's blowflies equation, Hutchinson's equation, an SIS epidemic model with delay, bacteria/phage dynamics, and glucose/insulin levels. Computational methods for approximating the SDDE models are described. Comparisons between computational solutions of the SDDEs and independently formulated Monte Carlo calculations support the accuracy of the derivations and of the computational methods.
Salvetti, Attilio; Applied Mathematics in Aerospace Science and Engineering
1994-01-01
This book contains the proceedings ofthe meeting on "Applied Mathematics in the Aerospace Field," held in Erice, Sicily, Italy from September 3 to September 10, 1991. The occasion of the meeting was the 12th Course of the School of Mathematics "Guido Stampacchia," directed by Professor Franco Giannessi of the University of Pisa. The school is affiliated with the International Center for Scientific Culture "Ettore Majorana," which is directed by Professor Antonino Zichichi of the University of Bologna. The objective of the course was to give a perspective on the state-of the-art and research trends concerning the application of mathematics to aerospace science and engineering. The course was structured with invited lectures and seminars concerning fundamental aspects of differential equa tions, mathematical programming, optimal control, numerical methods, per turbation methods, and variational methods occurring in flight mechanics, astrodynamics, guidance, control, aircraft design, fluid mechanic...
Applied Mathematics for agronomical engineers in Spain at UPM
Anton, J. M.; Grau, J. B.; Tarquis, A. M.; Fabregat, J.; Sanchez, M. E.
2009-04-01
Mathematics, created or discovered, are a global human conceptual endowment, containing large systems of knowledge, and varied skills to use definite parts of them, in creation or discovery, or for applications, e.g. in Physics, or notably in engineering behaviour. When getting upper intellectual levels in the 19th century, the agronomical science and praxis was noticeably or mainly organised in Spain in agronomical engineering schools and also in institutes, together with technician schools, also with different lower lever centres, and they have evolved with progress and they are much changing at present to a EEES schema (Bolonia process). They work in different lines that need some basis or skills from mathematics. The vocation to start such careers, that have varied curriculums, contains only some mathematics, and the number of credits for mathematics is restrained because time is necessary for other initial sciences such as applied chemistry, biology, ecology and soil sciences, but some basis and skill of maths are needed, also with Physics, at least for electricity, machines, construction, economics at initial ground levels, and also for Statistics that are here considered part of Applied Mathematics. The ways of teaching mathematical basis and skills are especial, and are different from the practical ways needed e. g. for Soil Sciences, and they involve especial efforts from students, and especial controls or exams that guide much learning. The mathematics have a very large accepted content that uses mostly a standard logic, and that is remarkably stable and international, rather similar notation and expressions being used with different main languages. For engineering the logical basis is really often not taught, but the use of it is transferred, especially for calculus that requires both adapted somehow simplified schemas and the learning of a specific skill to use it, and also for linear algebra. The basic forms of differential calculus in several
Talhaoui, Hicham; Menacer, Arezki; Kessal, Abdelhalim; Kechida, Ridha
2014-09-01
This paper presents new techniques to evaluate faults in case of broken rotor bars of induction motors. Procedures are applied with closed-loop control. Electrical and mechanical variables are treated using fast Fourier transform (FFT), and discrete wavelet transform (DWT) at start-up and steady state. The wavelet transform has proven to be an excellent mathematical tool for the detection of the faults particularly broken rotor bars type. As a performance, DWT can provide a local representation of the non-stationary current signals for the healthy machine and with fault. For sensorless control, a Luenberger observer is applied; the estimation rotor speed is analyzed; the effect of the faults in the speed pulsation is compensated; a quadratic current appears and used for fault detection. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.
Discrete computational structures
Korfhage, Robert R
1974-01-01
Discrete Computational Structures describes discrete mathematical concepts that are important to computing, covering necessary mathematical fundamentals, computer representation of sets, graph theory, storage minimization, and bandwidth. The book also explains conceptual framework (Gorn trees, searching, subroutines) and directed graphs (flowcharts, critical paths, information network). The text discusses algebra particularly as it applies to concentrates on semigroups, groups, lattices, propositional calculus, including a new tabular method of Boolean function minimization. The text emphasize
Research in applied mathematics, numerical analysis, and computer science
1984-01-01
Research conducted at the Institute for Computer Applications in Science and Engineering (ICASE) in applied mathematics, numerical analysis, and computer science is summarized and abstracts of published reports are presented. The major categories of the ICASE research program are: (1) numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; (2) control and parameter identification; (3) computational problems in engineering and the physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and (4) computer systems and software, especially vector and parallel computers.
Applying Lakatos' Theory to the Theory of Mathematical Problem Solving.
Nunokawa, Kazuhiko
1996-01-01
The relation between Lakatos' theory and issues in mathematics education, especially mathematical problem solving, is investigated by examining Lakatos' methodology of a scientific research program. (AIM)
Ward-Penny, Robert; Johnston-Wilder, Sue; Johnston-Wilder, Peter
2013-01-01
One-third of the current A-level mathematics curriculum is determined by choice, constructed out of "applied mathematics" modules in mechanics, statistics and decision mathematics. Although this choice arguably involves the most sizeable instance of choice in the current English school mathematics curriculum, and it has a significant…
The Threshold Hypothesis Applied to Spatial Skill and Mathematics
Freer, Daniel
2017-01-01
This cross-sectional study assessed the relation between spatial skills and mathematics in 854 participants across kindergarten, third grade, and sixth grade. Specifically, the study probed for a threshold for spatial skills when performing mathematics, above which spatial scores and mathematics scores would be significantly less related. This…
The Effects of Teacher Collaboration in Grade 9 Applied Mathematics
Egodawatte, Gunawardena; McDougall, Douglas; Stoilescu, Dorian
2011-01-01
The current emphasis of many mathematics education reform documents is on the need to change the environment of mathematics classrooms from the transmission of knowledge by the teacher to the transaction of knowledge between the teacher and the students which promotes mathematical investigation and exploration. In this article, we discuss the…
Notes for Applied Mathematics in Trigonometry and Earth Geometry/Navigation
Faulkner, Peter
2004-01-01
As time has progressed, the role of applied mathematics has become increasingly important. Indeed there are now more students enrolled in applied mathematics courses in senior high schools and colleges than in pure mathematics. Such courses become more relevant both to the student and to future employers, if the same constants and equations that…
Hartley, Lee; Roberts, David
2013-04-01
The Swedish Nuclear Fuel and Waste Management Company (SKB) is responsible for the development of a deep geological repository for spent nuclear fuel. The permitting of such a repository is informed by assessment studies to estimate the risks of the disposal method. One of the potential risks involves the transport of radionuclides in groundwater from defective canisters in the repository to the accessible environment. The Swedish programme for geological disposal of spent nuclear fuel has involved undertaking detailed surface-based site characterisation studies at two different sites, Forsmark and Laxemar-Simpevarp. A key component of the hydrogeological modelling of these two sites has been the development of Discrete Fracture Network (DFN) concepts of groundwater flow through the fractures in the crystalline rocks present. A discrete fracture network model represents some of the characteristics of fractures explicitly, such as their, orientation, intensity, size, spatial distribution, shape and transmissivity. This report summarises how the discrete fracture network methodology has been applied to model groundwater flow and transport at Forsmark and Laxemar. The account has involved summarising reports previously published by SKB between 2001 and 2011. The report describes the conceptual framework and assumptions used in interpreting site data, and in particular how data has been used to calibrate the various parameters that define the discrete fracture network representation of bedrock hydrogeology against borehole geologic and hydraulic data. Steps taken to confirm whether the developed discrete fracture network models provide a description of regional-scale groundwater flow and solute transport consistent with wider hydraulic tests hydrochemical data from Forsmark and Laxemar are discussed. It illustrates the use of derived hydrogeological DFN models in the simulations of the temperate period hydrogeology that provided input to radionuclide transport
Hartley, Lee; Roberts, David
2013-04-15
The Swedish Nuclear Fuel and Waste Management Company (SKB) is responsible for the development of a deep geological repository for spent nuclear fuel. The permitting of such a repository is informed by assessment studies to estimate the risks of the disposal method. One of the potential risks involves the transport of radionuclides in groundwater from defective canisters in the repository to the accessible environment. The Swedish programme for geological disposal of spent nuclear fuel has involved undertaking detailed surface-based site characterisation studies at two different sites, Forsmark and Laxemar-Simpevarp. A key component of the hydrogeological modelling of these two sites has been the development of Discrete Fracture Network (DFN) concepts of groundwater flow through the fractures in the crystalline rocks present. A discrete fracture network model represents some of the characteristics of fractures explicitly, such as their, orientation, intensity, size, spatial distribution, shape and transmissivity. This report summarises how the discrete fracture network methodology has been applied to model groundwater flow and transport at Forsmark and Laxemar. The account has involved summarising reports previously published by SKB between 2001 and 2011. The report describes the conceptual framework and assumptions used in interpreting site data, and in particular how data has been used to calibrate the various parameters that define the discrete fracture network representation of bedrock hydrogeology against borehole geologic and hydraulic data. Steps taken to confirm whether the developed discrete fracture network models provide a description of regional-scale groundwater flow and solute transport consistent with wider hydraulic tests hydrochemical data from Forsmark and Laxemar are discussed. It illustrates the use of derived hydrogeological DFN models in the simulations of the temperate period hydrogeology that provided input to radionuclide transport
Schindler, Maike; Mackrell, Kate; Pratt, Dave; Bakker, A.
2017-01-01
Schindler, M., Mackrell, K., Pratt, D., & Bakker, A. (2017). Applying contemporary philosophy in mathematics and statistics education: The perspective of inferentialism. In G. Kaiser (Ed.). Proceedings of the 13th International Congress on Mathematical Education, ICME-13
Applying Piaget's Theory of Cognitive Development to Mathematics Instruction
Ojose, Bobby
2008-01-01
This paper is based on a presentation given at National Council of Teachers of Mathematics (NCTM) in 2005 in Anaheim, California. It explicates the developmental stages of the child as posited by Piaget. The author then ties each of the stages to developmentally appropriate mathematics instruction. The implications in terms of not imposing…
Eremin, Yu. A.; Sveshnikov, A. G.
2018-04-01
The discrete source method is used to develop and implement a mathematical model for solving the problem of scattering electromagnetic waves by a three-dimensional plasmonic scatterer with nonlocal effects taken into account. Numerical results are presented whereby the features of the scattering properties of plasmonic particles with allowance for nonlocal effects are demonstrated depending on the direction and polarization of the incident wave.
McDougall, S R; Watson, M G; Devlin, A H; Mitchell, C A; Chaplain, M A J
2012-10-01
Pathological angiogenesis has been extensively explored by the mathematical modelling community over the past few decades, specifically in the contexts of tumour-induced vascularisation and wound healing. However, there have been relatively few attempts to model angiogenesis associated with normal development, despite the availability of animal models with experimentally accessible and highly ordered vascular topologies: for example, growth and development of the vascular plexus layers in the murine retina. The current study aims to address this issue through the development of a hybrid discrete-continuum mathematical model of the developing retinal vasculature in neonatal mice that is closely coupled with an ongoing experimental programme. The model of the functional vasculature is informed by a range of morphological and molecular data obtained over a period of several days, from 6 days prior to birth to approximately 8 days after birth. The spatio-temporal formation of the superficial retinal vascular plexus (RVP) in wild-type mice occurs in a well-defined sequence. Prior to birth, astrocytes migrate from the optic nerve over the surface of the inner retina in response to a chemotactic gradient of PDGF-A, formed at an earlier stage by migrating retinal ganglion cells (RGCs). Astrocytes express a variety of chemotactic and haptotactic proteins, including VEGF and fibronectin (respectively), which subsequently induce endothelial cell sprouting and modulate growth of the RVP. The developing RVP is not an inert structure; however, the vascular bed adapts and remodels in response to a wide variety of metabolic and biomolecular stimuli. The main focus of this investigation is to understand how these interacting cellular, molecular, and metabolic cues regulate RVP growth and formation. In an earlier one-dimensional continuum model of astrocyte and endothelial migration, we showed that the measured frontal velocities of the two cell types could be accurately reproduced
Studies in Mathematics, Volume X. Applied Mathematics in the High School.
Schiffer, Max M.
This publication contains a sequence of lectures given to high school mathematics teachers by the author. Applications of mathematics emphasized are elementary algebra, geometry, and matrix algebra. Included are: (1) an introduction concerning teaching applications of mathematics; (2) Chapter 1: Mechanics for the High School Student; (3) Chapter…
Literature Review of Applying Visual Method to Understand Mathematics
Yu Xiaojuan
2015-01-01
Full Text Available As a new method to understand mathematics, visualization offers a new way of understanding mathematical principles and phenomena via image thinking and geometric explanation. It aims to deepen the understanding of the nature of concepts or phenomena and enhance the cognitive ability of learners. This paper collates and summarizes the application of this visual method in the understanding of mathematics. It also makes a literature review of the existing research, especially with a visual demonstration of Euler’s formula, introduces the application of this method in solving relevant mathematical problems, and points out the differences and similarities between the visualization method and the numerical-graphic combination method, as well as matters needing attention for its application.
Annual report of the Center for Applied Mathematics, 1985
1986-01-01
Research on the mathematical aspects of wave propagation; particulate methods in fluid physics and mechanics; nonlinear problems; stochastic equations; martingales, and interacting particle systems; and computer programming and algorithms is presented [fr
Annual report of the Center for Applied Mathematics, 1986
1987-01-01
Research on the mathematical aspects of wave propagation; particulate methods in fluid physics and mechanics; nonlinear problems; stochastic equations; martingales, and interacting particle systems; and computer programming and algorithms is presented [fr
Guerrero-Ortiz, Carolina; Mena-Lorca, Jaime
2015-01-01
International audience; This study analyses the results obtained from comparing the paths shown by expert mathematicians on the one hand and mathematics teachers on the other, when addressing a hypothetical problem that requires the construction of a mathematical model. The research was conducted with a qualitative approach, applying a case study which involved a group of mathematics teachers and three experts from different mathematical areas. The results show that the process of constructin...
Lake, Warren; Wallin, Margie; Woolcott, Geoff; Boyd, Wendy; Foster, Alan; Markopoulos, Christos; Boyd, William
2017-02-01
Student mathematics performance and the need for work-ready graduates to be mathematics-competent is a core issue for many universities. While both student and teacher are responsible for learning outcomes, there is a need to explicitly acknowledge the weak mathematics foundation of many university students. A systematic literature review was undertaken of identified innovations and/or interventions that may lead to improvement in student outcomes for university mathematics-based units of study. The review revealed the importance of understanding the foundations of student performance in higher education mathematics learning, especially in first year. Pre-university mathematics skills were identified as significant in student retention and mathematics success at university, and a specific focus on student pre-university mathematics skill level was found to be more effective in providing help, rather than simply focusing on a particular at-risk group. Diagnostics tools were found to be important in identifying (1) student background and (2) appropriate intervention. The studies highlighted the importance of appropriate and validated interventions in mathematics teaching and learning, and the need to improve the learning model for mathematics-based subjects, communication and technology innovations.
Research in progress in applied mathematics, numerical analysis, and computer science
1990-01-01
Research conducted at the Institute in Science and Engineering in applied mathematics, numerical analysis, and computer science is summarized. The Institute conducts unclassified basic research in applied mathematics in order to extend and improve problem solving capabilities in science and engineering, particularly in aeronautics and space.
Applied mathematical sciences research at Argonne, April 1, 1981-March 31, 1982
Pieper, G.W.
1982-01-01
This report reviews the research activities in Applied Mathematical Sciences at Argonne National Laboratory for the period April 1, 1981, through March 31, 1982. The body of the report discusses various projects carried out in three major areas of research: applied analysis, computational mathematics, and software engineering. Information on section staff, visitors, workshops, and seminars is found in the appendices
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
Vladimir I. Volchikhin
2017-06-01
Full Text Available Introduction: The study promotes to decrease a number of errors of calculating the correlation coefficient in small test samples. Materials and Methods: We used simulation tool for the distribution functions of the density values of the correlation coefficient in small samples. A method for quantization of the data, allows obtaining a discrete spectrum states of one of the varieties of correlation functional. This allows us to consider the proposed structure as a mathematical correlation molecule, described by some analogue continuous-quantum Schrödinger equation. Results: The chi-squared Pearson’s molecule on small samples allows enhancing power of classical chi-squared test to 20 times. A mathematical correlation molecule described in the article has similar properties. It allows in the future reducing calculation errors of the classical correlation coefficients in small samples. Discussion and Conclusions: The authors suggest that there are infinitely many mathematical molecules are similar in their properties to the actual physical molecules. Schrödinger equations are not unique, their analogues can be constructed for each mathematical molecule. You can expect a mathematical synthesis of molecules for a large number of known statistical tests and statistical moments. All this should make it possible to reduce calculation errors due to quantum effects that occur in small test samples.
Applying mathematical finance tools to the competitive Nordic electricity market
Vehviläinen, Iivo
2004-01-01
This thesis models competitive electricity markets using the methods of mathematical finance. Fundamental problems of finance are market price modelling, derivative pricing, and optimal portfolio selection. The same questions arise in competitive electricity markets. The thesis presents an electricity spot price model based on the fundamental stochastic factors that affect electricity prices. The resulting price model has sound economic foundations, is able to explain spot market price mo...
Brown, Catherine A.; And Others
1988-01-01
Suggests that secondary school students seem to have reasonably good procedural knowledge in areas of mathematics as rational numbers, probability, measurement, and data organization and interpretation. It appears, however, that students are lacking the conceptual knowledge enabling them to successfully do the assessment items on applications,…
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…
Computational physics and applied mathematics capability review June 8-10, 2010
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
Applying science and mathematics to big data for smarter buildings.
Lee, Young M; An, Lianjun; Liu, Fei; Horesh, Raya; Chae, Young Tae; Zhang, Rui
2013-08-01
Many buildings are now collecting a large amount of data on operations, energy consumption, and activities through systems such as a building management system (BMS), sensors, and meters (e.g., submeters and smart meters). However, the majority of data are not utilized and are thrown away. Science and mathematics can play an important role in utilizing these big data and accurately assessing how energy is consumed in buildings and what can be done to save energy, make buildings energy efficient, and reduce greenhouse gas (GHG) emissions. This paper discusses an analytical tool that has been developed to assist building owners, facility managers, operators, and tenants of buildings in assessing, benchmarking, diagnosing, tracking, forecasting, and simulating energy consumption in building portfolios. © 2013 New York Academy of Sciences.
Applied Wave Mathematics Selected Topics in Solids, Fluids, and Mathematical Methods
Quak, Ewald
2009-01-01
This edited volume addresses the importance of mathematics in wave-related research, and its tutorial style contributions provide educational material for courses or seminars. It presents highlights from research carried out at the Centre for Nonlinear Studies in Tallinn, Estonia, the Centre of Mathematics for Applications in Oslo, Norway, and by visitors from the EU project CENS-CMA. The example applications discussed include wave propagation in inhomogeneous solids, liquid crystals in mesoscopic physics, and long ship waves in shallow water bodies. Other contributions focus on specific mathe
Applying mathematical finance tools to the competitive Nordic electricity market
Vehvilaeinen, I.
2004-01-01
This thesis models competitive electricity markets using the methods of mathematical finance. Fundamental problems of finance are market price modelling, derivative pricing, and optimal portfolio selection. The same questions arise in competitive electricity markets. The thesis presents an electricity spot price model based on the fundamental stochastic factors that affect electricity prices. The resulting price model has sound economic foundations, is able to explain spot market price movements, and offers a computationally efficient way of simulating spot prices. The thesis shows that the connection between spot prices and electricity forward prices is nontrivial because electricity is a commodity that must be consumed immediately. Consequently, forward prices of different times are based on the supply-demand conditions at those times. This thesis introduces a statistical model that captures the main characteristics of observed forward price movements. The thesis presents the pricing problems relating to the common Nordic electricity derivatives, as well as the pricing relations between electricity derivatives. The special characteristics of electricity make spot electricity market incomplete. The thesis assumes the existence of a risk-neutral martingale measure so that formal pricing results can be obtained. Some concepts introduced in financial markets are directly usable in the electricity markets. The risk management application in this thesis uses a static optimal portfolio selection framework where Monte Carlo simulation provides quantitative results. The application of mathematical finance requires careful consideration of the special characteristics of the electricity markets. Economic theory and reasoning have to be taken into account when constructing financial models in competitive electricity markets. (orig.)
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....
Applied Mathematical Sciences research at Argonne, October 1, 1978-March 31, 1980
Pieper, G. W. [ed.
1980-01-01
This report reviews the research activities of the Applied Mathematical Sciences Section for the period October 1, 1978, through March 31, 1980. The body of the report discusses various projects carried out in four major areas of research: applied analysis, computational mathematics, software engineering, and software clinics. Information on section staff, visitors, workshops, and seminars is found in the appendices. Descriptions of individual research topics are very brief.
A journey through discrete mathematics a tribute to Jiří Matoušek
Nešetřil, Jaroslav; Thomas, Robin
2017-01-01
This collection of high-quality articles in the field of combinatorics, geometry, algebraic topology and theoretical computer science is a tribute to Jiří Matoušek, who passed away prematurely in March 2015. It is a collaborative effort by his colleagues and friends, who have paid particular attention to clarity of exposition – something Jirka would have approved of. The original research articles, surveys and expository articles, written by leading experts in their respective fields, map Jiří Matoušek’s numerous areas of mathematical interest.
Recent progress and modern challenges in applied mathematics, modeling and computational science
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.
1st International Conference on Industrial and Applied Mathematics of the Indian Subcontinent
Kočvara, Michal
2002-01-01
An important objective of the study of mathematics is to analyze and visualize phenomena of nature and real world problems for its proper understanding. Gradually, it is also becoming the language of modem financial instruments. To project some of these developments, the conference was planned under the joint auspices of the Indian Society of Industrial and Applied mathematics (ISlAM) and Guru Nanak Dev University (G. N. D. U. ), Amritsar, India. Dr. Pammy Manchanda, chairperson of Mathematics Department, G. N. D. U. , was appointed the organizing secretary and an organizing committee was constituted. The Conference was scheduled in World Mathematics Year 2000 but, due one reason or the other, it could be held during 22. -25. January 2001. How ever, keeping in view the suggestion of the International Mathematics union, we organized two symposia, Role of Mathematics in industrial development and vice-versa and How image of Mathematics can be improved in public. These two symposia aroused great interest among...
Natal’ya Yur’evna Gorbunova
2017-06-01
Full Text Available We described several aspects of organizing student research work, as well as solving a number of mathematical modeling problems: professionally-oriented, multi-stage, etc. We underlined the importance of their economic content. Samples of using such problems in teaching Mathematics at agricultural university were given. Several questions connected with information material selection and peculiarities of research problems application were described. Purpose. The author aims to show the possibility and necessity of using professionally-oriented problems of mathematical modeling in teaching Mathematics at agricultural university. The subject of analysis is including such problems into educational process. Methodology. The main research method is dialectical method of obtaining knowledge of finding approaches to selection, writing and using mathematical modeling and professionally-oriented problems in educational process; the methodology is study of these methods of obtaining knowledge. Results. As a result of analysis of literature, students opinions, observation of students work, and taking into account personal teaching experience, it is possible to make conclusion about importance of using mathematical modeling problems, as it helps to systemize theoretical knowledge, apply it to practice, raise students study motivation in engineering sphere. Practical implications. Results of the research can be of interest for teachers of Mathematics in preparing Bachelor and Master students of engineering departments of agricultural university both for theoretical research and for modernization of study courses.
1994-01-01
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, 1993 through March 31, 1994. 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 acoustics and combustion; (3) experimental research in transition and turbulence and aerodynamics involving LaRC facilities and scientists; and (4) computer science.
An application of discrete mathematics in the design of an open pit mine
Caccetta, L.; Giannini, L.M.
1988-09-01
The determination of the 'optimum pit limit' of a mine is considered to be a fundamental problem in mine planning as it provides information which is essential in the evaluation of the economic potential of a mineral deposit, and in the formulation of long-, intermediate-, and short-range mine plans. A number of mathematical techniques have been proposed to solve this problem, some of the more elaborate ones posing considerable computational problems. In this paper we discuss the development and implementation of a graph-theoretic technique originally proposed by Lerchs and Grossman. Our implementation strategy involves the use of a dynamic programming technique to 'bound' the optimum. 19 refs., 4 figs.
An efficient permeability scaling-up technique applied to the discretized flow equations
Urgelli, D.; Ding, Yu [Institut Francais du Petrole, Rueil Malmaison (France)
1997-08-01
Grid-block permeability scaling-up for numerical reservoir simulations has been discussed for a long time in the literature. It is now recognized that a full permeability tensor is needed to get an accurate reservoir description at large scale. However, two major difficulties are encountered: (1) grid-block permeability cannot be properly defined because it depends on boundary conditions; (2) discretization of flow equations with a full permeability tensor is not straightforward and little work has been done on this subject. In this paper, we propose a new method, which allows us to get around both difficulties. As the two major problems are closely related, a global approach will preserve the accuracy. So, in the proposed method, the permeability up-scaling technique is integrated in the discretized numerical scheme for flow simulation. The permeability is scaled-up via the transmissibility term, in accordance with the fluid flow calculation in the numerical scheme. A finite-volume scheme is particularly studied, and the transmissibility scaling-up technique for this scheme is presented. Some numerical examples are tested for flow simulation. This new method is compared with some published numerical schemes for full permeability tensor discretization where the full permeability tensor is scaled-up through various techniques. Comparing the results with fine grid simulations shows that the new method is more accurate and more efficient.
Student School-Level Math Knowledge Influence on Applied Mathematics Study Courses
Rima Kriauzienė
2013-08-01
Full Text Available Purpose—to find out the influence of student school-level math knowledge on courses of applied mathematics studies: what is the importance of having a math maturity exam for students, an estimate of social science students’ motivation to learn math, and attendance of seminars. Students who did take the state exam attended more seminars than the students who did not take math exam, and vice versa. Design/methodology/approach—this work describes research which involved persistent MRU Public Administration degree program second-year students. Doing statistical analysis of the data will be a link between school-level mathematics knowledge and attendance activity in seminars and motivation to learn mathematics. Findings—the research is expected to establish a connection between school-level mathematics knowledge and student motivation to learn mathematics. It was found that there is no correlation between student opinions about school mathematics courses and result of their first test. Determine relationship between attendance of exercises and public examinations. Between the stored type of exam and test results are dependent. Determine relationship between exercise attendance and test results, as shown by the calculated correlation coefficient Based on the results, it’s recommended to increase the number of exercises. A more refined analysis of the data is subject to further investigation. Research limitations/implications—this method is just one of the possible ways of application. Practical implications—that kind of research and its methodology can be applied not only to the subject of applied mathematics studies, but also to other natural or social sciences. Originality/Value—empirical experiment data can be used in other studies of Educology nature analysis.
Student School-Level Math Knowledge Influence on Applied Mathematics Study Courses
Tadas Laukevičius
2011-12-01
Full Text Available Purpose—to find out the influence of student school-level math knowledge on courses of applied mathematics studies: what is the importance of having a math maturity exam for students, an estimate of social science students’ motivation to learn math, and attendance of seminars. Students who did take the state exam attended more seminars than the students who did not take math exam, and vice versa.Design/methodology/approach—this work describes research which involved persistent MRU Public Administration degree program second-year students. Doing statistical analysis of the data will be a link between school-level mathematics knowledge and attendance activity in seminars and motivation to learn mathematics.Findings—the research is expected to establish a connection between school-level mathematics knowledge and student motivation to learn mathematics.It was found that there is no correlation between student opinions about school mathematics courses and result of their first test.Determine relationship between attendance of exercises and public examinations.Between the stored type of exam and test results are dependent.Determine relationship between exercise attendance and test results, as shown by the calculated correlation coefficientBased on the results, it’s recommended to increase the number of exercises. A more refined analysis of the data is subject to further investigation.Research limitations/implications—this method is just one of the possible ways of application.Practical implications—that kind of research and its methodology can be applied not only to the subject of applied mathematics studies, but also to other natural or social sciences.Originality/Value—empirical experiment data can be used in other studies of Educology nature analysis.
Applying Mathematical Optimization Methods to an ACT-R Instance-Based Learning Model.
Said, Nadia; Engelhart, Michael; Kirches, Christian; Körkel, Stefan; Holt, Daniel V
2016-01-01
Computational models of cognition provide an interface to connect advanced mathematical tools and methods to empirically supported theories of behavior in psychology, cognitive science, and neuroscience. In this article, we consider a computational model of instance-based learning, implemented in the ACT-R cognitive architecture. We propose an approach for obtaining mathematical reformulations of such cognitive models that improve their computational tractability. For the well-established Sugar Factory dynamic decision making task, we conduct a simulation study to analyze central model parameters. We show how mathematical optimization techniques can be applied to efficiently identify optimal parameter values with respect to different optimization goals. Beyond these methodological contributions, our analysis reveals the sensitivity of this particular task with respect to initial settings and yields new insights into how average human performance deviates from potential optimal performance. We conclude by discussing possible extensions of our approach as well as future steps towards applying more powerful derivative-based optimization methods.
Soria Morillo, Luis M; Alvarez-Garcia, Juan A; Gonzalez-Abril, Luis; Ortega Ramírez, Juan A
2016-07-15
In this paper a new approach is applied to the area of marketing research. The aim of this paper is to recognize how brain activity responds during the visualization of short video advertisements using discrete classification techniques. By means of low cost electroencephalography devices (EEG), the activation level of some brain regions have been studied while the ads are shown to users. We may wonder about how useful is the use of neuroscience knowledge in marketing, or what could provide neuroscience to marketing sector, or why this approach can improve the accuracy and the final user acceptance compared to other works. By using discrete techniques over EEG frequency bands of a generated dataset, C4.5, ANN and the new recognition system based on Ameva, a discretization algorithm, is applied to obtain the score given by subjects to each TV ad. The proposed technique allows to reach more than 75 % of accuracy, which is an excellent result taking into account the typology of EEG sensors used in this work. Furthermore, the time consumption of the algorithm proposed is reduced up to 30 % compared to other techniques presented in this paper. This bring about a battery lifetime improvement on the devices where the algorithm is running, extending the experience in the ubiquitous context where the new approach has been tested.
Olav Slupphaug
2001-01-01
Full Text Available We present a mathematical programming approach to robust control of nonlinear systems with uncertain, possibly time-varying, parameters. The uncertain system is given by different local affine parameter dependent models in different parts of the state space. It is shown how this representation can be obtained from a nonlinear uncertain system by solving a set of continuous linear semi-infinite programming problems, and how each of these problems can be solved as a (finite series of ordinary linear programs. Additionally, the system representation includes control- and state constraints. The controller design method is derived from Lyapunov stability arguments and utilizes an affine parameter dependent quadratic Lyapunov function. The controller has a piecewise affine output feedback structure, and the design amounts to finding a feasible solution to a set of linear matrix inequalities combined with one spectral radius constraint on the product of two positive definite matrices. A local solution approach to this nonconvex feasibility problem is proposed. Complexity of the design method and some special cases such as state- feedback are discussed. Finally, an application of the results is given by proposing an on-line computationally feasible algorithm for constrained nonlinear state- feedback model predictive control with robust stability.
Committee on the Undergraduate Program in Mathematics, Berkeley, CA.
Proceedings from four sessions of the Summer Conference for College Teachers on Applied Mathematics are presented. The four sessions were: (1) Applications of Elementary Calculus, (2) Applications of Linear Algebra, (3) Applications of Elementary Differential Equations, and (4) Applications of Probability and Statistics. Nine lectures were given…
On the Formal-Logical Analysis of the Foundations of Mathematics Applied to Problems in Physics
Kalanov, Temur Z.
2016-03-01
Analysis of the foundations of mathematics applied to problems in physics was proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that critical analysis of the concept of mathematical quantity - central concept of mathematics - leads to the following conclusion: (1) The concept of ``mathematical quantity'' is the result of the following mental operations: (a) abstraction of the ``quantitative determinacy of physical quantity'' from the ``physical quantity'' at that the ``quantitative determinacy of physical quantity'' is an independent object of thought; (b) abstraction of the ``amount (i.e., abstract number)'' from the ``quantitative determinacy of physical quantity'' at that the ``amount (i.e., abstract number)'' is an independent object of thought. In this case, unnamed, abstract numbers are the only sign of the ``mathematical quantity''. This sign is not an essential sign of the material objects. (2) The concept of mathematical quantity is meaningless, erroneous, and inadmissible concept in science because it represents the following formal-logical and dialectical-materialistic error: negation of the existence of the essential sign of the concept (i.e., negation of the existence of the essence of the concept) and negation of the existence of measure of material object.
Batley, Richard; Ibáñez Rivas, Juan Nicolás
2013-01-01
in economics. Whilst some researchers were quick to see its practical potential (e.g. McFadden, 1968, 1975), it was not until the late 1970s and early 1980s that RUM was equipped with a reasonably comprehensive theoretical rationale in terms of the economics of consumption. An important tenet of this rationale......The apparatus of the Random Utility Model (RUM) first emerged in the early 1960s, with Marschak (1960) and Block and Marschak (1960) translating models originally developed for discriminant analysis in psychophysics (Thurstone, 1927) to the alternative domain of discrete choice analysis...
3D Discrete Dislocation Dynamics Applied to Interactions between Dislocation Walls and Particles
Záležák, Tomáš; Dlouhý, Antonín
2012-01-01
Roč. 122, č. 3 (2012), s. 450-452 ISSN 0587-4246. [International Symposium on Physics of Materials /12./ - ISPMA 12. Prague, 04.09.2011-08.09.2011] R&D Projects: GA ČR GD106/09/H035; GA ČR GA202/09/2073; GA MŠk OC 162 Institutional research plan: CEZ:AV0Z20410507 Keywords : 3D discrete dislocation dynamics * tilt boundary * migration * diffusion * pecipitation hardening Subject RIV: JG - Metallurgy Impact factor: 0.531, year: 2012
A simple mathematical model of society collapse applied to Easter Island
Bologna, M.; Flores, J. C.
2008-02-01
In this paper we consider a mathematical model for the evolution and collapse of the Easter Island society. Based on historical reports, the available primary resources consisted almost exclusively in the trees, then we describe the inhabitants and the resources as an isolated dynamical system. A mathematical, and numerical, analysis about the Easter Island community collapse is performed. In particular, we analyze the critical values of the fundamental parameters and a demographic curve is presented. The technological parameter, quantifying the exploitation of the resources, is calculated and applied to the case of another extinguished civilization (Copán Maya) confirming the consistency of the adopted model.
3rd International Conference on Computer Science, Applied Mathematics and Applications
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.
M. R. Sidi Ammi
2017-04-01
Full Text Available The International Workshop on Applied Mathematics, Errachidia (IWAM’2017 took place in Errachidia, Morocco at the Faculty of Sciences and Technics during March 13, 2017 (https://iwam2017.sciencesconf.org/. The workshop was held with the support of FST Errachidia, the University Moulay Isma¨ıl. It is aimed at celebrating the collaborative research in applied mathematics by the mathematicians of the FST Errachidia, the Systems and Control Group of CIDMA, University of Aveiro, and with the MIA Lab, University of La Rochelle. It was attended by about 100 Mathematicians and Ph.D. and M.S. students, coming from universities from diﬀerent countries, such as Algeria, Egypt, France, Portugal, and Morocco. The aim of IWAM’2017 is to bring researchers and professionals to discuss recent developments in both theoretical and applied mathematics, to create the knowledge exchange platform between mathematicians. The workshop is broad-based that covers several branches of engineering sciences, mathematics and interdisciplinary researches mainly in the ﬁelds of optimization and variational analysis, theoretical, asymptotic and numerical analysis of ordinary, partial and fractional diﬀerential equations
Discrete element method applied to the vibration process of coke particles
Majidi, Behzad
2012-01-01
Les propriétés physiques, mécaniques et chimiques des matières premières ont un effet majeur sur la qualité des anodes en carbone pour le procédé de production d’aluminium. Ce travail tente d’étudier la faisabilité de l’application de simulation de la Méthode des Élément Discrets (DEM) à la technologie de production d’anodes. L’effet de la forme des particules et de la distribution de leurs tailles sur la densité apparente vibrée (VBD) d’échantillons de coke sec est étudié. Les particules de ...
Wielandt method applied to the diffusion equations discretized by finite element nodal methods
Mugica R, A.; Valle G, E. del
2003-01-01
Nowadays the numerical methods of solution to the diffusion equation by means of algorithms and computer programs result so extensive due to the great number of routines and calculations that should carry out, this rebounds directly in the execution times of this programs, being obtained results in relatively long times. This work shows the application of an acceleration method of the convergence of the classic method of those powers that it reduces notably the number of necessary iterations for to obtain reliable results, what means that the compute times they see reduced in great measure. This method is known in the literature like Wielandt method and it has incorporated to a computer program that is based on the discretization of the neutron diffusion equations in plate geometry and stationary state by polynomial nodal methods. In this work the neutron diffusion equations are described for several energy groups and their discretization by means of those called physical nodal methods, being illustrated in particular the quadratic case. It is described a model problem widely described in the literature which is solved for the physical nodal grade schemes 1, 2, 3 and 4 in three different ways: to) with the classic method of the powers, b) method of the powers with the Wielandt acceleration and c) method of the powers with the Wielandt modified acceleration. The results for the model problem as well as for two additional problems known as benchmark problems are reported. Such acceleration method can also be implemented to problems of different geometry to the proposal in this work, besides being possible to extend their application to problems in 2 or 3 dimensions. (Author)
Validity of the Cauchy-Born rule applied to discrete cellular-scale models of biological tissues
Davit, Y.
2013-04-30
The development of new models of biological tissues that consider cells in a discrete manner is becoming increasingly popular as an alternative to continuum methods based on partial differential equations, although formal relationships between the discrete and continuum frameworks remain to be established. For crystal mechanics, the discrete-to-continuum bridge is often made by assuming that local atom displacements can be mapped homogeneously from the mesoscale deformation gradient, an assumption known as the Cauchy-Born rule (CBR). Although the CBR does not hold exactly for noncrystalline materials, it may still be used as a first-order approximation for analytic calculations of effective stresses or strain energies. In this work, our goal is to investigate numerically the applicability of the CBR to two-dimensional cellular-scale models by assessing the mechanical behavior of model biological tissues, including crystalline (honeycomb) and noncrystalline reference states. The numerical procedure involves applying an affine deformation to the boundary cells and computing the quasistatic position of internal cells. The position of internal cells is then compared with the prediction of the CBR and an average deviation is calculated in the strain domain. For center-based cell models, we show that the CBR holds exactly when the deformation gradient is relatively small and the reference stress-free configuration is defined by a honeycomb lattice. We show further that the CBR may be used approximately when the reference state is perturbed from the honeycomb configuration. By contrast, for vertex-based cell models, a similar analysis reveals that the CBR does not provide a good representation of the tissue mechanics, even when the reference configuration is defined by a honeycomb lattice. The paper concludes with a discussion of the implications of these results for concurrent discrete and continuous modeling, adaptation of atom-to-continuum techniques to biological
Voigt, Kristina; Scherb, Hagen; Bruggemann, Rainer; Schramm, Karl-Werner
2013-06-01
Sustainable/Green Chemistry is a chemical philosophy encouraging the design of products and processes that reduce or eliminate the use and generation of hazardous substances. In this respect, metrical scientific disciplines like Chemometrics are important, because they indicate criteria for chemicals being hazardous or not. We demonstrated that sustainable principles in the disciplines Green Chemistry, Green Engineering, and Sustainability in Information Technology have main aspects in common. The use of non-hazardous chemicals or the more efficient use of chemical substances is one of these aspects. We take a closer look on the topic of the hazards of chemical substances. Our research focuses on data analyses concerning environmental chemicals named Persistent Organic Pollutants (POPs), which are found all over the world and pose a large risk to environment as well as to humans. The evaluation of the data is a major step in the elucidation of the danger of these chemicals. The data analysis method demonstrated here, is based on the theory of partially ordered sets and provides a generalized ranking. In our approach we investigate data sets of breast milk samples of women in Denmark, Finland, and Turkey which contained measurable levels of 20 POPs. The goal is twofold: On the one side the hazardous chemicals are to be identified and on the other side possible differences among the three nations should be detected, because in that case possible different uptake mechanisms may be supposed. The data analysis is performed by the free available software package PyHasse, written by the third author. We conclude that the data analysis method can well be applied for distinguishing between more or less dangerous existing chemicals. Furthermore, it should be used in sustainable chemistry in the same manner for detecting more and less sustainable chemicals. Copyright © 2013 Elsevier B.V. All rights reserved.
Washback Effect of University Entrance exams in Applied Mathematics to Social Sciences.
Rodríguez-Muñiz, Luis J; Díaz, Patricia; Mier, Verónica; Alonso, Pedro
2016-01-01
Curricular issues of subject Applied Mathematics to Social Sciences are studied in relation to university entrance exams performed in several Spanish regions between 2009-2014. By using quantitative and qualitative analyses, it has been studied how these exams align with curriculum and how they produce a washback on curriculum and teachers' work. Additionally, one questionnaire about teachers' practices has been performed, in order to find out how the exams are influencing teaching methodology development. Main results obtained show that evaluation is producing a bias on the official curriculum, substantially simplifying the specific orientation that should guide applied mathematics. Furthermore, teachers' practices are influenced by the exams, and they usually approach their teaching methodology to the frequent types of exams. Also, slight differences among the teachers lead to distinguish two behavioral subgroups. Results can also be useful in an international context, because of the importance of standardized exit exams in OECD countries.
Washback Effect of University Entrance exams in Applied Mathematics to Social Sciences
Díaz, Patricia; Mier, Verónica; Alonso, Pedro
2016-01-01
Curricular issues of subject Applied Mathematics to Social Sciences are studied in relation to university entrance exams performed in several Spanish regions between 2009–2014. By using quantitative and qualitative analyses, it has been studied how these exams align with curriculum and how they produce a washback on curriculum and teachers’ work. Additionally, one questionnaire about teachers’ practices has been performed, in order to find out how the exams are influencing teaching methodology development. Main results obtained show that evaluation is producing a bias on the official curriculum, substantially simplifying the specific orientation that should guide applied mathematics. Furthermore, teachers’ practices are influenced by the exams, and they usually approach their teaching methodology to the frequent types of exams. Also, slight differences among the teachers lead to distinguish two behavioral subgroups. Results can also be useful in an international context, because of the importance of standardized exit exams in OECD countries. PMID:27936103
2016-01-01
This book provides a thorough introduction to the challenge of applying mathematics in real-world scenarios. Modelling tasks rarely involve well-defined categories, and they often require multidisciplinary input from mathematics, physics, computer sciences, or engineering. In keeping with this spirit of modelling, the book includes a wealth of cross-references between the chapters and frequently points to the real-world context. The book combines classical approaches to modelling with novel areas such as soft computing methods, inverse problems, and model uncertainty. Attention is also paid to the interaction between models, data and the use of mathematical software. The reader will find a broad selection of theoretical tools for practicing industrial mathematics, including the analysis of continuum models, probabilistic and discrete phenomena, and asymptotic and sensitivity analysis.
Mokhtar M. Metwally
2008-01-01
Full Text Available The aim of this paper is to formulate the mathematical relationship between firms potential ability and their applied efforts to attract the body of unattached customers. A method is devised in this paper by which management techniques imposed by a particular firm can evaluate its market share. This paper demonstrates the relationship between the applied marketing effort of management and the potential ability of the firm in determining its market share. This paper also investigates the effect of a number of simultaneous marketing impulses on the movement of the body of unattached customers and hence on the size of the market share.
Unified Modeling of Discrete Event and Control Systems Applied in Manufacturing
Amanda Arêas de Souza
2015-05-01
Full Text Available For the development of both a simulation modeland a control system, it is necessary to build, inadvance, a conceptual model. This is what isusually suggested by the methodologies applied inprojects of this nature. Some conceptual modelingtechniques allow for a better understanding ofthe simulation model, and a clear descriptionof the logic of control systems. Therefore, thispaper aims to present and evaluate conceptuallanguages for unified modeling of models ofdiscrete event simulation and control systemsapplied in manufacturing. The results show thatthe IDEF-SIM language can be applied both insimulation systems and in process control.
A scheme for designing extreme multistable discrete dynamical ...
A scheme for designing extreme multistable discrete dynamical systems ... Abstract. In this paper, we propose a scheme for designing discrete extreme multistable systems coupling two identical dynamical systems. Existence ... Department of Applied Mathematics, University of Calcutta, 92 APC Road, Kolkata 700 009, India ...
Applying Mathematical Optimization Methods to an ACT-R Instance-Based Learning Model.
Nadia Said
Full Text Available Computational models of cognition provide an interface to connect advanced mathematical tools and methods to empirically supported theories of behavior in psychology, cognitive science, and neuroscience. In this article, we consider a computational model of instance-based learning, implemented in the ACT-R cognitive architecture. We propose an approach for obtaining mathematical reformulations of such cognitive models that improve their computational tractability. For the well-established Sugar Factory dynamic decision making task, we conduct a simulation study to analyze central model parameters. We show how mathematical optimization techniques can be applied to efficiently identify optimal parameter values with respect to different optimization goals. Beyond these methodological contributions, our analysis reveals the sensitivity of this particular task with respect to initial settings and yields new insights into how average human performance deviates from potential optimal performance. We conclude by discussing possible extensions of our approach as well as future steps towards applying more powerful derivative-based optimization methods.
Georgios S. Stamatakos
2009-10-01
Full Text Available The tremendous rate of accumulation of experimental and clinical knowledge pertaining to cancer dictates the development of a theoretical framework for the meaningful integration of such knowledge at all levels of biocomplexity. In this context our research group has developed and partly validated a number of spatiotemporal simulation models of in vivo tumour growth and in particular tumour response to several therapeutic schemes. Most of the modeling modules have been based on discrete mathematics and therefore have been formulated in terms of rather complex algorithms (e.g. in pseudocode and actual computer code. However, such lengthy algorithmic descriptions, although sufficient from the mathematical point of view, may render it difficult for an interested reader to readily identify the sequence of the very basic simulation operations that lie at the heart of the entire model. In order to both alleviate this problem and at the same time provide a bridge to symbolic mathematics, we propose the introduction of the notion of hypermatrix in conjunction with that of a discrete operator into the already developed models. Using a radiotherapy response simulation example we demonstrate how the entire model can be considered as the sequential application of a number of discrete operators to a hypermatrix corresponding to the dynamics of the anatomic area of interest. Subsequently, we investigate the operators’ commutativity and outline the “summarize and jump” strategy aiming at efficiently and realistically address multilevel biological problems such as cancer. In order to clarify the actual effect of the composite discrete operator we present further simulation results which are in agreement with the outcome of the clinical study RTOG 83–02, thus strengthening the reliability of the model developed.
Stamatakos, Georgios S; Dionysiou, Dimitra D
2009-10-21
The tremendous rate of accumulation of experimental and clinical knowledge pertaining to cancer dictates the development of a theoretical framework for the meaningful integration of such knowledge at all levels of biocomplexity. In this context our research group has developed and partly validated a number of spatiotemporal simulation models of in vivo tumour growth and in particular tumour response to several therapeutic schemes. Most of the modeling modules have been based on discrete mathematics and therefore have been formulated in terms of rather complex algorithms (e.g. in pseudocode and actual computer code). However, such lengthy algorithmic descriptions, although sufficient from the mathematical point of view, may render it difficult for an interested reader to readily identify the sequence of the very basic simulation operations that lie at the heart of the entire model. In order to both alleviate this problem and at the same time provide a bridge to symbolic mathematics, we propose the introduction of the notion of hypermatrix in conjunction with that of a discrete operator into the already developed models. Using a radiotherapy response simulation example we demonstrate how the entire model can be considered as the sequential application of a number of discrete operators to a hypermatrix corresponding to the dynamics of the anatomic area of interest. Subsequently, we investigate the operators' commutativity and outline the "summarize and jump" strategy aiming at efficiently and realistically address multilevel biological problems such as cancer. In order to clarify the actual effect of the composite discrete operator we present further simulation results which are in agreement with the outcome of the clinical study RTOG 83-02, thus strengthening the reliability of the model developed.
Wollkind, David J
2017-01-01
This text demonstrates the process of comprehensive applied mathematical modeling through the introduction of various case studies. The case studies are arranged in increasing order of complexity based on the mathematical methods required to analyze the models. The development of these methods is also included, providing a self-contained presentation. To reinforce and supplement the material introduced, original problem sets are offered involving case studies closely related to the ones presented. With this style, the text’s perspective, scope, and completeness of the subject matter are considered unique. Having grown out of four self-contained courses taught by the authors, this text will be of use in a two-semester sequence for advanced undergraduate and beginning graduate students, requiring rudimentary knowledge of advanced calculus and differential equations, along with a basic understanding of some simple physical and biological scientific principles. .
Rancic, Milica
2016-01-01
This book highlights the latest advances in engineering mathematics with a main focus on the mathematical models, structures, concepts, problems and computational methods and algorithms most relevant for applications in modern technologies and engineering. It addresses mathematical methods of algebra, applied matrix analysis, operator analysis, probability theory and stochastic processes, geometry and computational methods in network analysis, data classification, ranking and optimisation. The individual chapters cover both theory and applications, and include a wealth of figures, schemes, algorithms, tables and results of data analysis and simulation. Presenting new methods and results, reviews of cutting-edge research, and open problems for future research, they equip readers to develop new mathematical methods and concepts of their own, and to further compare and analyse the methods and results discussed. The book consists of contributed chapters covering research developed as a result of a focused interna...
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 CP AM 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): (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; (2) Partial Differential Equations - The technical scope of this theme is the applied mathematics and numerical solution of partial
DISCRETE FIXED POINT THEOREMS AND THEIR APPLICATION TO NASH EQUILIBRIUM
Sato, Junichi; Kawasaki, Hidefumi
2007-01-01
Fixed point theorems are powerful tools in not only mathematics but also economic. In some economic problems, we need not real-valued but integer-valued equilibriums. However, classical fixed point theorems guarantee only real-valued equilibria. So we need discrete fixed point theorems in order to get discrete equilibria. In this paper, we first provide discrete fixed point theorems, next apply them to a non-cooperative game and prove the existence of a Nash equilibrium of pure strategies.
Bianchi, M.P.
1991-01-01
The discrete Boltzmann equation is a mathematical model in the kinetic theory of gases which defines the time and space evolution of a system of gas particles with a finite number of selected velocities. Discrete kinetic theory is an interesting field of research in mathematical physics and applied mathematics for several reasons. One of the relevant fields of application of the discrete Boltzmann equation is the analysis of nonlinear shock wave phenomena. Here, a new multiple collision regular plane model for binary gas mixtures is proposed within the discrete theory of gases and applied to the analysis of the classical problems of shock wave propagation
1992-01-01
Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, fluid mechanics including fluid dynamics, acoustics, and combustion, aerodynamics, and computer science during the period 1 Apr. 1992 - 30 Sep. 1992 is summarized.
Lorente, M.
2003-01-01
We explore the mathematical consequences of the assumption of a discrete space-time. The fundamental laws of physics have to be translated into the language of discrete mathematics. We find integral transformations that leave the lattice of any dimension invariant and apply these transformations to field equations.
Ayal, Carolina S.; Kusuma, Yaya S.; Sabandar, Jozua; Dahlan, Jarnawi Afgan
2016-01-01
Mathematical reasoning ability, are component that must be governable by the student. Mathematical reasoning plays an important role, both in solving problems and in conveying ideas when learning mathematics. In fact there ability are not still developed well, even in middle school. The importance of mathematical reasoning ability (KPM are…
Radiative transfer on discrete spaces
Preisendorfer, Rudolph W; Stark, M; Ulam, S
1965-01-01
Pure and Applied Mathematics, Volume 74: Radiative Transfer on Discrete Spaces presents the geometrical structure of natural light fields. This book describes in detail with mathematical precision the radiometric interactions of light-scattering media in terms of a few well established principles.Organized into four parts encompassing 15 chapters, this volume begins with an overview of the derivations of the practical formulas and the arrangement of formulas leading to numerical solution procedures of radiative transfer problems in plane-parallel media. This text then constructs radiative tran
[Geometry, analysis, and computation in mathematics and applied science]. Progress report
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.
Troldborg, Niels; Sørensen, Niels N.; Réthoré, Pierre-Elouan
2015-01-01
This paper describes a consistent algorithm for eliminating the numerical wiggles appearing when solving the finite volume discretized Navier-Stokes equations with discrete body forces in a collocated grid arrangement. The proposed method is a modification of the Rhie-Chow algorithm where the for...
Proceedings – Mathematical Sciences | Indian Academy of Sciences
Home; Journals; Proceedings – Mathematical Sciences; Volume 123; Issue 2. Notes on Discrete Subgroups of Möbius Transformations ... Department of Applied Mathematics, Hunan University, Changsha 410082, People's Republic of China; School of Mathematics and Computational Science, Wuyi University, Jiangmen, ...
Novikova, V.; Nikolaeva, O.
2017-11-01
In the article the authors consider a cognitive management method of the investment-building complex in the crisis conditions. The factors influencing the choice of an investment strategy are studied, the basic lines of the activity in the field of crisis-management from a position of mathematical modelling are defined. The general approach to decision-making on investment in real assets on the basis of the discrete systems based on the optimum control theory is offered. With the use of a discrete maximum principle the task in view of the decision is found. The numerical algorithm to define the optimum control is formulated by investments. Analytical decisions for the case of constant profitability of the basic means are obtained.
Mathematical Model and Artificial Intelligent Techniques Applied to a Milk Industry through DSM
Babu, P. Ravi; Divya, V. P. Sree
2011-08-01
The resources for electrical energy are depleting and hence the gap between the supply and the demand is continuously increasing. Under such circumstances, the option left is optimal utilization of available energy resources. The main objective of this chapter is to discuss about the Peak load management and overcome the problems associated with it in processing industries such as Milk industry with the help of DSM techniques. The chapter presents a generalized mathematical model for minimizing the total operating cost of the industry subject to the constraints. The work presented in this chapter also deals with the results of application of Neural Network, Fuzzy Logic and Demand Side Management (DSM) techniques applied to a medium scale milk industrial consumer in India to achieve the improvement in load factor, reduction in Maximum Demand (MD) and also the consumer gets saving in the energy bill.
Thomas Heckelei
2012-05-01
Full Text Available This paper reviews and discusses the more recent literature and application of Positive Mathematical Programming in the context of agricultural supply models. Specifically, advances in the empirical foundation of parameter specifications as well as the economic rationalisation of PMP models – both criticized in earlier reviews – are investigated. Moreover, the paper provides an overview on a larger set of models with regular/repeated policy application that apply variants of PMP. Results show that most applications today avoid arbitrary parameter specifications and rely on exogenous information on supply responses to calibrate model parameters. However, only few approaches use multiple observations to estimate parameters, which is likely due to the still considerable technical challenges associated with it. Equally, we found only limited reflection on the behavioral or technological assumptions that could rationalise the PMP model structure while still keeping the model’s advantages.
Kohaupt, Ludwig
2015-01-01
The discrete Fourier series is a valuable tool developed and used by mathematicians and engineers alike. One of the most prominent applications is signal processing. Usually, it is important that the signals be transmitted fast, for example, when transmitting images over large distances such as between the moon and the earth or when generating…
Samejima, Fumiko
In latent trait theory the latent space, or space of the hypothetical construct, is usually represented by some unidimensional or multi-dimensional continuum of real numbers. Like the latent space, the item response can either be treated as a discrete variable or as a continuous variable. Latent trait theory relates the item response to the latent…
LeMesurier, Brenton
2012-01-01
A new approach is described for generating exactly energy-momentum conserving time discretizations for a wide class of Hamiltonian systems of DEs with quadratic momenta, including mechanical systems with central forces; it is well-suited in particular to the large systems that arise in both spatial discretizations of nonlinear wave equations and lattice equations such as the Davydov System modeling energetic pulse propagation in protein molecules. The method is unconditionally stable, making it well-suited to equations of broadly “Discrete NLS form”, including many arising in nonlinear optics. Key features of the resulting discretizations are exact conservation of both the Hamiltonian and quadratic conserved quantities related to continuous linear symmetries, preservation of time reversal symmetry, unconditional stability, and respecting the linearity of certain terms. The last feature allows a simple, efficient iterative solution of the resulting nonlinear algebraic systems that retain unconditional stability, avoiding the need for full Newton-type solvers. One distinction from earlier work on conservative discretizations is a new and more straightforward nearly canonical procedure for constructing the discretizations, based on a “discrete gradient calculus with product rule” that mimics the essential properties of partial derivatives. This numerical method is then used to study the Davydov system, revealing that previously conjectured continuum limit approximations by NLS do not hold, but that sech-like pulses related to NLS solitons can nevertheless sometimes arise.
Lozi, René; Siddiqi, Abul
2017-01-01
The book discusses essential topics in industrial and applied mathematics such as image processing with a special focus on medical imaging, biometrics and tomography. Applications of mathematical concepts to areas like national security, homeland security and law enforcement, enterprise and e-government services, personal information and business transactions, and brain-like computers are also highlighted. These contributions – all prepared by respected academicians, scientists and researchers from across the globe – are based on papers presented at the international conference organized on the occasion of the Silver Jubilee of the Indian Society of Industrial and Applied Mathematics (ISIAM) held from 29 to 31 January 2016 at Sharda University, Greater Noida, India. The book will help young scientists and engineers grasp systematic developments in those areas of mathematics that are essential to properly understand challenging contemporary problems.
Nash, Jr, John Forbes
2016-01-01
The goal in putting together this unique compilation was to present the current status of the solutions to some of the most essential open problems in pure and applied mathematics. Emphasis is also given to problems in interdisciplinary research for which mathematics plays a key role. This volume comprises highly selected contributions by some of the most eminent mathematicians in the international mathematical community on longstanding problems in very active domains of mathematical research. A joint preface by the two volume editors is followed by a personal farewell to John F. Nash, Jr. written by Michael Th. Rassias. An introduction by Mikhail Gromov highlights some of Nash’s legendary mathematical achievements. The treatment in this book includes open problems in the following fields: algebraic geometry, number theory, analysis, discrete mathematics, PDEs, differential geometry, topology, K-theory, game theory, fluid mechanics, dynamical systems and ergodic theory, cryptography, theoretical computer sc...
Eringen, A Cemal
2013-01-01
Continuum Physics: Volume 1 - Mathematics is a collection of papers that discusses certain selected mathematical methods used in the study of continuum physics. Papers in this collection deal with developments in mathematics in continuum physics and its applications such as, group theory functional analysis, theory of invariants, and stochastic processes. Part I explains tensor analysis, including the geometry of subspaces and the geometry of Finsler. Part II discusses group theory, which also covers lattices, morphisms, and crystallographic groups. Part III reviews the theory of invariants th
Teachers' Views of the Challenges of Teaching Grade 9 Applied Mathematics in Toronto Schools
Stoilescu, Dorian; McDougall, Douglas; Egodawatte, Gunawardena
2016-01-01
Mathematics teachers, mathematics department heads, curriculum leaders, and administrators from 11 schools in four school boards from Toronto, Ontario, Canada, participated in a project to improve the teaching and learning in grade 9 mathematics classrooms. In each of these schools, an implementation team was created, so that at least three…
Validity of the Cauchy-Born rule applied to discrete cellular-scale models of biological tissues
Davit, Y.; Osborne, J. M.; Byrne, H. M.; Gavaghan, D.; Pitt-Francis, J.
2013-01-01
The development of new models of biological tissues that consider cells in a discrete manner is becoming increasingly popular as an alternative to continuum methods based on partial differential equations, although formal relationships between
Patahuddin, Sitti Maesuri; Puteri, Indira; Lowrie, Tom; Logan, Tracy; Rika, Baiq
2018-04-01
This study examined student mathematical engagement through the intended and enacted lessons taught by two teachers in two different middle schools in Indonesia. The intended lesson was developed using the ELPSA learning design to promote mathematical engagement. Based on the premise that students will react to the mathematical tasks in the forms of words and actions, the analysis focused on identifying the types of mathematical engagement promoted through the intended lesson and performed by students during the lesson. Using modified Watson's analytical tool (2007), students' engagement was captured from what the participants' did or said mathematically. We found that teachers' enacted practices had an influence on student mathematical engagement. The teacher who demonstrated content in explicit ways tended to limit the richness of the engagement; whereas the teacher who presented activities in an open-ended manner fostered engagement.
Stein, Sherman K
2010-01-01
Anyone can appreciate the beauty, depth, and vitality of mathematics with the help of this highly readable text, specially developed from a college course designed to appeal to students in a variety of fields. Readers with little mathematical background are exposed to a broad range of subjects chosen from number theory, topology, set theory, geometry, algebra, and analysis. Starting with a survey of questions on weight, the text discusses the primes, the fundamental theorem of arithmetic, rationals and irrationals, tiling, tiling and electricity, probability, infinite sets, and many other topi
Albert Corominas
Full Text Available A non-linear discrete-time mathematical program model is proposed to determining the optimal extraction policy for a single primary supplier of a durable non-renewable resource, such as gemstones or some metals. Karush, Kuhn and Tucker conditions allow obtaining analytic solutions and general properties of them in some specific settings. Moreover, provided that the objective function (i.e., the discounted value of the incomes throughout the planning horizon is concave, the model can be easily solved, even using standard commercial solver. However, the analysis of the solutions obtained for different assumptions of the values of the parameters show that the optimal extraction policies and the corresponding prices do not exhibit a general shape. Keywords: Durable non-renewable resources, Single primary supplier, Non-linear programming
Demazure, M.
1988-01-01
The 1988 progress report of the Mathematics center (Polytechnic School, France), is presented. The Center is composed of different research teams: analysis, Riemann geometry, group theory, formal calculus and algorithm geometry, dynamical systems, topology and singularity. For each team, the members, the research topics, the national and international cooperations, are given. The papers concerning the investigations carried out in 1988, are listed [fr
Applied & Computational MathematicsChallenges for the Design and Control of Dynamic Energy Systems
Brown, D L; Burns, J A; Collis, S; Grosh, J; Jacobson, C A; Johansen, H; Mezic, I; Narayanan, S; Wetter, M
2011-03-10
The Energy Independence and Security Act of 2007 (EISA) was passed with the goal 'to move the United States toward greater energy independence and security.' Energy security and independence cannot be achieved unless the United States addresses the issue of energy consumption in the building sector and significantly reduces energy consumption in buildings. Commercial and residential buildings account for approximately 40% of the U.S. energy consumption and emit 50% of CO{sub 2} emissions in the U.S. which is more than twice the total energy consumption of the entire U.S. automobile and light truck fleet. A 50%-80% improvement in building energy efficiency in both new construction and in retrofitting existing buildings could significantly reduce U.S. energy consumption and mitigate climate change. Reaching these aggressive building efficiency goals will not happen without significant Federal investments in areas of computational and mathematical sciences. Applied and computational mathematics are required to enable the development of algorithms and tools to design, control and optimize energy efficient buildings. The challenge has been issued by the U.S. Secretary of Energy, Dr. Steven Chu (emphasis added): 'We need to do more transformational research at DOE including computer design tools for commercial and residential buildings that enable reductions in energy consumption of up to 80 percent with investments that will pay for themselves in less than 10 years.' On July 8-9, 2010 a team of technical experts from industry, government and academia were assembled in Arlington, Virginia to identify the challenges associated with developing and deploying newcomputational methodologies and tools thatwill address building energy efficiency. These experts concluded that investments in fundamental applied and computational mathematics will be required to build enabling technology that can be used to realize the target of 80% reductions in energy
Applying Mathematical Concepts with Hands-On, Food-Based Science Curriculum
Roseno, Ashley T.; Carraway-Stage, Virginia G.; Hoerdeman, Callan; Díaz, Sebastián R.; Geist, Eugene; Duffrin, Melani W.
2015-01-01
This article addresses the current state of the mathematics education system in the United States and provides a possible solution to the contributing issues. As a result of lower performance in primary mathematics, American students are not acquiring the necessary quantitative literacy skills to become successful adults. This study analyzed the…
Applying Realistic Mathematics Education (RME) in teaching geometry in Indonesian primary schools
Fauzan, Ahmad
2002-01-01
Similar to other countries (see for example Niss, 1996; NCTM, 2000), the mathematics curriculum for primary schools in Indonesia pays much attention to several important aspects such as developing pupils' reasoning, activity, creativity and attitude, and providing pupils with mathematics skills so
Huseby, Arne B.; Natvig, Bent
2013-01-01
Discrete event models are frequently used in simulation studies to model and analyze pure jump processes. A discrete event model can be viewed as a system consisting of a collection of stochastic processes, where the states of the individual processes change as results of various kinds of events occurring at random points of time. We always assume that each event only affects one of the processes. Between these events the states of the processes are considered to be constant. In the present paper we use discrete event simulation in order to analyze a multistate network flow system of repairable components. In order to study how the different components contribute to the system, it is necessary to describe the often complicated interaction between component processes and processes at the system level. While analytical considerations may throw some light on this, a simulation study often allows the analyst to explore more details. By producing stable curve estimates for the development of the various processes, one gets a much better insight in how such systems develop over time. These methods are particulary useful in the study of advanced importancez measures of repairable components. Such measures can be very complicated, and thus impossible to calculate analytically. By using discrete event simulations, however, this can be done in a very natural and intuitive way. In particular significant differences between the Barlow–Proschan measure and the Natvig measure in multistate network flow systems can be explored
Vincent, Jill; Stacey, Kaye
2008-04-01
Australian eighth-grade mathematics lessons were shown by the 1999 TIMSS Video Study to use a high proportion of problems of low procedural complexity, with considerable repetition, and an absence of deductive reasoning. Using definitions from the Video Study, this study re-investigated this `shallow teaching syndrome' by examining the problems on three topics in nine eighth-grade textbooks from four Australian states for procedural complexity, type of solving processes, degree of repetition, proportion of `application' problems and proportion of problems requiring deductive reasoning. Overall, there was broad similarity between the characteristics of problems in the textbooks and in the Australian Video Study lessons. There were, however, considerable differences between textbooks and between topics within textbooks. In some books, including the best-selling textbooks in several states, the balance is too far towards repetitive problems of low procedural complexity.
Discrete Curvatures and Discrete Minimal Surfaces
Sun, Xiang
2012-06-01
This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.
Akimov Pavel
2016-01-01
Full Text Available The distinctive paper is devoted to the two-dimensional semi-analytical solution of boundary problems of analysis of shear walls with the use of discrete-continual finite element method (DCFEM. This approach allows obtaining the exact analytical solution in one direction (so-called “basic” direction, also decrease the size of the problem to one-dimensional common finite element analysis. The resulting multipoint boundary problem for the first-order system of ordinary differential equations with piecewise constant coefficients is solved analytically. The proposed method is rather efficient for evaluation of the boundary effect (such as the stress field near the concentrated force. DCFEM also has a completely computer-oriented algorithm, computational stability, optimal conditionality of resultant system and it is applicable for the various loads at an arbitrary point or a region of the wall.
Izadi, F A; Bagirov, G
2009-01-01
With its origins stretching back several centuries, discrete calculus is now an increasingly central methodology for many problems related to discrete systems and algorithms. The topics covered here usually arise in many branches of science and technology, especially in discrete mathematics, numerical analysis, statistics and probability theory as well as in electrical engineering, but our viewpoint here is that these topics belong to a much more general realm of mathematics; namely calculus and differential equations because of the remarkable analogy of the subject to this branch of mathemati
Proceedings – Mathematical Sciences | Indian Academy of Sciences
The discreteness of isometry groups in complex hyperbolic space is a fundamental problem. In this paper, the discreteness criteria of a -dimensional subgroup of S U ( n , 1 ) are investigated by using a test map which may not be in . Author Affiliations. Huani Qin1 2 Yueping Jiang1. College of Applied Mathematics, ...
Luther, Kenneth H.
2012-01-01
Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…
Using LabVIEW for Applying Mathematical Models in Representing Phenomena
Faraco, G.; Gabriele, L.
2007-01-01
Simulations make it possible to explore physical and biological phenomena, where conducting the real experiment is impracticable or difficult. The implementation of a software program describing and simulating a given physical situation encourages the understanding of a phenomenon itself. Fifty-nine students, enrolled at the Mathematical Methods…
Developing digital technologies for university mathematics by applying participatory design methods
Triantafyllou, Eva; Timcenko, Olga
2013-01-01
This paper presents our research efforts to develop digital technologies for undergraduate university mathematics. We employ participatory design methods in order to involve teachers and students in the design of such technologies. The results of the first round of our design are included...
Verschaffel, Lieven; Van Dooren, W.; Star, J.
2017-01-01
This special issue comprises contributions that address the breadth of current lines of recent research from cognitive psychology that appear promising for positively impacting students' learning of mathematics. More specifically, we included contributions (a) that refer to cognitive psychology based principles and techniques, such as explanatory…
Mathematical and Computational Aspects Related to Soil Modeling and Simulation
2017-09-26
and simulation challenges at the interface of applied math (homogenization, handling of discontinuous behavior, discrete vs. continuum representations...topics: a) Visco-elasto-plastic continuum models of geo-surface materials b) Discrete models of geo-surface materials (rocks/gravel/sand) c) Mixed...continuum- discrete representations. Coarse-graining and fine-graining mathematical formulations d) Multi-physics aspects related to the modeling of
Esther W de Bekker-Grob
Full Text Available To improve the information for and preparation of citizens at risk to hazardous material transport accidents, a first important step is to determine how different characteristics of hazardous material transport accidents will influence citizens' protective behaviour. However, quantitative studies investigating citizens' protective behaviour in case of hazardous material transport accidents are scarce.A discrete choice experiment was conducted among subjects (19-64 years living in the direct vicinity of a large waterway. Scenarios were described by three transport accident characteristics: odour perception, smoke/vapour perception, and the proportion of people in the environment that were leaving at their own discretion. Subjects were asked to consider each scenario as realistic and to choose the alternative that was most appealing to them: staying, seeking shelter, or escaping. A panel error component model was used to quantify how different transport accident characteristics influenced subjects' protective behaviour.The response was 44% (881/1,994. The predicted probability that a subject would stay ranged from 1% in case of a severe looking accident till 62% in case of a mild looking accident. All three transport accident characteristics proved to influence protective behaviour. Particularly a perception of strong ammonia or mercaptan odours and visible smoke/vapour close to citizens had the strongest positive influence on escaping. In general, 'escaping' was more preferred than 'seeking shelter', although stated preference heterogeneity among subjects for these protective behaviour options was substantial. Males were less willing to seek shelter than females, whereas elderly people were more willing to escape than younger people.Various characteristics of transport accident involving hazardous materials influence subjects' protective behaviour. The preference heterogeneity shows that information needs to be targeted differently depending on
On approximation of Lie groups by discrete subgroups
1Department of Mathematics, Faculty of Sciences at Sfax, University of Sfax,. Route Soukra ... Let S (G) denote the space of discrete co-compact subgroup of a Lie group G. We ..... For example, it suffices to apply the following fact: The mapping.
Spaces of fractional quotients, discrete operators, and their applications. II
Lifanov, I K; Poltavskii, L N
1999-01-01
The theory of discrete operators in spaces of fractional quotients is developed. A theorem on the stability of discrete operators under smooth perturbations is proved. On this basis, using special quadrature formulae of rectangular kind, the convergence of approximate solutions of hypersingular integral equations to their exact solutions is demonstrated and a mathematical substantiation of the method of closed discrete vortex frameworks is obtained. The same line of argument is also applied to difference equations arising in the solution of the homogeneous Dirichlet problem for a general second-order elliptic equation with variable coefficients
Firth, Jean M
1992-01-01
The analysis of signals and systems using transform methods is a very important aspect of the examination of processes and problems in an increasingly wide range of applications. Whereas the initial impetus in the development of methods appropriate for handling discrete sets of data occurred mainly in an electrical engineering context (for example in the design of digital filters), the same techniques are in use in such disciplines as cardiology, optics, speech analysis and management, as well as in other branches of science and engineering. This text is aimed at a readership whose mathematical background includes some acquaintance with complex numbers, linear differen tial equations, matrix algebra, and series. Specifically, a familiarity with Fourier series (in trigonometric and exponential forms) is assumed, and an exposure to the concept of a continuous integral transform is desirable. Such a background can be expected, for example, on completion of the first year of a science or engineering degree cour...
Mathematical models applied to the Cr(III) and Cr(VI) breakthrough curves.
Ramirez C, Margarita; Pereira da Silva, Mônica; Ferreira L, Selma G; Vasco E, Oscar
2007-07-19
Trivalent and hexavalent chromium continuous biosorption was studied using residual brewer Saccharomyces cerevisiae immobilized in volcanic rock. The columns used in the process had a diameter of 4.5 cm and a length of 140 cm, working at an inlet flow rate of 15 mL/min. Breakthrough curves were used to study the yeast biosorption behavior in the process. The saturation time (ts) was 21 and 45 h for Cr(III) and Cr(VI), respectively, and a breakthrough time (tb) of 4 h for Cr(III) and 5 h for Cr(VI). The uptake capacity of the biosorbent for Cr(III) and Cr(VI) were 48 and 60 mg/g, respectively. Two non-diffusional mathematical models with parameters t0 and sigma were used to adjust the experimental data obtained. Microsoft Excel tools were used for the mathematical solution of the two parameters used.
Jumpatong, Sutthaya; Yuenyong, Chokchai
2018-01-01
STEM education suggested that students should be enhanced to learn science with integration between Science, Technology, Engineering and Mathematics. To help Thai students make sense of relationship between Science, Technology, Engineering and Mathematics, this paper presents learning activities of STS Sound Pollution. The developing of STS Sound Pollution is a part of research that aimed to enhance students' perception of the relationship between Science Technology Engineering and Mathematics. This paper will discuss how to develop Sound Pollution through STS approach in framework of Yuenyong (2006) where learning activities were provided based on 5 stages. These included (1) identification of social issues, (2) identification of potential solutions, (3) need for knowledge, (4) decisionmaking, and (5) socialization stage. The learning activities could be highlighted as following. First stage, we use video clip of `Problem of people about Sound Pollution'. Second stage, students will need to identification of potential solutions by design Home/Factory without noisy. The need of scientific and other knowledge will be proposed for various alternative solutions. Third stage, students will gain their scientific knowledge through laboratory and demonstration of sound wave. Fourth stage, students have to make decision for the best solution of designing safety Home/Factory based on their scientific knowledge and others (e.g. mathematics, economics, art, value, and so on). Finally, students will present and share their Design Safety Home/Factory in society (e.g. social media or exhibition) in order to validate their ideas and redesigning. The paper, then, will discuss how those activities would allow students' applying knowledge of science technology engineering, mathematics and others (art, culture and value) for their possible solution of the STS issues.
建构主义教学法在离散数学教学中的应用初探%Application of Constructivism Teaching Method in Discrete Ma-thematics
刘峰; 唐存琛
2016-01-01
以建构主义教学理论为依据，采用抛锚方式应用于高校离散数学教学实践。通过对三个不同年级的跟踪实验，总结出建构主义教学法在离散数学教学中的优势。%The constructivism is introduced into Discrete Mathema-tics in this paper, which use the anchor teaching method to present the teaching contents. It is concluded that the constructivism theory can perform well in Discrete Mathematics by three experiments on diff erent grades.
Klerman, Elizabeth B; Beckett, Scott A; Landrigan, Christopher P
2016-09-13
In 2011 the U.S. Accreditation Council for Graduate Medical Education began limiting first year resident physicians (interns) to shifts of ≤16 consecutive hours. Controversy persists regarding the effectiveness of this policy for reducing errors and accidents while promoting education and patient care. Using a mathematical model of the effects of circadian rhythms and length of time awake on objective performance and subjective alertness, we quantitatively compared predictions for traditional intern schedules to those that limit work to ≤ 16 consecutive hours. We simulated two traditional schedules and three novel schedules using the mathematical model. The traditional schedules had extended duration work shifts (≥24 h) with overnight work shifts every second shift (including every third night, Q3) or every third shift (including every fourth night, Q4) night; the novel schedules had two different cross-cover (XC) night team schedules (XC-V1 and XC-V2) and a Rapid Cycle Rotation (RCR) schedule. Predicted objective performance and subjective alertness for each work shift were computed for each individual's schedule within a team and then combined for the team as a whole. Our primary outcome was the amount of time within a work shift during which a team's model-predicted objective performance and subjective alertness were lower than that expected after 16 or 24 h of continuous wake in an otherwise rested individual. The model predicted fewer hours with poor performance and alertness, especially during night-time work hours, for all three novel schedules than for either the traditional Q3 or Q4 schedules. Three proposed schedules that eliminate extended shifts may improve performance and alertness compared with traditional Q3 or Q4 schedules. Predicted times of worse performance and alertness were at night, which is also a time when supervision of trainees is lower. Mathematical modeling provides a quantitative comparison approach with potential to aid
Ioannis N. Mavridis
2017-12-01
Full Text Available The concept of stereotactically standard areas (SSAs within human brain nuclei belongs to the knowledge of the modern field of stereotactic brain microanatomy. These are areas resisting the individual variability of the nuclear location in stereotactic space. This paper summarizes the current knowledge regarding SSAs. A mathematical formula of SSAs was recently invented, allowing for their robust, reproducible, and accurate application to laboratory studies and clinical practice. Thus, SSAs open new doors for the application of stereotactic microanatomy to highly accurate brain targeting, which is mainly useful for minimally invasive neurosurgical procedures, such as deep brain stimulation.
Mavridis, Ioannis N
2017-12-11
The concept of stereotactically standard areas (SSAs) within human brain nuclei belongs to the knowledge of the modern field of stereotactic brain microanatomy. These are areas resisting the individual variability of the nuclear location in stereotactic space. This paper summarizes the current knowledge regarding SSAs. A mathematical formula of SSAs was recently invented, allowing for their robust, reproducible, and accurate application to laboratory studies and clinical practice. Thus, SSAs open new doors for the application of stereotactic microanatomy to highly accurate brain targeting, which is mainly useful for minimally invasive neurosurgical procedures, such as deep brain stimulation.
Dzierka, M.; Jurczak, P.
2015-12-01
In the paper, currently used methods for modeling the flow of the aqueous humor through eye structures are presented. Then a computational model based on rheological models of Newtonian and non-Newtonian fluids is proposed. The proposed model may be used for modeling the flow of the aqueous humor through the trabecular meshwork. The trabecular meshwork is modeled as an array of rectilinear parallel capillary tubes. The flow of Newtonian and non-Newtonian fluids is considered. As a results of discussion mathematical equations of permeability of porous media and velocity of fluid flow through porous media have been received.
Rhodes, Scott; Perez, Juan; Elborai, Shihab; Lee, Se-Hee; Zahn, Markus
2005-01-01
New flows and instabilities are presented for a ferrofluid drop contained in glass Hele-Shaw cells with simultaneously applied in-plane clockwise rotating and DC axial uniform magnetic fields. When a ferrofluid drop is stressed by a uniform DC axial magnetic field, up to ∼250 G in 0.9-1.4 mm gap Hele-Shaw cells, the drop forms a labyrinth pattern. With subsequent application of an in-plane uniform rotating magnetic field, up to ∼100 G rms at frequency 20-40 Hz, smooth spirals form from viscous shear due to ferrofluid flow. If the rotating magnetic field is applied first, the drop is held together without a labyrinth. Gradual increase of the DC axial magnetic field, to a critical magnetic field value, results in an abrupt phase transformation from a large drop to many small discrete droplets. A preliminary minimum magnetization and surface energy analysis is presented to model the phase transformation
Compatible Spatial Discretizations for Partial Differential Equations
Arnold, Douglas, N, ed.
2004-11-25
From May 11--15, 2004, the Institute for Mathematics and its Applications held a hot topics workshop on Compatible Spatial Discretizations for Partial Differential Equations. The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop was to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide variety of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic intrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE. Particular points of emphasis included: + Identification of intrinsic properties of PDE models that are critical for the fidelity of numerical
Herkül, Kristjan; Peterson, Anneliis; Paekivi, Sander
2017-06-01
Both basic science and marine spatial planning are in a need of high resolution spatially continuous data on seabed habitats and biota. As conventional point-wise sampling is unable to cover large spatial extents in high detail, it must be supplemented with remote sensing and modeling in order to fulfill the scientific and management needs. The combined use of in situ sampling, sonar scanning, and mathematical modeling is becoming the main method for mapping both abiotic and biotic seabed features. Further development and testing of the methods in varying locations and environmental settings is essential for moving towards unified and generally accepted methodology. To fill the relevant research gap in the Baltic Sea, we used multibeam sonar and mathematical modeling methods - generalized additive models (GAM) and random forest (RF) - together with underwater video to map seabed substrate and epibenthos of offshore shallows. In addition to testing the general applicability of the proposed complex of techniques, the predictive power of different sonar-based variables and modeling algorithms were tested. Mean depth, followed by mean backscatter, were the most influential variables in most of the models. Generally, mean values of sonar-based variables had higher predictive power than their standard deviations. The predictive accuracy of RF was higher than that of GAM. To conclude, we found the method to be feasible and with predictive accuracy similar to previous studies of sonar-based mapping.
Applying Mathematical Tools to Accelerate Vaccine Development: Modeling Shigella Immune Dynamics
Davis, Courtney L.; Wahid, Rezwanul; Toapanta, Franklin R.; Simon, Jakub K.
2013-01-01
We establish a mathematical framework for studying immune interactions with Shigella, a bacteria that kills over one million people worldwide every year. The long-term goal of this novel approach is to inform Shigella vaccine design by elucidating which immune components and bacterial targets are crucial for establishing Shigella immunity. Our delay differential equation model focuses on antibody and B cell responses directed against antigens like lipopolysaccharide in Shigella’s outer membrane. We find that antibody-based vaccines targeting only surface antigens cannot elicit sufficient immunity for protection. Additional boosting prior to infection would require a four-orders-of-magnitude increase in antibodies to sufficiently prevent epithelial invasion. However, boosting anti-LPS B memory can confer protection, which suggests these cells may correlate with immunity. We see that IgA antibodies are slightly more effective per molecule than IgG, but more total IgA is required due to spatial functionality. An extension of the model reveals that targeting both LPS and epithelial entry proteins is a promising avenue to advance vaccine development. This paper underscores the importance of multifaceted immune targeting in creating an effective Shigella vaccine. It introduces mathematical models to the Shigella vaccine development effort and lays a foundation for joint theoretical/experimental/clinical approaches to Shigella vaccine design. PMID:23589755
Applied Mathematics at the U.S. Department of Energy: Past, Present and a View to the Future
Brown, D.L; Bell, J.; Estep, D.; Gropp, W.; Hendrickson, B.; Keller-McNulty, S.; Keyes, D.; Oden, J.T.; Petzold, L.; Wright, M.
2008-01-01
Over the past half-century, the Applied Mathematics program in the U.S. Department of Energy's Office of Advanced Scientific Computing Research has made significant, enduring advances in applied mathematics that have been essential enablers of modern computational science. Motivated by the scientific needs of the Department of Energy and its predecessors, advances have been made in mathematical modeling, numerical analysis of differential equations, optimization theory, mesh generation for complex geometries, adaptive algorithms and other important mathematical areas. High-performance mathematical software libraries developed through this program have contributed as much or more to the performance of modern scientific computer codes as the high-performance computers on which these codes run. The combination of these mathematical advances and the resulting software has enabled high-performance computers to be used for scientific discovery in ways that could only be imagined at the program's inception. Our nation, and indeed our world, face great challenges that must be addressed in coming years, and many of these will be addressed through the development of scientific understanding and engineering advances yet to be discovered. The U.S. Department of Energy (DOE) will play an essential role in providing science-based solutions to many of these problems, particularly those that involve the energy, environmental and national security needs of the country. As the capability of high-performance computers continues to increase, the types of questions that can be answered by applying this huge computational power become more varied and more complex. It will be essential that we find new ways to develop and apply the mathematics necessary to enable the new scientific and engineering discoveries that are needed. In August 2007, a panel of experts in applied, computational and statistical mathematics met for a day and a half in Berkeley, California to understand the
Okuyama, Yoshifumi
2014-01-01
Discrete Control Systems establishes a basis for the analysis and design of discretized/quantized control systemsfor continuous physical systems. Beginning with the necessary mathematical foundations and system-model descriptions, the text moves on to derive a robust stability condition. To keep a practical perspective on the uncertain physical systems considered, most of the methods treated are carried out in the frequency domain. As part of the design procedure, modified Nyquist–Hall and Nichols diagrams are presented and discretized proportional–integral–derivative control schemes are reconsidered. Schemes for model-reference feedback and discrete-type observers are proposed. Although single-loop feedback systems form the core of the text, some consideration is given to multiple loops and nonlinearities. The robust control performance and stability of interval systems (with multiple uncertainties) are outlined. Finally, the monograph describes the relationship between feedback-control and discrete ev...
Operations research, engineering, and cyber security trends in applied mathematics and technology
Rassias, Themistocles
2017-01-01
Mathematical methods and theories with interdisciplinary applications are presented in this book. The eighteen contributions presented in this Work have been written by eminent scientists; a few papers are based on talks which took place at the International Conference at the Hellenic Artillery School in May 2015. Each paper evaluates possible solutions to long-standing problems such as the solvability of the direct electromagnetic scattering problem, geometric approaches to cyber security, ellipsoid targeting with overlap, non-equilibrium solutions of dynamic networks, measuring ballistic dispersion, elliptic regularity theory for the numerical solution of variational problems, approximation theory for polynomials on the real line and the unit circle, complementarity and variational inequalities in electronics, new two-slope parameterized achievement scalarizing functions for nonlinear multiobjective optimization, and strong and weak convexity of closed sets in a Hilbert space. Graduate students, scientists,...
6th World Conference on 21st Century Mathematics
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.
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 October 1, 1983 through March 31, 1984 is summarized.
1989-01-01
Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period October 1, 1988 through March 31, 1989 is summarized.
Mathematical methods for cancer evolution
Suzuki, Takashi
2017-01-01
The purpose of this monograph is to describe recent developments in mathematical modeling and mathematical analysis of certain problems arising from cell biology. Cancer cells and their growth via several stages are of particular interest. To describe these events, multi-scale models are applied, involving continuously distributed environment variables and several components related to particles. Hybrid simulations are also carried out, using discretization of environment variables and the Monte Carlo method for the principal particle variables. Rigorous mathematical foundations are the bases of these tools. The monograph is composed of four chapters. The first three chapters are concerned with modeling, while the last one is devoted to mathematical analysis. The first chapter deals with molecular dynamics occurring at the early stage of cancer invasion. A pathway network model based on a biological scenario is constructed, and then its mathematical structures are determined. In the second chapter mathematica...
Implementation of quantum and classical discrete fractional Fourier transforms
Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N.; Szameit, Alexander
2016-01-01
Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools. PMID:27006089
Implementation of quantum and classical discrete fractional Fourier transforms.
Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N; Szameit, Alexander
2016-03-23
Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.
Panagiotakopoulos, Chris T.
2011-01-01
Mathematics is an area of study that particularly lacks student enthusiasm. Nevertheless, with the help of educational games, any phobias concerning mathematics can be considerably decreased and mathematics can become more appealing. In this study, an educational game addressing mathematics was designed, developed and evaluated by a sample of 33…
Anton, Jose M.; Grau, Juan B.; Tarquis, Ana M.; Sanchez, Elena; Andina, Diego
2014-05-01
The authors were involved in the use of some Mathematical Decision Models, MDM, to improve knowledge and planning about some large natural or administrative areas for which natural soils, climate, and agro and forest uses where main factors, but human resources and results were important, natural hazards being relevant. In one line they have contributed about qualification of lands of the Community of Madrid, CM, administrative area in centre of Spain containing at North a band of mountains, in centre part of Iberian plateau and river terraces, and also Madrid metropolis, from an official study of UPM for CM qualifying lands using a FAO model from requiring minimums of a whole set of Soil Science criteria. The authors set first from these criteria a complementary additive qualification, and tried later an intermediate qualification from both using fuzzy logic. The authors were also involved, together with colleagues from Argentina et al. that are in relation with local planners, for the consideration of regions and of election of management entities for them. At these general levels they have adopted multi-criteria MDM, used a weighted PROMETHEE, and also an ELECTRE-I with the same elicited weights for the criteria and data, and at side AHP using Expert Choice from parallel comparisons among similar criteria structured in two levels. The alternatives depend on the case study, and these areas with monsoon climates have natural hazards that are decisive for their election and qualification with an initial matrix used for ELECTRE and PROMETHEE. For the natural area of Arroyos Menores at South of Rio Cuarto town, with at North the subarea of La Colacha, the loess lands are rich but suffer now from water erosions forming regressive ditches that are spoiling them, and use of soils alternatives must consider Soil Conservation and Hydraulic Management actions. The use of soils may be in diverse non compatible ways, as autochthonous forest, high value forest, traditional
Boix, Macarena; Cantó, Begoña
2013-04-01
Accurate image segmentation is used in medical diagnosis since this technique is a noninvasive pre-processing step for biomedical treatment. In this work we present an efficient segmentation method for medical image analysis. In particular, with this method blood cells can be segmented. For that, we combine the wavelet transform with morphological operations. Moreover, the wavelet thresholding technique is used to eliminate the noise and prepare the image for suitable segmentation. In wavelet denoising we determine the best wavelet that shows a segmentation with the largest area in the cell. We study different wavelet families and we conclude that the wavelet db1 is the best and it can serve for posterior works on blood pathologies. The proposed method generates goods results when it is applied on several images. Finally, the proposed algorithm made in MatLab environment is verified for a selected blood cells.
Emer Bernal
2017-01-01
Full Text Available In this paper we are presenting a method using fuzzy logic for dynamic parameter adaptation in the imperialist competitive algorithm, which is usually known by its acronym ICA. The ICA algorithm was initially studied in its original form to find out how it works and what parameters have more effect upon its results. Based on this study, several designs of fuzzy systems for dynamic adjustment of the ICA parameters are proposed. The experiments were performed on the basis of solving complex optimization problems, particularly applied to benchmark mathematical functions. A comparison of the original imperialist competitive algorithm and our proposed fuzzy imperialist competitive algorithm was performed. In addition, the fuzzy ICA was compared with another metaheuristic using a statistical test to measure the advantage of the proposed fuzzy approach for dynamic parameter adaptation.
Михаил Юрьевич Чернышов
2013-12-01
Full Text Available A software complex (SC elaborated by the authors on the basis of the language LMPL and representing a software tool intended for synthesis of applied software models and meta-models constructed on the basis of mathematical programming (MP principles is described. LMPL provides for an explicit form of declarative representation of MP-models, presumes automatic constructing and transformation of models and the capability of adding external software packages. The following software versions of the SC have been implemented: 1 a SC intended for representing the process of choosing an optimal hydroelectric power plant model (on the principles of meta-modeling and 2 a SC intended for representing the logic-sense relations between the models of a set of discourse formations in the discourse meta-model.
Quotable Quotes in Mathematics
Lo, Bruce W. N.
1983-01-01
As a way to dispel negative feelings toward mathematics, a variety of quotations are given. They are categorized by: what mathematics is, mathematicians, mathematics and other disciplines, different areas of mathematics, mathematics and humor, applications of mathematics, and pure versus applied mathematics. (MNS)
Homogenization of discrete media
Pradel, F.; Sab, K.
1998-01-01
Material such as granular media, beam assembly are easily seen as discrete media. They look like geometrical points linked together thanks to energetic expressions. Our purpose is to extend discrete kinematics to the one of an equivalent continuous material. First we explain how we build the localisation tool for periodic materials according to estimated continuum medium type (classical Cauchy, and Cosserat media). Once the bridge built between discrete and continuum media, we exhibit its application over two bidimensional beam assembly structures : the honey comb and a structural reinforced variation. The new behavior is then applied for the simple plan shear problem in a Cosserat continuum and compared with the real discrete solution. By the mean of this example, we establish the agreement of our new model with real structures. The exposed method has a longer range than mechanics and can be applied to every discrete problems like electromagnetism in which relationship between geometrical points can be summed up by an energetic function. (orig.)
Linear Elastic Waves - Series: Cambridge Texts in Applied Mathematics (No. 26)
Harris, John G.
2001-10-01
Wave propagation and scattering are among the most fundamental processes that we use to comprehend the world around us. While these processes are often very complex, one way to begin to understand them is to study wave propagation in the linear approximation. This is a book describing such propagation using, as a context, the equations of elasticity. Two unifying themes are used. The first is that an understanding of plane wave interactions is fundamental to understanding more complex wave interactions. The second is that waves are best understood in an asymptotic approximation where they are free of the complications of their excitation and are governed primarily by their propagation environments. The topics covered include reflection, refraction, the propagation of interfacial waves, integral representations, radiation and diffraction, and propagation in closed and open waveguides. Linear Elastic Waves is an advanced level textbook directed at applied mathematicians, seismologists, and engineers. Aimed at beginning graduate students Includes examples and exercises Has application in a wide range of disciplines
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
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.
Patahuddin, Sitti Maesuri; Puteri, Indira; Lowrie, Tom; Logan, Tracy; Rika, Baiq
2018-01-01
This study examined student mathematical engagement through the intended and enacted lessons taught by two teachers in two different middle schools in Indonesia. The intended lesson was developed using the ELPSA learning design to promote mathematical engagement. Based on the premise that students will react to the mathematical tasks in the forms…
Handbook of mathematical methods in imaging
2015-01-01
The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. This expanded and revised second edition contains updates to existing chapters and 16 additional entries on important mathematical methods such as graph cuts, morphology, discrete geometry, PDEs, conformal methods, to name a few. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 200 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and com...
Lubis, Asrin; Nasution, Andrea Arifsyah
2017-01-01
Mathematical reasoning in logical context has now received much attention in the mathematics curriculum documents of many countries, including Indonesia. In Indonesia, students start formally learning about logic when they pursue to senior-high school. Before, they previously have many experiences to deal with logic, but the earlier assignments do…
Modern approaches to discrete curvature
Romon, Pascal
2017-01-01
This book provides a valuable glimpse into discrete curvature, a rich new field of research which blends discrete mathematics, differential geometry, probability and computer graphics. It includes a vast collection of ideas and tools which will offer something new to all interested readers. Discrete geometry has arisen as much as a theoretical development as in response to unforeseen challenges coming from applications. Discrete and continuous geometries have turned out to be intimately connected. Discrete curvature is the key concept connecting them through many bridges in numerous fields: metric spaces, Riemannian and Euclidean geometries, geometric measure theory, topology, partial differential equations, calculus of variations, gradient flows, asymptotic analysis, probability, harmonic analysis, graph theory, etc. In spite of its crucial importance both in theoretical mathematics and in applications, up to now, almost no books have provided a coherent outlook on this emerging field.
Principles of discrete time mechanics
Jaroszkiewicz, George
2014-01-01
Could time be discrete on some unimaginably small scale? Exploring the idea in depth, this unique introduction to discrete time mechanics systematically builds the theory up from scratch, beginning with the historical, physical and mathematical background to the chronon hypothesis. Covering classical and quantum discrete time mechanics, this book presents all the tools needed to formulate and develop applications of discrete time mechanics in a number of areas, including spreadsheet mechanics, classical and quantum register mechanics, and classical and quantum mechanics and field theories. A consistent emphasis on contextuality and the observer-system relationship is maintained throughout.
Dina Aleksandrovna Kirillova
2015-12-01
Full Text Available The modern reform of the Russian higher education involves the implementation of competence-based approach, the main idea of which is the practical orientation of education. Mathematics is a universal language of description, modeling and studies of phenomena and processes of different nature. Therefore creating the fund of assessment tools for mathematical disciplines based on the applied problems is actual. The case method is the most appropriate mean of monitoring the learning outcomes, it is aimed at bridging the gap between theory and practice.The aim of the research is the development of methodical materials for the creating the fund of assessment tools that are based on the case-study for the mathematical analisis for direction «Applied Mathematics and Computer Science». The aim follows from the contradiction between the need for the introduction of case-method in the educational process in high school and the lack of study of the theoretical foundations of using of this method as applied to mathematical disciplines, insufficient theoretical basis and the description of the process of creating case-problems for use their in the monitoring of the learning outcomes.
Discrete stochastic processes and applications
Collet, Jean-François
2018-01-01
This unique text for beginning graduate students gives a self-contained introduction to the mathematical properties of stochastics and presents their applications to Markov processes, coding theory, population dynamics, and search engine design. The book is ideal for a newly designed course in an introduction to probability and information theory. Prerequisites include working knowledge of linear algebra, calculus, and probability theory. The first part of the text focuses on the rigorous theory of Markov processes on countable spaces (Markov chains) and provides the basis to developing solid probabilistic intuition without the need for a course in measure theory. The approach taken is gradual beginning with the case of discrete time and moving on to that of continuous time. The second part of this text is more applied; its core introduces various uses of convexity in probability and presents a nice treatment of entropy.
Eraslan, A.H.
1975-02-01
A far-field mathematical model is presented for numerical simulation of short-time (within tidal cycle) transient, two-dimensional temperature distributions in large coastal and offshore regions resulting from the condenser cooling water discharges of power plants. The Eulerian FLIDE (fluid-in-discrete-element) formulation employs the integral forms of the conservation principles for mass and thermal energy in variable-sized discrete elements that span the specific flow region. The contributions of vertical variations of the velocity components and temperature are rigorously incorporated in the development of depth-averaged, two-dimensional energy transport fluxes by spatially integrating the conservation equations over the enclosure surfaces of the discrete elements. The general mathematical formulation considers completely arbitrary, transient oceanic flow conditions, which include periodic tidal, geostrophic, and wind-induced currents, as locally specified inputs to the model. The thermal impact of a hypothetical, multiunit generating station in a coastal region is analyzed where the oceanic flow conditions are assumed to be strictly periodic tidal currents within any appreciable net drift of sufficient duration to remove the heated effluent. The numerical simulation indicates that the periodic flow conditions cause considerable variations in the temperature distributions during the day and the tidal cycles, which result in severe recirculation and re-entrainment of the heated water between the intakes and the discharges of the different units. This leads to a gradual, long-term increase of the temperatures in the immediate vicinity of the discharge structures and also in the far-field zone. (U.S.)
Advances in discrete differential geometry
2016-01-01
This is one of the first books on a newly emerging field of discrete differential geometry and an excellent way to access this exciting area. It surveys the fascinating connections between discrete models in differential geometry and complex analysis, integrable systems and applications in computer graphics. The authors take a closer look at discrete models in differential geometry and dynamical systems. Their curves are polygonal, surfaces are made from triangles and quadrilaterals, and time is discrete. Nevertheless, the difference between the corresponding smooth curves, surfaces and classical dynamical systems with continuous time can hardly be seen. This is the paradigm of structure-preserving discretizations. Current advances in this field are stimulated to a large extent by its relevance for computer graphics and mathematical physics. This book is written by specialists working together on a common research project. It is about differential geometry and dynamical systems, smooth and discrete theories, ...
Discrete and computational geometry
Devadoss, Satyan L
2011-01-01
Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also fe...
Marrero-Ponce, Yovani; Santiago, Oscar Martínez; López, Yoan Martínez; Barigye, Stephen J; Torrens, Francisco
2012-11-01
In this report, we present a new mathematical approach for describing chemical structures of organic molecules at atomic-molecular level, proposing for the first time the use of the concept of the derivative ([Formula: see text]) of a molecular graph (MG) with respect to a given event (E), to obtain a new family of molecular descriptors (MDs). With this purpose, a new matrix representation of the MG, which generalizes graph's theory's traditional incidence matrix, is introduced. This matrix, denominated the generalized incidence matrix, Q, arises from the Boolean representation of molecular sub-graphs that participate in the formation of the graph molecular skeleton MG and could be complete (representing all possible connected sub-graphs) or constitute sub-graphs of determined orders or types as well as a combination of these. The Q matrix is a non-quadratic and unsymmetrical in nature, its columns (n) and rows (m) are conditions (letters) and collection of conditions (words) with which the event occurs. This non-quadratic and unsymmetrical matrix is transformed, by algebraic manipulation, to a quadratic and symmetric matrix known as relations frequency matrix, F, which characterizes the participation intensity of the conditions (letters) in the events (words). With F, we calculate the derivative over a pair of atomic nuclei. The local index for the atomic nuclei i, Δ(i), can therefore be obtained as a linear combination of all the pair derivatives of the atomic nuclei i with all the rest of the j's atomic nuclei. Here, we also define new strategies that generalize the present form of obtaining global or local (group or atom-type) invariants from atomic contributions (local vertex invariants, LOVIs). In respect to this, metric (norms), means and statistical invariants are introduced. These invariants are applied to a vector whose components are the values Δ(i) for the atomic nuclei of the molecule or its fragments. Moreover, with the purpose of differentiating
Nuclear data compression and reconstruction via discrete wavelet transform
Park, Young Ryong; Cho, Nam Zin [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)
1997-12-31
Discrete Wavelet Transforms (DWTs) are recent mathematics, and begin to be used in various fields. The wavelet transform can be used to compress the signal and image due to its inherent properties. We applied the wavelet transform compression and reconstruction to the neutron cross section data. Numerical tests illustrate that the signal compression using wavelet is very effective to reduce the data saving spaces. 7 refs., 4 figs., 3 tabs. (Author)
Nuclear data compression and reconstruction via discrete wavelet transform
Park, Young Ryong; Cho, Nam Zin [Korea Advanced Institute of Science and Technology, Taejon (Korea, Republic of)
1998-12-31
Discrete Wavelet Transforms (DWTs) are recent mathematics, and begin to be used in various fields. The wavelet transform can be used to compress the signal and image due to its inherent properties. We applied the wavelet transform compression and reconstruction to the neutron cross section data. Numerical tests illustrate that the signal compression using wavelet is very effective to reduce the data saving spaces. 7 refs., 4 figs., 3 tabs. (Author)
Mesiar, Radko; Li, J.; Pap, E.
2013-01-01
Roč. 54, č. 3 (2013), s. 357-364 ISSN 0888-613X R&D Projects: GA ČR GAP402/11/0378 Institutional support: RVO:67985556 Keywords : concave integral * pseudo-addition * pseudo-multiplication Subject RIV: BA - General Mathematics Impact factor: 1.977, year: 2013 http://library.utia.cas.cz/separaty/2013/E/mesiar-discrete pseudo-integrals.pdf
Dilemma in Teaching Mathematics
Md Kamaruddin, Nafisah Kamariah; Md Amin, Zulkarnain
2012-01-01
The challenge in mathematics education is finding the best way to teach mathematics. When students learn the reasoning and proving in mathematics, they will be proficient in mathematics. Students must know mathematics before they can apply it. Symbolism and logic is the key to both the learning of mathematics and its effective application to…
Kirschner, Paul A.; Verschaffel, Lieven; Star, Jon; Van Dooren, Wim
2018-01-01
In this interview we asked Paul A. Kirschner about his comments and reflections regarding the idea to apply cognitive psychology-based instructional design principles to mathematics education and some related issues. With a main focus on cognitive psychology, educational psychology, educational
Kirschner, Paul A.; Verschaffel, Lieven; Star, Jon; Van Dooren, Wim
2017-01-01
In this interview we asked Paul A. Kirschner about his comments and reflections regarding the idea to apply cognitive psychology-based instructional design principles to mathematics education and some related issues. With a main focus on cognitive psychology, educational psychology, educational technology and instructional design, this…
Busch, Peter Andre; Zinner Henriksen, Helle
2018-01-01
discretion is suggested to reduce this footprint by influencing or replacing their discretionary practices using ICT. What is less researched is whether digital discretion can cause changes in public policy outcomes, and under what conditions such changes can occur. Using the concept of public service values......This study reviews 44 peer-reviewed articles on digital discretion published in the period from 1998 to January 2017. Street-level bureaucrats have traditionally had a wide ability to exercise discretion stirring debate since they can add their personal footprint on public policies. Digital......, we suggest that digital discretion can strengthen ethical and democratic values but weaken professional and relational values. Furthermore, we conclude that contextual factors such as considerations made by policy makers on the macro-level and the degree of professionalization of street...
Algorithmic Principles of Mathematical Programming
Faigle, Ulrich; Kern, Walter; Still, Georg
2002-01-01
Algorithmic Principles of Mathematical Programming investigates the mathematical structures and principles underlying the design of efficient algorithms for optimization problems. Recent advances in algorithmic theory have shown that the traditionally separate areas of discrete optimization, linear
Lesik, Sally A.
2007-01-01
The impact of academic programs--such as developmental mathematics programs--on student retention, has been a controversial topic for administrators, policy makers, and faculty in higher education. Despite deep interest in the effectiveness of these programs in retaining students, scholars have been unable to determine whether such programs have a…
Dimbylow, Peter
2006-01-01
This paper describes the development of 2 mm resolution hybrid voxel-mathematical models of the pregnant female. Mathematical models of the developing foetus at 8-, 13-, 26- and 38-weeks of gestation were converted into voxels and combined with the adult female model, NAOMI. This set of models was used to calculate induced current densities and electric fields in the foetus from applied 50 Hz magnetic and electric fields. The influence of foetal tissue conductivities was investigated and implications for electromagnetic field guidelines discussed
Basu, Uma; De, Soumen
2015-01-01
The book is based on research presentations at the international conference, “Emerging Trends in Applied Mathematics: In the Memory of Sir Asutosh Mookerjee, S.N. Bose, M.N. Saha, and N.R. Sen”, held at the Department of Applied Mathematics, University of Calcutta, during 12–14 February 2014. It focuses on various emerging and challenging topics in the field of applied mathematics and theoretical physics. The book will be a valuable resource for postgraduate students at higher levels and researchers in applied mathematics and theoretical physics. Researchers presented a wide variety of themes in applied mathematics and theoretical physics—such as emergent periodicity in a field of chaos; Ricci flow equation and Poincare conjecture; Bose–Einstein condensation; geometry of local scale invariance and turbulence; statistical mechanics of human resource allocation: mathematical modelling of job-matching in labour markets; contact problem in elasticity; the Saha equation; computational fluid dynamics with...
Mathematical foundation of the optimization-based fluid animation method
Erleben, Kenny; Misztal, Marek Krzysztof; Bærentzen, Jakob Andreas
2011-01-01
We present the mathematical foundation of a fluid animation method for unstructured meshes. Key contributions not previously treated are the extension to include diffusion forces and higher order terms of non-linear force approximations. In our discretization we apply a fractional step method to ...
A Mathematics Software Database Update.
Cunningham, R. S.; Smith, David A.
1987-01-01
Contains an update of an earlier listing of software for mathematics instruction at the college level. Topics are: advanced mathematics, algebra, calculus, differential equations, discrete mathematics, equation solving, general mathematics, geometry, linear and matrix algebra, logic, statistics and probability, and trigonometry. (PK)
The origin of discrete particles
Bastin, T
2009-01-01
This book is a unique summary of the results of a long research project undertaken by the authors on discreteness in modern physics. In contrast with the usual expectation that discreteness is the result of mathematical tools for insertion into a continuous theory, this more basic treatment builds up the world from the discrimination of discrete entities. This gives an algebraic structure in which certain fixed numbers arise. As such, one agrees with the measured value of the fine-structure constant to one part in 10,000,000 (10 7 ). Sample Chapter(s). Foreword (56 KB). Chapter 1: Introduction
Siri, Benoît; Berry, Hugues; Cessac, Bruno; Delord, Bruno; Quoy, Mathias
2008-12-01
We present a mathematical analysis of the effects of Hebbian learning in random recurrent neural networks, with a generic Hebbian learning rule, including passive forgetting and different timescales, for neuronal activity and learning dynamics. Previous numerical work has reported that Hebbian learning drives the system from chaos to a steady state through a sequence of bifurcations. Here, we interpret these results mathematically and show that these effects, involving a complex coupling between neuronal dynamics and synaptic graph structure, can be analyzed using Jacobian matrices, which introduce both a structural and a dynamical point of view on neural network evolution. Furthermore, we show that sensitivity to a learned pattern is maximal when the largest Lyapunov exponent is close to 0. We discuss how neural networks may take advantage of this regime of high functional interest.
Exarchakis, Georgios; Lücke, Jörg
2017-11-01
Sparse coding algorithms with continuous latent variables have been the subject of a large number of studies. However, discrete latent spaces for sparse coding have been largely ignored. In this work, we study sparse coding with latents described by discrete instead of continuous prior distributions. We consider the general case in which the latents (while being sparse) can take on any value of a finite set of possible values and in which we learn the prior probability of any value from data. This approach can be applied to any data generated by discrete causes, and it can be applied as an approximation of continuous causes. As the prior probabilities are learned, the approach then allows for estimating the prior shape without assuming specific functional forms. To efficiently train the parameters of our probabilistic generative model, we apply a truncated expectation-maximization approach (expectation truncation) that we modify to work with a general discrete prior. We evaluate the performance of the algorithm by applying it to a variety of tasks: (1) we use artificial data to verify that the algorithm can recover the generating parameters from a random initialization, (2) use image patches of natural images and discuss the role of the prior for the extraction of image components, (3) use extracellular recordings of neurons to present a novel method of analysis for spiking neurons that includes an intuitive discretization strategy, and (4) apply the algorithm on the task of encoding audio waveforms of human speech. The diverse set of numerical experiments presented in this letter suggests that discrete sparse coding algorithms can scale efficiently to work with realistic data sets and provide novel statistical quantities to describe the structure of the data.
Triantafyllou, Eva; Timcenko, Olga
2013-01-01
As a result of changes in society and education, assumptions about the knowledge of entrants to university have become obsolete. One area in which this seems to be true is mathematics. This paper presents our research aiming at tackling with this problem by developing digital educational material...... for mathematics education, which will be student-driven, dynamic, and multimodal. Our approach will be supported by the theories of Constructionism and PBL. The impact of its use will be evaluated in university settings. It is expected that the evaluation will demonstrate an improvement in student engagement...
Handbook on modelling for discrete optimization
Pitsoulis, Leonidas; Williams, H
2006-01-01
The primary objective underlying the Handbook on Modelling for Discrete Optimization is to demonstrate and detail the pervasive nature of Discrete Optimization. While its applications cut across an incredibly wide range of activities, many of the applications are only known to specialists. It is the aim of this handbook to correct this. It has long been recognized that "modelling" is a critically important mathematical activity in designing algorithms for solving these discrete optimization problems. Nevertheless solving the resultant models is also often far from straightforward. In recent years it has become possible to solve many large-scale discrete optimization problems. However, some problems remain a challenge, even though advances in mathematical methods, hardware, and software technology have pushed the frontiers forward. This handbook couples the difficult, critical-thinking aspects of mathematical modeling with the hot area of discrete optimization. It will be done in an academic handbook treatment...
Aksu, Hasan Hüseyin
2014-01-01
This study aims to investigate, in terms of different variables, the views of prospective Mathematics teachers on tablet computers to be used in schools as an outcome of the Fatih Project, which was initiated by the Ministry of National Education. In the study, scanning model, one of the quantitative research methods, was used. In the population…
Hickendorff, Marian
2013-01-01
The results of an exploratory study into measurement of elementary mathematics ability are presented. The focus is on the abilities involved in solving standard computation problems on the one hand and problems presented in a realistic context on the other. The objectives were to assess to what extent these abilities are shared or distinct, and…
Chen, P. Daniel; Simpson, Patricia A.
2015-01-01
This study utilized John Holland's personality typology and the Social Cognitive Career Theory (SCCT) to examine the factors that may affect students' self-selection into science, technology, engineering, and mathematics (STEM) majors. Results indicated that gender, race/ethnicity, high school achievement, and personality type were statistically…
The Spectrum of Mathematical Models.
Karplus, Walter J.
1983-01-01
Mathematical modeling problems encountered in many disciplines are discussed in terms of the modeling process and applications of models. The models are classified according to three types of abstraction: continuous-space-continuous-time, discrete-space-continuous-time, and discrete-space-discrete-time. Limitations in different kinds of modeling…
Caltagirone, Jean-Paul
2014-01-01
This book presents the fundamental principles of mechanics to re-establish the equations of Discrete Mechanics. It introduces physics and thermodynamics associated to the physical modeling. The development and the complementarity of sciences lead to review today the old concepts that were the basis for the development of continuum mechanics. The differential geometry is used to review the conservation laws of mechanics. For instance, this formalism requires a different location of vector and scalar quantities in space. The equations of Discrete Mechanics form a system of equations where the H
Lee, T.D.
1985-01-01
This paper reviews the role of time throughout all phases of mechanics: classical mechanics, non-relativistic quantum mechanics, and relativistic quantum theory. As an example of the relativistic quantum field theory, the case of a massless scalar field interacting with an arbitrary external current is discussed. The comparison between the new discrete theory and the usual continuum formalism is presented. An example is given of a two-dimensional random lattice and its duel. The author notes that there is no evidence that the discrete mechanics is more appropriate than the usual continuum mechanics
Homogenization of discrete media
Pradel, F.; Sab, K. [CERAM-ENPC, Marne-la-Vallee (France)
1998-11-01
Material such as granular media, beam assembly are easily seen as discrete media. They look like geometrical points linked together thanks to energetic expressions. Our purpose is to extend discrete kinematics to the one of an equivalent continuous material. First we explain how we build the localisation tool for periodic materials according to estimated continuum medium type (classical Cauchy, and Cosserat media). Once the bridge built between discrete and continuum media, we exhibit its application over two bidimensional beam assembly structures : the honey comb and a structural reinforced variation. The new behavior is then applied for the simple plan shear problem in a Cosserat continuum and compared with the real discrete solution. By the mean of this example, we establish the agreement of our new model with real structures. The exposed method has a longer range than mechanics and can be applied to every discrete problems like electromagnetism in which relationship between geometrical points can be summed up by an energetic function. (orig.) 7 refs.
Positivity for Convective Semi-discretizations
Fekete, Imre; Ketcheson, David I.; Loczi, Lajos
2017-01-01
We propose a technique for investigating stability properties like positivity and forward invariance of an interval for method-of-lines discretizations, and apply the technique to study positivity preservation for a class of TVD semi-discretizations
Wuensche, Andrew
DDLab is interactive graphics software for creating, visualizing, and analyzing many aspects of Cellular Automata, Random Boolean Networks, and Discrete Dynamical Networks in general and studying their behavior, both from the time-series perspective — space-time patterns, and from the state-space perspective — attractor basins. DDLab is relevant to research, applications, and education in the fields of complexity, self-organization, emergent phenomena, chaos, collision-based computing, neural networks, content addressable memory, genetic regulatory networks, dynamical encryption, generative art and music, and the study of the abstract mathematical/physical/dynamical phenomena in their own right.
Jothi, A Lenin
2009-01-01
Financial services, particularly banking and insurance services is the prominent sector for the development of a nation. After the liberalisation of financial sector in India, the scope of getting career opportunities has been widened. It is heartening to note that various universities in India have introduced professional courses on banking and insurance. A new field of applied mathematics has come into prominence under the name of Financial Mathematics. Financial mathematics has attained much importance in the recent years because of the role played by mathematical concepts in decision - m
A necessary condition for dispersal driven growth of populations with discrete patch dynamics.
Guiver, Chris; Packman, David; Townley, Stuart
2017-07-07
We revisit the question of when can dispersal-induced coupling between discrete sink populations cause overall population growth? Such a phenomenon is called dispersal driven growth and provides a simple explanation of how dispersal can allow populations to persist across discrete, spatially heterogeneous, environments even when individual patches are adverse or unfavourable. For two classes of mathematical models, one linear and one non-linear, we provide necessary conditions for dispersal driven growth in terms of the non-existence of a common linear Lyapunov function, which we describe. Our approach draws heavily upon the underlying positive dynamical systems structure. Our results apply to both discrete- and continuous-time models. The theory is illustrated with examples and both biological and mathematical conclusions are drawn. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.
Mathematics without boundaries surveys in pure mathematics
Pardalos, Panos
2014-01-01
The contributions in this volume have been written by eminent scientists from the international mathematical community and present significant advances in several theories, methods and problems of Mathematical Analysis, Discrete Mathematics, Geometry and their Applications. The chapters focus on both old and recent developments in Functional Analysis, Harmonic Analysis, Complex Analysis, Operator Theory, Combinatorics, Functional Equations, Differential Equations as well as a variety of Applications. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical Sciences, and especially to graduate students looking for the latest information.
Lyudmyla Shishko
2016-01-01
Full Text Available The current state of formation of mathematical knowledge in universities insufficiently focused on their further use in professional activities. Students not formed the ability to apply mathematical knowledge to study general professional and special disciplines. In this article: –\tconsidered features of formation of a professional orientation of teaching mathematics using structured content multimedia information system for educational purposes (MISEP; –\tfound psychologo-pedagogical features of teaching mathematics of students IT specialties; –\tconsidered methodical aspects of MISEP in teaching the course "Discrete Mathematics" for students of IT specialties
Discrete Tomography and Imaging of Polycrystalline Structures
Alpers, Andreas
High resolution transmission electron microscopy is commonly considered as the standard application for discrete tomography. While this has yet to be technically realized, new applications with a similar flavor have emerged in materials science. In our group at Ris� DTU (Denmark's National...... Laboratory for Sustainable Energy), for instance, we study polycrystalline materials via synchrotron X-ray diffraction. Several reconstruction problems arise, most of them exhibit inherently discrete aspects. In this talk I want to give a concise mathematical introduction to some of these reconstruction...... problems. Special focus is on their relationship to classical discrete tomography. Several open mathematical questions will be mentioned along the way....
GENERAL TASKS OF MATHEMATICAL EDUCATION DEVELOPMENT
V. A. Testov
2014-01-01
Full Text Available The paper discusses basic implementation aspects of the Mathematical Education Development Concept, adopted by the Russian Government in 2013. According to the above document, the main problems of mathematical education include: low motivation of secondary and higher school students for studying the discipline, resulted from underestimation of mathematical knowledge; and outdated educational content, overloaded by technical elements. In the author’s opinion, a number of important new mathematical fields, developed over the last years, - the graph theory, discrete mathematics, encoding theory, fractal geometry, etc – have a large methodological and applied educational potential. However, these new subdisciplines have very little representation both in the secondary and higher school mathematical curricula. As a solution for overcoming the gap between the latest scientific achievements and pedagogical practices, the author recommends integration of the above mentioned mathematical disciplines in educational curricula instead of some outdated technical issues. In conclusion, the paper emphasizes the need for qualified mathematical teachers’ training for solving the problems of students’ motivation development and content updates.
Avilner Rafael Páez Pereira
2017-11-01
Full Text Available The purpose of the study was to train LB "José Véliz" teacher for the teaching of mathematics through the application of super-learning techniques, based on the Research Participatory Action modality, proposed by López de Ceballos, (2008, following the model of the Lewin cycles of action (1946, quoted by Latorre (2007, based on the theories of humanism, Martínez (2009; multiple intelligence, Armstrong (2006; the Super learning of Sambrano and Stainer, (2003. Within the framework of the Critical - Social paradigm, in the type Qualitative Research, a plan of approach to the group was made, where through brainstorming and informal interviews the main problems were listed, which were hierarchized and then carried out an awareness - raising process. formulation of an overall plan of action. Among the results were 6 training workshops on techniques of breathing, relaxation, aromatherapy, music therapy, positive programming, color in the classroom, song in mathematical algorithms, in which processes of reflection were established on the benefits or obstacles obtained in the application of these in the transformation of the educational reality, elaborating a didactic strategy product of the experiences reached.
Masiello, Emiliano; Martin, Brunella; Do, Jean-Michel
2011-01-01
A new development for the IDT solver is presented for large reactor core applications in XYZ geometries. The multigroup discrete-ordinate neutron transport equation is solved using a Domain-Decomposition (DD) method coupled with the Coarse-Mesh Finite Differences (CMFD). The later is used for accelerating the DD convergence rate. In particular, the external power iterations are preconditioned for stabilizing the oscillatory behavior of the DD iterative process. A set of critical 2-D and 3-D numerical tests on a single processor will be presented for the analysis of the performances of the method. The results show that the application of the CMFD to the DD can be a good candidate for large 3D full-core parallel applications. (author)
Non-Lipschitz Dynamics Approach to Discrete Event Systems
Zak, M.; Meyers, R.
1995-01-01
This paper presents and discusses a mathematical formalism for simulation of discrete event dynamics (DED) - a special type of 'man- made' system designed to aid specific areas of information processing. A main objective is to demonstrate that the mathematical formalism for DED can be based upon the terminal model of Newtonian dynamics which allows one to relax Lipschitz conditions at some discrete points.
Brunetti, Federico Alberto
2014-01-01
It will be soon presented to the public a new version of stereoscopic viewers designed for observing files and video projected images through a system of transparent optical prisms which allow the simultaneous perception of the surrounding environment. The real challenge for applied mathematics and visual design will be to prefigure how to use them and their applications, since these new devices can actually enable a deeper visual experience. A specific case study concerns the visualizations of the collisions at the LHC at CERN, selected to verify the traces of the boson theorized by Francois Englert and Peter Higgs, with Robert Brout, who recently (2013) received the Nobel Prize for their research.
Mesquita, C.H. de; Hamada, M.M.
1987-09-01
A mathematical model is described to fit the decomposition rate of labelled RIA compounds. The model was formulated using four parameters: one parameter correlated with the radioactive decay constant; the chemical decomposition rate 'K * ' of the radiolabelled molecules; the natural chemical decomposition rate 'K' and; the fraction 'f * ' of the labelled molecules in the substrate. According to the particular values that these parameters can assume, ten cases were discussed. To determine one of these cases which fit the experimental data, three types of samples were need: radioactive; simulated radiotracer ('false radiolabelled') and; on labelled common substrate. The radioinsulin 125 I was used as an example to illustrate the model application. The experimental data substantiate that the insulin labelled according to the substorchiometric procedures and kept at freezer temperature were degraded with K=0.45% per day. (Author) [pt
Parker, R Gary
1988-01-01
This book treats the fundamental issues and algorithmic strategies emerging as the core of the discipline of discrete optimization in a comprehensive and rigorous fashion. Following an introductory chapter on computational complexity, the basic algorithmic results for the two major models of polynomial algorithms are introduced--models using matroids and linear programming. Further chapters treat the major non-polynomial algorithms: branch-and-bound and cutting planes. The text concludes with a chapter on heuristic algorithms.Several appendixes are included which review the fundamental ideas o
Observability of discretized partial differential equations
Cohn, Stephen E.; Dee, Dick P.
1988-01-01
It is shown that complete observability of the discrete model used to assimilate data from a linear partial differential equation (PDE) system is necessary and sufficient for asymptotic stability of the data assimilation process. The observability theory for discrete systems is reviewed and applied to obtain simple observability tests for discretized constant-coefficient PDEs. Examples are used to show how numerical dispersion can result in discrete dynamics with multiple eigenvalues, thereby detracting from observability.
Introducing philosophy of mathematics
Friend, Michele
2014-01-01
What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual acc
Discrete gradients in discrete classical mechanics
Renna, L.
1987-01-01
A simple model of discrete classical mechanics is given where, starting from the continuous Hamilton equations, discrete equations of motion are established together with a proper discrete gradient definition. The conservation laws of the total discrete momentum, angular momentum, and energy are demonstrated
Sufahani, Suliadi; Mohamad, Mahathir; Roslan, Rozaini; Ghazali Kamardan, M.; Che-Him, Norziha; Ali, Maselan; Khalid, Kamal; Nazri, E. M.; Ahmad, Asmala
2018-04-01
Boarding school student needs to eat well balanced nutritious food which includes proper calories, vitality and supplements for legitimate development, keeping in mind the end goal is to repair and support the body tissues and averting undesired ailments and disease. Serving healthier menu is a noteworthy stride towards accomplishing that goal. Be that as it may, arranging a nutritious and adjusted menu physically is confounded, wasteful and tedious. This study intends to build up a scientific mathematical model for eating routine arranging that improves and meets the vital supplement consumption for boarding school student aged 13-18 and in addition saving the financial plan. It likewise gives the adaptability for the cook to change any favoured menu even after the ideal arrangement has been produced. A recalculation procedure will be performed in view of the ideal arrangement. The information was gathered from the the Ministry of Education and boarding schools’ authorities. Menu arranging is a notable enhancement issue and part of well-established optimization problem. The model was fathomed by utilizing Binary Programming and “Delete-Reshuffle-Reoptimize Algortihm (DDRA)”.
Diamond difference method with hybrid angular quadrature applied to neutron transport problems
Zani, Jose H.; Barros, Ricardo C.; Alves Filho, Hermes
2005-01-01
In this work we presents the results for the calculations of the disadvantage factor in thermal nuclear reactor physics. We use the one-group discrete ordinates (S N ) equations to mathematically model the flux distributions in slab lattices. We apply the diamond difference method with source iteration iterative scheme to numerically solve the discretized systems equations. We used special interface conditions to describe the method with hybrid angular quadrature. We show numerical results to illustrate the accuracy of the hybrid method. (author)
Real-Time Exponential Curve Fits Using Discrete Calculus
Rowe, Geoffrey
2010-01-01
An improved solution for curve fitting data to an exponential equation (y = Ae(exp Bt) + C) has been developed. This improvement is in four areas -- speed, stability, determinant processing time, and the removal of limits. The solution presented avoids iterative techniques and their stability errors by using three mathematical ideas: discrete calculus, a special relationship (be tween exponential curves and the Mean Value Theorem for Derivatives), and a simple linear curve fit algorithm. This method can also be applied to fitting data to the general power law equation y = Ax(exp B) + C and the general geometric growth equation y = Ak(exp Bt) + C.
Gadalla, Tahany M.
The equivalence of multiple-choice (MC) and constructed response (discrete) (CR-D) response formats as applied to mathematics computation at grade levels two to six was tested. The difference between total scores from the two response formats was tested for statistical significance, and the factor structure of items in both response formats was…
New Challenges in the Teaching of Mathematics.
Bourguignon, Jean Pierre
The manifold but discrete presence of mathematics in many objects or services imposes new constraints to the teaching of mathematics. If citizens need to be comfortable in various situations with a variety of mathematical tools, the learning of mathematics requires that one starts with simple concepts. This paper proposes some solutions to solve…
Mathematical modeling and applications in nonlinear dynamics
Merdan, Hüseyin
2016-01-01
The book covers nonlinear physical problems and mathematical modeling, including molecular biology, genetics, neurosciences, artificial intelligence with classical problems in mechanics and astronomy and physics. The chapters present nonlinear mathematical modeling in life science and physics through nonlinear differential equations, nonlinear discrete equations and hybrid equations. Such modeling can be effectively applied to the wide spectrum of nonlinear physical problems, including the KAM (Kolmogorov-Arnold-Moser (KAM)) theory, singular differential equations, impulsive dichotomous linear systems, analytical bifurcation trees of periodic motions, and almost or pseudo- almost periodic solutions in nonlinear dynamical systems. Provides methods for mathematical models with switching, thresholds, and impulses, each of particular importance for discontinuous processes Includes qualitative analysis of behaviors on Tumor-Immune Systems and methods of analysis for DNA, neural networks and epidemiology Introduces...
Application of network methods for understanding evolutionary dynamics in discrete habitats.
Greenbaum, Gili; Fefferman, Nina H
2017-06-01
In populations occupying discrete habitat patches, gene flow between habitat patches may form an intricate population structure. In such structures, the evolutionary dynamics resulting from interaction of gene-flow patterns with other evolutionary forces may be exceedingly complex. Several models describing gene flow between discrete habitat patches have been presented in the population-genetics literature; however, these models have usually addressed relatively simple settings of habitable patches and have stopped short of providing general methodologies for addressing nontrivial gene-flow patterns. In the last decades, network theory - a branch of discrete mathematics concerned with complex interactions between discrete elements - has been applied to address several problems in population genetics by modelling gene flow between habitat patches using networks. Here, we present the idea and concepts of modelling complex gene flows in discrete habitats using networks. Our goal is to raise awareness to existing network theory applications in molecular ecology studies, as well as to outline the current and potential contribution of network methods to the understanding of evolutionary dynamics in discrete habitats. We review the main branches of network theory that have been, or that we believe potentially could be, applied to population genetics and molecular ecology research. We address applications to theoretical modelling and to empirical population-genetic studies, and we highlight future directions for extending the integration of network science with molecular ecology. © 2017 John Wiley & Sons Ltd.
Fundamental structures of algebra and discrete mathematics
Foldes, Stephan
2011-01-01
Introduces and clarifies the basic theories of 12 structural concepts, offering a fundamental theory of groups, rings and other algebraic structures. Identifies essentials and describes interrelationships between particular theories. Selected classical theorems and results relevant to current research are proved rigorously within the theory of each structure. Throughout the text the reader is frequently prompted to perform integrated exercises of verification and to explore examples.
Exploring Discrete Mathematics with American Football
Muldoon Brown, Tricia; Kahn, Eric B.
2015-01-01
This paper presents an extended project that offers, through American football, an application of concepts from enumerative combinatorics and an introduction to proofs course. The questions in this paper and subsequent details concerning equivalence relations and counting techniques can be used to reinforce these new topics to students in such a…
A discrete control model of PLANT
Mitchell, C. M.
1985-01-01
A model of the PLANT system using the discrete control modeling techniques developed by Miller is described. Discrete control models attempt to represent in a mathematical form how a human operator might decompose a complex system into simpler parts and how the control actions and system configuration are coordinated so that acceptable overall system performance is achieved. Basic questions include knowledge representation, information flow, and decision making in complex systems. The structure of the model is a general hierarchical/heterarchical scheme which structurally accounts for coordination and dynamic focus of attention. Mathematically, the discrete control model is defined in terms of a network of finite state systems. Specifically, the discrete control model accounts for how specific control actions are selected from information about the controlled system, the environment, and the context of the situation. The objective is to provide a plausible and empirically testable accounting and, if possible, explanation of control behavior.
Virdi, Surinder; Virdi, Narinder Kaur
2014-01-01
Construction Mathematics is an introductory level mathematics text, written specifically for students of construction and related disciplines. Learn by tackling exercises based on real-life construction maths. Examples include: costing calculations, labour costs, cost of materials and setting out of building components. Suitable for beginners and easy to follow throughout. Learn the essential basic theory along with the practical necessities. The second edition of this popular textbook is fully updated to match new curricula, and expanded to include even more learning exercises. End of chapter exercises cover a range of theoretical as well as practical problems commonly found in construction practice, and three detailed assignments based on practical tasks give students the opportunity to apply all the knowledge they have gained. Construction Mathematics addresses all the mathematical requirements of Level 2 construction NVQs from City & Guilds/CITB and Edexcel courses, including the BTEC First Diploma in...
Eck, Christof; Knabner, Peter
2017-01-01
Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.
Exploring Differential Effects of Mathematics Courses on Mathematics Achievement
Ma, Xin; McIntyre, Laureen J.
2005-01-01
Using data from the Longitudinal Study of Mathematics Participation (N = 1,518 students from 34 schools), we investigated the effects of pure and applied mathematics courses on mathematics achievement, controlling for prior mathematics achievement. Results of multilevel modelling showed that the effects of pure mathematics were significant after…
Foundations of a discrete physics
McGoveran, D.; Noyes, P.
1988-01-01
Starting from the principles of finiteness, discreteness, finite computability and absolute nonuniqueness, we develop the ordering operator calculus, a strictly constructive mathematical system having the empirical properties required by quantum mechanical and special relativistic phenomena. We show how to construct discrete distance functions, and both rectangular and spherical coordinate systems(with a discrete version of ''π''). The richest discrete space constructible without a preferred axis and preserving translational and rotational invariance is shown to be a discrete 3-space with the usual symmetries. We introduce a local ordering parameter with local (proper) time-like properties and universal ordering parameters with global (cosmological) time-like properties. Constructed ''attribute velocities'' connect ensembles with attributes that are invariant as the appropriate time-like parameter increases. For each such attribute, we show how to construct attribute velocities which must satisfy the '' relativistic Doppler shift'' and the ''relativistic velocity composition law,'' as well as the Lorentz transformations. By construction, these velocities have finite maximum and minimum values. In the space of all attributes, the minimum of these maximum velocities will predominate in all multiple attribute computations, and hence can be identified as a fundamental limiting velocity, General commutation relations are constructed which under the physical interpretation are shown to reduce to the usual quantum mechanical commutation relations. 50 refs., 18 figs
Discrete Curvatures and Discrete Minimal Surfaces
Sun, Xiang
2012-01-01
This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads
2004-01-01
All the mechanical and electronic components for the zero power splitable machine (the critical facility) arrived in excellent condition from France. Installation began and good progress was made on the mechanical side where the base and tables were successfully assembled and are being adjusted to meet the exacting specification. Power transients arising from the insertion of short reactivity steps were studied for the reactors, HIFAR, MOATA and the critical facility. Some effort was also devoted to the study of blowdown accidents in light water reactors and calculations of some Italian experiments were made successfully. The measurements of fast fission factor and initial conversion ratios for a range of natural uranium heavy water reactors were completed, and good progress is being made with neutron streaming in aluminium-water lattices. Many other investigators of this problem appear to have neglected or given insufficient attention to the case where the neutron beam is parallel to the plates. It is difficult to fit a cosine curve uniquely as coarse and fine features can not be separated. Previous analysis of the moisture content of soils and concrete by neutron scattering was successfully applied to obtain information on the variation of the moisture in large coal stacks as a function of time. This work was done in conjunction with Electricity Commission of N.S.W. Although a small Pu/Be source was found adequate for the above work, development continued on producing neutron pulses by means of a coaxial plasma focus device. Neutron pulses were produced regularly, but the output was variable; the fault was traced to breakdowns at the breech end of the device where restriking occurs. Although discrepancies of about 2% exist between V-bar for spontaneous fission of 252 Cf as measured by the liquid scintillation method and by the Manganese bath method, this important quantity is being measured locally using the liquid scintillator method. Preliminary results suggest
Jalnapurkar, Sameer M; Leok, Melvin; Marsden, Jerrold E; West, Matthew
2006-01-01
This paper develops the theory of Abelian Routh reduction for discrete mechanical systems and applies it to the variational integration of mechanical systems with Abelian symmetry. The reduction of variational Runge-Kutta discretizations is considered, as well as the extent to which symmetry reduction and discretization commute. These reduced methods allow the direct simulation of dynamical features such as relative equilibria and relative periodic orbits that can be obscured or difficult to identify in the unreduced dynamics. The methods are demonstrated for the dynamics of an Earth orbiting satellite with a non-spherical J 2 correction, as well as the double spherical pendulum. The J 2 problem is interesting because in the unreduced picture, geometric phases inherent in the model and those due to numerical discretization can be hard to distinguish, but this issue does not appear in the reduced algorithm, where one can directly observe interesting dynamical structures in the reduced phase space (the cotangent bundle of shape space), in which the geometric phases have been removed. The main feature of the double spherical pendulum example is that it has a non-trivial magnetic term in its reduced symplectic form. Our method is still efficient as it can directly handle the essential non-canonical nature of the symplectic structure. In contrast, a traditional symplectic method for canonical systems could require repeated coordinate changes if one is evoking Darboux' theorem to transform the symplectic structure into canonical form, thereby incurring additional computational cost. Our method allows one to design reduced symplectic integrators in a natural way, despite the non-canonical nature of the symplectic structure
Mathematics and Computer Science | Argonne National Laboratory
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
On the physical relevance of the discrete Fourier transform
Greben, JM
1991-11-01
Full Text Available This paper originated from the author's dissatisfaction with the way the discrete Fourier transform is usually presented in the literature. Although mathematically correct, the physical meaning of the common representation is unsatisfactory...
Johnson, K. D.; Pinder, G. F.
2013-12-01
The objective of the project is the creation of a new, computationally based, approach to the collection, evaluation and use of data for the purpose of determining optimal strategies for investment in the solution of remediation of contaminant source areas and similar environmental problems. The research focuses on the use of existing mathematical tools assembled in a unique fashion. The area of application of this new capability is optimal (least-cost) groundwater contamination source identification; we wish to identify the physical environments wherein it may be cost-prohibitive to identify a contaminant source, the optimal strategy to protect the environment from additional insult and formulate strategies for cost-effective environmental restoration. The computational underpinnings of the proposed approach encompass the integration into a unique of several known applied-mathematical tools. The resulting tool integration achieves the following: 1) simulate groundwater flow and contaminant transport under uncertainty, that is when the physical parameters such as hydraulic conductivity are known to be described by a random field; 2) define such a random field from available field data or be able to provide insight into the sampling strategy needed to create such a field; 3) incorporate subjective information, such as the opinions of experts on the importance of factors such as locations of waste landfills; 4) optimize a search strategy for finding a potential source location and to optimally combine field information with model results to provide the best possible representation of the mean contaminant field and its geostatistics. Our approach combines in a symbiotic manner methodologies found in numerical simulation, random field analysis, Kalman filtering, fuzzy set theory and search theory. Testing the algorithm for this stage of the work, we will focus on fabricated field situations wherein we can a priori specify the degree of uncertainty associated with the
Data assimilation a mathematical introduction
Law, Kody; Zygalakis, Konstantinos
2015-01-01
This book provides a systematic treatment of the mathematical underpinnings of work in data assimilation, covering both theoretical and computational approaches. Specifically the authors develop a unified mathematical framework in which a Bayesian formulation of the problem provides the bedrock for the derivation, development and analysis of algorithms; the many examples used in the text, together with the algorithms which are introduced and discussed, are all illustrated by the MATLAB software detailed in the book and made freely available online. The book is organized into nine chapters: the first contains a brief introduction to the mathematical tools around which the material is organized; the next four are concerned with discrete time dynamical systems and discrete time data; the last four are concerned with continuous time dynamical systems and continuous time data and are organized analogously to the corresponding discrete time chapters. This book is aimed at mathematical researchers interested in a sy...
Discrete-Time Nonlinear Control of VSC-HVDC System
TianTian Qian
2015-01-01
Full Text Available Because VSC-HVDC is a kind of strong nonlinear, coupling, and multi-input multioutput (MIMO system, its control problem is always attracting much attention from scholars. And a lot of papers have done research on its control strategy in the continuous-time domain. But the control system is implemented through the computer discrete sampling in practical engineering. It is necessary to study the mathematical model and control algorithm in the discrete-time domain. The discrete mathematical model based on output feedback linearization and discrete sliding mode control algorithm is proposed in this paper. And to ensure the effectiveness of the control system in the quasi sliding mode state, the fast output sampling method is used in the output feedback. The results from simulation experiment in MATLAB/SIMULINK prove that the proposed discrete control algorithm can make the VSC-HVDC system have good static, dynamic, and robust characteristics in discrete-time domain.
Transversals in non-discrete groups
Transversals in non-discrete groups. RAMJI LAL and R P SHUKLA. Department of Mathematics, University of Allahabad, Allahabad 211 002, India. E-mail: ramjilal@mri.ernet.in; rps@mri.ernet.in. MS received 2 August 2004; revised 4 August 2005. Abstract. The concept of 'topological right transversal' is introduced to study ...
Attractors for discrete periodic dynamical systems
John E. Franke; James F. Selgrade
2003-01-01
A mathematical framework is introduced to study attractors of discrete, nonautonomous dynamical systems which depend periodically on time. A structure theorem for such attractors is established which says that the attractor of a time-periodic dynamical system is the unin of attractors of appropriate autonomous maps. If the nonautonomous system is a perturbation of an...
Discrete expansions of continuum wave functions
Bang, J.; Ershov, S.N.; Gareev, F.A.; Kazacha, G.S.
1980-01-01
Different methods of expanding continuum wave functions in terms of discrete basis sets are discussed. The convergence properties of these expansions are investigated, both from a mathematical and a numerical point of view, for the case of potentials of Woods-Saxon and square well type. (orig.)
Evaluation, Dissemination and Assessment Center, Dallas.
This Spanish language teacher's edition of a practical mathematics text for the intermediate grades contains three components which can be structured in different combinations according to different student needs. Built around a review of selected objectives in the mathematics basic curriculum, the material is intended to stimulate interest in…
Evaluation, Dissemination and Assessment Center, Dallas.
This Spanish language teacher's edition of a practical mathematics text for the intermediate grades contains three components which can be structured in different combinations according to different student needs. Built around a review of selected objectives in the mathematics basic curriculum, the material is intended to stimulate interest in…
Evaluation, Dissemination and Assessment Center, Dallas.
This Spanish language teacher's edition of a practical mathematics text for the intermediate grades contains three components which can be structured in different combinations according to different student needs. Built around a review of selected objectives in the mathematics basic curriculum, the material is intended to stimulate interest in…
A discretized algorithm for the solution of a constrained, continuous ...
A discretized algorithm for the solution of a constrained, continuous quadratic control problem. ... The results obtained show that the Discretized constrained algorithm (DCA) is much more accurate and more efficient than some of these techniques, particularly the FSA. Journal of the Nigerian Association of Mathematical ...
On the application of Discrete Time Optimal Control Concepts to ...
On the application of Discrete Time Optimal Control Concepts to Economic Problems. ... Journal of the Nigerian Association of Mathematical Physics ... Abstract. An extension of the use of the maximum principle to solve Discrete-time Optimal Control Problems (DTOCP), in which the state equations are in the form of general ...
On the discrete reconciliation of relativity and quantum mechanics
Noyes, H.P.
1987-03-01
A way is sketched to replace physics based on arbitrary units of mass, length, and time by counting in terms of these quantized values and to replace continuum mathematical physics by computer science. The consequences of such a discrete physics are summarized. These are obtained by postulating finiteness, discreteness, finite computability, absolute non-uniqueness, and additivity
Identification of parameters of discrete-continuous models
Cekus, Dawid; Warys, Pawel
2015-01-01
In the paper, the parameters of a discrete-continuous model have been identified on the basis of experimental investigations and formulation of optimization problem. The discrete-continuous model represents a cantilever stepped Timoshenko beam. The mathematical model has been formulated and solved according to the Lagrange multiplier formalism. Optimization has been based on the genetic algorithm. The presented proceeding’s stages make the identification of any parameters of discrete-continuous systems possible
Identification of parameters of discrete-continuous models
Cekus, Dawid, E-mail: cekus@imipkm.pcz.pl; Warys, Pawel, E-mail: warys@imipkm.pcz.pl [Institute of Mechanics and Machine Design Foundations, Czestochowa University of Technology, Dabrowskiego 73, 42-201 Czestochowa (Poland)
2015-03-10
In the paper, the parameters of a discrete-continuous model have been identified on the basis of experimental investigations and formulation of optimization problem. The discrete-continuous model represents a cantilever stepped Timoshenko beam. The mathematical model has been formulated and solved according to the Lagrange multiplier formalism. Optimization has been based on the genetic algorithm. The presented proceeding’s stages make the identification of any parameters of discrete-continuous systems possible.
Discrete calculus methods for counting
Mariconda, Carlo
2016-01-01
This book provides an introduction to combinatorics, finite calculus, formal series, recurrences, and approximations of sums. Readers will find not only coverage of the basic elements of the subjects but also deep insights into a range of less common topics rarely considered within a single book, such as counting with occupancy constraints, a clear distinction between algebraic and analytical properties of formal power series, an introduction to discrete dynamical systems with a thorough description of Sarkovskii’s theorem, symbolic calculus, and a complete description of the Euler-Maclaurin formulas and their applications. Although several books touch on one or more of these aspects, precious few cover all of them. The authors, both pure mathematicians, have attempted to develop methods that will allow the student to formulate a given problem in a precise mathematical framework. The aim is to equip readers with a sound strategy for classifying and solving problems by pursuing a mathematically rigorous yet ...
Mimetic discretization methods
Castillo, Jose E
2013-01-01
To help solve physical and engineering problems, mimetic or compatible algebraic discretization methods employ discrete constructs to mimic the continuous identities and theorems found in vector calculus. Mimetic Discretization Methods focuses on the recent mimetic discretization method co-developed by the first author. Based on the Castillo-Grone operators, this simple mimetic discretization method is invariably valid for spatial dimensions no greater than three. The book also presents a numerical method for obtaining corresponding discrete operators that mimic the continuum differential and
The Effects of Constructivist Learning Environment on Prospective Mathematics Teachers' Opinions
Narli, Serkan; Baser, Nes'e
2010-01-01
To explore the effects of constructivist learning environment on prospective teachers' opinions about "mathematics, department of mathematics, discrete mathematics, countable and uncountable infinity" taught under the subject of Cantorian Set Theory in discrete mathematics class, 60 first-year students in the Division of Mathematics…
3-D discrete analytical ridgelet transform.
Helbert, David; Carré, Philippe; Andres, Eric
2006-12-01
In this paper, we propose an implementation of the 3-D Ridgelet transform: the 3-D discrete analytical Ridgelet transform (3-D DART). This transform uses the Fourier strategy for the computation of the associated 3-D discrete Radon transform. The innovative step is the definition of a discrete 3-D transform with the discrete analytical geometry theory by the construction of 3-D discrete analytical lines in the Fourier domain. We propose two types of 3-D discrete lines: 3-D discrete radial lines going through the origin defined from their orthogonal projections and 3-D planes covered with 2-D discrete line segments. These discrete analytical lines have a parameter called arithmetical thickness, allowing us to define a 3-D DART adapted to a specific application. Indeed, the 3-D DART representation is not orthogonal, It is associated with a flexible redundancy factor. The 3-D DART has a very simple forward/inverse algorithm that provides an exact reconstruction without any iterative method. In order to illustrate the potentiality of this new discrete transform, we apply the 3-D DART and its extension to the Local-DART (with smooth windowing) to the denoising of 3-D image and color video. These experimental results show that the simple thresholding of the 3-D DART coefficients is efficient.
Time-Discrete Higher-Order ALE Formulations: Stability
Bonito, Andrea
2013-01-01
Arbitrary Lagrangian Eulerian (ALE) formulations deal with PDEs on deformable domains upon extending the domain velocity from the boundary into the bulk with the purpose of keeping mesh regularity. This arbitrary extension has no effect on the stability of the PDE but may influence that of a discrete scheme. We examine this critical issue for higher-order time stepping without space discretization. We propose time-discrete discontinuous Galerkin (dG) numerical schemes of any order for a time-dependent advection-diffusion-model problem in moving domains, and study their stability properties. The analysis hinges on the validity of the Reynold\\'s identity for dG. Exploiting the variational structure and assuming exact integration, we prove that our conservative and nonconservative dG schemes are equivalent and unconditionally stable. The same results remain true for piecewise polynomial ALE maps of any degree and suitable quadrature that guarantees the validity of the Reynold\\'s identity. This approach generalizes the so-called geometric conservation law to higher-order methods. We also prove that simpler Runge-Kutta-Radau methods of any order are conditionally stable, that is, subject to a mild ALE constraint on the time steps. Numerical experiments corroborate and complement our theoretical results. © 2013 Society for Industrial and Applied Mathematics.
Souza, Manoelito M. de
1997-01-01
We discuss the physical meaning and the geometric interpretation of implementation in classical field theories. The origin of infinities and other inconsistencies in field theories is traced to fields defined with support on the light cone; a finite and consistent field theory requires a light-cone generator as the field support. Then, we introduce a classical field theory with support on the light cone generators. It results on a description of discrete (point-like) interactions in terms of localized particle-like fields. We find the propagators of these particle-like fields and discuss their physical meaning, properties and consequences. They are conformally invariant, singularity-free, and describing a manifestly covariant (1 + 1)-dimensional dynamics in a (3 = 1) spacetime. Remarkably this conformal symmetry remains even for the propagation of a massive field in four spacetime dimensions. We apply this formalism to Classical electrodynamics and to the General Relativity Theory. The standard formalism with its distributed fields is retrieved in terms of spacetime average of the discrete field. Singularities are the by-products of the averaging process. This new formalism enlighten the meaning and the problem of field theory, and may allow a softer transition to a quantum theory. (author)
Mathematics related anxiety: Mathematics bogeyman or not?
Videnović Marina
2011-01-01
Full Text Available Data of the PISA 2003 survey indicate high levels of mathematics anxiety of students in Serbia. More than half of our students worry whether they will have difficulties in mathematics class or whether they will earn poor marks. Aims of this study therefore are: examining relationship between math anxiety and achievement at mathematics literacy scale; establishing possible predictors of math anxiety and identification of students' groups in relations to their relationship towards mathematics as a subject. Mathematics anxiety is statistically negatively correlated with school achievement and achievement at mathematics literacy scale. Socio-demographic factors, motivational and cognitive aspects related to learning mathematics, perception of school and classroom climate explain 40% variance of mathematics anxiety. Based on students' relationship towards mathematics they cam be divided into three groups; while dimensions that apart them are uninterested-interested in mathematics and presence-absence of anxiety. The group displaying anxiety scores lowest among the three. Applying qualitative analysis students' and teachers' attitudes on specific issues related to teaching and learning mathematics was examined.
Dios, R.A.
1984-01-01
This dissertation focuses upon the field of probabilistic risk assessment and its development. It investigates the development of probabilistic risk assessment in nuclear engineering. To provide background for its development, the related areas of population dynamics (demography), epidemiology and actuarial science are studied by presenting information upon how risk has been viewed in these areas over the years. A second major problem involves presenting an overview of the mathematical models related to risk analysis to mathematics educators and making recommendations for presenting this theory in classes of probability and statistics for mathematics and engineering majors at the undergraduate and graduate levels
Time Discretization Techniques
Gottlieb, S.; Ketcheson, David I.
2016-01-01
The time discretization of hyperbolic partial differential equations is typically the evolution of a system of ordinary differential equations obtained by spatial discretization of the original problem. Methods for this time evolution include
Inferring gene networks from discrete expression data
Zhang, L.; Mallick, B. K.
2013-01-01
graphical models applied to continuous data, which give a closedformmarginal likelihood. In this paper,we extend network modeling to discrete data, specifically data from serial analysis of gene expression, and RNA-sequencing experiments, both of which
An analysis of the Simpson Discrete Hartley transform | Ramsunder ...
The relatively new Simpson Discrete Hartley Transform (SDHT) has interesting mathematical properties, which are crucial for applications. These are developed and proved in this paper. This analysis gives one a comprehensive understanding of the transform. Mathematics Subject Classication (2010): 43A32. Key words: ...
Gabriel R. Bitran
1995-12-01
Full Text Available Este artigo apresenta a segunda (e última parte do nosso exame dos modelos de redes de filas abertas aplicados a sistemas de manufatura discretos. Nosso enfoque é em modelos de projeto e planejamento de job-shops. Na primeira parte (BITRAN & MORABITO, 1995b revisamos métodos de decomposição exatos e aproximados para modelos de avaliação de desempenho em sistemas com múltiplas classes de produtos e diversas estações de trabalho. Nesta segunda parte examinamos modelos de otimização de três categorias de problemas: a primeira minimiza o investimento de capital de maneira a atingir uma medida de desempenho (estoque em processo ou leadtime, a segunda busca otimizar a medida de desempenho sujeito às restrições de recursos, e a terceira explora resultados de pesquisas recentes com a redução de complexidade mediante reprojeto da planta e da partição de produtos.This paper presents the second (and last part of our survey on open queueing network models applied to discrete manufacturing systems. We focus on design and planning for job-shops. In the first part (Bitran and Morabito, 1995b we reviewed exact and approximate decomposition methods for performance evaluation models for single and multiple product class systems. The second part reviews optimization models of three categories of problems: the first minimizes capital investment subject to attaining a performance measure (WIP or leadtime, the second seeks to optimize the performance measure subject to resource constraints, and the third explores recent research developments in complexity reduction through shop redesign and products partitioning.
Discrete tomography in neutron radiography
Kuba, Attila; Rodek, Lajos; Kiss, Zoltan; Rusko, Laszlo; Nagy, Antal; Balasko, Marton
2005-01-01
Discrete tomography (DT) is an imaging technique for reconstructing discrete images from their projections using the knowledge that the object to be reconstructed contains only a few homogeneous materials characterized by known discrete absorption values. One of the main reasons for applying DT is that we will hopefully require relatively few projections. Using discreteness and some a priori information (such as an approximate shape of the object) we can apply two DT methods in neutron imaging by reducing the problem to an optimization task. The first method is a special one because it is only suitable if the object is composed of cylinders and sphere shapes. The second method is a general one in the sense that it can be used for reconstructing objects of any shape. Software was developed and physical experiments performed in order to investigate the effects of several reconstruction parameters: the number of projections, noise levels, and complexity of the object to be reconstructed. We give a summary of the experimental results and make a comparison of the results obtained using a classical reconstruction technique (FBP). The programs we developed are available in our DT reconstruction program package DIRECT
Visualization and mathematics III
Polthier, Konrad
2003-01-01
This research book on Mathematical Visualization contains state of the art presentations on visualization problems in mathematics, on fundamental mathematical research in computer graphics, and on software frameworks for the application of visualization to real-world problems. All contributions were written by leading experts in the field and peer-refereed by an international editorial team. The book grew out of the third international workshop "Visualization and Mathematics", which was held from May 22-25, 2002 in Berlin. The themes of the book cover important recent developments on - Geometry and Combinatorics of Meshes - Discrete Vector Fields and Topology - Geometric Modelling - Image Based Visualization - Software Environments and Applications - Education and Communication The variety of topics makes the book a suitable resource for researchers, lecturers, and practitioners; http://www-sfb288.math.tu-berlin.de/vismath/
Synchronization Of Parallel Discrete Event Simulations
Steinman, Jeffrey S.
1992-01-01
Adaptive, parallel, discrete-event-simulation-synchronization algorithm, Breathing Time Buckets, developed in Synchronous Parallel Environment for Emulation and Discrete Event Simulation (SPEEDES) operating system. Algorithm allows parallel simulations to process events optimistically in fluctuating time cycles that naturally adapt while simulation in progress. Combines best of optimistic and conservative synchronization strategies while avoiding major disadvantages. Algorithm processes events optimistically in time cycles adapting while simulation in progress. Well suited for modeling communication networks, for large-scale war games, for simulated flights of aircraft, for simulations of computer equipment, for mathematical modeling, for interactive engineering simulations, and for depictions of flows of information.
Mathematical problems for chemistry students
Pota, Gyorgy
2011-01-01
Mathematical Problems for Chemistry Students has been compiled and written (a) to help chemistrystudents in their mathematical studies by providing them with mathematical problems really occurring in chemistry (b) to help practising chemists to activate their applied mathematical skills and (c) to introduce students and specialistsof the chemistry-related fields (physicists, mathematicians, biologists, etc.) intothe world of the chemical applications.Some problems of the collection are mathematical reformulations of those in the standard textbooks of chemistry, others we
1991-02-01
international Colloquium on Automata. Languages, and Programming, T Ottmann. ed , Karlsruhe, Federal Republic of Germany, July 1987 (E41 Eisenhart . L P...present mathematical knowledge in the form of problem reduction rules (" theo - rems"). For example, an "algorithm" for limes computations could be
Jazby, Dan
2014-01-01
Research into human decision making (DM) processes from outside of education paint a different picture of DM than current DM models in education. This pilot study assesses the use of critical decision method (CDM)--developed from observations of firefighters' DM -- in the context of primary mathematics teachers' in-class DM. Preliminary results…
1989-02-01
Groebner Bases Moss Sweedler ...................................................... 699 Using Macsyma in a Generalized Harmonic Balance Method for a Problem...Doing Mathiematics by Comnputer, Addison-Wesley Publishing Company, 1988. 698 Groebner Bases GROEBNER BASES Moss Sweedler Mathematical Sciences...Institute Cornell University Ithaca NY 14853 ABSTRACT Groebner bases are remarkable sets of polynomials which permit effec- tive manipulation of multivariate
Mathematical Background of Public Key Cryptography
Frey, Gerhard; Lange, Tanja
2005-01-01
The two main systems used for public key cryptography are RSA and protocols based on the discrete logarithm problem in some cyclic group. We focus on the latter problem and state cryptographic protocols and mathematical background material.......The two main systems used for public key cryptography are RSA and protocols based on the discrete logarithm problem in some cyclic group. We focus on the latter problem and state cryptographic protocols and mathematical background material....
Stokes phenomena in discrete Painlevé II.
Joshi, N; Lustri, C J; Luu, S
2017-02-01
We consider the asymptotic behaviour of the second discrete Painlevé equation in the limit as the independent variable becomes large. Using asymptotic power series, we find solutions that are asymptotically pole-free within some region of the complex plane. These asymptotic solutions exhibit Stokes phenomena, which is typically invisible to classical power series methods. We subsequently apply exponential asymptotic techniques to investigate such phenomena, and obtain mathematical descriptions of the rapid switching behaviour associated with Stokes curves. Through this analysis, we determine the regions of the complex plane in which the asymptotic behaviour is described by a power series expression, and find that the behaviour of these asymptotic solutions shares a number of features with the tronquée and tri-tronquée solutions of the second continuous Painlevé equation.
Exact discretization of Schrödinger equation
Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru
2016-01-08
There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.
Exact discretization of Schrödinger equation
Tarasov, Vasily E.
2016-01-01
There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.
Mathematics and Computer Science: Exploring a Symbiotic Relationship
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…
Geometry and Hamiltonian mechanics on discrete spaces
Talasila, V; Clemente-Gallardo, J; Schaft, A J van der
2004-01-01
Numerical simulation is often crucial for analysing the behaviour of many complex systems which do not admit analytic solutions. To this end, one either converts a 'smooth' model into a discrete (in space and time) model, or models systems directly at a discrete level. The goal of this paper is to provide a discrete analogue of differential geometry, and to define on these discrete models a formal discrete Hamiltonian structure-in doing so we try to bring together various fundamental concepts from numerical analysis, differential geometry, algebraic geometry, simplicial homology and classical Hamiltonian mechanics. For example, the concept of a twisted derivation is borrowed from algebraic geometry for developing a discrete calculus. The theory is applied to a nonlinear pendulum and we compare the dynamics obtained through a discrete modelling approach with the dynamics obtained via the usual discretization procedures. Also an example of an energy-conserving algorithm on a simple harmonic oscillator is presented, and its effect on the Poisson structure is discussed
Nielsen, Erland Hejn
2000-01-01
During the last 1-2 decades, simulation optimisation of discrete event dynamic systems (DEDS) has made considerable theoretical progress with respect to computational efficiency. The score-function (SF) method and the infinitesimal perturbation analysis (IPA) are two candidates belonging to this ...
An introduction to mathematical cryptography
Hoffstein, Jeffrey; Silverman, Joseph H
2014-01-01
This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra, number theory, and probability are introduced and developed as required. This text provides an ideal introduction for mathematics and computer science students to the mathematical foundations of modern cryptography. The book includes an extensive bibliography and index; supplementary materials are available online. The book covers a variety of topics that are considered central to mathematical cryptography. Key topics include: classical cryptographic constructions, such as Diffie–Hellmann key exchange, discrete logarithm-based cryptosystems, the RSA cryptosystem, and digital signatures; fundamental mathematical tools for cr...
MATHEMATICS CONNECTION aims at providing a forum topromote the development of Mathematics Education in Ghana. Articles that seekto enhance the teaching and/or learning of mathematics at all levels of theeducational system are welcome.
The ultimatum game: Discrete vs. continuous offers
Dishon-Berkovits, Miriam; Berkovits, Richard
2014-09-01
In many experimental setups in social-sciences, psychology and economy the subjects are requested to accept or dispense monetary compensation which is usually given in discrete units. Using computer and mathematical modeling we show that in the framework of studying the dynamics of acceptance of proposals in the ultimatum game, the long time dynamics of acceptance of offers in the game are completely different for discrete vs. continuous offers. For discrete values the dynamics follow an exponential behavior. However, for continuous offers the dynamics are described by a power-law. This is shown using an agent based computer simulation as well as by utilizing an analytical solution of a mean-field equation describing the model. These findings have implications to the design and interpretation of socio-economical experiments beyond the ultimatum game.
"Minesweeper" and spectrum of discrete Laplacians
German, Oleg; Lakshtanov, Evgeny
2008-01-01
The paper is devoted to a problem inspired by the "Minesweeper" computer game. It is shown that certain configurations of open cells guarantee the existence and the uniqueness of solution. Mathematically the problem is reduced to some spectral properties of discrete differential operators. It is shown how the uniqueness can be used to create a new game which preserves the spirit of "Minesweeper" but does not require a computer.
Trojanowicz, Karol; Wójcik, Wtodzimierz
2014-01-01
The description of a biofilm mathematical model application for dimensioning an aerated fixed bed biofilm reactor (ASFBBR) for petrochemical wastewater polishing is presented. A simple one-dimensional model of biofilm, developed by P Harremöes, was chosen for this purpose. The model was calibrated and verified under conditions of oil-refinery effluent. The results of ASFBBR dimensioning on the basis of the biofilm model were compared with the bioreactor dimensions determined by application of...
Discrete-Time Biomedical Signal Encryption
Victor Grigoraş
2017-12-01
Full Text Available Chaotic modulation is a strong method of improving communication security. Analog and discrete chaotic systems are presented in actual literature. Due to the expansion of digital communication, discrete-time systems become more efficient and closer to actual technology. The present contribution offers an in-depth analysis of the effects chaos encryption produce on 1D and 2D biomedical signals. The performed simulations show that modulating signals are precisely recovered by the synchronizing receiver if discrete systems are digitally implemented and the coefficients precisely correspond. Channel noise is also applied and its effects on biomedical signal demodulation are highlighted.
Baecklund transformations for discrete Painleve equations: Discrete PII-PV
Sakka, A.; Mugan, U.
2006-01-01
Transformation properties of discrete Painleve equations are investigated by using an algorithmic method. This method yields explicit transformations which relates the solutions of discrete Painleve equations, discrete P II -P V , with different values of parameters. The particular solutions which are expressible in terms of the discrete analogue of the classical special functions of discrete Painleve equations can also be obtained from these transformations
Discrete Gabor transform and discrete Zak transform
Bastiaans, M.J.; Namazi, N.M.; Matthews, K.
1996-01-01
Gabor's expansion of a discrete-time signal into a set of shifted and modulated versions of an elementary signal or synthesis window is introduced, along with the inverse operation, i.e. the Gabor transform, which uses an analysis window that is related to the synthesis window and with the help of
Discrete symmetries and coset space dimensional reduction
Kapetanakis, D.; Zoupanos, G.
1989-01-01
We consider the discrete symmetries of all the six-dimensional coset spaces and we apply them in gauge theories defined in ten dimensions which are dimensionally reduced over these homogeneous spaces. Particular emphasis is given in the consequences of the discrete symmetries on the particle content as well as on the symmetry breaking a la Hosotani of the resulting four-dimensional theory. (orig.)
Kuipers, L
1969-01-01
International Series of Monographs in Pure and Applied Mathematics, Volume 99: Handbook of Mathematics provides the fundamental mathematical knowledge needed for scientific and technological research. The book starts with the history of mathematics and the number systems. The text then progresses to discussions of linear algebra and analytical geometry including polar theories of conic sections and quadratic surfaces. The book then explains differential and integral calculus, covering topics, such as algebra of limits, the concept of continuity, the theorem of continuous functions (with examp
Aydin, Alhun; Sisman, Altug
2016-01-01
By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they're almost completely flattened out after summation or integration operation. It's seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl's conjecture always preserve their lower error characteristic. - Highlights: • Discrete density of states considering minimum energy difference is proposed. • Analytical DOS and NOS formulas based on Weyl conjecture are given. • Discrete DOS and NOS functions are examined for various dimensions. • Relative errors of analytical formulas are much better than the conventional ones.
Aydin, Alhun; Sisman, Altug, E-mail: sismanal@itu.edu.tr
2016-03-22
By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they're almost completely flattened out after summation or integration operation. It's seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl's conjecture always preserve their lower error characteristic. - Highlights: • Discrete density of states considering minimum energy difference is proposed. • Analytical DOS and NOS formulas based on Weyl conjecture are given. • Discrete DOS and NOS functions are examined for various dimensions. • Relative errors of analytical formulas are much better than the conventional ones.
Discrete repulsive oscillator wavefunctions
Munoz, Carlos A; Rueda-Paz, Juvenal; Wolf, Kurt Bernardo
2009-01-01
For the study of infinite discrete systems on phase space, the three-dimensional Lorentz algebra and group, so(2,1) and SO(2,1), provide a discrete model of the repulsive oscillator. Its eigenfunctions are found in the principal irreducible representation series, where the compact generator-that we identify with the position operator-has the infinite discrete spectrum of the integers Z, while the spectrum of energies is a double continuum. The right- and left-moving wavefunctions are given by hypergeometric functions that form a Dirac basis for l 2 (Z). Under contraction, the discrete system limits to the well-known quantum repulsive oscillator. Numerical computations of finite approximations raise further questions on the use of Dirac bases for infinite discrete systems.
Morris, J; Johnson, S
2007-12-03
The Distinct Element Method (also frequently referred to as the Discrete Element Method) (DEM) is a Lagrangian numerical technique where the computational domain consists of discrete solid elements which interact via compliant contacts. This can be contrasted with Finite Element Methods where the computational domain is assumed to represent a continuum (although many modern implementations of the FEM can accommodate some Distinct Element capabilities). Often the terms Discrete Element Method and Distinct Element Method are used interchangeably in the literature, although Cundall and Hart (1992) suggested that Discrete Element Methods should be a more inclusive term covering Distinct Element Methods, Displacement Discontinuity Analysis and Modal Methods. In this work, DEM specifically refers to the Distinct Element Method, where the discrete elements interact via compliant contacts, in contrast with Displacement Discontinuity Analysis where the contacts are rigid and all compliance is taken up by the adjacent intact material.
Discrete symmetries in the MSSM
Schieren, Roland
2010-12-02
The use of discrete symmetries, especially abelian ones, in physics beyond the standard model of particle physics is discussed. A method is developed how a general, abelian, discrete symmetry can be obtained via spontaneous symmetry breaking. In addition, anomalies are treated in the path integral approach with special attention to anomaly cancellation via the Green-Schwarz mechanism. All this is applied to the minimal supersymmetric standard model. A unique Z{sup R}{sub 4} symmetry is discovered which solves the {mu}-problem as well as problems with proton decay and allows to embed the standard model gauge group into a simple group, i.e. the Z{sup R}{sub 4} is compatible with grand unification. Also the flavor problem in the context of minimal flavor violation is addressed. Finally, a string theory model is presented which exhibits the mentioned Z{sup R}{sub 4} symmetry and other desirable features. (orig.)
Discrete symmetries in the MSSM
Schieren, Roland
2010-01-01
The use of discrete symmetries, especially abelian ones, in physics beyond the standard model of particle physics is discussed. A method is developed how a general, abelian, discrete symmetry can be obtained via spontaneous symmetry breaking. In addition, anomalies are treated in the path integral approach with special attention to anomaly cancellation via the Green-Schwarz mechanism. All this is applied to the minimal supersymmetric standard model. A unique Z R 4 symmetry is discovered which solves the μ-problem as well as problems with proton decay and allows to embed the standard model gauge group into a simple group, i.e. the Z R 4 is compatible with grand unification. Also the flavor problem in the context of minimal flavor violation is addressed. Finally, a string theory model is presented which exhibits the mentioned Z R 4 symmetry and other desirable features. (orig.)
Ascarrunz, F G; Kisley, M A; Flach, K A; Hamilton, R W; MacGregor, R J
1995-07-01
This paper applies a general mathematical system for characterizing and scaling functional connectivity and information flow across the diffuse (EC) and discrete (DG) input junctions to the CA3 hippocampus. Both gross connectivity and coordinated multiunit informational firing patterns are quantitatively characterized in terms of 32 defining parameters interrelated by 17 equations, and then scaled down according to rules for uniformly proportional scaling and for partial representation. The diffuse EC-CA3 junction is shown to be uniformly scalable with realistic representation of both essential spatiotemporal cooperativity and coordinated firing patterns down to populations of a few hundred neurons. Scaling of the discrete DG-CA3 junction can be effected with a two-step process, which necessarily deviates from uniform proportionality but nonetheless produces a valuable and readily interpretable reduced model, also utilizing a few hundred neurons in the receiving population. Partial representation produces a reduced model of only a portion of the full network where each model neuron corresponds directly to a biological neuron. The mathematical analysis illustrated here shows that although omissions and distortions are inescapable in such an application, satisfactorily complete and accurate models the size of pattern modules are possible. Finally, the mathematical characterization of these junctions generates a theory which sees the DG as a definer of the fine structure of embedded traces in the hippocampus and entire coordinated patterns of sequences of 14-cell links in CA3 as triggered by the firing of sequences of individual neurons in DG.
Mathematical Footprints Discovering Mathematics Everywhere
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
Rami Ahmad El-Nabulsi
2015-08-01
Full Text Available Recently, non-standard Lagrangians have gained a growing importance in theoretical physics and in the theory of non-linear differential equations. However, their formulations and implications in general relativity are still in their infancies despite some advances in contemporary cosmology. The main aim of this paper is to fill the gap. Though non-standard Lagrangians may be defined by a multitude form, in this paper, we considered the exponential type. One basic feature of exponential non-standard Lagrangians concerns the modified Euler-Lagrange equation obtained from the standard variational analysis. Accordingly, when applied to spacetime geometries, one unsurprisingly expects modified geodesic equations. However, when taking into account the time-like paths parameterization constraint, remarkably, it was observed that mutually discrete gravity and discrete spacetime emerge in the theory. Two different independent cases were obtained: A geometrical manifold with new spacetime coordinates augmented by a metric signature change and a geometrical manifold characterized by a discretized spacetime metric. Both cases give raise to Einstein’s field equations yet the gravity is discretized and originated from “spacetime discreteness”. A number of mathematical and physical implications of these results were discussed though this paper and perspectives are given accordingly.
Mabile, C.; Rey Fabre, I.; Benjelloun-Touimi-Dabaghi, Z. [Institut Francais du Petrole (IFP), 92 - Rueil-Malmaison (France)
1997-04-01
During the rotary drilling, drill pipes and bits are submitted to physical stresses which are all the more important that the well is deep. The aim of the study is then to physically understand these phenomena in order to prevent the effects as the pre-wear, the rupture of the drill pipes or the destruction of the measure instruments used at the bottom during the drilling of the well. Computers are used to establish a mathematical model which correspond to reality and which should be directly used on offshore platforms. (O.M.)
Methods of mathematical modeling using polynomials of algebra of sets
Kazanskiy, Alexandr; Kochetkov, Ivan
2018-03-01
The article deals with the construction of discrete mathematical models for solving applied problems arising from the operation of building structures. Security issues in modern high-rise buildings are extremely serious and relevant, and there is no doubt that interest in them will only increase. The territory of the building is divided into zones for which it is necessary to observe. Zones can overlap and have different priorities. Such situations can be described using formulas algebra of sets. Formulas can be programmed, which makes it possible to work with them using computer models.
Mathematical biodescriptors of proteomics maps: background and applications.
Basak, Subhash C; Gute, Brian D
2008-05-01
This article reviews recent developments in the formulation and application of biodescriptors to characterize proteomics maps. Such biodescriptors can be derived by applying techniques from discrete mathematics (graph theory, linear algebra and information theory). This review focuses on the development of biodescriptors for proteomics maps derived from 2D gel electrophoresis. Preliminary results demonstrated that such descriptors have a reasonable ability to differentiate between proteomics patterns that result from exposure to closely related individual chemicals and complex mixtures, such as the jet fuel JP-8. Further research is required to evaluate the utility of these proteomics-based biodescriptors for drug discovery and predictive toxicology.
Applied research into direct numerical control of A-1 reactor temperature
Karpeta, C.; Volf, K.
1974-01-01
Partial results of research efforts aimed at applying modern control theory in the control of the reactor of the A-1 nuclear power station are presented. A mathematical model of the process dynamics was developed. Some parameters of the model were determined using the results of an experimentally performed reactor scram. The optimal stochastic discrete regulator was determined and closed-loop transients were studied. The possibilities of implementing control routines were investigated using the RPP-16 computer. (author)
Experimental Mathematics and Computational Statistics
Bailey, David H.; Borwein, Jonathan M.
2009-04-30
The field of statistics has long been noted for techniques to detect patterns and regularities in numerical data. In this article we explore connections between statistics and the emerging field of 'experimental mathematics'. These includes both applications of experimental mathematics in statistics, as well as statistical methods applied to computational mathematics.
Teaching Mathematics in Geography Degrees
Bennett, Robert
1978-01-01
Examines ways of developing college students' motivation for mathematical training; describes the type of mathematical knowledge required in the geography discipline; and explores an applied approach to mathematics teaching based on a systems concept. For journal availability, see SO 506 224. (Author/AV)
User interface to an ICAI system that teaches discrete math
Calcote, Roy Keith.; Howard, Richard Anthony
1990-01-01
Approved for public release; distribution is unlimited. The main thrust of this thesis is the design of a usable Intelligent Computer Aided Instruction (ICAI) user interface that does not use a natural language processor and runs on a personal computer. Discrete Mathematics is the knowledge domain for this project and the Discrete Math Tutor (DMT) is the name of the tutoring system. The DMT will allow the average student to benefit from a tutoring system now and not have to wait until the ...
Discrete gauge symmetries in discrete MSSM-like orientifolds
Ibáñez, L.E.; Schellekens, A.N.; Uranga, A.M.
2012-01-01
Motivated by the necessity of discrete Z N symmetries in the MSSM to insure baryon stability, we study the origin of discrete gauge symmetries from open string sector U(1)'s in orientifolds based on rational conformal field theory. By means of an explicit construction, we find an integral basis for the couplings of axions and U(1) factors for all simple current MIPFs and orientifolds of all 168 Gepner models, a total of 32 990 distinct cases. We discuss how the presence of discrete symmetries surviving as a subgroup of broken U(1)'s can be derived using this basis. We apply this procedure to models with MSSM chiral spectrum, concretely to all known U(3)×U(2)×U(1)×U(1) and U(3)×Sp(2)×U(1)×U(1) configurations with chiral bi-fundamentals, but no chiral tensors, as well as some SU(5) GUT models. We find examples of models with Z 2 (R-parity) and Z 3 symmetries that forbid certain B and/or L violating MSSM couplings. Their presence is however relatively rare, at the level of a few percent of all cases.
Symmetric discrete coherent states for n-qubits
Muñoz, C; Klimov, A B; Sánchez-Soto, L L
2012-01-01
We put forward a method of constructing discrete coherent states for n qubits. After establishing appropriate displacement operators, the coherent states appear as displaced versions of a fiducial vector that is fixed by imposing a number of natural symmetry requirements on its Q-function. Using these coherent states, we establish a partial order in the discrete phase space, which allows us to picture some n-qubit states as apparent distributions. We also analyze correlations in terms of sums of squared Q-functions. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)
Kang, Li; Tang, Sanyi
2016-01-01
Highlights: • The discrete single species and multiple species models with random perturbation are proposed. • The complex dynamics and interesting bifurcation behavior have been investigated. • The reverse effects of random perturbation on discrete systems have been discussed and revealed. • The main results can be applied for pest control and resources management. - Abstract: The natural species are likely to present several interesting and complex phenomena under random perturbations, which have been confirmed by simple mathematical models. The important questions are: how the random perturbations influence the dynamics of the discrete population models with multiple steady states or multiple species interactions? and is there any different effects for single species and multiple species models with random perturbation? To address those interesting questions, we have proposed the discrete single species model with two stable equilibria and the host-parasitoid model with Holling type functional response functions to address how the random perturbation affects the dynamics. The main results indicate that the random perturbation does not change the number of blurred orbits of the single species model with two stable steady states compared with results for the classical Ricker model with same random perturbation, but it can strength the stability. However, extensive numerical investigations depict that the random perturbation does not influence the complexities of the host-parasitoid models compared with the results for the models without perturbation, while it does increase the period of periodic orbits doubly. All those confirm that the random perturbation has a reverse effect on the dynamics of the discrete single and multiple population models, which could be applied in reality including pest control and resources management.
Finite Discrete Gabor Analysis
Søndergaard, Peter Lempel
2007-01-01
frequency bands at certain times. Gabor theory can be formulated for both functions on the real line and for discrete signals of finite length. The two theories are largely the same because many aspects come from the same underlying theory of locally compact Abelian groups. The two types of Gabor systems...... can also be related by sampling and periodization. This thesis extends on this theory by showing new results for window construction. It also provides a discussion of the problems associated to discrete Gabor bases. The sampling and periodization connection is handy because it allows Gabor systems...... on the real line to be well approximated by finite and discrete Gabor frames. This method of approximation is especially attractive because efficient numerical methods exists for doing computations with finite, discrete Gabor systems. This thesis presents new algorithms for the efficient computation of finite...
Adaptive Discrete Hypergraph Matching.
Yan, Junchi; Li, Changsheng; Li, Yin; Cao, Guitao
2018-02-01
This paper addresses the problem of hypergraph matching using higher-order affinity information. We propose a solver that iteratively updates the solution in the discrete domain by linear assignment approximation. The proposed method is guaranteed to converge to a stationary discrete solution and avoids the annealing procedure and ad-hoc post binarization step that are required in several previous methods. Specifically, we start with a simple iterative discrete gradient assignment solver. This solver can be trapped in an -circle sequence under moderate conditions, where is the order of the graph matching problem. We then devise an adaptive relaxation mechanism to jump out this degenerating case and show that the resulting new path will converge to a fixed solution in the discrete domain. The proposed method is tested on both synthetic and real-world benchmarks. The experimental results corroborate the efficacy of our method.
Goodrich, Christopher
2015-01-01
This text provides the first comprehensive treatment of the discrete fractional calculus. Experienced researchers will find the text useful as a reference for discrete fractional calculus and topics of current interest. Students who are interested in learning about discrete fractional calculus will find this text to provide a useful starting point. Several exercises are offered at the end of each chapter and select answers have been provided at the end of the book. The presentation of the content is designed to give ample flexibility for potential use in a myriad of courses and for independent study. The novel approach taken by the authors includes a simultaneous treatment of the fractional- and integer-order difference calculus (on a variety of time scales, including both the usual forward and backwards difference operators). The reader will acquire a solid foundation in the classical topics of the discrete calculus while being introduced to exciting recent developments, bringing them to the frontiers of the...
Williams, Ruth M
2006-01-01
A review is given of a number of approaches to discrete quantum gravity, with a restriction to those likely to be relevant in four dimensions. This paper is dedicated to Rafael Sorkin on the occasion of his sixtieth birthday
Drew, D.A.; Flaherty, J.E.
1986-01-01
The mathematical analysis of fluid mechanics and stability and its applications in science and engineering are examined in reviews and reports. Topics addressed include Taylor-vortex flow, isothermal fluid-film lubrication theories, the morphology of spiral galaxies, rotating-fluid problems in ballistics, coupled Lorenz oscillators, the connection between chaos and turbulence, plane-front alloy solidification versus free-surface Benard convection, and the nonlinear stability of spiral flow between rotating cylinders with a small gap. Consideration is given to resonance conditions for forced two-dimensional channel flows, the secondary bifurcation of standing surface waves in rectangular basins, instability in the flow of granular materials, and the supercritical dynamics of baroclinic disturbances
Stenta, Herman Roberto; Riccardi, Gerardo A; Basile, Pedro A [Universidad Nacional de Rosario (Mexico)
2008-07-15
Distributed hydrological models are suitable for the determination of time and space variability of hydrological responses within a given watershed. In a watershed, the model can be implemented with different levels of space resolution, mainly as a function of data availability, objectives of the numerical study, and requirements of the system to be modeled. In this paper, the effects on landscape representation due to different cell sizes are analyzed and scaling of parameters in a lower spatial resolution level is proposed in order to obtain similarity in hydrological responses between different degrees of discretization. The comparison was made in terms of maximum discharge, maximum flow velocity, and maximum water depth by simulating a number of observed and hypothetical hydrological events. The concept of total equilibrium state of the watershed was used. Under these circumstances, the roughness coefficients associated to overland and stream flow and the storage function of each discretization element were adjusted separately for the lower spatial resolution level. The results show that the similarity in hydrological responses, in terms of maximum water depth, obtained by adjusting the storage function of the cells, is better than that corresponding to the adjustment of roughness coefficients. [Spanish] Los modelos matematicos de parametros distribuidos resultan particularmente apropiados para determinar la variabilidad espacial y temporal de las respuestas hidrologicas dentro de un determinado sistema hidrico. En una cuenca es posible realizar la constitucion de un modelo con diferentes niveles de detalle en funcion principalmente de la disponibilidad de informacion de entrada necesaria, de los objetivos de estudio y de los requerimientos de modelado del sistema. En el presente trabajo se analizan los efectos producidos en la representacion del relieve debido a los diferentes tamanos de celda en que se ha discretizado una cuenca de llanura y se propone el
Andreescu, Titu; Tetiva, Marian
2017-01-01
Building bridges between classical results and contemporary nonstandard problems, Mathematical Bridges embraces important topics in analysis and algebra from a problem-solving perspective. Blending old and new techniques, tactics and strategies used in solving challenging mathematical problems, readers will discover numerous genuine mathematical gems throughout that will heighten their appreciation of the inherent beauty of mathematics. Most of the problems are original to the authors and are intertwined in a well-motivated exposition driven by representative examples. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics. Instructors and educators teaching problem-solving courses or organizing mathematics clubs, as well as motivated mathematics students from high school juniors to college seniors, will find Mathematical Bri...
Core-Plus Mathematics. What Works Clearinghouse Intervention Report
What Works Clearinghouse, 2010
2010-01-01
"Core-Plus Mathematics" is a four-year curriculum that replaces the traditional sequence with courses that each feature interwoven strands of algebra and functions, statistics and probability, geometry and trigonometry, and discrete mathematics. The first three courses in the series provide a common core of broadly useful mathematics,…
Discrete Painlevé equations from Y-systems
Hone, Andrew N W; Inoue, Rei
2014-01-01
We consider T-systems and Y-systems arising from cluster mutations applied to quivers that have the property of being periodic under a sequence of mutations. The corresponding nonlinear recurrences for cluster variables (coefficient-free T-systems) were described in the work of Fordy and Marsh, who completely classified all such quivers in the case of period 1, and characterized them in terms of the skew-symmetric exchange matrix B that defines the quiver. A broader notion of periodicity in general cluster algebras was introduced by Nakanishi, who also described the corresponding Y-systems, and T-systems with coefficients. A result of Fomin and Zelevinsky says that the coefficient-free T-system provides a solution of the Y-system. In this paper, we show that in general there is a discrepancy between these two systems, in the sense that the solution of the former does not correspond to the general solution of the latter. This discrepancy is removed by introducing additional non-autonomous coefficients into the T-system. In particular, we focus on the period 1 case and show that, when the exchange matrix B is degenerate, discrete Painlevé equations can arise from this construction. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Cluster algebras in mathematical physics’. (paper)
3-D discrete shearlet transform and video processing.
Negi, Pooran Singh; Labate, Demetrio
2012-06-01
In this paper, we introduce a digital implementation of the 3-D shearlet transform and illustrate its application to problems of video denoising and enhancement. The shearlet representation is a multiscale pyramid of well-localized waveforms defined at various locations and orientations, which was introduced to overcome the limitations of traditional multiscale systems in dealing with multidimensional data. While the shearlet approach shares the general philosophy of curvelets and surfacelets, it is based on a very different mathematical framework, which is derived from the theory of affine systems and uses shearing matrices rather than rotations. This allows a natural transition from the continuous setting to the digital setting and a more flexible mathematical structure. The 3-D digital shearlet transform algorithm presented in this paper consists in a cascade of a multiscale decomposition and a directional filtering stage. The filters employed in this decomposition are implemented as finite-length filters, and this ensures that the transform is local and numerically efficient. To illustrate its performance, the 3-D discrete shearlet transform is applied to problems of video denoising and enhancement, and compared against other state-of-the-art multiscale techniques, including curvelets and surfacelets.
A study of discrete nonlinear systems
Dhillon, H.S.
2001-04-01
An investigation of various spatially discrete time-independent nonlinear models was undertaken. These models are generically applicable to many different physical systems including electron-phonon interactions in solids, magnetic multilayers, layered superconductors and classical lattice systems. To characterise the possible magnetic structures created on magnetic multilayers a model has been formulated and studied. The Euler-Lagrange equation for this model is a discrete version of the Sine-Gordon equation. Solutions of this equation are generated by applying the methods of Chaotic Dynamics - treating the space variable associated with the layer number as a discrete time variable. The states found indicate periodic, quasiperiodic and chaotic structures. Analytic solutions to the discrete nonlinear Schroedinger Equation (DNSE) with cubic nonlinearity are presented in the strong coupling limit. Using these as a starting point, a procedure is developed to determine the wave function and the energy eigenvalue for moderate coupling. The energy eigenvalues of the different structures of the wave function are found to be in excellent agreement with the exact strong coupling result. The solutions to the DNSE indicate commensurate and incommensurate spatial structures associated with different localisation patterns of the wave function. The states which arise may be fractal, periodic, quasiperiodic or chaotic. This work is then extended to solve a first order discrete nonlinear equation. The exact solutions for both the first and second order discrete nonlinear equations with cubic nonlinearity suggests that this method of studying discrete nonlinear equations may be applied to solve discrete equations with any order difference and cubic nonlinearity. (author)
Continuum mechanics the birthplace of mathematical models
Allen, Myron B
2015-01-01
Continuum mechanics is a standard course in many graduate programs in engineering and applied mathematics as it provides the foundations for the various differential equations and mathematical models that are encountered in fluid mechanics, solid mechanics, and heat transfer. This book successfully makes the topic more accessible to advanced undergraduate mathematics majors by aligning the mathematical notation and language with related courses in multivariable calculus, linear algebra, and differential equations; making connections with other areas of applied mathematics where parial differe
Le Hardy, D. [Université de Nantes, LTN UMR CNRS 6607 (France); Favennec, Y., E-mail: yann.favennec@univ-nantes.fr [Université de Nantes, LTN UMR CNRS 6607 (France); Rousseau, B. [Université de Nantes, LTN UMR CNRS 6607 (France); Hecht, F. [Sorbonne Universités, UPMC Université Paris 06, UMR 7598, inria de Paris, Laboratoire Jacques-Louis Lions, F-75005, Paris (France)
2017-04-01
The contribution of this paper relies in the development of numerical algorithms for the mathematical treatment of specular reflection on borders when dealing with the numerical solution of radiative transfer problems. The radiative transfer equation being integro-differential, the discrete ordinates method allows to write down a set of semi-discrete equations in which weights are to be calculated. The calculation of these weights is well known to be based on either a quadrature or on angular discretization, making the use of such method straightforward for the state equation. Also, the diffuse contribution of reflection on borders is usually well taken into account. However, the calculation of accurate partition ratio coefficients is much more tricky for the specular condition applied on arbitrary geometrical borders. This paper presents algorithms that calculate analytically partition ratio coefficients needed in numerical treatments. The developed algorithms, combined with a decentered finite element scheme, are validated with the help of comparisons with analytical solutions before being applied on complex geometries.
Advanced engineering mathematics
Jeffrey, Alan
2001-01-01
Advanced Engineering Mathematics provides comprehensive and contemporary coverage of key mathematical ideas, techniques, and their widespread applications, for students majoring in engineering, computer science, mathematics and physics. Using a wide range of examples throughout the book, Jeffrey illustrates how to construct simple mathematical models, how to apply mathematical reasoning to select a particular solution from a range of possible alternatives, and how to determine which solution has physical significance. Jeffrey includes material that is not found in works of a similar nature, such as the use of the matrix exponential when solving systems of ordinary differential equations. The text provides many detailed, worked examples following the introduction of each new idea, and large problem sets provide both routine practice, and, in many cases, greater challenge and insight for students. Most chapters end with a set of computer projects that require the use of any CAS (such as Maple or Mathematica) th...
... this page: //medlineplus.gov/ency/article/001534.htm Mathematics disorder To use the sharing features on this page, please enable JavaScript. Mathematics disorder is a condition in which a child's ...
Gaponenko, A. M.; Kagramanova, A. A.
2017-11-01
The opportunity of application of Stirling engine with non-conventional and renewable sources of energy. The advantage of such use. The resulting expression for the thermal efficiency of the Stirling engine. It is shown that the work per cycle is proportional to the quantity of matter, and hence the pressure of the working fluid, the temperature difference and, to a lesser extent, depends on the expansion coefficient; efficiency of ideal Stirling cycle coincides with the efficiency of an ideal engine working on the Carnot cycle, which distinguishes a Stirling cycle from the cycles of Otto and Diesel underlying engine. It has been established that the four input parameters, the only parameter which can be easily changed during operation, and which effectively affects the operation of the engine is the phase difference. Dependence of work per cycle of the phase difference, called the phase characteristic, visually illustrates mode of operation of Stirling engine. The mathematical model of the cycle of Schmidt and the analysis of operation of Stirling engine in the approach of Schmidt with the aid of numerical analysis. To conduct numerical experiments designed program feature in the language MathLab. The results of numerical experiments are illustrated by graphical charts.
García-Rojo, A M; Martínez-Sánchez, A; López, R; García de la Vega, J M; Rica, M; González, M; Disney, R H L
2013-09-10
We present a forensic case associated with skeletonized human remains found inside a cistern in a coastal town located in the eastern Iberian Peninsula (Valencian Regional Government, Spain). In order to analyse the particular environmental conditions that occurred during oviposition and development of the collected insects, estimated temperatures at the crime scene were calculated by a predictive mathematical model. This model analyses the correlation between the variability of the internal temperature depending on the variability of the external ones. The amplitude of the temperature oscillations inside the tank and the containment of the enclosure is reduced by the presence of water. Such variation occurred within about 2h due to the time required for heat exchange. The differential equations employed to model differences between outdoor and indoor temperatures were an essential tool which let us estimate the post-mortem interval (PMI) that was carried out by the study of the insect succession and the development time of the collected Diptera specimens under the adjusted temperatures. The presence of live larvae and pupae of Sarcophagidae and empty pupae of Calliphoridae, Sarcophagidae, Fanniidae, Muscidae, Phoridae and Piophilidae and the decomposition stage suggested the possibility that the remains were in the tank at least a year. We highlight the absence of Calliphora and Lucilia spp., and the first occurrence of the phorid Conicera similis in a human cadaver among the entomological evidence. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.
Sur, Chiranjib; Shukla, Anupam
2018-03-01
Bacteria Foraging Optimisation Algorithm is a collective behaviour-based meta-heuristics searching depending on the social influence of the bacteria co-agents in the search space of the problem. The algorithm faces tremendous hindrance in terms of its application for discrete problems and graph-based problems due to biased mathematical modelling and dynamic structure of the algorithm. This had been the key factor to revive and introduce the discrete form called Discrete Bacteria Foraging Optimisation (DBFO) Algorithm for discrete problems which exceeds the number of continuous domain problems represented by mathematical and numerical equations in real life. In this work, we have mainly simulated a graph-based road multi-objective optimisation problem and have discussed the prospect of its utilisation in other similar optimisation problems and graph-based problems. The various solution representations that can be handled by this DBFO has also been discussed. The implications and dynamics of the various parameters used in the DBFO are illustrated from the point view of the problems and has been a combination of both exploration and exploitation. The result of DBFO has been compared with Ant Colony Optimisation and Intelligent Water Drops Algorithms. Important features of DBFO are that the bacteria agents do not depend on the local heuristic information but estimates new exploration schemes depending upon the previous experience and covered path analysis. This makes the algorithm better in combination generation for graph-based problems and combination generation for NP hard problems.
Trinajstić, Nenad; Gutman, Ivan
2002-01-01
A brief description is given of the historical development of mathematics and chemistry. A path leading to the meeting of these two sciences is described. An attempt is made to define mathematical chemistry, and journals containing the term mathematical chemistry in their titles are noted. In conclusion, the statement is made that although chemistry is an experimental science aimed at preparing new compounds and materials, mathematics is very useful in chemistry, among other things, to produc...
Kilpatrick, Jeremy
2014-01-01
This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares…
Discrete non-parametric kernel estimation for global sensitivity analysis
Senga Kiessé, Tristan; Ventura, Anne
2016-01-01
This work investigates the discrete kernel approach for evaluating the contribution of the variance of discrete input variables to the variance of model output, via analysis of variance (ANOVA) decomposition. Until recently only the continuous kernel approach has been applied as a metamodeling approach within sensitivity analysis framework, for both discrete and continuous input variables. Now the discrete kernel estimation is known to be suitable for smoothing discrete functions. We present a discrete non-parametric kernel estimator of ANOVA decomposition of a given model. An estimator of sensitivity indices is also presented with its asymtotic convergence rate. Some simulations on a test function analysis and a real case study from agricultural have shown that the discrete kernel approach outperforms the continuous kernel one for evaluating the contribution of moderate or most influential discrete parameters to the model output. - Highlights: • We study a discrete kernel estimation for sensitivity analysis of a model. • A discrete kernel estimator of ANOVA decomposition of the model is presented. • Sensitivity indices are calculated for discrete input parameters. • An estimator of sensitivity indices is also presented with its convergence rate. • An application is realized for improving the reliability of environmental models.
Mathematical Modeling in the High School Curriculum
Hernández, Maria L.; Levy, Rachel; Felton-Koestler, Mathew D.; Zbiek, Rose Mary
2016-01-01
In 2015, mathematics leaders and instructors from the Society for Industrial and Applied Mathematics (SIAM) and the Consortium for Mathematics and Its Applications (COMAP), with input from NCTM, came together to write the "Guidelines for Assessment and Instruction in Mathematical Modeling Education" (GAIMME) report as a resource for…
Mathematical methods in neutronics
Planchard, J.
1995-01-01
This book presents the mathematical theory of nuclear reactors. It applies to engineers in neutronics and applied mathematicians. After a recall of the elementary notions of neutronics and of diffusion-type partial derivative equations, the theory of reactors criticality calculation is described. (J.S.)
Mugica R, A.; Valle G, E. del [IPN, ESFM, 07738 Mexico D.F. (Mexico)]. e-mail: mugica@esfm.ipn.mx
2003-07-01
Nowadays the numerical methods of solution to the diffusion equation by means of algorithms and computer programs result so extensive due to the great number of routines and calculations that should carry out, this rebounds directly in the execution times of this programs, being obtained results in relatively long times. This work shows the application of an acceleration method of the convergence of the classic method of those powers that it reduces notably the number of necessary iterations for to obtain reliable results, what means that the compute times they see reduced in great measure. This method is known in the literature like Wielandt method and it has incorporated to a computer program that is based on the discretization of the neutron diffusion equations in plate geometry and stationary state by polynomial nodal methods. In this work the neutron diffusion equations are described for several energy groups and their discretization by means of those called physical nodal methods, being illustrated in particular the quadratic case. It is described a model problem widely described in the literature which is solved for the physical nodal grade schemes 1, 2, 3 and 4 in three different ways: to) with the classic method of the powers, b) method of the powers with the Wielandt acceleration and c) method of the powers with the Wielandt modified acceleration. The results for the model problem as well as for two additional problems known as benchmark problems are reported. Such acceleration method can also be implemented to problems of different geometry to the proposal in this work, besides being possible to extend their application to problems in 2 or 3 dimensions. (Author)
Discrete Dynamical Systems Meet the Classic Monkey-and-the-Bananas Problem.
Gannon, Gerald E.; Martelli, Mario U.
2001-01-01
Presents a solution of the three-sailors-and-the-bananas problem and attempts a generalization. Introduces an interesting way of looking at the mathematics with an idea drawn from discrete dynamical systems. (KHR)
Continuous/discrete non parametric Bayesian belief nets with UNICORN and UNINET
Cooke, R.M.; Kurowicka, D.; Hanea, A.M.; Morales Napoles, O.; Ababei, D.A.; Ale, B.J.M.; Roelen, A.
2007-01-01
Hanea et al. (2006) presented a method for quantifying and computing continuous/discrete non parametric Bayesian Belief Nets (BBN). Influences are represented as conditional rank correlations, and the joint normal copula enables rapid sampling and conditionalization. Further mathematical background
Hybrid discrete-time neural networks.
Cao, Hongjun; Ibarz, Borja
2010-11-13
Hybrid dynamical systems combine evolution equations with state transitions. When the evolution equations are discrete-time (also called map-based), the result is a hybrid discrete-time system. A class of biological neural network models that has recently received some attention falls within this category: map-based neuron models connected by means of fast threshold modulation (FTM). FTM is a connection scheme that aims to mimic the switching dynamics of a neuron subject to synaptic inputs. The dynamic equations of the neuron adopt different forms according to the state (either firing or not firing) and type (excitatory or inhibitory) of their presynaptic neighbours. Therefore, the mathematical model of one such network is a combination of discrete-time evolution equations with transitions between states, constituting a hybrid discrete-time (map-based) neural network. In this paper, we review previous work within the context of these models, exemplifying useful techniques to analyse them. Typical map-based neuron models are low-dimensional and amenable to phase-plane analysis. In bursting models, fast-slow decomposition can be used to reduce dimensionality further, so that the dynamics of a pair of connected neurons can be easily understood. We also discuss a model that includes electrical synapses in addition to chemical synapses with FTM. Furthermore, we describe how master stability functions can predict the stability of synchronized states in these networks. The main results are extended to larger map-based neural networks.
Prateek Sharma
2015-04-01
Full Text Available Abstract Simulation can be regarded as the emulation of the behavior of a real-world system over an interval of time. The process of simulation relies upon the generation of the history of a system and then analyzing that history to predict the outcome and improve the working of real systems. Simulations can be of various kinds but the topic of interest here is one of the most important kind of simulation which is Discrete-Event Simulation which models the system as a discrete sequence of events in time. So this paper aims at introducing about Discrete-Event Simulation and analyzing how it is beneficial to the real world systems.
Discrete systems and integrability
Hietarinta, J; Nijhoff, F W
2016-01-01
This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and Bäcklund transformations; difference equations and special functions; multidimensional consistency of integrable lattice equations; associated linear problems (Lax pairs); connections with Padé approximants and convergence algorithms; singularities and geometry; Hirota's bilinear formalism for lattices; intriguing properties of discrete Painlevé equations; and the novel theory of Lagrangian multiforms. The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples. Written by respected experts in the field, the numerous exercises and the thoroug...
Progress in Industrial Mathematics at ECMI 96
mathematicians get inspiration from industrial demands. The European Consortium for Mathematics in Industry aims to create contact between industry and academia, and to promote research in industrial mathematics. This book contains a broad spectrum of mathematics applied to industrial problems. Applied...... mathematics, case studies, and review papers in the following fields are included: Environmental modelling, railway systems, industrial processes, electronics, ships, oil industry, optimization, machine dynamics, fluids in industry. Applied mathematicians and other professionals working in academia...
Mathematical modelling techniques
Aris, Rutherford
1995-01-01
""Engaging, elegantly written."" - Applied Mathematical ModellingMathematical modelling is a highly useful methodology designed to enable mathematicians, physicists and other scientists to formulate equations from a given nonmathematical situation. In this elegantly written volume, a distinguished theoretical chemist and engineer sets down helpful rules not only for setting up models but also for solving the mathematical problems they pose and for evaluating models.The author begins with a discussion of the term ""model,"" followed by clearly presented examples of the different types of mode
Abu Darda
2016-01-01
Full Text Available The objective of mathematics education is not only preparingmathematicians but making well-informed citizens. This is a broad generalterms for objective of the teaching of mathematics. And, this might beimplemented as “accurate thorough knowledge” or “original logicalthinking”. So, teaching mathematics is not the conversation andtransmission of mathematical knowledge, but on the aim of preparing wellinformedcitizens trained in independent, critical thinking.By the mathematics, sciences become simple, clearer, and easier to bedeveloped. The mathematics is often applied for solving any problem ofother field of sciences, either in the physics such as astronomy, chemistry,technique; or social sciences such as economy, demography, and assurance.Those all need an analysis reading ability.Mathematical skill, therefore, relates strongly with the analysisreading ability in the human intellectual structure. This study is about therelationship between them. And, result of the study shows us as below:Both Mathematical skill and analysis reading ability possess the “high type”of thinking operation. Both also involve the same content of the abstractintelligent, i.e. symbolic and semantic contents. Last but not least, both alsouse the same product of thinking, i.e. units, classes, relations, and systems.Both can be transformed and have an implication.
Nakamura, Yoshimasa; Sekido, Hiroto
2018-04-01
The finite or the semi-infinite discrete-time Toda lattice has many applications to various areas in applied mathematics. The purpose of this paper is to review how the Toda lattice appears in the Lanczos algorithm through the quotient-difference algorithm and its progressive form (pqd). Then a multistep progressive algorithm (MPA) for solving linear systems is presented. The extended Lanczos parameters can be given not by computing inner products of the extended Lanczos vectors but by using the pqd algorithm with highly relative accuracy in a lower cost. The asymptotic behavior of the pqd algorithm brings us some applications of MPA related to eigenvectors.
If You Had To Tell an Alien What Math Is...: Construct of Mathematics and SQUARE ONE TV.
Debold, Elizabeth
The ideas of the nature, purpose, and scope of mathematics held by students is an issue of interest to the mathematics education community. Movement from a mathematics as discrete operations perspective to a mathematics as problem-solving perspective is a desired change in mathematics education reform. A pretest/posttest experimental design study…
Prateek Sharma
2015-01-01
Abstract Simulation can be regarded as the emulation of the behavior of a real-world system over an interval of time. The process of simulation relies upon the generation of the history of a system and then analyzing that history to predict the outcome and improve the working of real systems. Simulations can be of various kinds but the topic of interest here is one of the most important kind of simulation which is Discrete-Event Simulation which models the system as a discrete sequence of ev...
Positivity for Convective Semi-discretizations
Fekete, Imre
2017-04-19
We propose a technique for investigating stability properties like positivity and forward invariance of an interval for method-of-lines discretizations, and apply the technique to study positivity preservation for a class of TVD semi-discretizations of 1D scalar hyperbolic conservation laws. This technique is a generalization of the approach suggested in Khalsaraei (J Comput Appl Math 235(1): 137–143, 2010). We give more relaxed conditions on the time-step for positivity preservation for slope-limited semi-discretizations integrated in time with explicit Runge–Kutta methods. We show that the step-size restrictions derived are sharp in a certain sense, and that many higher-order explicit Runge–Kutta methods, including the classical 4th-order method and all non-confluent methods with a negative Butcher coefficient, cannot generally maintain positivity for these semi-discretizations under any positive step size. We also apply the proposed technique to centered finite difference discretizations of scalar hyperbolic and parabolic problems.
Cycles of a discrete time bipolar artificial neural network
Cheng Suisun; Chen, J.-S.; Yueh, W.-C.
2009-01-01
A discrete time bipolar neural network depending on two parameters is studied. It is observed that its dynamical behaviors can be classified into six cases. For each case, the long time behaviors can be summarized in terms of fixed points, periodic points, basin of attractions, and related initial distributions. Mathematical reasons are supplied for these observations and applications in cellular automata are illustrated.
a pyramid algorithm for the haar discrete wavelet packet transform
PROF EKWUEME
computer-aided signal processing of non-stationary signals, this paper develops a pyramid algorithm for the discrete wavelet packet ... Edith T. Luhanga, School of Computational and Communication Sciences and Engineering, Nelson Mandela African. Institute of ..... Mathematics, Washington University. 134. EDITH T.
Modular Control of Discrete-Event Systems with Coalgebra
Komenda, Jan; van Schuppen, J. H.
2008-01-01
Roč. 53, č. 2 (2008), s. 447-460 ISSN 0018-9286 R&D Projects: GA AV ČR(CZ) KJB100190609 Institutional research plan: CEZ:AV0Z10190503 Keywords : discrete-event systems * modular supervisory control * coalgebra Subject RIV: BA - General Mathematics Impact factor: 3.293, year: 2008
Blomhøj, Morten
2004-01-01
Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...... modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive...
Mathematical Modeling and Pure Mathematics
Usiskin, Zalman
2015-01-01
Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…
Fair value accounting and managerial discretion
Byrne, A.; Clacher, I.; Hillier, D.; Hodgson, A.
2008-01-01
We analyse the extent to which managers exercise discretion under fair value accounting and the value relevance of these disclosures. Utilising a sample of firms that apply the UK fair value pension accounting standard, (FRS-17), we examine the main determinants of the assumptions managers use to
Reproductive Health Services Discrete-Event Simulation
Lee, Sungjoo; Giles, Denise F.; Goldsman, David; Cook, Douglas A.; Mishra, Ninad; McCarthy, Brian
2006-01-01
Low resource healthcare environments are often characteristic of patient flow patterns with varying patient risks, extensive patient waiting times, uneven workload distributions, and inefficient service delivery. Models from industrial and systems engineering allow for a greater examination of processes by applying discrete-event computer simulation techniques to evaluate and optimize hospital performance.
Huaiqin Wu
2012-01-01
Full Text Available By combing the theories of the switched systems and the interval neural networks, the mathematics model of the switched interval neural networks with discrete and distributed time-varying delays of neural type is presented. A set of the interval parameter uncertainty neural networks with discrete and distributed time-varying delays of neural type are used as the individual subsystem, and an arbitrary switching rule is assumed to coordinate the switching between these networks. By applying the augmented Lyapunov-Krasovskii functional approach and linear matrix inequality (LMI techniques, a delay-dependent criterion is achieved to ensure to such switched interval neural networks to be globally asymptotically robustly stable in terms of LMIs. The unknown gain matrix is determined by solving this delay-dependent LMIs. Finally, an illustrative example is given to demonstrate the validity of the theoretical results.
Control of discrete-event systems with modular or distributed structure
Komenda, Jan; van Schuppen, J. H.
2007-01-01
Roč. 388, č. 3 (2007), s. 199-226 ISSN 0304-3975 R&D Projects: GA AV ČR(CZ) KJB100190609 Institutional research plan: CEZ:AV0Z10190503 Keywords : supervisory control * modular discrete-event system * distributed discrete-event system Subject RIV: BA - General Mathematics Impact factor: 0.735, year: 2007
On the relationship of steady states of continuous and discrete models arising from biology.
Veliz-Cuba, Alan; Arthur, Joseph; Hochstetler, Laura; Klomps, Victoria; Korpi, Erikka
2012-12-01
For many biological systems that have been modeled using continuous and discrete models, it has been shown that such models have similar dynamical properties. In this paper, we prove that this happens in more general cases. We show that under some conditions there is a bijection between the steady states of continuous and discrete models arising from biological systems. Our results also provide a novel method to analyze certain classes of nonlinear models using discrete mathematics.
We also describe discrete-time systems in terms of difference ... A more modern alternative, especially for larger systems, is to convert ... In other words, ..... picture?) State-variable equations are also called state-space equations because the ...
Discrete Lorentzian quantum gravity
Loll, R.
2000-01-01
Just as for non-abelian gauge theories at strong coupling, discrete lattice methods are a natural tool in the study of non-perturbative quantum gravity. They have to reflect the fact that the geometric degrees of freedom are dynamical, and that therefore also the lattice theory must be formulated
Stöltzner, Michael
Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.
Discrete Exterior Calculus Discretization of Incompressible Navier-Stokes Equations
Mohamed, Mamdouh S.; Hirani, Anil N.; Samtaney, Ravi
2017-01-01
A conservative discretization of incompressible Navier-Stokes equations over surface simplicial meshes is developed using discrete exterior calculus (DEC). Numerical experiments for flows over surfaces reveal a second order accuracy
Mayari, R.; Espinosa, M. C.; Ruiz, M. [Centro Nacional de Investigaciones Ceintificas. La Habana (Cuba); Romero, E. [Universidad de Huelva (Spain)
2000-07-01
This work shows as specific methodology for the determination of dissolved oxygen in saline waters that allows to consider the variations of temperature and of concentration of salts. Both factors influence the solubility of the gases in water, making possible in place measurements, in bodies of water with content of salts unto of the concentration of sea water, with greater dependability. The mathematical models obtained are shown, the errors due to equipment, as well as the results obtained when applying this methodology in saline waters with diverse levels of contamination this allows to discern when the decrease of dissolved oxygen levels is due to an increase in the salinity or to an increase in the contamination of the water body. (Author) 7 refs.
Discrete mKdV and discrete sine-Gordon flows on discrete space curves
Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro
2014-01-01
In this paper, we consider the discrete deformation of the discrete space curves with constant torsion described by the discrete mKdV or the discrete sine-Gordon equations, and show that it is formulated as the torsion-preserving equidistant deformation on the osculating plane which satisfies the isoperimetric condition. The curve is reconstructed from the deformation data by using the Sym–Tafel formula. The isoperimetric equidistant deformation of the space curves does not preserve the torsion in general. However, it is possible to construct the torsion-preserving deformation by tuning the deformation parameters. Further, it is also possible to make an arbitrary choice of the deformation described by the discrete mKdV equation or by the discrete sine-Gordon equation at each step. We finally show that the discrete deformation of discrete space curves yields the discrete K-surfaces. (paper)
Mathematical statistics and stochastic processes
Bosq, Denis
2013-01-01
Generally, books on mathematical statistics are restricted to the case of independent identically distributed random variables. In this book however, both this case AND the case of dependent variables, i.e. statistics for discrete and continuous time processes, are studied. This second case is very important for today's practitioners.Mathematical Statistics and Stochastic Processes is based on decision theory and asymptotic statistics and contains up-to-date information on the relevant topics of theory of probability, estimation, confidence intervals, non-parametric statistics and rob
African Journal of Educational Studies in Mathematics and Sciences ...
African Journal of Educational Studies in Mathematics and Sciences. ... The level of detail varies; some disciplines produce manuscripts that comprise discrete .... Duplicate publication, sometimes called self-plagiarism, occurs when an author ...
Aigner, Martin; Spain, Philip G
2010-01-01
Mathematics is all around us. Often we do not realize it, though. Mathematics Everywhere is a collection of presentations on the role of mathematics in everyday life, through science, technology, and culture. The common theme is the unique position of mathematics as the art of pure thought and at the same time as a universally applicable science. The authors are renowned mathematicians; their presentations cover a wide range of topics. From compact discs to the stock exchange, from computer tomography to traffic routing, from electronic money to climate change, they make the "math inside" unde
Pappas, Theoni
1997-01-01
In this highly readable volume of vignettes of mathematical scandals and gossip, Theoni Pappas assembles 29 fascinating stories of intrigue and the bizarre ? in short, the human background of the history of mathematics. Might a haberdasher have changed Einstein's life? Why was the first woman mathematician murdered? How come there's no Nobel Prize in mathematics?Mathematics is principally about numbers, equations, and solutions, all of them precise and timeless. But, behind this arcane matter lies the sometimes sordid world of real people, whose rivalries and deceptions
Stroud, K A
2013-01-01
A groundbreaking and comprehensive reference that's been a bestseller since it first debuted in 1970, the new seventh edition of Engineering Mathematics has been thoroughly revised and expanded. Providing a broad mathematical survey, this innovative volume covers a full range of topics from the very basic to the advanced. Whether you're an engineer looking for a useful on-the-job reference or want to improve your mathematical skills, or you are a student who needs an in-depth self-study guide, Engineering Mathematics is sure to come in handy time and time again.
An algebra of discrete event processes
Heymann, Michael; Meyer, George
1991-01-01
This report deals with an algebraic framework for modeling and control of discrete event processes. The report consists of two parts. The first part is introductory, and consists of a tutorial survey of the theory of concurrency in the spirit of Hoare's CSP, and an examination of the suitability of such an algebraic framework for dealing with various aspects of discrete event control. To this end a new concurrency operator is introduced and it is shown how the resulting framework can be applied. It is further shown that a suitable theory that deals with the new concurrency operator must be developed. In the second part of the report the formal algebra of discrete event control is developed. At the present time the second part of the report is still an incomplete and occasionally tentative working paper.
Acceleration techniques for the discrete ordinate method
Efremenko, Dmitry; Doicu, Adrian; Loyola, Diego; Trautmann, Thomas
2013-01-01
In this paper we analyze several acceleration techniques for the discrete ordinate method with matrix exponential and the small-angle modification of the radiative transfer equation. These techniques include the left eigenvectors matrix approach for computing the inverse of the right eigenvectors matrix, the telescoping technique, and the method of false discrete ordinate. The numerical simulations have shown that on average, the relative speedup of the left eigenvector matrix approach and the telescoping technique are of about 15% and 30%, respectively. -- Highlights: ► We presented the left eigenvector matrix approach. ► We analyzed the method of false discrete ordinate. ► The telescoping technique is applied for matrix operator method. ► Considered techniques accelerate the computations by 20% in average.
mathematical models for estimating radio channels utilization
2017-08-08
Aug 8, 2017 ... Mathematical models for radio channels utilization assessment by real-time flows transfer in ... data transmission networks application having dynamic topology ..... Journal of Applied Mathematics and Statistics, 56(2): 85–90.
Proceedings – Mathematical Sciences | Indian Academy of Sciences
Department of Applied Mathematics, Andhra University, Visakhapatnam 530 003, India; Department of Mathematics, Gayatri Vidya Parishad College of Engineering for Women, Madhurawada, Visakhapatnam 530 048, India; Department of Mathematics, Sri Prakash College of Engineering, Tuni 533 401, India ...
Snow, D.R.
1975-01-01
This paper provides mathematicians and other persons interested in energy problems with some ideas of the kinds of mathematics being applied and a few ideas for further investigation both in the relevant mathematics and in mathematical modeling. This paper is not meant to be an extensive bibliography on the subject, but references are provided. The Conference emphasized large scale and economic considerations related to energy rather than specific technologies, but additional mathematical problems arising in current and future technologies are suggested. Several of the papers dealt with linear programming models of large scale systems related to energy. These included economic models, policy models, energy sector models for supply and demand and environmental concerns. One of the economic models utilized variational techniques including such things as the Hamiltonian, the Euler-Lagrange differential equation, transversality and natural boundary conditions
Modern problems in insurance mathematics
Martin-Löf, Anders
2014-01-01
This book is a compilation of 21 papers presented at the International Cramér Symposium on Insurance Mathematics (ICSIM) held at Stockholm University in June, 2013. The book comprises selected contributions from several large research communities in modern insurance mathematics and its applications. The main topics represented in the book are modern risk theory and its applications, stochastic modelling of insurance business, new mathematical problems in life and non-life insurance, and related topics in applied and financial mathematics. The book is an original and useful source of inspiration and essential reference for a broad spectrum of theoretical and applied researchers, research students and experts from the insurance business. In this way, Modern Problems in Insurance Mathematics will contribute to the development of research and academy–industry co-operation in the area of insurance mathematics and its applications.
Roberts, Fred; Thrall, Robert
1983-01-01
The purpose of this four volume series is to make available for college teachers and students samples of important and realistic applications of mathematics which can be covered in undergraduate programs. The goal is to provide illustrations of how modem mathematics is actually employed to solve relevant contemporary problems. Although these independent chapters were prepared primarily for teachers in the general mathematical sciences, they should prove valuable to students, teachers, and research scientists in many of the fields of application as well. Prerequisites for each chapter and suggestions for the teacher are provided. Several of these chapters have been tested in a variety of classroom settings, and all have undergone extensive peer review and revision. Illustrations and exercises be covered in one class, are included in most chapters. Some units can whereas others provide sufficient material for a few weeks of class time. Volume 1 contains 23 chapters and deals with differential equations and, in ...
2002-01-01
Discrete geometry investigates combinatorial properties of configurations of geometric objects. To a working mathematician or computer scientist, it offers sophisticated results and techniques of great diversity and it is a foundation for fields such as computational geometry or combinatorial optimization. This book is primarily a textbook introduction to various areas of discrete geometry. In each area, it explains several key results and methods, in an accessible and concrete manner. It also contains more advanced material in separate sections and thus it can serve as a collection of surveys in several narrower subfields. The main topics include: basics on convex sets, convex polytopes, and hyperplane arrangements; combinatorial complexity of geometric configurations; intersection patterns and transversals of convex sets; geometric Ramsey-type results; polyhedral combinatorics and high-dimensional convexity; and lastly, embeddings of finite metric spaces into normed spaces. Jiri Matousek is Professor of Com...
Time Discretization Techniques
Gottlieb, S.
2016-10-12
The time discretization of hyperbolic partial differential equations is typically the evolution of a system of ordinary differential equations obtained by spatial discretization of the original problem. Methods for this time evolution include multistep, multistage, or multiderivative methods, as well as a combination of these approaches. The time step constraint is mainly a result of the absolute stability requirement, as well as additional conditions that mimic physical properties of the solution, such as positivity or total variation stability. These conditions may be required for stability when the solution develops shocks or sharp gradients. This chapter contains a review of some of the methods historically used for the evolution of hyperbolic PDEs, as well as cutting edge methods that are now commonly used.
Introduction to the mathematics of finance from risk management to options pricing
Roman, Steven
2004-01-01
The Mathematics of Finance has become a hot topic in applied mathematics ever since the discovery of the Black-Scholes option pricing formulas in 1973. Unfortunately, there are very few undergraduate textbooks in this area. This book is specifically written for upper division undergraduate or beginning graduate students in mathematics, finance or economics. With the exception of an optional chapter on the Capital Asset Pricing Model, the book concentrates on discrete derivative pricing models, culminating in a careful and complete derivation of the Black-Scholes option pricing formulas as a limiting case of the Cox-Ross-Rubinstein discrete model. The final chapter is devoted to American options. The mathematics is not watered down but is appropriate for the intended audience. No measure theory is used and only a small amount of linear algebra is required. All necessary probability theory is developed in several chapters throughout the book, on a "need-to-know" basis. No background in finance is required, sinc...
Discrete variational Hamiltonian mechanics
Lall, S; West, M
2006-01-01
The main contribution of this paper is to present a canonical choice of a Hamiltonian theory corresponding to the theory of discrete Lagrangian mechanics. We make use of Lagrange duality and follow a path parallel to that used for construction of the Pontryagin principle in optimal control theory. We use duality results regarding sensitivity and separability to show the relationship between generating functions and symplectic integrators. We also discuss connections to optimal control theory and numerical algorithms
Discrete port-Hamiltonian systems
Talasila, V.; Clemente-Gallardo, J.; Schaft, A.J. van der
2006-01-01
Either from a control theoretic viewpoint or from an analysis viewpoint it is necessary to convert smooth systems to discrete systems, which can then be implemented on computers for numerical simulations. Discrete models can be obtained either by discretizing a smooth model, or by directly modeling
A paradigm for discrete physics
Noyes, H.P.; McGoveran, D.; Etter, T.; Manthey, M.J.; Gefwert, C.
1987-01-01
An example is outlined for constructing a discrete physics using as a starting point the insight from quantum physics that events are discrete, indivisible and non-local. Initial postulates are finiteness, discreteness, finite computability, absolute nonuniqueness (i.e., homogeneity in the absence of specific cause) and additivity
Mastering mathematics for Edexcel GCSE
Davis, Heather; Liggett, Linda
2015-01-01
Help students to develop their knowledge, skills and understanding so that they can reason mathematically, communicate mathematical information and apply mathematical techniques in solving problems; with resources developed specifically for the Edexcel GCSE 2015 specification with leading Assessment Consultant Keith Pledger and a team of subject specialists. - Supports you and your students through the new specifications, with topic explanations and new exam-style questions, to support the new assessment objectives. - Builds understanding and measures progress throughout the course with plenty
Discrete variational methods and their application to electronic structures
Ellis, D.E.
1987-01-01
Some general concepts concerning Discrete Variational methods are developed and applied to problems of determination of eletronic spectra, charge densities and bonding of free molecules, surface-chemisorbed species and bulk solids. (M.W.O.) [pt
Conference on "Mathematical Technology of Networks"
2015-01-01
Bringing together leading researchers in the fields of functional analysis, mathematical physics and graph theory, as well as natural scientists using networks as a tool in their own research fields, such as neuroscience and machine learning, this volume presents recent advances in functional, analytical, probabilistic, and spectral aspects in the study of graphs, quantum graphs, and complex networks. The contributors to this volume explore the interplay between theoretical and applied aspects of discrete and continuous graphs. Their work helps to close the gap between different avenues of research on graphs, including metric graphs and ramified structures. All papers were presented at the conference "Mathematical Technology of Networks," held December 4–7, 2013 at the Zentrum für interdisziplinäre Forschung (ZiF) in Bielefeld, Germany, and are supplemented with detailed figures illustrating both abstract concepts as well as their real-world applications. Dynamical models on graphs or random graphs a...
Kleene, Stephen Cole
1967-01-01
Undergraduate students with no prior instruction in mathematical logic will benefit from this multi-part text. Part I offers an elementary but thorough overview of mathematical logic of 1st order. Part II introduces some of the newer ideas and the more profound results of logical research in the 20th century. 1967 edition.
Huckstep, Peter
2002-01-01
Contends teachers must resist the temptation to suggest that, while children can create stories and melodies, they cannot create mathematics. Quotes mathematician G. H. Hardy: "A mathematician, like a painter or poet, is a 'maker' of patterns." Considers mathematics should be able to stand up for itself. (BT)
Batchelder, William H
2010-09-01
Mathematical psychology is a sub-field of psychology that started in the 1950s and has continued to grow as an important contributor to formal psychological theory, especially in the cognitive areas of psychology such as learning, memory, classification, choice response time, decision making, attention, and problem solving. In addition, there are several scientific sub-areas that were originated by mathematical psychologists such as the foundations of measurement, stochastic memory models, and psychologically motivated reformulations of expected utility theory. Mathematical psychology does not include all uses of mathematics and statistics in psychology, and indeed there is a long history of such uses especially in the areas of perception and psychometrics. What is most unique about mathematical psychology is its approach to theory construction. While accepting the behaviorist dictum that the data in psychology must be observable and replicable, mathematical models are specified in terms of unobservable formal constructs that can predict detailed aspects of data across multiple experimental and natural settings. By now almost all the substantive areas of cognitive and experimental psychology have formal mathematical models and theories, and many of these are due to researchers that identify with mathematical psychology. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website. Copyright © 2010 John Wiley & Sons, Ltd.
Kodaira, Kunihiko
1996-01-01
This is the translation from the Japanese textbook for the grade 11 course, "General Mathematics". It is part of the easier of the three elective courses in mathematics offered at this level and is taken by about 40% of students. The book covers basic notions of probability and statistics, vectors, exponential, logarithmic, and trigonometric functions, and an introduction to differentiation and integration.
Discrete wavelet transform: a tool in smoothing kinematic data.
Ismail, A R; Asfour, S S
1999-03-01
Motion analysis systems typically introduce noise to the displacement data recorded. Butterworth digital filters have been used to smooth the displacement data in order to obtain smoothed velocities and accelerations. However, this technique does not yield satisfactory results, especially when dealing with complex kinematic motions that occupy the low- and high-frequency bands. The use of the discrete wavelet transform, as an alternative to digital filters, is presented in this paper. The transform passes the original signal through two complementary low- and high-pass FIR filters and decomposes the signal into an approximation function and a detail function. Further decomposition of the signal results in transforming the signal into a hierarchy set of orthogonal approximation and detail functions. A reverse process is employed to perfectly reconstruct the signal (inverse transform) back from its approximation and detail functions. The discrete wavelet transform was applied to the displacement data recorded by Pezzack et al., 1977. The smoothed displacement data were twice differentiated and compared to Pezzack et al.'s acceleration data in order to choose the most appropriate filter coefficients and decomposition level on the basis of maximizing the percentage of retained energy (PRE) and minimizing the root mean square error (RMSE). Daubechies wavelet of the fourth order (Db4) at the second decomposition level showed better results than both the biorthogonal and Coiflet wavelets (PRE = 97.5%, RMSE = 4.7 rad s-2). The Db4 wavelet was then used to compress complex displacement data obtained from a noisy mathematically generated function. Results clearly indicate superiority of this new smoothing approach over traditional filters.
Murray, James D
1993-01-01
The book is a textbook (with many exercises) giving an in-depth account of the practical use of mathematical modelling in the biomedical sciences. The mathematical level required is generally not high and the emphasis is on what is required to solve the real biological problem. The subject matter is drawn, e.g. from population biology, reaction kinetics, biological oscillators and switches, Belousov-Zhabotinskii reaction, reaction-diffusion theory, biological wave phenomena, central pattern generators, neural models, spread of epidemics, mechanochemical theory of biological pattern formation and importance in evolution. Most of the models are based on real biological problems and the predictions and explanations offered as a direct result of mathematical analysis of the models are important aspects of the book. The aim is to provide a thorough training in practical mathematical biology and to show how exciting and novel mathematical challenges arise from a genuine interdisciplinary involvement with the biosci...
Parshall, Karen Hunger
2002-01-01
Although today's mathematical research community takes its international character very much for granted, this "global nature" is relatively recent, having evolved over a period of roughly 150 years-from the beginning of the nineteenth century to the middle of the twentieth century. During this time, the practice of mathematics changed from being centered on a collection of disparate national communities to being characterized by an international group of scholars for whom the goal of mathematical research and cooperation transcended national boundaries. Yet, the development of an international community was far from smooth and involved obstacles such as war, political upheaval, and national rivalries. Until now, this evolution has been largely overlooked by historians and mathematicians alike. This book addresses the issue by bringing together essays by twenty experts in the history of mathematics who have investigated the genesis of today's international mathematical community. This includes not only develo...
Discrete bipolar universal integrals
Greco, S.; Mesiar, Radko; Rindone, F.
2014-01-01
Roč. 252, č. 1 (2014), s. 55-65 ISSN 0165-0114 R&D Projects: GA ČR GAP402/11/0378 Institutional support: RVO:67985556 Keywords : bipolar integral * universal integral * Choquet integral Subject RIV: BA - General Mathematics Impact factor: 1.986, year: 2014 http://library.utia.cas.cz/separaty/2014/E/mesiar-0432224.pdf
Discrete dynamic modeling of cellular signaling networks.
Albert, Réka; Wang, Rui-Sheng
2009-01-01
Understanding signal transduction in cellular systems is a central issue in systems biology. Numerous experiments from different laboratories generate an abundance of individual components and causal interactions mediating environmental and developmental signals. However, for many signal transduction systems there is insufficient information on the overall structure and the molecular mechanisms involved in the signaling network. Moreover, lack of kinetic and temporal information makes it difficult to construct quantitative models of signal transduction pathways. Discrete dynamic modeling, combined with network analysis, provides an effective way to integrate fragmentary knowledge of regulatory interactions into a predictive mathematical model which is able to describe the time evolution of the system without the requirement for kinetic parameters. This chapter introduces the fundamental concepts of discrete dynamic modeling, particularly focusing on Boolean dynamic models. We describe this method step-by-step in the context of cellular signaling networks. Several variants of Boolean dynamic models including threshold Boolean networks and piecewise linear systems are also covered, followed by two examples of successful application of discrete dynamic modeling in cell biology.
Sead Rešić
2015-09-01
Full Text Available It is very difficult to motivate students when it comes to a school subject like Mathematics. Teachers spend a lot of time trying to find something that will arouse interest in students. It is particularly difficult to find materials that are motivating enough for students that they eagerly wait for the next lesson. One of the solutions may be found in Vedic Mathematics. Traditional methods of teaching Mathematics create fear of this otherwise interesting subject in the majority of students. Fear increases failure. Often the traditional, conventional mathematical methods consist of very long lessons which are difficult to understand. Vedic Mathematics is an ancient system that is very flexible and encourages the development of intuition and innovation. It is a mental calculating tool that does not require a calculator because the calculator is embedded in each of us. Starting from the above problems of fear and failure in Mathematics, the goal of this paper is to do research with the control and the experimental group and to compare the test results. Two tests should be done for each of the groups. The control group would do the tests in the conventional way. The experimental group would do the first test in a conventional manner and then be subjected to different treatment, that is to say, be taught on the basis of Vedic Mathematics. After that, the second group would do the second test according to the principles of Vedic Mathematics. Expectations are that after short lectures on Vedic mathematics results of the experimental group would improve and that students will show greater interest in Mathematics.
How to discretize differential systems in a systematic way
Murata, M; Satsuma, J; Ramani, A; Grammaticos, B
2010-01-01
We present a systematic approach to the construction of discrete analogues for differential systems. Our method is tailored to first-order differential equations and relies on a formal linearization, followed by a Pade-like rational approximation of an exponential evolution operator. We apply our method to a host of systems for which there exist discretization results obtained by what we call the 'intuitive' method and compare the discretizations obtained. A discussion of our method as compared to one of the Mickens is also presented. Finally we apply our method to a system of coupled Riccati equations with emphasis on the preservation of the integrable character of the differential system.
Two new discrete integrable systems
Chen Xiao-Hong; Zhang Hong-Qing
2013-01-01
In this paper, we focus on the construction of new (1+1)-dimensional discrete integrable systems according to a subalgebra of loop algebra Ã 1 . By designing two new (1+1)-dimensional discrete spectral problems, two new discrete integrable systems are obtained, namely, a 2-field lattice hierarchy and a 3-field lattice hierarchy. When deriving the two new discrete integrable systems, we find the generalized relativistic Toda lattice hierarchy and the generalized modified Toda lattice hierarchy. Moreover, we also obtain the Hamiltonian structures of the two lattice hierarchies by means of the discrete trace identity
Strategy Instruction in Mathematics.
Goldman, Susan R.
1989-01-01
Experiments in strategy instruction for mathematics have been conducted using three models (direct instruction, self-instruction, and guided learning) applied to the tasks of computation and word problem solving. Results have implications for effective strategy instruction for learning disabled students. It is recommended that strategy instruction…
Towards mathematical philosophy
Hendricks, Vincent F
2008-01-01
Logical investigations in cognitive science have successfully utilized methods and systems of belief revision, non-monotonic logic and dynamic epistemic logic. This title deals with focal issues of belief revision. It contains a collection of articles applying methods of logic or, more generally, of mathematics to solve problems.
An application of a discrete fixed point theorem to the Cournot model
Sato, Junichi
2008-01-01
In this paper, we apply a discrete fixed point theorem of [7] to the Cournot model [1]. Then we can deal with the Cournot model where the production of the enterprises is discrete. To handle it, we define a discrete Cournot-Nash equilibrium, and prove its existence.
Pontrjagin, Lev Semenovič
1984-01-01
Lev Semenovic Pontrjagin (1908) is one of the outstanding figures in 20th century mathematics. In a long career he has made fundamental con tributions to many branches of mathematics, both pure and applied. He has received every honor that a grateful government can bestow. Though in no way constrained to do so, he has through the years taught mathematics courses at Moscow State University. In the year 1975 he set himself the task of writing a series of books on secondary school and beginning university mathematics. In his own words, "I wished to set forth the foundations of higher mathematics in a form that would have been accessible to myself as a lad, but making use of all my experience as a scientist and a teacher, ac cumulated over many years. " The present volume is a translation of the first two out of four moderately sized volumes on this theme planned by Pro fessor Pontrjagin. The book begins at the beginning of modern mathematics, analytic ge ometry in the plane and 3-dimensional space. Refin...
Bird, John
2014-01-01
A practical introduction to the core mathematics required for engineering study and practiceNow in its seventh edition, Engineering Mathematics is an established textbook that has helped thousands of students to succeed in their exams.John Bird's approach is based on worked examples and interactive problems. This makes it ideal for students from a wide range of academic backgrounds as the student can work through the material at their own pace. Mathematical theories are explained in a straightforward manner, being supported by practical engineering examples and applications in order to ensure