Download or read book Combinatorial Functional Equations written by Yanpei Liu and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-10-21 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume set presents combinatorial functional equations using an algebraic approach, and illustrates their applications in combinatorial maps, graphs, networks, etc. The first volume mainly presents basic concepts and the theoretical background. Differential (ordinary and partial) equations and relevant topics are discussed in detail.
Download or read book Combinatorial Functional Equations written by Yanpei Liu and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-12-16 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume set presents combinatorial functional equations using an algebraic approach, and illustrates their applications in combinatorial maps, graphs, networks, etc. The second volume mainly presents several kinds of meson functional equations which are divided into three types: outer, inner and surface. It is suited for a wide readership, including pure and applied mathematicians, and also computer scientists.
Download or read book Weyl Group Multiple Dirichlet Series written by Ben Brubaker and published by Princeton University Press. This book was released on 2011-07-05 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number theory. By contrast, these Weyl group multiple Dirichlet series may be functions of several complex variables and their groups of functional equations may be arbitrary finite Weyl groups. Furthermore, their coefficients are multiplicative up to roots of unity, generalizing the notion of Euler products. This book proves foundational results about these series and develops their combinatorics. These interesting functions may be described as Whittaker coefficients of Eisenstein series on metaplectic groups, but this characterization doesn't readily lead to an explicit description of the coefficients. The coefficients may be expressed as sums over Kashiwara crystals, which are combinatorial analogs of characters of irreducible representations of Lie groups. For Cartan Type A, there are two distinguished descriptions, and if these are known to be equal, the analytic properties of the Dirichlet series follow. Proving the equality of the two combinatorial definitions of the Weyl group multiple Dirichlet series requires the comparison of two sums of products of Gauss sums over lattice points in polytopes. Through a series of surprising combinatorial reductions, this is accomplished. The book includes expository material about crystals, deformations of the Weyl character formula, and the Yang-Baxter equation.
Download or read book 102 Combinatorial Problems written by Titu Andreescu and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: "102 Combinatorial Problems" consists of carefully selected problems that have been used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Key features: * Provides in-depth enrichment in the important areas of combinatorics by reorganizing and enhancing problem-solving tactics and strategies * Topics include: combinatorial arguments and identities, generating functions, graph theory, recursive relations, sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinatorial and advanced geometry, functional equations and classical inequalities The book is systematically organized, gradually building combinatorial skills and techniques and broadening the student's view of mathematics. Aside from its practical use in training teachers and students engaged in mathematical competitions, it is a source of enrichment that is bound to stimulate interest in a variety of mathematical areas that are tangential to combinatorics.
Download or read book Lectures on Functional Equations and Their Applications written by J. Aczel and published by Courier Corporation. This book was released on 2006-02-01 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerous detailed proofs highlight this treatment of functional equations. Starting with equations that can be solved by simple substitutions, the book then moves to equations with several unknown functions and methods of reduction to differential and integral equations. Also includes composite equations, equations with several unknown functions of several variables, vector and matrix equations, more. 1966 edition.
Download or read book Weyl Group Multiple Dirichlet Series written by Ben Brubaker and published by . This book was released on 2011 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Weyl group multiple Dirichlet series are generalizations of the Riemann zeta function. Like the Riemann zeta function, they are Dirichlet series with analytic continuation and functional equations, having applications to analytic number theory. By contrast, these Weyl group multiple Dirichlet series may be functions of several complex variables and their groups of functional equations may be arbitrary finite Weyl groups. Furthermore, their coefficients are multiplicative up to roots of unity, generalizing the notion of Euler products. This book proves foundational results about these series and develops their combinatorics. These interesting functions may be described as Whittaker coefficients of Eisenstein series on metaplectic groups, but this characterization doesn't readily lead to an explicit description of the coefficients. The coefficients may be expressed as sums over Kashiwara crystals, which are combinatorial analogs of characters of irreducible representations of Lie groups. For Cartan Type A, there are two distinguished descriptions, and if these are known to be equal, the analytic properties of the Dirichlet series follow. Proving the equality of the two combinatorial definitions of the Weyl group multiple Dirichlet series requires the comparison of two sums of products of Gauss sums over lattice points in polytopes. Through a series of surprising combinatorial reductions, this is accomplished. The book includes expository material about crystals, deformations of the Weyl character formula, and the Yang-Baxter equation.
Download or read book Stability of Functional Equations in Several Variables written by D.H. Hyers and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of stability of functional equations of several variables in the sense used here had its origins more than half a century ago when S. Ulam posed the fundamental problem and Donald H. Hyers gave the first significant partial solution in 1941. The subject has been revised and de veloped by an increasing number of mathematicians, particularly during the last two decades. Three survey articles have been written on the subject by D. H. Hyers (1983), D. H. Hyers and Th. M. Rassias (1992), and most recently by G. L. Forti (1995). None of these works included proofs of the results which were discussed. Furthermore, it should be mentioned that wider interest in this subject area has increased substantially over the last years, yet the pre sentation of research has been confined mainly to journal articles. The time seems ripe for a comprehensive introduction to this subject, which is the purpose of the present work. This book is the first to cover the classical results along with current research in the subject. An attempt has been made to present the material in an integrated and self-contained fashion. In addition to the main topic of the stability of certain functional equa tions, some other related problems are discussed, including the stability of the convex functional inequality and the stability of minimum points. A sad note. During the final stages of the manuscript our beloved co author and friend Professor Donald H. Hyers passed away.
Download or read book Analytic Combinatorics written by Marni Mishna and published by CRC Press. This book was released on 2019-11-29 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytic Combinatorics: A Multidimensional Approach is written in a reader-friendly fashion to better facilitate the understanding of the subject. Naturally, it is a firm introduction to the concept of analytic combinatorics and is a valuable tool to help readers better understand the structure and large-scale behavior of discrete objects. Primarily, the textbook is a gateway to the interactions between complex analysis and combinatorics. The study will lead readers through connections to number theory, algebraic geometry, probability and formal language theory. The textbook starts by discussing objects that can be enumerated using generating functions, such as tree classes and lattice walks. It also introduces multivariate generating functions including the topics of the kernel method, and diagonal constructions. The second part explains methods of counting these objects, which involves deep mathematics coming from outside combinatorics, such as complex analysis and geometry. Features Written with combinatorics-centric exposition to illustrate advanced analytic techniques Each chapter includes problems, exercises, and reviews of the material discussed in them Includes a comprehensive glossary, as well as lists of figures and symbols About the author Marni Mishna is a professor of mathematics at Simon Fraser University in British Columbia. Her research investigates interactions between discrete structures and many diverse areas such as representation theory, functional equation theory, and algebraic geometry. Her specialty is the development of analytic tools to study the large-scale behavior of discrete objects.
Download or read book Combinatorial Species and Tree like Structures written by François Bergeron and published by Cambridge University Press. This book was released on 1998 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: The combinatorial theory of species, introduced by Joyal in 1980, provides a unified understanding of the use of generating functions for both labelled and unlabelled structures and as a tool for the specification and analysis of these structures. Of particular importance is their capacity to transform recursive definitions of tree-like structures into functional or differential equations, and vice versa. The goal of this book is to present the basic elements of the theory and to give a unified account of its developments and applications. It offers a modern introduction to the use of various generating functions, with applications to graphical enumeration, Polya theory and analysis of data structures in computer science, and to other areas such as special functions, functional equations, asymptotic analysis and differential equations. This book will be a valuable reference to graduate students and researchers in combinatorics, analysis, and theoretical computer science.
Download or read book A Short Course on Functional Equations written by J. Aczél and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently I taught short courses on functional equations at several universities (Barcelona, Bern, Graz, Hamburg, Milan, Waterloo). My aim was to introduce the most important equations and methods of solution through actual (not artifi cial) applications which were recent and with which I had something to do. Most of them happened to be related to the social or behavioral sciences. All were originally answers to questions posed by specialists in the respective applied fields. Here I give a somewhat extended version of these lectures, with more recent results and applications included. As previous knowledge just the basic facts of calculus and algebra are supposed. Parts where somewhat more (measure theory) is needed and sketches of lengthier calcula tions are set in fine print. I am grateful to Drs. J. Baker (Waterloo, Ont.), W. Forg-Rob (Innsbruck, Austria) and C. Wagner (Knoxville, Tenn.) for critical remarks and to Mrs. Brenda Law for care ful computer-typing of the manuscript (in several versions). A note on numbering of statements and references: The numbering of Lemmata, Propositions, Theorems, Corollaries and (separately) formulae starts anew in each section. If quoted in another section, the section number is added, e.g. (2.10) or Theorem 1.2. References are quoted by the last names of the authors and the last two digits of the year, e.g. Daroczy-Losonczi [671. 1 1. An aggregation theorem for allocation problems. Cauchy equation for single-and multiplace functions. Two extension theorems.
Download or read book Functional Equations Inequalities and Applications written by Themistocles RASSIAS and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional Equations, Inequalities and Applications provides an extensive study of several important equations and inequalities, useful in a number of problems in mathematical analysis. Subjects dealt with include the generalized Cauchy functional equation, the Ulam stability theory in the geometry of partial differential equations, stability of a quadratic functional equation in Banach modules, functional equations and mean value theorems, isometric mappings, functional inequalities of iterative type, related to a Cauchy functional equation, the median principle for inequalities and applications, Hadamard and Dragomir-Agarwal inequalities, the Euler formulae and convex functions and approximate algebra homomorphisms. Also included are applications to some problems of pure and applied mathematics. This book will be of particular interest to mathematicians and graduate students whose work involves functional equations, inequalities and applications.
Download or read book On Applications and Theory of Functional Equations written by J. Aczél and published by . This book was released on 1969 with total page 72 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Functional Equations in Mathematical Analysis written by Themistocles M. Rassias and published by Springer Science & Business Media. This book was released on 2011-09-18 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: The stability problem for approximate homomorphisms, or the Ulam stability problem, was posed by S. M. Ulam in the year 1941. The solution of this problem for various classes of equations is an expanding area of research. In particular, the pursuit of solutions to the Hyers-Ulam and Hyers-Ulam-Rassias stability problems for sets of functional equations and ineqalities has led to an outpouring of recent research. This volume, dedicated to S. M. Ulam, presents the most recent results on the solution to Ulam stability problems for various classes of functional equations and inequalities. Comprised of invited contributions from notable researchers and experts, this volume presents several important types of functional equations and inequalities and their applications to problems in mathematical analysis, geometry, physics and applied mathematics. "Functional Equations in Mathematical Analysis" is intended for researchers and students in mathematics, physics, and other computational and applied sciences.
Download or read book Stability of Functional Equations in Random Normed Spaces written by Yeol Je Cho and published by Springer Science & Business Media. This book was released on 2013-08-27 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the rapidly developing subject of mathematical analysis that deals primarily with stability of functional equations in generalized spaces. The fundamental problem in this subject was proposed by Stan M. Ulam in 1940 for approximate homomorphisms. The seminal work of Donald H. Hyers in 1941 and that of Themistocles M. Rassias in 1978 have provided a great deal of inspiration and guidance for mathematicians worldwide to investigate this extensive domain of research. The book presents a self-contained survey of recent and new results on topics including basic theory of random normed spaces and related spaces; stability theory for new function equations in random normed spaces via fixed point method, under both special and arbitrary t-norms; stability theory of well-known new functional equations in non-Archimedean random normed spaces; and applications in the class of fuzzy normed spaces. It contains valuable results on stability in random normed spaces, and is geared toward both graduate students and research mathematicians and engineers in a broad area of interdisciplinary research.
Download or read book Analytic Combinatorics written by Philippe Flajolet and published by Cambridge University Press. This book was released on 2009-01-15 with total page 825 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
Download or read book Complex Vector Functional Equations written by Valery Covachev and published by World Scientific. This book was released on 2001-11-28 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of complex vector functional equations is a new area in the theory of functional equations. This monograph provides a systematic overview of the authors' recently obtained results concerning both linear and nonlinear complex vector functional equations, in all aspects of their utilization. It is intended for mathematicians, physicists and engineers who use functional equations in their investigations.
Download or read book A Combinatorial Perspective on Quantum Field Theory written by Karen Yeats and published by Springer. This book was released on 2016-11-23 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores combinatorial problems and insights in quantum field theory. It is not comprehensive, but rather takes a tour, shaped by the author’s biases, through some of the important ways that a combinatorial perspective can be brought to bear on quantum field theory. Among the outcomes are both physical insights and interesting mathematics. The book begins by thinking of perturbative expansions as kinds of generating functions and then introduces renormalization Hopf algebras. The remainder is broken into two parts. The first part looks at Dyson-Schwinger equations, stepping gradually from the purely combinatorial to the more physical. The second part looks at Feynman graphs and their periods. The flavour of the book will appeal to mathematicians with a combinatorics background as well as mathematical physicists and other mathematicians.
