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Exponential Sums And Differential Equations
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Book Synopsis Exponential Sums and Differential Equations. (AM-124), Volume 124 by : Nicholas M. Katz
Download or read book Exponential Sums and Differential Equations. (AM-124), Volume 124 written by Nicholas M. Katz and published by Princeton University Press. This book was released on 2016-03-02 with total page 445 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differential equations in one complex variable with polynomial coefficients, and the theory of one parameter families of exponential sums over finite fields. After reviewing some results from representation theory, the book discusses results about differential equations and their differential galois groups (G) and one-parameter families of exponential sums and their geometric monodromy groups (G). The final part of the book is devoted to comparison theorems relating G and G of suitably "corresponding" situations, which provide a systematic explanation of the remarkable "coincidences" found "by hand" in the hypergeometric case.
Book Synopsis Exponential Sums and Differential Equations by : Nicholas M. Katz
Download or read book Exponential Sums and Differential Equations written by Nicholas M. Katz and published by Princeton University Press. This book was released on 1990-09-21 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with two areas of mathematics, at first sight disjoint, and with some of the analogies and interactions between them. These areas are the theory of linear differential equations in one complex variable with polynomial coefficients, and the theory of one parameter families of exponential sums over finite fields. After reviewing some results from representation theory, the book discusses results about differential equations and their differential galois groups (G) and one-parameter families of exponential sums and their geometric monodromy groups (G). The final part of the book is devoted to comparison theorems relating G and G of suitably "corresponding" situations, which provide a systematic explanation of the remarkable "coincidences" found "by hand" in the hypergeometric case.
Book Synopsis Van Der Corput's Method of Exponential Sums by : S. W. Graham
Download or read book Van Der Corput's Method of Exponential Sums written by S. W. Graham and published by Cambridge University Press. This book was released on 1991-01-25 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a self-contained account of the one- and two-dimensional van der Corput method and its use in estimating exponential sums. These arise in many problems in analytic number theory. It is the first cohesive account of much of this material and will be welcomed by graduates and professionals in analytic number theory. The authors show how the method can be applied to problems such as upper bounds for the Riemann-Zeta function. the Dirichlet divisor problem, the distribution of square free numbers, and the Piatetski-Shapiro prime number theorem.
Book Synopsis Fractional Differential Equations by : Zhi-Zhong Sun
Download or read book Fractional Differential Equations written by Zhi-Zhong Sun and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-08-24 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with an introduction to fractional derivatives and numerical approximations, this book presents finite difference methods for fractional differential equations, including time-fractional sub-diffusion equations, time-fractional wave equations, and space-fractional differential equations, among others. Approximation methods for fractional derivatives are developed and approximate accuracies are analyzed in detail.
Book Synopsis Sieve Methods, Exponential Sums, and Their Applications in Number Theory by : G. R. H. Greaves
Download or read book Sieve Methods, Exponential Sums, and Their Applications in Number Theory written by G. R. H. Greaves and published by Cambridge University Press. This book was released on 1997-01-30 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: State-of-the-art analytic number theory proceedings.
Book Synopsis p-adic Differential Equations by : Kiran S. Kedlaya
Download or read book p-adic Differential Equations written by Kiran S. Kedlaya and published by Cambridge University Press. This book was released on 2010-06-10 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to number theory and to computer science. This book, the first comprehensive and unified introduction to the subject, improves and simplifies existing results as well as including original material. Based on a course given by the author at MIT, this modern treatment is accessible to graduate students and researchers. Exercises are included at the end of each chapter to help the reader review the material, and the author also provides detailed references to the literature to aid further study.
Book Synopsis Partial Differential Equations by : Walter A. Strauss
Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Book Synopsis Exponential Data Fitting and Its Applications by : Victor Pereyra
Download or read book Exponential Data Fitting and Its Applications written by Victor Pereyra and published by Bentham Science Publishers. This book was released on 2010 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Real and complex exponential data fitting is an important activity in many different areas of science and engineering, ranging from Nuclear Magnetic Resonance Spectroscopy and Lattice Quantum Chromodynamics to Electrical and Chemical Engineering, Vision a"
Book Synopsis Applied Stochastic Differential Equations by : Simo Särkkä
Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Book Synopsis Character Sums with Exponential Functions and Their Applications by : Sergei Konyagin
Download or read book Character Sums with Exponential Functions and Their Applications written by Sergei Konyagin and published by Penguin Group. This book was released on 1999-09-02 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: A treatment of a lively topic from number theory for graduate students and researchers.
Book Synopsis Computational and Algorithmic Problems in Finite Fields by : Igor Shparlinski
Download or read book Computational and Algorithmic Problems in Finite Fields written by Igor Shparlinski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents an exhaustive treatment of computation and algorithms for finite fields. Topics covered include polynomial factorization, finding irreducible and primitive polynomials, distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types, and new applications of finite fields to other araes of mathematics. For completeness, also included are two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number generators, modular arithmetic etc.), and computational number theory (primality testing, factoring integers, computing in algebraic number theory, etc.) The problems considered here have many applications in computer science, coding theory, cryptography, number theory and discrete mathematics. The level of discussion presuppose only a knowledge of the basic facts on finite fields, and the book can be recommended as supplementary graduate text. For researchers and students interested in computational and algorithmic problems in finite fields.
Book Synopsis Recipes for Continuation by : Harry Dankowicz
Download or read book Recipes for Continuation written by Harry Dankowicz and published by SIAM. This book was released on 2013-01-01 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to the mathematical methodology of parameter continuation, the computational analysis of families of solutions to nonlinear mathematical equations. It develops a systematic formalism for constructing abstract representations of continuation problems and for implementing these in an existing computational platform. Recipes for Continuation lends equal importance to theoretical rigor, algorithm development, and software engineering; demonstrates the use of fully developed toolbox templates for single- and multisegment boundary-value problems to the analysis of periodic orbits in smooth and hybrid dynamical systems, quasi-periodic invariant tori, and homoclinic and heteroclinic connecting orbits between equilibria and/or periodic orbits; shows the use of vectorization for optimal computational efficiency, an object-oriented paradigm for the modular construction of continuation problems, and adaptive discretization algorithms for guaranteed bounds on estimated errors; and contains extensive and fully worked examples that illustrate the application of the MATLAB®-based Computational Continuation Core (COCO) to problems from recent research literature that are relevant to dynamical system models from mechanics, electronics, biology, economics, and neuroscience.
Book Synopsis Dynamical Systems and Probabilistic Methods in Partial Differential Equations by : Percy Deift
Download or read book Dynamical Systems and Probabilistic Methods in Partial Differential Equations written by Percy Deift and published by American Mathematical Soc.. This book was released on 1996 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains some of the lectures presented in June 1994 during the AMS-SIAM Summer Seminar at the Mathematical Sciences Research Institute in Berkeley. The goal of the seminar was to introduce participants to as many interesting and active applications of dynamical systems and probabilistic methods to problems in applied mathematics as possible. As a result, this book covers a great deal of ground. Nevertheless, the pedagogical orientation of the lectures has been retained, and therefore the book will serve as an ideal introduction to these varied and interesting topics.
Book Synopsis Differential Equations And The Stokes Phenomenon by : B L J Braaksma
Download or read book Differential Equations And The Stokes Phenomenon written by B L J Braaksma and published by World Scientific. This book was released on 2002-12-10 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the record of a workshop on differential equations and the Stokes phenomenon, held in May 2001 at the University of Groningen. It contains expanded versions of most of the lectures given at the workshop. To a large extent, both the workshop and the book may be regarded as a sequel to a conference held in Groningen in 1995 which resulted in the book The Stokes Phenomenon and Hilbert's 16th Problem (B L J Braaksma, G K Immink and M van der Put, editors), also published by World Scientific (1996).Both books offer a snapshot concerning the state of the art in the areas of differential, difference and q-difference equations. Apart from the asymptotics of solutions, Painlevé properties and the algebraic theory, new topics addressed in the second book include arithmetic theory of linear equations, and Galois theory and Lie symmetries of nonlinear differential equations.
Book Synopsis Proceedings of the Conference on Differential Equations and the Stokes Phenomenon by : Boele Lieuwe Jan Braaksma
Download or read book Proceedings of the Conference on Differential Equations and the Stokes Phenomenon written by Boele Lieuwe Jan Braaksma and published by World Scientific. This book was released on 2002 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a snapshot concerning the state of the art in the areas of differential, difference and q-difference equations.
Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Book Synopsis Technical Abstract Bulletin by : Defense Documentation Center (U.S.)
Download or read book Technical Abstract Bulletin written by Defense Documentation Center (U.S.) and published by . This book was released on 1961-04 with total page 1746 pages. Available in PDF, EPUB and Kindle. Book excerpt:
