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Asymptotic Combinatorics With Application To Mathematical Physics
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Book Synopsis Asymptotic Combinatorics with Application to Mathematical Physics by : V.A. Malyshev
Download or read book Asymptotic Combinatorics with Application to Mathematical Physics written by V.A. Malyshev and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: New and striking results obtained in recent years from an intensive study of asymptotic combinatorics have led to a new, higher level of understanding of related problems: the theory of integrable systems, the Riemann-Hilbert problem, asymptotic representation theory, spectra of random matrices, combinatorics of Young diagrams and permutations, and even some aspects of quantum field theory.
Book Synopsis Asymptotic Combinatorics with Applications to Mathematical Physics by : Anatoly M. Vershik
Download or read book Asymptotic Combinatorics with Applications to Mathematical Physics written by Anatoly M. Vershik and published by Springer. This book was released on 2003-07-03 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the Summer School Saint Petersburg 2001, the main lecture courses bore on recent progress in asymptotic representation theory: those written up for this volume deal with the theory of representations of infinite symmetric groups, and groups of infinite matrices over finite fields; Riemann-Hilbert problem techniques applied to the study of spectra of random matrices and asymptotics of Young diagrams with Plancherel measure; the corresponding central limit theorems; the combinatorics of modular curves and random trees with application to QFT; free probability and random matrices, and Hecke algebras.
Book Synopsis Asymptotic Combinatorics with Applications to Mathematical Physics by : Anatoly M. Vershik
Download or read book Asymptotic Combinatorics with Applications to Mathematical Physics written by Anatoly M. Vershik and published by . This book was released on 2014-01-15 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Methods in Equations of Mathematical Physics by : B Vainberg
Download or read book Asymptotic Methods in Equations of Mathematical Physics written by B Vainberg and published by CRC Press. This book was released on 1989-02-25 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Typed English translation of a monograph first published (in Russian) in 1982. Provides graduate students and researchers with usefully detailed discussion of most of the asymptotic methods standard these days to the work of mathematical physicists. The author prefers not to dwell in the heights of abstraction; he has written a broadly intelligble book, which is informed at every point by his secure command of major physical applications. An expensive but valuable contribution to the literature of an important but too-little-written- about field. Twelve chapters, references. (NW) Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Asymptotic Expansions by : E. T. Copson
Download or read book Asymptotic Expansions written by E. T. Copson and published by Cambridge University Press. This book was released on 2004-06-03 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic representation of a function os of great importance in many branches of pure and applied mathematics.
Book Synopsis Graphs in Perturbation Theory by : Michael Borinsky
Download or read book Graphs in Perturbation Theory written by Michael Borinsky and published by Springer. This book was released on 2018-11-04 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first systematic study of graphical enumeration and the asymptotic algebraic structures in perturbative quantum field theory. Starting with an exposition of the Hopf algebra structure of generic graphs, it reviews and summarizes the existing literature. It then applies this Hopf algebraic structure to the combinatorics of graphical enumeration for the first time, and introduces a novel method of asymptotic analysis to answer asymptotic questions. This major breakthrough has combinatorial applications far beyond the analysis of graphical enumeration. The book also provides detailed examples for the asymptotics of renormalizable quantum field theories, which underlie the Standard Model of particle physics. A deeper analysis of such renormalizable field theories reveals their algebraic lattice structure. The pedagogical presentation allows readers to apply these new methods to other problems, making this thesis a future classic for the study of asymptotic problems in quantum fields, network theory and far beyond.
Book Synopsis Asymptotic Methods for Wave and Quantum Problems by : M. V. Karasev
Download or read book Asymptotic Methods for Wave and Quantum Problems written by M. V. Karasev and published by American Mathematical Soc.. This book was released on 2003 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The collection consists of four papers in different areas of mathematical physics united by the intrinsic coherence of the asymptotic methods used. The papers describe both the known results and most recent achievements, as well as new concepts and ideas in mathematical analysis of quantum and wave problems. In the introductory paper ``Quantization and Intrinsic Dynamics'' a relationship between quantization of symplectic manifolds and nonlinear wave equations is described and discussed from the viewpoint of the weak asymptotics method (asymptotics in distributions) and the semiclassical approximation method. It also explains a hidden dynamic geometry that arises when using these methods. Three other papers discuss applications of asymptotic methods to the construction of wave-type solutions of nonlinear PDE's, to the theory of semiclassical approximation (in particular, the Whitham method) for nonlinear second-order ordinary differential equations, and to the study of the Schrodinger type equations whose potential wells are sufficiently shallow that the discrete spectrum contains precisely one point. All the papers contain detailed references and are oriented not only to specialists in asymptotic methods, but also to a wider audience of researchers and graduate students working in partial differential equations and mathematical physics.
Book Synopsis Idempotent Mathematics and Mathematical Physics by : Grigoriĭ Lazarevich Litvinov
Download or read book Idempotent Mathematics and Mathematical Physics written by Grigoriĭ Lazarevich Litvinov and published by American Mathematical Soc.. This book was released on 2005 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Idempotent mathematics is a rapidly developing new branch of the mathematical sciences that is closely related to mathematical physics. The existing literature on the subject is vast and includes numerous books and journal papers. A workshop was organized at the Erwin Schrodinger Institute for Mathematical Physics (Vienna) to give a snapshot of modern idempotent mathematics. This volume contains articles stemming from that event. Also included is an introductory paper by G. Litvinov and additional invited contributions. The resulting volume presents a comprehensive overview of the state of the art. It is suitable for graduate students and researchers interested in idempotent mathematics and tropical mathematics.
Book Synopsis Combinatorics and Finite Fields by : Kai-Uwe Schmidt
Download or read book Combinatorics and Finite Fields written by Kai-Uwe Schmidt and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-07-08 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics and finite fields are of great importance in modern applications such as in the analysis of algorithms, in information and communication theory, and in signal processing and coding theory. This book contains survey articles on topics such as difference sets, polynomials, and pseudorandomness.
Book Synopsis Introduction to Asymptotic Methods by : David Y. Gao
Download or read book Introduction to Asymptotic Methods written by David Y. Gao and published by CRC Press. This book was released on 2006-05-03 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the theoretical methods for solving many problems of applied mathematics, physics, and technology, asymptotic methods often provide results that lead to obtaining more effective algorithms of numerical evaluation. Presenting the mathematical methods of perturbation theory, Introduction to Asymptotic Methods reviews the most important m
Book Synopsis Asymptotic Expansions by : Edward Thomas Copson
Download or read book Asymptotic Expansions written by Edward Thomas Copson and published by . This book was released on 1976 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Advanced Mathematical Methods for Scientists and Engineers I by : Carl M. Bender
Download or read book Advanced Mathematical Methods for Scientists and Engineers I written by Carl M. Bender and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.
Book Synopsis Asymptotics for Dissipative Nonlinear Equations by : Nakao Hayashi
Download or read book Asymptotics for Dissipative Nonlinear Equations written by Nakao Hayashi and published by Springer. This book was released on 2006-08-29 with total page 557 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book in world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
Book Synopsis Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications by : Yves Achdou
Download or read book Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications written by Yves Achdou and published by Springer. This book was released on 2013-05-24 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Lecture Notes contain the material relative to the courses given at the CIME summer school held in Cetraro, Italy from August 29 to September 3, 2011. The topic was "Hamilton-Jacobi Equations: Approximations, Numerical Analysis and Applications". The courses dealt mostly with the following subjects: first order and second order Hamilton-Jacobi-Bellman equations, properties of viscosity solutions, asymptotic behaviors, mean field games, approximation and numerical methods, idempotent analysis. The content of the courses ranged from an introduction to viscosity solutions to quite advanced topics, at the cutting edge of research in the field. We believe that they opened perspectives on new and delicate issues. These lecture notes contain four contributions by Yves Achdou (Finite Difference Methods for Mean Field Games), Guy Barles (An Introduction to the Theory of Viscosity Solutions for First-order Hamilton-Jacobi Equations and Applications), Hitoshi Ishii (A Short Introduction to Viscosity Solutions and the Large Time Behavior of Solutions of Hamilton-Jacobi Equations) and Grigory Litvinov (Idempotent/Tropical Analysis, the Hamilton-Jacobi and Bellman Equations).
Book Synopsis Random Matrices, Random Processes and Integrable Systems by : John Harnad
Download or read book Random Matrices, Random Processes and Integrable Systems written by John Harnad and published by Springer Science & Business Media. This book was released on 2011-05-06 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the remarkable connections between two domains that, a priori, seem unrelated: Random matrices (together with associated random processes) and integrable systems. The relations between random matrix models and the theory of classical integrable systems have long been studied. These appear mainly in the deformation theory, when parameters characterizing the measures or the domain of localization of the eigenvalues are varied. The resulting differential equations determining the partition function and correlation functions are, remarkably, of the same type as certain equations appearing in the theory of integrable systems. They may be analyzed effectively through methods based upon the Riemann-Hilbert problem of analytic function theory and by related approaches to the study of nonlinear asymptotics in the large N limit. Associated with studies of matrix models are certain stochastic processes, the "Dyson processes", and their continuum diffusion limits, which govern the spectrum in random matrix ensembles, and may also be studied by related methods. Random Matrices, Random Processes and Integrable Systems provides an in-depth examination of random matrices with applications over a vast variety of domains, including multivariate statistics, random growth models, and many others. Leaders in the field apply the theory of integrable systems to the solution of fundamental problems in random systems and processes using an interdisciplinary approach that sheds new light on a dynamic topic of current research.
Book Synopsis The Mathematical Legacy of Richard P. Stanley by : Patricia Hersh
Download or read book The Mathematical Legacy of Richard P. Stanley written by Patricia Hersh and published by American Mathematical Soc.. This book was released on 2016-12-08 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Richard Stanley's work in combinatorics revolutionized and reshaped the subject. His lectures, papers, and books inspired a generation of researchers. In this volume, these researchers explain how Stanley's vision and insights influenced and guided their own perspectives on the subject. As a valuable bonus, this book contains a collection of Stanley's short comments on each of his papers. This book may serve as an introduction to several different threads of ongoing research in combinatorics as well as giving historical perspective.
Book Synopsis Spectral Theory and Geometric Analysis by : Mikhail Aleksandrovich Shubin
Download or read book Spectral Theory and Geometric Analysis written by Mikhail Aleksandrovich Shubin and published by American Mathematical Soc.. This book was released on 2011-02-10 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume cover important topics in spectral theory and geometric analysis such as resolutions of smooth group actions, spectral asymptotics, solutions of the Ginzburg-Landau equation, scattering theory, Riemann surfaces of infinite genus and tropical mathematics.