The Stokes Phenomenon Borel Summation And Mellin Barnes Regularisation

Author : Victor Kowalenko
Publisher : Bentham Science Publishers
Page : 262 pages
File Size : 42,7 Mb
Release : 2009
Category : Mathematics
ISBN : 9781608050109

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The Stokes Phenomenon, Borel Summation and Mellin-Barnes Regularisation by Victor Kowalenko Pdf

The Stokes phenomenon refers to the emergence of jump discontinuities in asymptotic expansions at specific rays in the complex plane. This book presents a radical theory for the phenomenon by introducing the concept of regularization. Two methods of regularization, Borel summation and Mellin-Barnes regularization, are used to derive general expressions for the regularized values of asymptotic expansions throughout the complex plane. Though different, both yield identical values, which, where possible, agree with the original functions. Consequently, asymptotics has been elevated to a true disc

Author : Bruce H. J. McKellar,Ken Amos
Publisher : World Scientific
Page : 240 pages
File Size : 42,5 Mb
Release : 2010
Category : Science
ISBN : 9789814293662

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In Celebration of K.C. Hines by Bruce H. J. McKellar,Ken Amos Pdf

This book presents a comprehensive review of a diverse range of subjects in physics written by physicists who have all been taught by or are associated with K C Hines. Ken Hines was a great mentor with far-reaching influence on his students who later went on to make outstanding contributions to physics in their careers. The papers provide significant insights into statistical physics, plasma physics from fluorescent lighting to quantum pair plasmas, cosmic ray physics, nuclear reactions, and many other fields. Sample Chapter(s). Chapter 1: Concerning Ken Hines... (358 KB). Contents: Resonant X-Ray Scattering and X-Ray Absorption: Closing the Circle? (Z Barnea et al.); The Screened Field of a Test Particle (R L Dewar); Aspects of Plasma Physics (R J Hosking); The Boltzmann Equation in Fluorescent Lamp Theory (G Lister); Pair Modes in Relativistic Quantum Plasmas (D B Melrose & J McOrist); Neutrons from the Galactic Centre (R R Volkas); Quaternions and Octonions in Nature (G C Joshi); Accretion onto the Supermassive Black Hole at the Centre of Our Galaxy (F Melia); and other papers. Readership: Academics and graduate students interested in physics.

Author : Tapas Kumar Chandra
Publisher : Springer Science & Business Media
Page : 114 pages
File Size : 46,8 Mb
Release : 2012-07-04
Category : Mathematics
ISBN : 9788132206774

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The Borel-Cantelli Lemma by Tapas Kumar Chandra Pdf

This monograph provides an extensive treatment of the theory and applications of the celebrated Borel-Cantelli Lemma. Starting from some of the basic facts of the axiomatic probability theory, it embodies the classical versions of these lemma, together with the well known as well as the most recent extensions of them due to Barndorff-Nielsen, Balakrishnan and Stepanov, Erdos and Renyi, Kochen and Stone, Petrov and the present author. The versions of the second Borel-Cantelli Lemma for pair wise negative quadrant dependent sequences, weakly *-mixing sequences, mixing sequences (due to Renyi) and for many other dependent sequences are all included. The special feature of the book is a detailed discussion of a strengthened form of the second Borel-Cantelli Lemma and the conditional form of the Borel-Cantelli Lemmas due to Levy, Chen and Serfling. All these results are well illustrated by means of many interesting examples. All the proofs are rigorous, complete and lucid. An extensive list of research papers, some of which are forthcoming, is provided. The book can be used for a self study and as an invaluable research reference on the present topic.

Author : Michael Borinsky
Publisher : Springer
Page : 173 pages
File Size : 52,9 Mb
Release : 2018-11-04
Category : Science
ISBN : 9783030035419

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Graphs in Perturbation Theory by Michael Borinsky Pdf

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.

Author : Victor Kowalenko
Publisher : Academic Press
Page : 322 pages
File Size : 49,7 Mb
Release : 2017-01-19
Category : Mathematics
ISBN : 9780128045114

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The Partition Method for a Power Series Expansion by Victor Kowalenko Pdf

The Partition Method for a Power Series Expansion: Theory and Applications explores how the method known as 'the partition method for a power series expansion', which was developed by the author, can be applied to a host of previously intractable problems in mathematics and physics. In particular, this book describes how the method can be used to determine the Bernoulli, cosecant, and reciprocal logarithm numbers, which appear as the coefficients of the resulting power series expansions, then also extending the method to more complicated situations where the coefficients become polynomials or mathematical functions. From these examples, a general theory for the method is presented, which enables a programming methodology to be established. Finally, the programming techniques of previous chapters are used to derive power series expansions for complex generating functions arising in the theory of partitions and in lattice models of statistical mechanics. Explains the partition method by presenting elementary applications involving the Bernoulli, cosecant, and reciprocal logarithm numbers Compares generating partitions via the BRCP algorithm with the standard lexicographic approaches Describes how to program the partition method for a power series expansion and the BRCP algorithm

Author : Rolf-Peter Holzapfel,Muhammed Uludag,M. Yoshida
Publisher : Birkhäuser
Page : 0 pages
File Size : 50,6 Mb
Release : 2007-01-22
Category : Mathematics
ISBN : 376438283X

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Arithmetic and Geometry Around Hypergeometric Functions by Rolf-Peter Holzapfel,Muhammed Uludag,M. Yoshida Pdf

This volume comprises lecture notes, survey and research articles originating from the CIMPA Summer School Arithmetic and Geometry around Hypergeometric Functions held at Galatasaray University, Istanbul, June 13-25, 2005. It covers a wide range of topics related to hypergeometric functions, thus giving a broad perspective of the state of the art in the field.

Author : Vic Kowalenko,N. E. Frankel,L. Glasser,T. Taucher
Publisher : Cambridge University Press
Page : 146 pages
File Size : 54,6 Mb
Release : 1995-09-14
Category : Mathematics
ISBN : 0521497981

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Generalised Euler-Jacobi Inversion Formula and Asymptotics Beyond All Orders by Vic Kowalenko,N. E. Frankel,L. Glasser,T. Taucher Pdf

This work presents exciting new developments in understanding the subdominant exponential terms of asymptotic expansions which have previously been neglected.

Author : Keith B. Oldham,Jan Myland,Jerome Spanier
Publisher : Springer Science & Business Media
Page : 737 pages
File Size : 45,7 Mb
Release : 2010-07-15
Category : Mathematics
ISBN : 9780387488073

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An Atlas of Functions by Keith B. Oldham,Jan Myland,Jerome Spanier Pdf

This book comprehensively covers several hundred functions or function families. In chapters that progress by degree of complexity, it starts with simple, integer-valued functions then moves on to polynomials, Bessel, hypergeometric and hundreds more.

Author : T. K. Chandra
Publisher : Alpha Science International, Limited
Page : 256 pages
File Size : 53,5 Mb
Release : 1999-01-01
Category : Mathematics
ISBN : 817319260X

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A First Course in Asymptotic Theory of Statistics by T. K. Chandra Pdf

Starting with elementary notions of calculus, statistics and probability, the author introduces in this book the basic results of asymptotic theory through intuitive and motivated approaches with excellent exposure to various problems. Many theoretical and numerical examples have been worked out along with results that are not available in other books.

Author : Chretien de Troyes,Chrétien (de Troyes)
Publisher : Yale University Press
Page : 244 pages
File Size : 52,6 Mb
Release : 1987-09-10
Category : Poetry
ISBN : 9780300038385

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Yvain by Chretien de Troyes,Chrétien (de Troyes) Pdf

A twelfth-century poem by the creator of the Arthurian romance describes the courageous exploits and triumphs of a brave lord who tries to win back his deserted wife's love

Author : Joseph A. Gallian
Publisher : MAA
Page : 344 pages
File Size : 49,7 Mb
Release : 2010
Category : Mathematics
ISBN : 9780883853498

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Mathematics and Sports by Joseph A. Gallian Pdf

This is an eclectic compendium of the essays solicited for the 2010 Mathematics Awareness Month Web page on the theme of 'Mathematics and Sports'. In keeping with the goal of promoting mathematics awareness to a broad audience, all of the articles are accessible to university-level mathematics students and many are accessible to the general public. The book is divided into sections by the kind of sports. The section on American football includes an article that evaluates a method for reducing the advantage of the winner to a coin flip in an NFL overtime game; the section on track and field examines the ultimate limit on how fast a human can run 100 metres; the section on baseball includes an article on the likelihood of streaks; the section on golf has an article that describes the double-pendulum model of a golf swing and an article on modelling Tiger Woods' career.

Author : Edward Thomas Copson
Publisher : Unknown
Page : 448 pages
File Size : 45,9 Mb
Release : 1970
Category : Functions of complex variables
ISBN : LCCN:86001115

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An Introduction to the Theory of Functions of a Complex Variable by Edward Thomas Copson Pdf

Author : Stephen Wolfram
Publisher : Unknown
Page : 994 pages
File Size : 44,8 Mb
Release : 1991
Category : Electronic
ISBN : 0201515024

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Mathematica by Stephen Wolfram Pdf

Author : Michael Ruzhansky,Durvudkhan Suragan
Publisher : Springer
Page : 579 pages
File Size : 43,5 Mb
Release : 2019-07-02
Category : Mathematics
ISBN : 9783030028954

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Hardy Inequalities on Homogeneous Groups by Michael Ruzhansky,Durvudkhan Suragan Pdf

This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.

Author : John J. Benedetto
Publisher : CRC Press
Page : 592 pages
File Size : 41,6 Mb
Release : 2021-07-28
Category : Mathematics
ISBN : 9781000443462

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Wavelets by John J. Benedetto Pdf

Wavelets is a carefully organized and edited collection of extended survey papers addressing key topics in the mathematical foundations and applications of wavelet theory. The first part of the book is devoted to the fundamentals of wavelet analysis. The construction of wavelet bases and the fast computation of the wavelet transform in both continuous and discrete settings is covered. The theory of frames, dilation equations, and local Fourier bases are also presented. The second part of the book discusses applications in signal analysis, while the third part covers operator analysis and partial differential equations. Each chapter in these sections provides an up-to-date introduction to such topics as sampling theory, probability and statistics, compression, numerical analysis, turbulence, operator theory, and harmonic analysis. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise. It will be an especially useful reference for harmonic analysts, partial differential equation researchers, signal processing engineers, numerical analysts, fluids researchers, and applied mathematicians.