The Stokes Phenomenon Borel Summation And Mellin Barnes Regularisation

Author : Victor Kowalenko
Publisher : Bentham Science Publishers
ISBN 13 : 1608050106
Total Pages : 262 pages
Book Rating : 4.09/5 ( download)

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Download or read book The Stokes Phenomenon, Borel Summation and Mellin-Barnes Regularisation written by Victor Kowalenko and published by Bentham Science Publishers. This book was released on 2009 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : World Scientific
ISBN 13 : 9814293660
Total Pages : 240 pages
Book Rating : 4.62/5 ( download)

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Download or read book In Celebration of K.C. Hines written by Bruce H. J. McKellar and published by World Scientific. This book was released on 2010 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 8132206770
Total Pages : 114 pages
Book Rating : 4.74/5 ( download)

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Download or read book The Borel-Cantelli Lemma written by Tapas Kumar Chandra and published by Springer Science & Business Media. This book was released on 2012-07-04 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 3030035417
Total Pages : 173 pages
Book Rating : 4.19/5 ( download)

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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.

Author : Victor Kowalenko
Publisher : Academic Press
ISBN 13 : 0128045116
Total Pages : 322 pages
Book Rating : 4.14/5 ( download)

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Download or read book The Partition Method for a Power Series Expansion written by Victor Kowalenko and published by Academic Press. This book was released on 2017-01-19 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : Birkhäuser
ISBN 13 : 9783764382834
Total Pages : 0 pages
Book Rating : 4.3X/5 ( download)

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Download or read book Arithmetic and Geometry Around Hypergeometric Functions written by Rolf-Peter Holzapfel and published by Birkhäuser. This book was released on 2007-01-22 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Publisher : Cambridge University Press
ISBN 13 : 9780521497985
Total Pages : 146 pages
Book Rating : 4.81/5 ( download)

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Download or read book Generalised Euler-Jacobi Inversion Formula and Asymptotics Beyond All Orders written by Vic Kowalenko and published by Cambridge University Press. This book was released on 1995-09-14 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents exciting new developments in understanding the subdominant exponential terms of asymptotic expansions which have previously been neglected.

Author : T. K. Chandra
Publisher : Alpha Science International, Limited
ISBN 13 : 9788173192609
Total Pages : 256 pages
Book Rating : 4.0X/5 ( download)

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Download or read book A First Course in Asymptotic Theory of Statistics written by T. K. Chandra and published by Alpha Science International, Limited. This book was released on 1999-01-01 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Keith B. Oldham
Publisher : Springer Science & Business Media
ISBN 13 : 0387488073
Total Pages : 737 pages
Book Rating : 4.73/5 ( download)

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Download or read book An Atlas of Functions written by Keith B. Oldham and published by Springer Science & Business Media. This book was released on 2010-07-15 with total page 737 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Chretien de Troyes
Publisher : Yale University Press
ISBN 13 : 0300038380
Total Pages : 244 pages
Book Rating : 4.85/5 ( download)

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Download or read book Yvain written by Chretien de Troyes and published by Yale University Press. This book was released on 1987-09-10 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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