Recent Advances in Orthogonal Polynomials, Special Functions, and Their Applications
Recent Advances in Orthogonal Polynomials, Special Functions, and Their Applications

Author: Jorge Arvesœ

Publisher: American Mathematical Soc.

Published: 2012-09-11

Total Pages: 266

ISBN-13: 0821868969

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This volume contains the proceedings of the 11th International Symposium on Orthogonal Polynomials, Special Functions, and their Applications, held August 29-September 2, 2011, at the Universidad Carlos III de Madrid in Leganes, Spain. The papers cover asymptotic properties of polynomials on curves of the complex plane, universality behavior of sequences of orthogonal polynomials for large classes of measures and its application in random matrix theory, the Riemann-Hilbert approach in the study of Pade approximation and asymptotics of orthogonal polynomials, quantum walks and CMV matrices, spectral modifications of linear functionals and their effect on the associated orthogonal polynomials, bivariate orthogonal polynomials, and optimal Riesz and logarithmic energy distribution of points. The methods used include potential theory, boundary values of analytic functions, Riemann-Hilbert analysis, and the steepest descent method.

Recent Advances in Scientific Computing and Applications
Recent Advances in Scientific Computing and Applications

Author: Jichun Li

Publisher: American Mathematical Soc.

Published: 2013-04-24

Total Pages: 397

ISBN-13: 0821887378

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This volume contains the proceedings of the Eighth International Conference on Scientific Computing and Applications, held April 1-4, 2012, at the University of Nevada, Las Vegas. The papers in this volume cover topics such as finite element methods, multiscale methods, finite difference methods, spectral methods, collocation methods, adaptive methods, parallel computing, linear solvers, applications to fluid flow, nano-optics, biofilms, finance, magnetohydrodynamics flow, electromagnetic waves, the fluid-structure interaction problem, and stochastic PDEs. This book will serve as an excellent reference for graduate students and researchers interested in scientific computing and its applications.

Recent Advances in Real Complexity and Computation
Recent Advances in Real Complexity and Computation

Author: Luis M. Pardo

Publisher: American Mathematical Soc.

Published: 2014-11-12

Total Pages: 202

ISBN-13: 0821891502

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This volume is composed of six contributions derived from the lectures given during the UIMP-RSME Lluis Santalo Summer School on ``Recent Advances in Real Complexity and Computation'', held July 16-20, 2012, in Santander, Spain. The goal of this Summer School was to present some of the recent advances on Smale's 17th Problem: ``Can a zero of $n$ complex polynomial equations in $n$ unknowns be found approximately, on the average, in polynomial time with a uniform algorithm?'' These papers cover several aspects of this problem: from numerical to symbolic methods in polynomial equation solving, computational complexity aspects (both worse and average cases and both upper and lower complexity bounds) as well as aspects of the underlying geometry of the problem. Some of the contributions also deal with either real or multiple solutions solving.

Special Functions
Special Functions

Author: George E. Andrews

Publisher: Cambridge University Press

Published: 1999

Total Pages: 684

ISBN-13: 9780521789882

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An overview of special functions, focusing on the hypergeometric functions and the associated hypergeometric series.

Toeplitz Operators and Random Matrices
Toeplitz Operators and Random Matrices

Author: Estelle Basor

Publisher: Springer Nature

Published: 2023-01-01

Total Pages: 606

ISBN-13: 3031138511

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This volume is dedicated to the memory of Harold Widom (1932–2021), an outstanding mathematician who has enriched mathematics with his ideas and ground breaking work since the 1950s until the present time. It contains a biography of Harold Widom, personal notes written by his former students or colleagues, and also his last, previously unpublished paper on domain walls in a Heisenberg–Ising chain. Widom's most famous contributions were made to Toeplitz operators and random matrices. While his work on random matrices is part of almost all the present-day research activities in this field, his work in Toeplitz operators and matrices was done mainly before 2000 and is therefore described in a contribution devoted to his achievements in just this area. The volume contains 18 invited and refereed research and expository papers on Toeplitz operators and random matrices. These present new results or new perspectives on topics related to Widom's work.

Orthogonal Polynomials and Continued Fractions
Orthogonal Polynomials and Continued Fractions

Author: S. V. Khrushchev

Publisher:

Published: 2008

Total Pages: 478

ISBN-13: 9781107101586

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"This new and exciting historical book tells how Euler introduced the idea of orthogonal polynomials and how he combined them with continued fractions, as well as how Brouncker's formula of 1655 can be derived from Euler's efforts in Special Functions and Orthogonal Polynomials. The most interesting applications of this work are discussed, including the great Markoff's Theorem on the Lagrange spectrum, Abel's Theorem on integration in finite terms, Chebyshev's Theory of Orthogonal Polynomials, and very recent advances in Orthogonal Polynomials on the unit circle. As continued fractions become more important again, in part due to their use in finding algorithms in approximation theory, this timely book revives the approach of Wallis, Brouncker and Euler and illustrates the continuing significance of their influence. A translation of Euler's famous paper 'Continued Fractions, Observation' is included as an Addendum."--Publisher's description.

Advances in Ultrametric Analysis
Advances in Ultrametric Analysis

Author: Khodr Shamseddine

Publisher: American Mathematical Soc.

Published: 2013

Total Pages: 305

ISBN-13: 0821891421

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This volume contains papers based on lectures given at the 12th International Conference on p-adic Functional Analysis, which was held at the University of Manitoba on July 2-6, 2012. Through a combination of new research articles and survey papers, this book provides the reader with an overview of current developments and techniques in non-archimedean analysis as well as a broad knowledge of some of the sub-areas of this exciting and fast-developing research area.

Special Functions & Their Applications
Special Functions & Their Applications

Author: N. N. Lebedev

Publisher: Courier Corporation

Published: 2012-04-30

Total Pages: 340

ISBN-13: 0486139891

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Famous Russian work discusses the application of cylinder functions and spherical harmonics; gamma function; probability integral and related functions; Airy functions; hyper-geometric functions; more. Translated by Richard Silverman.

Recent Trends in Nonlinear Partial Differential Equations II
Recent Trends in Nonlinear Partial Differential Equations II

Author: James Serrin

Publisher: American Mathematical Soc.

Published: 2013

Total Pages: 354

ISBN-13: 0821898612

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This book is the second of two volumes which contain the proceedings of the Workshop on Nonlinear Partial Differential Equations, held from May 28-June 1, 2012, at the University of Perugia in honour of Patrizia Pucci's 60th birthday. The workshop brought together leading experts and researchers in nonlinear partial differential equations to promote research and to stimulate interactions among the participants.

Recent Trends in Nonlinear Partial Differential Equations I
Recent Trends in Nonlinear Partial Differential Equations I

Author: James B. Serrin

Publisher: American Mathematical Soc.

Published: 2013-07-22

Total Pages: 323

ISBN-13: 082188736X

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This book is the first of two volumes which contain the proceedings of the Workshop on Nonlinear Partial Differential Equations, held from May 28-June 1, 2012, at the University of Perugia in honor of Patrizia Pucci's 60th birthday. The workshop brought t