The H-Function

The H-Function
Author: A.M. Mathai
Publisher: Springer Science & Business Media
Total Pages: 276
Release: 2009-10-10
Genre: Science
ISBN: 1441909168

TheH-function or popularly known in the literature as Fox’sH-function has recently found applications in a large variety of problems connected with reaction, diffusion, reaction–diffusion, engineering and communication, fractional differ- tial and integral equations, many areas of theoretical physics, statistical distribution theory, etc. One of the standard books and most cited book on the topic is the 1978 book of Mathai and Saxena. Since then, the subject has grown a lot, mainly in the elds of applications. Due to popular demand, the authors were requested to - grade and bring out a revised edition of the 1978 book. It was decided to bring out a new book, mostly dealing with recent applications in statistical distributions, pa- way models, nonextensive statistical mechanics, astrophysics problems, fractional calculus, etc. and to make use of the expertise of Hans J. Haubold in astrophysics area also. It was decided to con ne the discussion toH-function of one scalar variable only. Matrix variable cases and many variable cases are not discussed in detail, but an insight into these areas is given. When going from one variable to many variables, there is nothing called a unique bivariate or multivariate analogue of a givenfunction. Whatever be the criteria used, there may be manydifferentfunctions quali ed to be bivariate or multivariate analogues of a given univariate function. Some of the bivariate and multivariateH-functions, currently in the literature, are also questioned by many authors.

Lectures on Random Lozenge Tilings

Lectures on Random Lozenge Tilings
Author: Vadim Gorin
Publisher: Cambridge University Press
Total Pages: 261
Release: 2021-09-09
Genre: Language Arts & Disciplines
ISBN: 1108843964

This is the first book dedicated to reviewing the mathematics of random tilings of large domains on the plane.

The Scientific Legacy of Poincare

The Scientific Legacy of Poincare
Author: Éric Charpentier
Publisher: American Mathematical Soc.
Total Pages: 410
Release: 2010
Genre: Biography & Autobiography
ISBN: 082184718X

Henri Poincare (1854-1912) was one of the greatest scientists of his time, perhaps the last one to have mastered and expanded almost all areas in mathematics and theoretical physics. In this book, twenty world experts present one part of Poincare's extraordinary work. Each chapter treats one theme, presenting Poincare's approach, and achievements.

Special Functions and the Theory of Group Representations

Special Functions and the Theory of Group Representations
Author: Naum I͡Akovlevich Vilenkin
Publisher: American Mathematical Soc.
Total Pages: 613
Release: 1968
Genre: Mathematics
ISBN: 9780821815724

A standard scheme for a relation between special functions and group representation theory is the following: certain classes of special functions are interpreted as matrix elements of irreducible representations of a certain Lie group, and then properties of special functions are related to (and derived from) simple well-known facts of representation theory. The book combines the majority of known results in this direction. In particular, the author describes connections between the exponential functions and the additive group of real numbers (Fourier analysis), Legendre and Jacobi polynomials and representations of the group $SU(2)$, and the hypergeometric function and representations of the group $SL(2,R)$, as well as many other classes of special functions.

Special Functions & Their Applications

Special Functions & Their Applications
Author: N. N. Lebedev
Publisher: Courier Corporation
Total Pages: 340
Release: 2012-04-30
Genre: Mathematics
ISBN: 0486139891

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.

Stochastic Processes in Physics and Engineering

Stochastic Processes in Physics and Engineering
Author: Sergio Albeverio
Publisher: Springer Science & Business Media
Total Pages: 418
Release: 2012-12-06
Genre: Mathematics
ISBN: 9400928939

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. O. K. Chesterton. The Scandal of Father 'The Hermit Qad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu!ik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

The Anomalous Magnetic Moment of the Muon

The Anomalous Magnetic Moment of the Muon
Author: Fred Jegerlehner
Publisher: Springer Science & Business Media
Total Pages: 433
Release: 2008
Genre: Science
ISBN: 3540726330

This book reviews the present state of knowledge of the anomalous magnetic moment a=(g-2)/2 of the muon. The muon anomalous magnetic moment is one of the most precisely measured quantities in elementary particle physics and provides one of the most stringent tests of relativistic quantum field theory as a fundamental theoretical framework. It allows for an extremely precise check of the standard model of elementary particles and of its limitations.

Calogero-Moser Systems and Representation Theory

Calogero-Moser Systems and Representation Theory
Author: Pavel I. Etingof
Publisher: European Mathematical Society
Total Pages: 108
Release: 2007
Genre: Mathematics
ISBN: 9783037190340

Calogero-Moser systems, which were originally discovered by specialists in integrable systems, are currently at the crossroads of many areas of mathematics and within the scope of interests of many mathematicians. More specifically, these systems and their generalizations turned out to have intrinsic connections with such fields as algebraic geometry (Hilbert schemes of surfaces), representation theory (double affine Hecke algebras, Lie groups, quantum groups), deformation theory (symplectic reflection algebras), homological algebra (Koszul algebras), Poisson geometry, etc. The goal of the present lecture notes is to give an introduction to the theory of Calogero-Moser systems, highlighting their interplay with these fields. Since these lectures are designed for non-experts, the author gives short introductions to each of the subjects involved and provides a number of exercises.