Ellis, Richard S.
Entropy, Large Deviations, and Statistical Mechanics
Series: Classics in Mathematics
Reprint of the 1st ed. Springer-Verlag New York 1985, 2006,
XVIII, 364 p., Softcover
ISBN: 3-540-29059-1
About this book
From the reviews:
"... Besides the fact that the author's treatment of large deviations
is a nice contribution to the literature on the subject, his book has the
virue that it provides a beautifully unified and mathematically appealing
account of certain aspects of statistical mechanics. ... Furthermore, he
does not make the mistake of assuming that his mathematical audience will
be familiar with the physics and has done an admireable job of explaining
the necessary physical background. Finally, it is clear that the author's
book is the product of many painstaking hours of work; and the reviewer
is confident that its readers will benefit from his efforts." D. Stroock
in Mathematical Reviews 1985
"... Each chapter of the book is followed by a notes section
and by a problems section. There are over 100 problems, many of
which have hints. The book may be recommended as a text, it
provides a completly self-contained reading ..." S. Pogosian
in Zentralblatt fur Mathematik 1986
Table of contents
Large Deviations and Statistical Mechanics: Introduction to Large
Deviations.- Large Deviation Property and Asymptotics of
Integrals.- Large Deviations and the Discrete Ideal Gas.-
Ferromagnetic Models on Z.- Magnetic Models on ZD and on the
Circle. Convexity and Proofs of Large Deviation Theorems: Convex
Functions and the Legendre-Fenchel Transform.- Large Deviations
for Random Vectors.- Level-2 Large Deviations for I.I.D. Random
Vectors.- Level-3 Large Deviations for I.I.D. Random Vectors.
Appendices: Probability.- Proofs to Two Theorems in Section II.7.-
Equivalent Notions of Infinite-Volume Measures for Spin Systems.-
Existence of the Specific Gibbs Free Energy.
Ghorpade, Sudhir R., Limaye, Balmohan
A Course in Calculus and Real Analysis
Series: Undergraduate Texts in Mathematics
2005, Approx. 510 p. 75 illus., Hardcover
ISBN: 0-387-30530-0
About this textbook
Real analysis may be regarded as a formidable counterpart to
calculus. It is a subject where one revisits notions encountered
in calculus, but with greater rigor and sometimes with greater
generality. Here, the authors provide a self-contained and
rigorous introduction to the calculus of functions of one
variable. The presentation and sequencing of topics emphasizes
the structural development of calculus. At the same time, due
importance is given to computational techniques and applications.
Table of contents
* Numbers and Functions * Sequences * Continuity and Limits *
Differentiation * Applications of Differentiation * Integration *
Elementary Transcendental Functions * Applications of Integration
* Infinite Series and Improper Integrals * Partial
Differentiation * Multiple Integrals and their Applications *
Appendix A: Construction of Real Numbers * Appendix B: Algebra *
Bibliography * Index
Stroock, Daniel W., Varadhan, S.R.S.
Multidimensional Diffusion Processes
Series: Classics in Mathematics
Reprint of the 1st ed. Berlin Heidelberg New York 1979, 2006,
XII, 338 p., Hardcover
ISBN: 3-540-28998-4
About this book
"This book is an excellent presentation of the application of martingale theory to the theory of Markov processes, especially multidimensional diffusions. This approach was initiated by Stroock and Varadhan in their famous papers. (...) The proofs and techniques are presented in such a way that an adaptation in other contexts can be easily done. (...) The reader must be familiar with standard probability theory and measure theory which are summarized at the beginning of the book. This monograph can be recommended to graduate students and research workers but also to all interested in Markov processes from a more theoretical point of view." Mathematische Operationsforschung und Statistik, 1981
Table of contents
Preliminary Material: Extension Theorems, Martingales, and
Compactness.- Markov Processes, Regularity of Their Sample Paths,
and the Wiener Measure.- Parabolic Partial Differential Equations.-
The Stochastic Calculus of Diffusion Theory.- Stochastic
Differential Equations.- The Martingale Formulation.- Uniqueness.-
Itofs Uniqueness and Uniqueness to the Martingale Problem.-
Some Estimates on the Transition Probability Functions.-
Explosion.- Limit Theorems.- The Non-Unique Case
Huang, Sha, Qiao, Yu Ying, Wen, Guo Chun
Real and Complex Clifford Analysis
Series: Advances in Complex Analysis and Its Applications, Vol.
5
2006, X, 246 p., Hardcover
ISBN: 0-387-24535-9
About this book
Clifford analysis, a branch of mathematics that has been
developed since about 1970, has important theoretical value and
several applications. In this book, the authors introduce many
properties of regular functions and generalized regular functions
in real Clifford analysis, as well as harmonic functions in
complex Clifford analysis. It covers important developments in
handling the incommutativity of multiplication in Clifford
algebra, the definitions and computations of high-order singular
integrals, boundary value problems, and so on. In addition, the
book considers harmonic analysis and boundary value problems in
four kinds of characteristic fields proposed by Luogeng Hua for
complex analysis of several variables. The great majority of the
contents originate in the authorsf investigations, and this new
monograph will be interesting for researchers studying the theory
of functions.
Table of contents
General Regular and Harmonic Functions in Real and Complex
Clifford Analysis.- Boundary Value Problems of Generalized
Regular Functions and Hyperbolical Harmonic Functions in Real
Clifford Analysis.- Nonlinear Boundary Value Problems for
Generalized Biregular Functions in Real Clifford Analysis.-
Boundary Value Problems of two Order Partial Differential
Equations for Classical Domains in Clifford Analysis.- The
Integrals Dependent on Parameter and Singular Integral Equations
in Real Clifford Analysis.- Several Kinds of High Order Singular
Integrals and Differential Integral Equations in Real Clifford
Analysis.- Relation Between Clifford Analysis and Elliptic
Equations.- References.- Index.
Tanigawa, Yoshio; Zhang, Wenpeng (Eds.)
Number Theory
Tradition and Modernization
Series: Developments in Mathematics, Vol. 15
2006, XIV, 242 p. 5 illus., Hardcover
ISBN: 0-387-30414-2
About this book
Number Theory: Tradition and Modernization is a collection of
survey and research papers on various topics in number theory.
Though the topics and descriptive details appear varied, they are
unified by two underlying principles: first, making everything
readable as a book, and second, making a smooth transition from
traditional approaches to modern ones by providing a rich array
of examples.
The chapters are presented in quite different in depth and cover
a variety of descriptive details, but the underlying editorial
principle enables the reader to have a unified glimpse of the
developments of number theory. Thus, on the one hand, the
traditional approach is presented in great detail, and on the
other, the modernization of the methods in number theory is
elaborated. The book emphasizes a few common features such as
functional equations for various zeta-functions, modular forms,
congruence conditions, exponential sums, and algorithmic aspects.
Table of contents
Preface
About the book and the conference
List of participants
Positive finiteness of number systems (S. Akiyama)
On a distribution property of the resudual order of a (mod p) ?IV
(K. Chinen and L. Murata)
Diagonalizing gbadh Hecke operators on spaces of cusp forms (Y.-J.
Choie and W. Kohnen)
On the Hilbert-Kamke and the Vinogradov problems in additive
number theory (V. N. Chubarikov)
The Goldbach-Vinogradov theorem in arithmetic progressions (Z.
Cui)
Densities of sets of primes related to decimal expansion of
rational numbers (T. Hadano, Y. Kitaoka, T. Kubota and M. Nozaki)
Spherical functions on p-adic homogeneous spaces (Y. Hironaka)
On modular forms of weight (6n + 1)=5 satisfying a certain
differential equation (M. Kaneko)
Some aspects of the modular relation (S. Kanemitsu, Y. Tanigawa,
H. Tsukada and M. Yoshimoto)
Zeros of automorphic L-functions and noncyclic base change (J.
Liu and Y. Ye)
Analytic properties of multiple zeta-functions in several
variables (K. Matsumoto)
Cubic fields and Mordell curves (K. Miyake)
Towards the reciprocity of quartic theta-Weyl sums, and beyond (Y.-N.
Nakai)
Explicit congruences for Euler polynomials (Z.-W. Sun)
Square-free integers as sums of two squares (W. Zhai)
Some applications of L-functions to the mean value of the
Dedekind sums and Cochrane sums (W. Zhang)
Index