Frank den Hollander, Nijmegen University, Netherlands
Large Deviations
Description
This volume offers an introduction to large deviations. It is divided into two parts: theory and applications. Basic large deviation theorems are presented for i.i.d. sequences, Markov sequences, and sequences with moderate dependence. The rate function is computed explicitly. The theory is explained without too much emphasis on technicalities. Also included is an outline of general definitions and theorems. The goal is to expose the unified theme that gives large deviation theory its overallstructure, which can be made to work in many concrete cases. The section on applications focuses on recent work in statistical physics and random media.
This book contains 60 exercises (with solutions) that should elucidate the content and engage the reader. Prerequisites for the book are a strong background in probabilityand analysis and some knowledge of statistical physics. It would make an excellent textbook for a special topics course in large deviations.
Contents
Theory
Large deviations for i.i.d. sequences: Part 1
Large deviations for i.i.d. sequences: Part 2
General theory
Large deviations for Markov sequences
Large deviations for dependent sequences
Applications
Statistical hypothesis testing
Random walk in random environment
Heat conduction with random sources and sinks
Polymer chains
Interacting diffusions
Solutions to the exercises
Bibliography
Index
Glossary of symbols
Details:
Publisher: American Mathematical Society
Series: Fields Institute Monographs, Volume: 14
Publication Year: 2000
ISBN: 0-8218-1989-5
Paging: 143 pp.
Binding: Hardcover
Edited by: Mourad E. H. Ismail, University of South Florida, Tampa, FL,
and Dennis W. Stanton, University of Minnesota, Minneapolis, MN
q-Series from a Contemporary Perspective
Description
This volume presents the proceedings of the Joint Summer Research Conference on q-series, combinatorics and computer algebra held at Mount Holyoke College(Hadley, MA). All of the papers were contributed by participants and offer original research on topics of current interest.
Articles in the book reflect the diversity of areas that overlap with q-series, as well as the usefulness of q-series across the mathematical sciences. The conference was held in honor of Richard Askey on the occasion of his 65th birthday and the proceedings contain an article about Askey's contributions to special functions.
Contents
K. Alladi -- Reformulations of a partition theorem of G?llnitz and q-series identities
G. E. Andrews -- Schur's theorem, partitions with odd parts and the Al-Salam-Carlitz polynomials
K. Aomoto and K. Iguchi -- Singularity and monodromy of quasi-hypergeometric functions
B. C. Berndt, H. H. Chan, and S.-S. Huang -- Incomplete elliptic integrals in Ramanujan's lost notebook
W. C. Connett and A. L. Schwartz -- Measure algebras associated with orthogonal polynomials
D. Foata and G. Han -- Word straightening and q-Eulerian calculus
O. Foda, K. S. M. Lee, Y. Pugai, and T. A. Welsh -- Path generating transforms
G. Gasper -- q-extensions of Erd?lyi's fractional integral representations for hypergeometric functions and some summation formulas for double q-Kamp deFriet series
R. Wm. Gosper, Jr. and S. K. Suslov -- Numerical investigation of basic Fourier series
M. D. Hirschhorn -- An identity of Ramanujan, and applications
M. E. H. Ismail and D. W. Stanton -- Addition theorems for the q-exponential function
K. W. J. Kadell -- The Schur functions for partitions with complex parts
J. Kaneko -- On Forrester's generalization of Morris constant term identity
A. N. Kirillov -- New combinatorial formula for modified Hall-Littlewood polynomials
C. Krattenthaler -- Schur function identities and the number of perfect matchings of Holey Aztec rectangles
S. C. Milne -- A new U(n) generalization of the Jacobi triple product identity
H. Rosengren -- A new quantum algebraic interpretation of the Askey-Wilson polynomials
S. Sahi -- Some properties of Koornwinder polynomials
M. Schlosser -- A new multidimensional matrix inversion in A_r
Details:
Publisher: American Mathematical Society
Series: Contemporary Mathematics, Volume: 254
Publication Year: 2000
ISBN: 0-8218-1150-9
Paging: approximately 454 pp.
Binding: Softcover
W. J. Kaczor and M. T. Nowak, Marie Curie-Sklodowska University, Lublin, Poland
Problems in Mathematical Analysis I: Real Numbers, Sequences and Series
Description
We learn by doing. We learn mathematics by doing problems. This book is the first volume of a series of books of problems in mathematical analysis. It is mainly intended for students studying the basic principles of analysis. However, given its organization, level, and selection of problems, it would also be an ideal choice for tutorial or
problem-solving seminars, particularly those geared toward the Putnam exam. The volume is also suitable for self-study.
Each section of the book begins with relatively simple exercises, yet may also contain quite challenging problems. Very often several consecutive exercises are concerned with different aspects of one mathematical problem or theorem. This presentation of material is designed to help student comprehension and to encourage them to ask
their own questions and to start research. The collection of problems in the book is also intended to help teachers who wish to incorporate the problems into lectures. Solutions for all the problems are provided.
The book covers three topics: real numbers, sequences, and series, and is divided into two parts: exercises and/or problems, and solutions. Specific topics covered in this volume include the following: basic properties of real numbers, continued fractions, monotonic sequences, limits of sequences, Stolz's theorem, summation of series, tests for convergence, double series, arrangement of series, Cauchy product, and infinite products.
Contents
Problems
Real numbers
Sequence of real numbers
Series of real numbers
Solutions
Real numbers
Sequences of real numbers
Series of real numbers
Bibliography
Details:
Publisher: American Mathematical Society
Series: Student Mathematical Library, Volume: 4
Publication Year: 2000
ISBN: 0-8218-2050-8
Paging: approximately 384 pp.
Binding: Softcover
Edited by: Charles N. Delzell and James J. Madden, Louisiana State University, Baton Rouge, LA
Real Algebraic Geometry and Ordered Structures
Description
This volume contains 16 carefully refereed articles by participants in the Special Session on Real Algebraic Geometry and Ordered Algebraic Structures at the Sectional Meeting of the AMS in Baton Rouge, April 1996, and the associated Special Semester in the spring of 1996 at Louisiana State University and Southern University, Baton
Rouge. The 23 contributors to this volume were among the 75 mathematicians from 15 countries who participated.
Topics include the topology of real algebraic curves (Hilbert's 16th problem), moduli of real algebraic curves, effective sums of squares of real forms (Hilbert's 17th problem), efficient real quantifier elimination, subanalytic sets and stratifications, semialgebraic singularity theory, radial vector fields, exponential functions and valuations
on nonarchimedean ordered fields, valued field extensions, partially ordered and lattice-ordered rings, rings of continuous functions, spectra of rings, and abstract spaces of (higher-level) orderings and real places.
This volume provides a good overview of the state of the art in this area in the 1990s. It includes both expository and original research papers by top workers in this thriving field. The authors and editors strived to make the volume useful to a wide audience (including students and researchers) interested in real algebraic geometry and ordered structures--two subjects that are obviously related, but seldom brought together.
Contents
M. E. Alonso and M. P. V?lez -- On real involutions and ramification of real valuations
E. Becker, V. Powers, and T. W?rmann -- Deciding positivity of real polynomials
J.-P. Brasselet -- Radial vector fields and the Poincar?-Hopf theorem
S. Finashin -- A generalization of the Arnold-Viro inequalities for real singular algebraic curves
P. M. Gilmer -- Floppy curves, with applications to real algebraic curves
D. Gondard and M. Marshall -- Towards an abstract description of the space of real places
L. Gonzalez-Vega -- A special quantifier elimination algorithm for Pham systems
M. Henriksen and F. A. Smith -- A look at biseparating maps from an algebraic point of view
J. Huisman -- Real Teichm?ller spaces and moduli of real algebraic curves
J. Huisman -- Correction to "A real algebraic vector bundle is strongly algebraic whenever its total space is affine"
F.-V. Kuhlmann and S. Kuhlmann -- The exponential rank of nonarchimedean exponential fields
L. Noirel and D. Trotman -- Subanalytic and semialgebraic realisations of abstract stratified sets
J. Ohm -- On the vector space defect for valued field extensions
G. M. Polotovskii -- On the classification of decomposable 7-th degree curves
M. J. de la Puente -- The complex spectrum of a ring
B. Reznick -- Some concrete aspects of Hilbert's 17th problem
M. Shiota -- Semialgebraic singularity theory
Details:
Publisher: American Mathematical Society
Series: Contemporary Mathematics, Volume: 253
Publication Year: 2000
ISBN: 0-8218-0804-4
Paging: 287 pp.
Binding: Softcover
Edited by Cornelius T. Leondes University of California, Los Angeles
Title: Knowledge-Based Systems : Techniques and Applications
ISBN: 0-12-443875-X
Cover: CaseBound
GENERAL DESCRIPTION
The design of knowledge systems is finding myriad applications from corporate databases to general decision support in areas as diverse as engineering, manufacturing and other industrial processes, medicine, business, and economics. In engineering, for example, knowledge bases can be utilized for reliable electric power system operation.
In medicine they support complex diagnoses, while in business they inform the process of strategic planning. Programmed securities trading and the defeat of chess champion Kasparov by IBM's Big Blue are two familiar examples of dedicated knowledge bases in combination with an expert system for decision-making. With volumes covering "Implementation," "Optimization," "Computer Techniques," and "Systems and Applications," this comprehensive set constitutes a unique reference source for students, practitioners, and researchers in computer science, engineering, and the broad range of applications areas for knowledge-based systems.
Edited by Howard E.A. Tinsley University of Florida,
Gainesville Steven D. Brown Loyola University Chicago, Wilmette, Illinois
Handbook of Applied Multivariate Statistics and Mathematical Modeling
ISBN: 0126913609
Cover: CaseBound
GENERAL DESCRIPTION
Multivariate statistics and mathematical models provide flexible and powerful tools essential in most disciplines. Nevertheless, many practicing researchers lack an adequate knowledge of these techniques, or did once know the techniques, but have not been able to keep abreast of new developments.
The Handbook of Applied Multivariate Statistics and Mathematical Modeling explains the appropriate uses of multivariate procedures and mathematical modeling techniques, and prescribe practices that will enable applied researchers to use these procedures effectively without needing to concern themselves with the mathematical basis. The Handbook emphasizes using models and statistics as tools.
The objective of the book is to inform readers about which tool to use to accomplish which task.
Each chapter begins with a discussion of what kinds of questions a particular technique can and cannot answer.
As multivariate statistics and modeling techniques are useful across disciplines, these examples include issues of concern in biological and social sciences as well as the humanities.