Translations of Mathematical Monographs, Volume: 120
2007; 183 pp; softcover
ISBN-13: 978-0-8218-4358-1
Aimed at students and researchers in mathematics, communications engineering,
and economics, this book describes the probabilistic structure of a Gaussian
process in terms of its canonical representation (or its innovation process).
Multiple Markov properties of a Gaussian process and equivalence problems
of Gaussian processes are clearly presented. The authors' approach is unique,
involving causality in time evolution and information-theoretic aspects.
Because the book is self-contained and only requires background in the
fundamentals of probability theory and measure theory, it would be suitable
as a textbook at the senior undergraduate or graduate level.
Senior-level and graduate-level mathematics students. Students and researchers in communications engineering. Researchers in economics.
"Each part of the exposition progresses from the simple to the more sophisticated, thus avoiding the perils of plunging the reader straight into the deep waters of the more advanced theory. No specialized knowledge is required on the part of the reader, other than a good command of the general theory of probability."
-- Mathematical Reviews
CRM Proceedings & Lecture Notes, Volume: 44
2008; 267 pp; softcover
ISBN-13: 978-0-8218-4350-5
Expected publication date is May 8, 2008.
This book contains papers presented at the "Workshop on Singularities
in PDE and the Calculus of Variations" at the CRM in July 2006. The
main theme of the meeting was the formation of geometrical singularities
in PDE problems with a variational formulation. These equations typically
arise in some applications (to physics, engineering, or biology, for example)
and their resolution often requires a combination of methods coming from
areas such as functional and harmonic analysis, differential geometry and
geometric measure theory. Among the PDE problems discussed were: the Cahn-Hilliard
model of phase transitions and domain walls; vortices in Ginzburg-Landau
type models for superconductivity and superfluidity; the Ohna-Kawasaki
model for di-block copolymers; models of image enhancement; and Monge-Ampere
functions. The articles give a sampling of problems and methods in this
diverse area of mathematics, which touches a large part of modern mathematics
and its applications.
Graduate students and research mathematicians interested in PDEs and calculus of variation.
CRM Proceedings & Lecture Notes, Volume: 45
2008; 234 pp; softcover
ISBN-13: 978-0-8218-4352-9
Expected publication date is May 10, 2008.
Data mining aims at finding interesting, useful or profitable information in very large databases. The enormous increase in the size of available scientific and commercial databases (data avalanche) as well as the continuing and exponential growth in performance of present day computers make data mining a very active field. In many cases, the burgeoning volume of data sets has grown so large that it threatens to overwhelm rather than enlighten scientists. Therefore, traditional methods are revised and streamlined, complemented by many new methods to address challenging new problems. Mathematical Programming plays a key role in this endeavor. It helps us to formulate precise objectives (e.g., a clustering criterion or a measure of discrimination) as well as the constraints imposed on the solution (e.g., find a partition, a covering or a hierarchy in clustering). It also provides powerful mathematical tools to build highly performing exact or approximate algorithms.
This book is based on lectures presented at the workshop on "Data Mining and Mathematical Programming" (October 10-13, 2006, Montreal) and will be a valuable scientific source of information to faculty, students, and researchers in optimization, data analysis and data mining, as well as people working in computer science, engineering and applied mathematics.
Graduate students and research mathematicians interested in optimization, data analysis, and data mining.
E. Carrizosa -- Support vector machines and distance minimization
H. Chen and J. Peng -- 0-1 semidefinite programming for graph-cut clustering: Modelling and approximation
Z. Csizmadia, P. L. Hammer, and B. Vizvari -- Artificial attributes in analyzing biomedical databases
Y.-J. Fan, C. Iyigun, and W. A. Chaovalitwongse -- Recent advances in mathematical programming for classification and cluster analysis
P. G. Georgiev -- Nonlinear skeletons of data sets and applications--Methods based on subspace clustering
M. R. Guarracino, S. Cuciniello, D. Feminiano, G. Toraldo, and P. M. Pardalos -- Current classification algorithms for biomedical applications
G. Kunapuli, K. P. Bennett, J. Hu, and J.-S. Pang -- Bilevel model selection for support vector machines
V. Makarenkov, A. Boc, A. Boubacar Diallo, and A. Banire Diallo -- Algorithms for detecting complete and partial horizontal gene transfers: Theory and practice
O. L. Mangasarian and E. W. Wild -- Nonlinear knowledge in kernel machines
F. Murtagh -- Ultrametric embedding: Application to data fingerprinting and to fast data clustering
O. Seref, O. E. Kundakcioglu, and P. M. Pardalos -- Selective linear and nonlinear classification
Graduate Studies in Mathematics, Volume: 91
2008; approx. 620 pp; hardcover
ISBN-13: 978-0-8218-4153-2
Expected publication date is July 27, 2008.
This book is a companion volume to Graduate Algebra: Commutative View (published as volume 73 in this series). The main and most important feature of the book is that it presents a unified approach to many important topics, such as group theory, ring theory, Lie algebras, and gives conceptual proofs of many basic results of noncommutative algebra. There are also a number of major results in noncommutative algebra that are usually found only in technical works, such as Zelmanov's proof of the restricted Burnside problem in group theory, word problems in groups, Tits's alternative in algebraic groups, PI algebras, and many of the roles that Coxeter diagrams play in algebra.
The first half of the book can serve as a one-semester course on noncommutative algebra, whereas the remaining part of the book describes some of the major directions of research in the past 100 years. The main text is extended through several appendices, which permits the inclusion of more advanced material, and numerous exercises. The only prerequisite for using the book is an undergraduate course in algebra; whenever necessary, results are quoted from Graduate Algebra: Commutative View.
Graduate students and research mathematicians interested in various topics of noncommutative algebra.
Fundamental concepts in ring theory
Semisimple modules and rings and the Wedderburn-Artin theorem
The Jacobson program applied to left Artinian rings
Noetherian rings and the role of prime rings
Algebras in terms of generators and relations
Tensor products
Exercises-Part IV
Group representations and group algebras
Characters of finite groups
Lie algebras and other nonassociative algebras
Dynkin diagrams (Coxeter-Dynkin graphs and Coxeter groups)
Exercises-Part V
Polynomial identities and representable algebras
Central simple algebras and the Brauer group
Homological algebra and categories of modules
Hopf algebras
Exercises-Part VI
Bibliography
Index
Translations of Mathematical Monographs, Volume: 236
2008; approx. 505 pp; hardcover
ISBN-13: 978-0-8218-4265-2
Expected publication date is June 2, 2008.
This book contains a comprehensive exposition of the Nevanlinna theory of meromorphic functions of one complex variable, with detailed study of deficiencies, value distribution, and asymptotic properties of meromorphic functions.
A self-contained exposition of the inverse problem for meromorphic functions of finite order with finitely many deficiencies is given in full detail. Many results included in the book belong to the authors, and were previously available only in journal articles.
The main body of the book is a translation of the Russian original published in 1970, which has been one of the most popular sources in this field since then. New references and footnotes related to recent achievements in the topics considered in the original edition have been added and a few corrections made. A new Appendix with a survey of the results obtained after 1970 and extensive bibliography has been written by Alexandre Eremenko and James K. Langley for this English edition.
The only prerequisite for understanding material of this book is an undergraduate course in the theory of functions of one complex variable.
Graduate students and research mathematicians interested in complex analysis.
Characteristics of the behavior of a meromorphic function and the first fundamental theorem
Meromorphic functions of finite order
The second fundamental theorem
Deficient values
Asymptotic properties of meromorphic functions and deficiencies
Value distribution with respect to the arguments
Applications of Riemann surfaces to value distribution
On the magnitude of an entire function
Notes
A survey of some results after 1970
Bibliography
Author index
Subject index
Notation index
University Lecture Series, Volume: 44
2008; approx. 236 pp; softcover
ISBN-13: 978-0-8218-4453-3
Expected publication date is July 3, 2008.
Over the last 20 years, the theory of Borel equivalence relations and related topics have been very active areas of research in set theory and have important interactions with other fields of mathematics, like ergodic theory and topological dynamics, group theory, combinatorics, functional analysis, and model theory. The book presents, for the first time in mathematical literature, all major aspects of this theory and its applications.
This book should be of interest to a wide spectrum of mathematicians working in set theory as well as the other areas mentioned. It provides a systematic exposition of results that so far have been only available in journals or are even unpublished. The book presents unified and in some cases significantly streamlined proofs of several difficult results, especially dichotomy theorems. It has rather minimal overlap with other books published in this subject.
Graduate students and research mathematicians interested in logic, set theory, and applications.
Introduction
Descriptive set theoretic background
Some theorems of descriptive set theory
Borel ideals
Introduction to equivalence relations
Borel reducibility of equivalence relations
"Elementary" results
Introduction to countable equivalence relations
Hyperfinite equivalence relations
More on countable equivalence relations
The 1st and 2nd dichotomy theorems
Ideal {\mathscr I}_1 and the equivalence relation {\mathsf E}_1
Actions of the infinite symmetric group
Turbulent group actions
The ideal \mathscr{I}_3 and the equivalence relation \mathsf{E}_3
Summable equivalence relations
\mathsf{c}_0-equalities
Pinned equivalence relations
Reduction of Borel equivalence relations to Borel ideals
On Cohen and Gandy-Harrington forcing over countable models
Bibliography
Index
American Mathematical Society Translations--Series 2, Volume: 223
2008; approx. 194 pp; hardcover
ISBN-13: 978-0-8218-3928-7
Expected publication date is July 31, 2008.
This volume contains translations of papers that originally appeared in the Japanese journal Sugaku. The papers range over a variety of topics, including operator algebras, analysis, and statistics.
This volume is suitable for graduate students and research mathematicians interested in analysis and its applications.
Graduate students and research mathematicians interested in analysis and its applications.
M. Takesaki -- Entrance to operator algebras
M. Izumi -- Classification of C*-algebras
A. Miyachi -- Weighted Hardy spaces and Jacobi series
S. Igari -- Legacy of J. Marcinkiewicz to real analysis in the 20th century
H. Tanaka -- The Kakeya conjecture
T. Kumagai -- Recent developments of analysis on fractals
S. Akiyama -- Symbolic dynamical system and number theoretical tilings
N. Obata -- Notions of independence in quantum probability and spectral analysis of graphs
K. Tanaka -- On various applications of the wavelet analysis to statistics
H. Tanaka -- Bhattacharyya type inequalities