Freddy Van Oystaeyen, University of Antwerp, UIA, Belgium
Algebraic Geometry for Associative Algebras
series: Pure and Applied Mathematics volume: 232
06/06/2000
Hardcover, 302 Pages, Illustrated
ISBN:0-8247-0424-X
description:
Focuses on the association of methods from topology, category and sheaf theory, algebraic geometry, noncommutative and homological algebra, quantum groups and spaces, rings of differential operators, cech and sheaf cohomology theories, and dimension theories to create a new blend of noncommutative algebraic geometry!
This innovative reference/text facilitates the origin of a noncommutative topology that provides, for the first time, the possibility to define an underlying space where geometric properties can be phrased and studied? resulting in a scheme theory that sustains the duality between algebraic geometry and commuative algebra to the noncommutative level.
Constructs the scheme theory from the interaction between graded and filtered algebras appearing as a general deformation principle among geometries!
Algebraic Geometry for Associative Algebras fully introduces
noncommutative topology / deformation of structure schemes / new cohomological methods /
homological algebra and regularity conditions / divisor theory using noncommutative valuations /
reductions of algebras / microlocalization and quantum sections / formal completion along subvarieties
and more!
Enriched with numerous examples, Algebraic Geometry for Associative Algebras serves as an important research reference for pure and applied mathematicians, particularly algebraists, number theorists, ring theorists, geometers, and topologists, as well as a stimulating text for upper-level undergraduate and graduate students in these disciplines.
contents:
Introduction
The Noncommutative Site
Structure Sheaves and their Sections
Regular Algebras
Valuations and Divisors
Cohomology Theories
A Functorial Approach
Formalizing the Topology
Edited by: Tian-Xiao He, Illinois Wesleyan University, Bloomington, Illinois
Wavelet Analysis and Multiresolution Methods
series: Lecture Notes in Pure and Applied Mathematics volume: 212
05/05/2000
Softcover, 396 Pages, Illustrated
ISBN:0-8247-0417-7
description:
This volume contains a selection of papers presented at the Wavelet Analysis and Multiresolution Methods Session of the American Mathematical Society meeting held recently at the University of Illinois at Urbana-Champaign.
Offering self-contained papers that include an introduction to a major topic in wavelet analysis, recent research results, analysis of key historical developments, and a detailed list of references, Wavelet Analysis and Multiresolution Methods explores the construction, analysis, computation, and application of multiwavelets scaling vectors nonhomogeneous refinement multivariate orthogonal and biorthogonal wavelets and much more.
Wavelet Analysis and Multiresolution Methods is a noteworthy acquisition for pure, applied, and industrial mathematicians; computer scientists; optical, electrical, and electronics engineers; and upper-level undergraduate and graduate students in these disciplines.
contents:
Higher Order Multivariate Wavelet Type Approximation/ George A. Anastassiou
Nonlinear Haar Approximation of Functions with Bounded Mixed Derivative/ Alexander V. Andrianov
Wavelet Coefficients Associate with Translation and Rotation Transform/ Yu Dai and Yunshi Zhou
Multiwavelet Construction via the Lifting Scheme/ Geoffrey M. Davis, Vasily Strela, and Radka Turcajov
Methods in Nonhomogeneous Refinement/ Thomas B. Dinsenbacher
Construction of Multivariate Biorthogonal Wavelets by CBC Algorithm/ Bin Han
Construction of Prewavelets with Minimum Support over Triangulations / Don Hong and Yuchun Anna Mu
Wavelet Analysis: Applications in Industry/ Mei Kobayashi
Divergence-Free Multiwavelets on Rectangular Domains / Joseph D. Lakey and Marie Cristina Pereyra
Multiwavelet Solutions for the Dirichlet Problem / En-Bing Lin and Zhengchu Xiao
Calculating the Spectral Radius of a Set of Matrices/ Mohsen Maesumi
Polynomial Frames for the Detection of Singularities / N. H. Mhaskar and J. Prestin
Sampling Bounds and Stability / Joseph M. Rosenblatt
On the Construction of Positive Scaling Vectors/ David K. Ruch and Patrick J. Van Fleet
A Geometric Approach to Ergodic Non-Homogeneous Markov Chains / Jianhong Shen
Conversion between Orthogonal and Biorthogonal Wavelets/ Jun Tian and Raymond O. Wells, Jr.
D. F. Andrews, Department of Statistics, University of Toronto, Canada,
J. E. Stafford, Department of Public Health Sciences, University of Toronto, Canada
Symbolic Computation for Statistical Inference
171 pages, line figures, 234mm x 156mm
Series: Oxford Statistical Science Series
Hardback (laminated boards),
0-19-850705-4
Publication date: 29 June 2000
Description
Readership: Graduate students and research statisticians.
The development of statistical computing has had a huge impact on the subject, freeing statisticians from the need to perform tedious calculations and allowing researchers to perform progressively more complex operations. This book gives a coherent presentation of the theory underlying the computations, and provides a
framework where computer algorithms are used to do much of the calculation inherent in statistics. Beginning with an outline of algorithms to cover much of an undergraduate course in probability and statistics, it then goes on to discuss various common distributions, likelihood, bootstrap and sampling.
Contents/contributors
1 Introduction
2 Probability and random variables
3 Fundamental procedures
4 Asymptotic expansions
5 Expansions of expectations, cumulants, and unbiased estimates
6 Expansions of distributions
7 Expansions for likelihood quantities
8 The analytic bootstrap
9 Sample surveys
10 Intersection matrices
Rebolledo, R., Pontifica
Universidad Catholica de Chile, Santiago, Chile (Ed.)
Stochastic Analysis and Mathematical Physics
ANESTOC '98, Proceedings of the Third International Workshop
Trends in Mathematics
2000. 176 pages. Hardcover
ISBN 0-8176-4185-8
This work highlights emergent research in the area of quantum probability.
Several papers present a qualitative analysis of quantum dynamical semigroups and new results on q-deformed oscillator algebras, while others stress the application of classical stochastic processes in quantum modeling.
All of the contributions have been thoroughly refereed and are an outgrowth of an international workshop in Stochastic Analysis and Mathematical Physics. The book targets an audience of mathematical physicists as
well as specialists in probability theory, stochastic analysis, and operator algebras.
Ryan, J., University of Arkansas, Fayettevilee, USA,
Sprossig, W., TU-Bergakademie Freiberg, Germany (Eds.)
Clifford Algebras and their Applications in Mathematical Physics
Volume 2: Clifford Analysis
Progress in Physics
2000. 320 pages. Hardcover
ISBN 0-8176-4183-1
Leading experts in the rapidly evolving field of Clifford (geometric) algebras have contributed to this comprehensive two-volume text.
Consisting of thematically organized chapters, the volume is a broad overview of cutting-edge topics in mathematical physics and the physical applications of Clifford algebras.
Volume 2
Clifford Analysis is an up-to-date survey of most aspects of modern-day Clifford analysis.
Topics range from applications such as complex-distance potential theory, supersymmetry, and fluid dynamics to Fourier analysis, the study of boundary value problems, and applications to mathematical physics and Schwarzian derivatives in Euclidean space.
Among the mathematical topics examined are generalized Dirac operators, holonomy groups, monogenic and
hypermonogenic functions and their derivatives, quaternionic Beltrami equations, Fourier theory under Möbius transformations, Cauchy-Riemann operators, and Cauchy type integrals.
A careful balance of mathematical theory and applications to physics, the two volumes are accessible to both graduate students and specialists in the general area of Clifford algebras and their applications.