Aref'eva, Irina; Sternheimer, Daniel (Eds.)
Modern Encyclopedia of Mathematical Physics
2007
ISBN: 1-4020-5050-X
About this book
The goal of this major undertaking is to support and enhance the
interactions between mathematics and physics by making full use
of the modern information technologies. Indeed, the 20th century
was full of dramatic discoveries in each domain. And the
important advances of that century in Mathematical Physics
demonstrate clearly that physics is much closer to deep problems
in mathematics than one could imagine by studying textbooks in
our universities, and that physical ideas and concepts are often
seminal in mathematics.
The Modern Encyclopedia of Mathematical Physics (MEMPhys) is a
truly 21st century scientific encyclopedia, emphasizing
mathematical physics as opposed to mathematics on one side and
physics on the other. The central idea is to create a modern
version of Maimonides’ Guide for the Perplexed, albeit limited
to this multidisciplinary field. Indeed nowadays, increasingly
so, the problem (especially in science) is not so much the
existence or availability of information, but the ability to
find, when the need occurs, pertinent and reliable information.
So MEMPhys seeks to be a model for locating authoritative
overviews and an efficient starting point for researchers and
students at any level.
Moreover, mathematical physics is not just an intersection of
mathematics with physics, and certainly not a disjoint union of
topics in both, but the discipline has an intrinsic value and
existence that is articulated throughout this work. Accordingly,
the contributions are written in precise mathematical language
with clear indication of heuristic aspects, with physical
interpretations or applications serving as examples. The ability
to interrelate distinct items in MEMPhys (such as connecting an
entry from the Encyclopedia with material from a handbook as well
as with many texts existing in electronic form) enhance that
characteristic of MEMPhys. Since this reference anticipates and
seeks as wide a scientific audience as possible, students of
mathematical physics, physics, and mathematics readily find
concise summaries of recent profound ideas and to get an
stimulating idea of their interrelations
Table of contents
Rao, M.M.
Random and Vector Measures
Theory and Applications
Series: Probability and its Applications
2008, Approx. 400 p., 10 illus., Hardcover
ISBN: 0-8176-4517-9
About this textbook
This comprehensive text treats the complementary subjects of
random and vector measures. A vector-valued measure is a function
on a ring of sets taking values in a vector space, and a random
measure is a subclass of vector measures whose value spaces are
built on a probability space. There is a common foundation for
both, yet each has different application potentials.
The book examines the representations of random and vector
measures, random measures on probability (i.e., Frechet, Banach,
and Hilbert) spaces, the bimeasures associated with random
measures and the extension to polymeasures, boundedness
principles, and the importance of random and vector measures in
applications. The interaction between random and vector measures
is explained, thus helping to understand the deeper aspects of
vector-valued analysis.
This comparative and distinctive text is ideal for either
graduate students in the classroom setting, or for researchers in
mathematics, statistics, and engineering.
Table of contents
Introduction and motivation.-Second order random measures and
their representations.-Random measures admitting controls.-Random
measures in Banach spaces and their integrals.-Stable random
measures in Frechet spaces and integrals.-Vector measures on d-rings
and their use in integral representations of vector functions.-Bimeasures
associated with random measures and extensions to polymeasures.-Integral
representations of random processes by vector measures.-Random
measures and stable stochastic integrals.-Martingale measures and
applications.-Generalized Poisson measures and counting processes.-Applications
to random (trigonometric) series.-Multiple random integrals and
measures.-Chaos (Hida-) expansions and summability.-Abstract
Wiener integral and its analysis.-References.-Index.
Czaja, Wojciech, Speegle, Darrin
Wave Packets and Related Transforms
Series: Applied and Numerical Harmonic Analysis
2009, Approx. 350 p., 10 illus., Hardcover
ISBN: 0-8176-4490-3
About this textbook
Time-frequency and time-scale analysis, two of the most important
aspects of signal analysis, are developed for the first time in
book form as special cases of the more general wave packets. This
theory, initiated by Cordoba and Fefferman, has proved to be a
valuable tool in operator theory and partial differential
equations. Fine decompositions of signals by means of wave
packets are also a new and promising tool in signal processing.
The book begins with a refresher on basic wavelet and Gabor
analysis, followed by the general theory of discrete and
continuous wave packets. The presentation is distinguished by its
focus on wave packets as objects worthy of independent study
Table of contents
Preface.- Time-Frequency and Time-Scale Analyses. Fourier
Transforms. Wavelet Transforms. Gabor and Short-time Fourier
Transforms. Wigner Transform, Wigner Distribution, Rihaczek
Transform. Curvelet Transform. Discretization. Other Examples of
Transforms Analyzing the TFS Content (radar ambiguity function).-
The Continuous Wave Packet Transform. Definition/Examples (Continuous
Wavelet Transform/Windowed Fourier Transform). Reproducing
Formulas. Approximate Plancherel Theorems. Changing the
Parameters Defining a Surface.- Discrete Wave Packet Transform.
Definition/Examples (Wavelets, Gabor Systems). Reproducing
Systems. Necessary Conditions on the Analyzing Function.
Sufficient Conditions on the Analyzing Function. Necessary
Conditions on Parameter Set. Sufficient Conditions on Parameter
Set. Characterizations.- Between Time-Frequency and Time-scale
Analyses. $/Alpha$-Modulation Spaces. Flexible Gabor-Wavelet
Decompositions. Atomic Decompositions and Banach Frames in
Coorbit Spaces.- Bilinear Hilbert Transform. Introduction. Lacey-Thiele
Proof of the Boundedness of BHT. A Wave Packet Proof of
Carleson's Theorem.
Giaquinta, Mariano, Modica, Giuseppe
Mathematical Analysis
Linear and Metric Structures and Continuity
Volume package: Mathematical Analysis
2007, XVIII, 470 p., 128 illus., Softcover
ISBN: 0-8176-4375-3
About this textbook
This self-contained work on linear and metric structures focuses
on studying continuity and its applications to finite- and
infinite-dimensional spaces.
The book is divided into three parts. The first part introduces
the basic ideas of linear and metric spaces, including the Jordan
canonical form of matrices and the spectral theorem for self-adjoint
and normal operators. The second part examines the role of
general topology in the context of metric spaces and includes the
notions of homotopy and degree. The third and final part is a
discussion on Banach spaces of continuous functions, Hilbert
spaces and the spectral theory of compact operators.
Mathematical Analysis: Linear and Metric Structures and
Continuity motivates the study of linear and metric structures
with examples, observations, exercises, and illustrations. It may
be used in the classroom setting or for self-study by advanced
undergraduate and graduate students and as a valuable reference
for researchers in mathematics, physics, and engineering.
Other books recently published by the authors include:
Mathematical Analysis: Functions of One Variable, and
Mathematical Analysis: Approximation and Discrete Processes. This
book builds upon the discussion in these books to provide the
reader with a strong foundation in modern-day analysis.
Table of contents
Preface.-Part I: Linear Algebra.-Vectors, Matrices and Linear
Systems.-Vector Spaces and Linear Maps.-Euclidean and Hermitian
Spaces.-Self-Adjoint Operators.-Part II: Metrics and Topology.-Metric
Spaces and Continuous Functions.-Compactness and Connectedness.-Curves.-Some
Topics from the Topology of Rn.-Part III.-Continuity in Infinite-Dimensional
Spaces.-Spaces of Continuous functions, Banach Spaces and
Abstract Equations.-Hilbert Spaces, Dirichlet’s Principle and
Linear compact Operators.-Some Applications.-A. Mathematicians
and Other Scientists.-B. Bibliographical Notes.-C. Index.
James W. Hardin / University of South Carolina, Columbia, South Carolina, USA
Joseph M. Hilbe / Arizona State University, Tempe, Arizona, USA
Generalized Linear Models and Extensions, Second Edition
ISBN: 1597180149
Publication Date: 8/15/2006
Presents a thorough examination of GLM estimation methods
Derives all major GLM families, including Gaussian, gamma,
inverse Gaussian, binomial, Poisson, geometric, and negative
binomial
Includes models developed on GLM theory, such as GAM, multinomial
logit and probit, GEE, and random intercept
Emphasizes model development and goodness-of-fit
Provides numerous examples using Stata
Generalized Linear Models and Extensions, Second Edition presents
a thorough examination of generalized linear model (GLM)
estimation methods as well as the derivation of all major GLM
families and meaningful links. Examined families include
Gaussian, gamma, inverse Gaussian, binomial, Poisson, geometric,
and negative binomial. The text also provides an excellent
overview of the various models that have been developed on the
basis of GLM theory, including GAM, ordered binomial models,
multinomial logit and probit models, GEE and other quasi-likelihood
models, fixed and random effects models, and random intercept and
random parameter models. Throughout the book, the authors
emphasize issues of model development and goodness-of-fit.
Numerous examples are given to assist you in applying the models
to your own data situations. All examples are presented using
Stata.
Table of contents