Series: Springer Monographs in Mathematics
2015, XX, 710 p.
Hardcover
ISBN 978-3-319-19421-9
* Highlights the importance of homological algebra and set theory in
the modern theory of abelian groups
* Exposes the reader to the key ideas and modern methods of the
subject
* Provides a convenient reference for results scattered throughout the
literature
Written by one of the subjectfs foremost experts, this book focuses on the central
developments and modern methods of the advanced theory of abelian groups, while
remaining accessible, as an introduction and reference, to the non-specialist. It provides a
coherent source for results scattered throughout the research literature with lots of new
proofs.
The presentation highlights major trends that have radically changed the modern
character of the subject, in particular, the use of homological methods in the structure
theory of various classes of abelian groups, and the use of advanced set-theoretical
methods in the study of undecidability problems. The treatment of the latter trend
includes Shelahfs seminal work on the undecidability in ZFC of Whiteheadfs Problem;
while the treatment of the former trend includes an extensive (but non-exhaustive)
study of p-groups, torsion-free groups, mixed groups, and important classes of groups
arising from ring theory. To prepare the reader to tackle these topics, the book reviews
the fundamentals of abelian group theory and provides some background material from
category theory, set theory, topology, and homological algebra.
An abundance of exercises are included to test the readerfs comprehension, and to
explore noteworthy extensions and related sidelines of the main topics. A list of open
problems and questions, in each chapter, invite the reader to take an active part in the
subjectfs further development.
Series: Developments in Mathematics, Vol. 41
2015, XVI, 432 p. 2 illus.
Hardcover
ISBN 978-3-319-20770-4
* A novel theory of pseudo-differential operators and equations with
symbols singular in dual variables is presented systematically
* Recent developments in the theory of fractional order differential
equations and their various applications are studied
* Fractional Fokker-Planck-Kolmogorov equations and their
connection with the associated stochastic differential equations
driven by a time-changed process are discussed in detail
The book systematically presents the theories of pseudo-differential operators with
symbols singular in dual variables, fractional order derivatives, distributed and variable
order fractional derivatives, random walk approximants, and applications of these theories
to various initial and multi-point boundary value problems for pseudo-differential
equations. Fractional Fokker-Planck-Kolmogorov equations associated with a large class of
stochastic processes are presented. A complex version of the theory of pseudo-differential
operators with meromorphic symbols based on the recently introduced complex Fourier
transform is developed and applied for initial and boundary value problems for systems of
complex differential and pseudo-differential equations.
Series: Springer Series in Statistics
2015, XXVIII, 587 p. 103 illus., 100 illus. in color.
Hardcover
ISBN 978-1-4939-2817-0
* First comprehensive book on Vector Generalized Linear Models
* Builds on success of VGAM R package, which is used to show
applications of the methodology
* Techniques on regression and parametric and non-parametric
methods covered in detail along with gamut of mathematical
calculations
This book presents a statistical framework that expands generalized linear models (GLMs)
for regression modelling. The framework shared in this book allows analyses based on
many semi-traditional applied statistics models to be performed as a coherent whole. This
is possible through the approximately half-a-dozen major classes of statistical models
included in the book and the software infrastructure component, which makes the models
easily operable.
The bookfs methodology and accompanying software (the extensive VGAM R package)
are directed at these limitations, and this is the first time the methodology and software
are covered comprehensively in one volume. Since their advent in 1972, GLMs have
unified important distributions under a single umbrella with enormous implications. The
demands of practical data analysis, however, require a flexibility that GLMs do not have.
Data-driven GLMs, in the form of generalized additive models (GAMs), are also largely
confined to the exponential family. This book treats distributions and classical models as
generalized regression models, and the result is a much broader application base for GLMs
and GAMs.
The book may be used in senior undergraduate and first-year postgraduate courses on
GLMs and regression modeling, including categorical data analysis. It may also serve as a
reference on vector generalized linear models and as a methodology resource for VGAM
users. The methodological contribution of this book stands alone and does not require
use of the VGAM package. In the second part of the book, the R package VGAM makes
applications of the methodology immediate. R code is integrated in the text, and datasets
are used throughout. Potential applications include ecology, finance, biostatistics, and
social sciences.
Series: Lecture Notes in Mathematics, Vol. 2146
2015, XIII, 338 p. 46 illus., 41 illus. in color.
Softcover
ISBN 978-3-319-19014-3
* First volume in the new CEMPI subseries
Focusing on the interface between mathematics and physics, this book offers an
introduction to the physics, the mathematics, and the numerical simulation of nonlinear
systems in optics and atomic physics. The text covers a wide spectrum of current
research on the subject, which is an extremely active field in physics and mathematical
physics, with a very broad range of implications, both for fundamental science and
technological applications: light propagation in microstructured optical fibers, Bose-
Einstein condensates, disordered systems, and the newly emerging field of nonlinear
quantum mechanics.
Accessible to PhD students, this book will also be of interest to post-doctoral researchers
and seasoned academics.