A Study of a Class of Totally Disconnected Topological Groups
This authoritative book on periodic locally compact groups is divided into three
parts. The first part covers the necessary background material on locally
compact groups, the second part develops a general structure theory of locally
compact near abelian groups, while the third part uses this theory for a complete
and novel presentation of Mukhin's results which generalized Iwasawa's work
for abstract groups in the case of locally compact groups.
* An authoritative monograph on locally compact periodic groups.
* Written by well-known experts in the field.
* Of interest to researchers and graduate students in group theory and algebra.
De Gruyter Studies in Mathematics
xii, 320 pages, 15 Figures (bw)
Hardcover:
ISBN 978-3-11-059847-6
Date of Publication: September 2018
Language of Publication: English
Subjects: Algebra and Number Theory
Of interest to: Researchers and graduate students in mathematics.
Introduction to Dynamical Systems and Geometric Mechanics provides a
comprehensive tour of two fields that are intimately entwined: dynamical
systems is the study of the behavior of physical systems that may be described
by a set of nonlinear first-order ordinary differential equations in Euclidean
space, whereas geometric mechanics explores similar systems that instead
evolve on differentiable manifolds.
In the first we discuss linearization and stability of trajectories and fixed points,
invariant manifold theory, periodic orbits, Poincare maps, Floquet theory, the
Poincare-Bendixson theorem, bifurcations, and chaos. The second part of the
text begins with a self-contained chapter on differential geometry that introduces
notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and
differential forms.
* Chapters conclude with useful applications.
* Insightful case-studies.
* Well-presented examples and exercises.
De Gruyter Studies in Mathematical Physics
2nd ed., Approx. xx, 350 pages,
50 Figures (bw), 50 Figures (c)
Hardcover:
ISBN 978-3-11-059729-5
Date of Publication: September 2018
Language of Publication: English
Subjects: Differential Equations and Dynamical Systems
Mechanics and Fluid Dynamics
Theoretical and Mathematical Physics
Of interest to: Researchers in Mathematical and Theoretical Physics, and Mathematics.
This volume provides an introduction to modern space-time discretization
methods such as finite and boundary elements and isogeometric analysis for
time-dependent initial-boundary value problems of parabolic and hyperbolic
type. Particular focus is given on stable formulations, error estimates, adaptivity
in space and time, efficient solution algorithms, parallelization of the solution
pipeline, and applications in science and engineering.
* A collection of original survey articles on space-time discretization methods.
* Presents the state of the art of the theory along with applications.
* Of interest to applied mathematicians as well as to applied scientists and
engineers.
Radon Series on Computational and Applied Mathematics
Approx. xii, 300 pages, 30 Figures (bw),
30 Figures (c), 10 Schedule (bw)
Hardcover:
ISBN 978-3-11-054787-0
Date of Publication: November 2018
Language of Publication: English
Subjects: Applied Mathematics
Differential Equations and Dynamical Systems
Numerical and Computational Mathematics
Of interest to: Researchers and graduate students in applied and computational
mathematics, physics, and engineering.
Fractional calculus is a rapidly growing field of research, at the interface
between probability, differential equations, and mathematical physics. It is used
to model anomalous diffusion, in which a cloud of particles spreads in a
different manner than traditional diffusion. This monograph develops the basic
theory of fractional calculus and anomalous diffusion, from the point of view of
probability.
In this book, we will see how fractional calculus and anomalous diffusion can
be understood at a deep and intuitive level, using ideas from probability. It
covers basic limit theorems for random variables and random vectors with heavy
tails. This includes regular variation, triangular arrays, infinitely divisible laws,
random walks, and stochastic process convergence in the Skorokhod topology.
The basic ideas of fractional calculus and anomalous diffusion are closely
connected with heavy tail limit theorems. Heavy tails are applied in finance,
insurance, physics, geophysics, cell biology, ecology, medicine, and computer
engineering.
The goal of this book is to prepare graduate students in probability for research
in the area of fractional calculus, anomalous diffusion, and heavy tails. Many
interesting problems in this area remain open. This book will guide the
motivated reader to understand the essential background needed to read and
unerstand current research papers, and to gain the insights and techniques
needed to begin making their own contributions to this rapidly growing field.
* Develops the theory of fractional calculus and anomalous diffusion using
probability theory.
* Revised and updated edition with a new chapter on numerical methods,
including examples and computer codes.
* With applications in many applied contexts.
De Gruyter Studies in Mathematics
rev. and ext., Approx. xii, 450 pages ,
90 Figures (bw)
Hardcover:
ISBN 978-3-11-055907-1
Date of Publication: December 2018
Language of Publication: English
Subjects: Probability and Statistics
Of interest to: Graduate students and researchers in probability and stochastics.
Hardback
This item is not yet published, but may be pre-ordered now for delivery when available.
Published: 13 September 2018 (Estimated)
256 Pages | 30
234x156mm
ISBN: 9780198827351
Kazimierz Goebel and Stanislaw Prus
Provides a concise introduction to the theory to help non-specialists gain a deeper understanding of the subject
Includes numerous examples to direct study
One of the subjects of functional analysis is classification of Banach spaces depending on various properties of the unit ball. The need of such considerations comes from a number of applications to problems of mathematical analysis. The list of subjects includes: differential calculus in normed spaces, approximation theory, weak topologies and reflexivity, general theory of convexity and convex functions, metric fixed point theory and others. The book presents basic facts from this field.
1: Basics and prerequisites
2: Low dimensional spaces
3: Strict and uniform convexity
4: Smoothness and uniform smoothness
5: Uniform smoothness vs uniform convexity
6: Projections on balls and convex sets
7: More moduli and coefficients
8: Radius vs diameter
9: Three special topics
10: Measures of noncompactness and related properties
11: The case of Banach lattices
*