Series: Operator Theory: Advances and Applications , Vol. 170
2006, Approx. 245 p., Hardcover.
ISBN: 3-7643-7736-4
Due: October 2006
About this book
This volume is dedicated to the eminent Russian mathematician I.B.
Simonenko on the occasion of his 70th birthday. It presents
recent results in Fredholm theory for singular integral and
convolution operators, estimates for singular integral operators
on Carleson curves acting in Lp spaces with variable exponents,
the finite sections method for band-dominated and Toeplitz
operators, Szego type theorems, the averaging method for
nonlinear equations, among others. All papers are contributed by
leading experts, many of whom are connected with I.B. Simonenko
as students or collaborators. The book testifies the wide
mathematical interest of I.B. Simonenko and includes a biography,
his list of publications and a list of his Ph.D. students.
Written for:
Graduates, postgraduates and researchers in mathematics and
related fields
Table of contents
Editorial Introduction.- Contributions by A.B. Antonevich, A.
Bottcher, L.P. Castro, R.G. Douglas, R. Duduchava, I. Feldman, C.
Foias, I. Gohberg, S.M. Grudsky, M.A. Kaashoek, Yu.I. Karlovich,
V. Kokilashvili, N. Krupnik, L. Lerer, V.B. Levenshtam, A.
Markus, V. Paatashvili, V.S. Rabinovich, S. Roch, S. Samko, B.
Silbermann, F.-O. Speck, N. Vasilevski, D. Wenzel, H. Widom.
Series: Springer Monographs in Mathematics
2007, Approx. 250 p., 20 illus., Softcover.
ISBN: 0-387-35156-6
About this textbook
This text treats the classical theory of quadratic diophantine
equations and guides the reader through the last two decades of
computational techniques and progress in the area. These new
techniques combined with the latest increases in computational
power shed new light on important open problems.
Key features:
Motivates the study of quadratic diophantine equations with
excellent examples and open problems
Examines Pell’s equation and its generalizations
Presents important quadratic diophantine equations and
applications
Computational techniques solve classical and outstanding problems
The book is intended for advanced undergraduate and graduate
students as well as researchers. It challenges the reader to
apply not only specific techniques and strategies, but also to
employ methods and tools from other areas of mathematics, such as
algebra and analysis.
Written for:
Advanced undergraduate and graduate students, and researchers in
mathematics
Table of contents
Introduction.-Why Pell’s equation?.-Two useful techniques:
continued fractions and quadratic rings.-Pell’s equation.-General
Pell’s equation.-Equations reducible to Pell’s equation.-Diophantine
representations of some sequences.-Other applications.-Glossary.-References.-Index.
Volume package: Mathematical Analysis
2007, XVIII, 470 p., 128 illus., Hardcover.
ISBN: 0-8176-4374-5
Due: November 2006
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.
Written for:
Advanced undergraduates, graduate students, researchers
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.
2007, Approx. 300 p., 10 illus., Softcover.
ISBN: 0-8176-4497-0
Due: December 2006
About this textbook
Probability with Statistical Applications targets non-mathematics
students, undergraduate and graduates, who do not need an
exhaustive treatment of the subject. While the presentation is
rigorous and contains theorems and proofs, linear algebra is
largely avoided and only a minimal amount of multivariable
calculus is needed.
Key features:
* Clear definitions, simplified notation and techniques of
statistical anaylsis, combined with well chosen examples and
exercises, motivate the exposition
* Theory and applications carefully balanced
* Topics include random phenomena -- discrete and continuous
random variables -- expectations and variance, and common
probability distributions such as the binomial, Poisson, and
normal
* Combinatorial principles involve all four arithmetic
operations; emphasis on tree diagrams
* References to more advanced concepts throughout the book, but
may be safely skipped, depending on the reader
For students in a variety of disciplines, including computer
science, engineering, natural and social sciences.
Written for:
Advanced undergraduate and graduate students in computer science,
engineering, natural and social sciences
Table of contents
Preface.- The Algebra of Events.- Combinatorial Problems.-
Probabilities.- Random Variables.- Expectation, Variance, Moments.-
Some Special Distributions.- The Elements of Mathematical
Statistics.- Bibliography.- Index.
Series: Problem Books in Mathematics
2007, Approx. 130 p., 14 illus., Hardcover.
ISBN: 0-387-34534-5
Due: January 2007
About this textbook
Over the years, a number of books have been written on the theory
of functional equations. However, very little has been published
which helps readers to solve functional equations in mathematics
competitions and mathematical problem solving. This book fills
that gap. The student who encounters a functional equation on a
mathematics contest will need to investigate solutions to the
equation by finding all solutions (if any) or by showing that all
solutions have a particular property. Our emphasis will be on the
development of those tools which are most useful in giving a
family of solutions to each functional equation in explicit form.
At the end of each chapter, readers will find a list of problems
associated with the material in that chapter. The problems vary
greatly diffculty, with the easiest problems being accessible to
any high school student who has read the chapter carefully. The
most diffcult problems will be a reasonable challenge to advanced
students studying for the International Mathematical Olympiad at
the high school level or the William Lowell Putnam Competition
for university undergraduates.
The modern theory of functional equations can occur in a very
abstract setting that is quite inappropriate for the most high
school students. However, the abstraction of some parts of the
modern theory reflects the fact that functional equations can
occur in diverse settings: functions on the natural numbers, the
integers, the reals, or the complex numbers can all be studied
within the subject area of functional equations. Most of the
time, the functions in this book are real-valued functions of a
single real variable. However, readers will also find functions
with complex arguments and functions defined on natural numbers
in these pages. In some cases, equations for functions between
circles will also crop up. The book ends with an appendix
containing topics that provide a springboard for further
investigation of the concepts of limits, infinite series and
continuity.
Written for:
Advanced high school students, undergraduates, participants of
mathematical Olympiads and William Lowell Putnam competitions
Table of contents
Preface.- An historical introduction.- Functional equations with
two variables.- Functional equations with one variable.-
Miscellaneous methods for functional equations.- Some closing
heuristics.- Appendix: Hamel bases.- Hints and partial solutions
to problems.- Bibliography.- Index.
2007, Approx. 455 p., 300 illus..
ISBN: 1-84628-039-7
Due: May 2007
About this book
A coherent framework is presented for understanding the dynamics
of piecewise-smooth and hybrid systems. An informal introduction
motivates the ubiquity of such models via examples from
mechanics, electronics, control theory and physiology. The main
thrust is to classify complex behaviour via bifurcation theory,
in a systematic yet applicable way. The key concept is that of
discontinuity-induced bifurcation, which generalises diverse
phenomena such as grazing, border-collision, sliding, chattering
and the period-adding route to chaos. The results are presented
in an informal style, illustrated via many examples, both
theoretical and experimental.
The book is aimed at a wide audience of applied mathematicians,
engineers and scientists at the beginning postgraduate level.
Almost no mathematical background is assumed other than basic
calculus and algebra. The inclusion of a comprehensive
bibliography and many open questions should also serve as a
stimulus for future research.
Written for:
Postgraduate students; Researchers
Table of contents
Introduction
Technical Background
Border-Collisions in Piecewise Linear Maps
Other Piecewise Smooth Maps
Non-smooth Equilibrium Bifurcations
Hybrid Systems and their Limit-Cycle Bifurcations
Grazing bifurcations in Piecewise-Smooth Flows
Sliding Bifurcations in Fillipov Systems
Global Issues
Further Applications
Series: Applied Mathematical Sciences , Vol. 162
Approx. 600 p., Hardcover.
ISBN: 0-387-35779-3
Due: May 2007
About this book
The present monograph is the successor of "Direct methods in
the calculus of variations" which was published in the
Applied Mathematical Sciences series and is currently out of
print. Although the core and the structure of the present book is
similar to the old one, it is much more than a revised version.
Fifteen years have passed since the publication of the "Direct
methods in the calculus of variations" book and since the
subject is a very active one, almost half of the book presently
consists of new material. The perspective has also slightly
changed, which is reflected in the change of the title. Indeed a
new subject, "quasiconvex analysis" has now been
developed. The present monograph, which is essentially a
reference book on the subject of quasiconvex analysis, can be
used, as was the earlier book for an advanced course on the
calculus of variations.
Written for:
Researchers, graduate students
Table of contents
Introduction.- The scalar case.- Convex sets and convex functions.-
Lower semicontinuity and existence theorems.- The one dimensional
case.- The vectorial case.- Polyconvex, quasiconvex and rank one
convex functions.- Polyconvex, quasiconvex and rank one convex
envelopes.- Polyconvex, quasiconvex and rank one convex sets.-
Lower semi continuity and existence theorems in the vectorial
case.- Relaxation and non convex problems.- Relaxation theorems.-
Implicit partial differential equations.- Existence of minima for
non quasiconvex integrands.- Miscellaneous.- Function spaces.-
Singular values.- Some underdetermined partial differential
equations.- Extension of Lipschitz functions on Banach spaces