Series: Lecture Notes in Physics
2003, XV, 246 p., Hardcover
ISBN: 3-540-20307-9
About this book
The present volume, published at the occasion
of his 100th
birthday anniversary, is a collection of
articles that reviews
the impact of Kolomogorov's work in the physical
sciences and
provides an introduction to the modern developments
that have
been triggered in this way to encompass recent
applications in
biology, chemistry, information sciences
and finance. This book
addresses scientists and postgraduate students
in applied
mathematics and theoretical physics.
Written for:
Scientists, postgraduate students
Table of contents
Part I: Chaos and Dynamical Systems.- Part
II: Algorithmic
Complexity and Information Theory.- Part
III: Turbulence.- Part
IV: Applications of Probability Theory.
Series: Lecture Notes in Mathematics
Series: Fondazione C.I.M.E., Firenze
2004, XIV, 349 p., Softcover
ISBN: 3-540-20357-5
About this book
Noncommutative Geometry is one of the most
deep and vital
research subjects of present-day Mathematics.
Its development,
mainly due to Alain Connes, is providing
an increasing number of
applications and deeper insights for instance
in Foliations, K-Theory,
Index Theory, Number Theory but also in Quantum
Physics of
elementary particles. The purpose of the
Summer School in Martina
Franca was to offer a fresh invitation to
the subject and closely
related topics; the contributions in this
volume include the four
main lectures, cover advanced developments
and are delivered by
prominent specialists.
Written for:
Researchers and graduate students
Table of contents
Preface.- A. Connes: Cyclic Cohomology, Noncommutative
Geometry
and Quantum Group Symmetries.- J. Cuntz:
Cyclic Theory and the
Bivariant Chern-Connes Character.- N. Higson,
E. Guentner: Group
C*-Algebras and K-Theory.- E. Guentner, J.
Kaminker: Geometric
and Analytic Properties of Groups.- J.E.
Roberts: More Lectures
on Algebraic Quantum Field Theory.
Series: Lecture Notes in Mathematics
2004, IX, 280 p., Softcover
ISBN: 3-540-20611-6
About this book
This volume provides a systematic mathematical
exposition of the
conceptual problems of nonequilibrium statistical
physics, such
as entropy production, irreversibility, and
ordered phenomena.
Markov chains, diffusion processes, and hyperbolic
dynamical
systems are used as mathematical models of
physical systems. A
measure-theoretic definition of entropy production
rate and its
formulae in various cases are given. It vanishes
if and only if
the stationary system is reversible and in
equilibrium. Moreover,
in the cases of Markov chains and diffusion
processes on
manifolds, it can be expressed in terms of
circulations on
directed cycles. Regarding entropy production
fluctuations, the
Gallavotti-Cohen fluctuation theorem is rigorously
proved.
Written for:
Researchers and graduate students
Table of contents
Preface.- Introduction.- Circulation Distribution,
Entropy
Production and Irreversibility of Denumerable
Markov Chains.-
Circulation Distribution, Entropy Production
and Irreversibility
of Finite Markov Chains with Continuous Parameter.-
General
Minimal Diffusion Process: its Construction,
Invariant Measure,
Entropy Production and Irreversibility.-
Measure-theoretic
Discussion on Entropy Production of Diffusion
Processes and
Fluctuation-dissipation Theorem.- Entropy
Production, Rotation
Numbers and Irreversibility of Diffusion
Processes on Manifolds.-
On a System of Hyperstable Frequency Locking
Persistence under
White Noise.- Entropy Production and Information
Gain in Axiom A
Systems.- Lyapunov Exponents of Hyperbolic
Attractors.- Entropy
Production, Information Gain and Lyapunov
Exponents of Random
Hyperbolic Dynamical Systems.- References.-
Index.
Series: Problem Books in Mathematics
3rd ed., 2004, Approx. 610 p. 42 illus.,
Hardcover
ISBN: 0-387-20429-6
About this book
In 1977 the Mathematics Department at the
University of
California, Berkeley, instituted a written
examination as one of
the first major requirements toward the Ph.D.
degree in
Mathematics. Its purpose was to determine
whether first-year
students in the Ph.D. program had successfully
mastered basic
mathematics in order to continue in the program
with the
likelihood of success. Since its inception,
the exam has become a
major hurdle to overcome in the pursuit of
the degree. The
purpose of this book is to publicize the
material and aid in the
preparation for the examination during the
undergraduate years.
The book is a compilation of over 1,250 problems
which have
appeared on the preliminary exams in Berkeley
over the last
twenty-five years. It is an invaluable source
of problems and
solutions for every mathematics student who
plans to enter a Ph.D.
program. Students who work through this book
will develop problem-solving
skills in areas such as real analysis, multivariable
calculus,
differential equations, metric spaces, complex
analysis, algebra,
and linear algebra. The problems are organized
by subject and
ordered in an increasing level of difficulty.
Tags with the exact
exam year provide the opportunity to rehearse
complete
examinations. The appendix includes instructions
on accessing
electronic versions of the exams as well
as a syllabus and
statistics of passing scores. This new edition
has been updated
with the most recent exams, including exams
given during the Fall
2003 semester. There are numerous new problems
and solutions
which were not included in previous editions.
Written for:
Undergraduate and graduate students in mathematics
Table of contents
Preface.- Problems.- Real Analysis.- Multivariable
Calculus.-
Differential Equations.- Metric Spaces.-
Complex Analysis.-
Algebra.- Linear Algebra.- Solutions.- Real
Analysis.-
Multivariable Calculus.- Differential Equations.-
Metric Spaces.-
Complex Analysis.- Algebra.- Linear Algebra.-
Appendices.-
References.- Index.
2003, XII, 234 pp., Hardcover
ISBN: 3-540-20482-2
About this textbook
This is a readily accessible introduction
to the theory of
stochastic processes with emphasis on processes
with independent
increments and Markov processes. After preliminaries
on
infinitely divisible distributions and martingales,
Chapter 1
gives a thorough treatment of the decomposition
of paths of
processes with independent increments, today
called the Levy-Ito
decomposition, in a form close to Ito's original
paper from 1942.
Chapter 2 contains a detailed treatment of
time-homogeneous
Markov processes from the viewpoint of probability
measures on
path space. Two separate Sections present
about 70 exercises and
their complete solutions. The text and exercises
are carefully
edited and footnoted, while retaining the
style of the original
lecture notes from Aarhus University.
Written for:
Graduate students and researchers
Table of contents
Preliminaries.- Additive Processes (Processes
with Independent
Increments).- Markov Processes.- Exercises.-
Solutions of
Exercises.
2004, XIX, 459 p., Softcover
ISBN: 3-540-20466-0
About this book
This book represents the refereed proceedings
of the Fifth
International Conference on Monte Carlo and
Quasi-Monte Carlo
Methods in Scientific Computing which was
held at the National
University of Singapore in the year 2002.
An important feature
are invited surveys of the state of the art
in key areas such as
multidimensional numerical integration, low-discrepancy
point
sets, computational complexity, finance,
and other applications
of Monte Carlo and quasi-Monte Carlo methods.
These proceedings
also include carefully selected contributed
papers on all aspects
of Monte Carlo and quasi-Monte Carlo methods.
The reader will be
informed about current research in this very
active area.
Written for:
Researchers, graduate students