2006, Approx. 295 p. 120 illus., Softcover
ISBN: 0-8176-4484-9
About this textbook
Graph theory continues to be one of the fastest growing areas of
modern mathematics because of its wide applicability in such
diverse discliplines as computer science, engineering, chemistry,
management science, social science, and resource planning. Graphs
arise as mathematical models in these fields, and the theory of
graphs provides a spectrum of methods of proof. This concisely
written textbook is intended for an introductory course in graph
theory for undergraduate mathematics majors or advanced
undergraduate and graduate students from the many fields that
benefit from graph-theoretic applications.
Table of contents
Preface.- Preface to the First Edition.- List of Figures.- Graphs.-
Walks, Paths, and Cycles.- Connectivity.- Trees.- Linear Spaces
Associated with Graphs.- Factorizations.- Graph Colorings.-
Planarity.- Labeling.- Ramsey Theory.- Digraphs.- Critical Paths.-
Flows in Networks.- Computational Considerations.- Communication
Networks and Small Worlds.- References.- Hints.- Answers and
Solutions
Series: International Series of Numerical Mathematics , Vol.
154
2006, Hardcover
ISBN: 3-7643-7718-6
About this book
This book gathers a collection of refereed articles containing
original results reporting the recent contributions of the
lectures and communications presented at the Free Boundary
Problems Conference that took place at the University of Coimbra,
Portugal, from June 7 to 12, 2005 (FBP2005). They deal with the
mathematics of a broad class of models and problems involving
nonlinear partial differential equations arising in physics,
engineering, biology and finance. Among the main topics, the
talks considered free boundary problems in biomedicine, in porous
media, in thermodynamic modeling, in fluid mechanics, in image
processing, in financial mathematics or in computations for inter-scale
problems.
Table of contents
Preface.- 43 original research articles on free boundary problems
in biomedicine, in porous media, in thermodynamic modeling, in
fluid mechanics, in image processing, in financial mathematics
and in computations for inter-scale problems.
Series: Graduate Texts in Mathematics , Vol. 236
2006, Approx. 440 p. 31 illus., Hardcover
ISBN: 0-387-33621-4
About this textbook
"This book is an account of the theory of Hardy spaces in
one dimension, with emphasis on some of the exciting developments
of the past two decades or so. The last seven of the ten chapters
are devoted in the main to these recent developments. The motif
of the theory of Hardy spaces is the interplay between real,
complex, and abstract analysis. While paying proper attention to
each of the three aspects, the author has underscored the
effectiveness of the methods coming from real analysis, many of
them developed as part of a program to extend the theory to
Euclidean spaces, where the complex methods are not available...Each
chapter ends with a section called Notes and another called
Exercises and further results. The former sections contain brief
historical comments and direct the reader to the original sources
for the material in the text."
Table of contents
Preliminaries.- H_p spaces.- Conjugate functions.- Some extremal
problems.- Some uniform algebra.- Bounded mean oscillation.-
Interpolating sequences.- The corona construction.- Douglas
algebras.- Interpolating sequences and Maximal Ideals.-
Bibliography.- Index.-
Series: International Series of Numerical Mathematics , Vol.
155
2006, Approx. 350 p., Hardcover
ISBN: 3-7643-7720-8
About this book
Proceedings of the 2005 Oberwolfach Conference on “Optimal
Control of Coupled Systems of Partial Differential Equations“.
Contributions by many leading researchers in this fast-growing
research area.
Written for:
Researchers interested in Optimal control of coupled systems of
PDEs
Table of contents
Introduction.- Wave Control.- Boundary Controllability.- Quantum
Control.- Shape Optimization.- Navier-Stokes Equations.
Series: Progress in Mathematics , Preliminary entry 950
2006, Approx. 350 p. 20 illus., Hardcover
ISBN: 0-8176-4496-2
About this book
Eisenstein series are an essential ingredient in the spectral
theory of automorphic forms and an important tool in the theory
of L-functions. They have also been exploited extensively by
number theorists for many arithmetic purposes. Bringing together
contributions from areas which are not usually interacting with
each other, this volume will introduce diverse users of
Eisenstein series to a variety of important applications. With
this juxtaposition of perspectives, the reader obtains deeper
insights into the arithmetic of Eisenstein series.
The central theme of the exposition focuses on the common
structural properties of Eisenstein series occurring in many
related applications that have arisen in several recent
developments in arithmetic: Arakelov intersection theory on
Shimura varieties, special values of L-functions and Iwasawa
theory, and equidistribution of rational/integer points on
homogeneous varieties. Key questions that are considered include:
Is it possible to identify a class of Eisenstein series whose
Fourier coefficients (resp. special values) encode significant
arithmetic information? Do such series fit into p-adic families?
and, Are the Eisenstein series that arise in counting problems of
this type?
Table of contents
Preface.- Part I: Introductory Papers.- D. Bump: Multiple
Dirichlet Series.- M. Emerton: p-adic Langlands Program.- W.T.
Gan: Eisenstein series.- W.T. Gan: Saito--Kurokawa Lifting.- S.S.
Kudla: Siegel--Weil Formula.- E. Lapid: Analytic Theory of
Eisenstein Series.- J. Schwermer: Eisenstein Cohomology.- C.M.
Skinner: p-adic Modular Forms and Applications.- R. Takloo-Bighash
and Y. Tschinkel: Counting Rational Points.- Part II: Research
Papers.- J. Franke.- J. Funke.- M. Harris.- D.H. Jiang.- W.
Kohnen.- K. Prasanna.- F. Shahidi.- B. Speh.
Series: Progress in Mathematical Physics , Preliminary entry
1300
2007, Approx. 255 p. 40 illus., Hardcover
ISBN: 0-8176-4400-8
About this book
Quantization in quantum mechanics deals with the problem of
correct defining various classical structures, for example,
quantum-mechanical observables such as Hamiltonian, momentum,
self-adjoint operators in some Hilbert space and so on. Though
there exists a naive treatment, based on experience in finite-dimensional
algebra or even infinite-dimensional algebra with bounded
operators, it results in paradoxes and inaccuracies. This
exposition is devoted to a consistent treatment of such problems,
based on appealing to some nontrivial items of functional
analysis concerning the theory of linear operators in Hilbert
spaces.
It begins by considering quantization problems in general,
emphasizing the non-triviality of consistent operator
construction by presenting paradoxes to the naive treatment. It
then builds the necessary mathematical background following it by
the theory of self-adjoint extensions. By considering several
problems such as the one-dimensional Calogero problem, the
Aharonov-Bohm problem, the problem of delta-like potentials and
relativistic Coulomb problem it then shows how quantization
problems associated with correct definition of observables can be
treated consistently for comparatively simple quantum-mechanical
systems. In the end, related problems in quantum field theory are
briefly introduced.
This well organized text is most suitable for students and post
graduates interested in deepening their understanding of
mathematical problems in quantum mechanics. However, scientists
in mathematical and theoretical physics and mathematicians will
also find it useful.
Table of contents
Introduction.- Self-adjoint extensions of symmetric operators.-
Consistent quantization of simple methods.- Quantum mechanical
problems with delta-like potentials.- Relativistic and
nonrelativistic particles in Aharonov-Bohm field.- The problem of
supercritical point charge. Particle creation on the charge.-
Discussion.- Subject Index.- Bibliography