August 2002, ISBN 1-4020-0793-0, Paperback
Book Series: NATO SCIENCE SERIES: II: Mathematics, Physics and
Chemistry : Volume 77
New and striking results obtained in recent years from an
intensive study of asymptotic combinatorics have led to a new,
higher level of understanding of related problems: the theory of
integrable systems, the Riemann-Hilbert problem, asymptotic
representation theory, spectra of random matrices, combinatorics
of Young diagrams and permutations, and even some aspects of
quantum field theory.
Contents and Contributors
Preface. Program. List of participants. Part One: Matrix Models
and Graph Enumeration. Matrix Quantum Mechanics; V. Kazakov.
Introduction to matrix models; E. Brezin. A Class of the Multi-Interval
Eigenvalue Distributions of Matrix Models and Related Structures;
V. Buslaev, L. Pastur. Combinatorics and Probability of Maps; V.A.
Malyshev. The Combinatorics of Alternating Tangles: from theory
to computerized enumeration; J.L. Jacobsen, P. Zinn-Justin.
Invariance Principles for Non-uniform Random Mappings and Trees;
D. Aldous, J. Pitman. Part Two: Integrable Models (of Statistical
Physics and Quantum Field Theory). Renormalization group solution
of fermionic Dyson model; M.D. Missarov. Statistical Mechanics
and Number Theory; H.E. Boos, V.E. Korepin. Quantization of
Thermodynamics and the Bardeen-Cooper-Schriffer-Bogolyubov
Equation; V.P. Maslov. Approximate Distribution of Hitting
Probabilities for a Regular Surface with Compact Support in 2D; D.S.
Grebenkov. Part Three: Representation Theory. Notes on
homogeneous vector bundles over complex flag manifolds; S. Igonin.
Representation Theory and Doubles of Yangians of Classical Lie
Superalgebras; V. Stukopin. Idempotent (asymptotic) Mathematics
and the Representation theory; G.L. Litvinov, et al. A new
approach to Berezin kernels and canonical representations; G. van
Dijk. Theta Hypergeometric Series; V.P. Spiridonov.
December 2002, ISBN 1-4020-1015-X, Hardbound
Tensor Analysis and Nonlinear Tensor Functions embraces the basic
fields of tensor calculus: tensor algebra, tensor analysis,
tensor description of curves and surfaces, tensor integral
calculus, the basis of tensor calculus in Riemannian spaces and
affinely connected spaces, - which are used in mechanics and
electrodynamics of continua, crystallophysics, quantum chemistry
etc.
The book suggests a new approach to definition of a tensor in
space 3, which allows us to show a geometric representation of a
tensor and operations on tensors. Based on this approach, the
author gives a mathematically rigorous definition of a tensor as
an individual object in arbitrary linear, Riemannian and other
spaces for the first time.
It is the first book to present a systematized theory of tensor
invariants, a theory of nonlinear anisotropic tensor functions
and a theory of indifferent tensors describing the physical
properties of continua.
The book will be useful for students and postgraduates of
mathematical, mechanical engineering and physical departments of
universities and also for investigators and academic scientists
working in continuum mechanics, solid physics, general
relativity, crystallophysics, quantum chemistry of solids and
material science.
Contents
Preface. Sources of Tensor Calculus. Introduction. 1. Tensor
Algebra. 2. Tensors in Linear Spaces. 3. Groups of
Transformations. 4. Indifferent Tensors and Invariants. 5. Tensor
Functions. 6. Tensor Analysis. 7. Geometry of Curves and Surfaces.
8. Tensors in Riemannian Spaces and Affinely Connected Spaces. 9.
Integration of Tensors. 10. Tensors in Continuum Mechanics. 11.
Tensor Functions in Continuum Mechanics. References. Subject
Index.
November 2002, ISBN 0-306-47422-0, Hardbound
Book Series: INTERNATIONAL MATHEMATICAL SERIES : Volume 2
The main topics reflect the fields of mathematics in which
Professor O.A. Ladyzhenskaya obtained her most influential
results.
One of the main topics considered in the volume is the Navier-Stokes
equations. This subject is investigated in many different
directions. In particular, the existence and uniqueness results
are obtained for the Navier-Stokes equations in spaces of low
regularity. A sufficient condition for the regularity of
solutions to the evolution Navier-Stokes equations in the three-dimensional
case is derived and the stabilization of a solution to the Navier-Stokes
equations to the steady-state solution and the realization of
stabilization by a feedback boundary control are discussed in
detail. Connections between the regularity problem for the Navier-Stokes
equations and a backward uniqueness problem for the heat operator
are also clarified.
Generalizations and modified Navier-Stokes equations modeling
various physical phenomena such as the mixture of fluids and
isotropic turbulence are also considered. Numerical results for
the Navier-Stokes equations, as well as for the porous medium
equation and the heat equation, obtained by the diffusion
velocity method are illustrated by computer graphs.
Some other models describing various processes in continuum
mechanics are studied from the mathematical point of view. In
particular, a structure theorem for divergence-free vector fields
in the plane for a problem arising in a micromagnetics model is
proved. The absolute continuity of the spectrum of the elasticity
operator appearing in a problem for an isotropic periodic elastic
medium with constant shear modulus (the Hill body) is established.
Time-discretization problems for generalized Newtonian fluids are
discussed, the unique solvability of the initial-value problem
for the inelastic homogeneous Boltzmann equation for hard
spheres, with a diffusive term representing a random background
acceleration is proved and some qualitative properties of the
solution are studied. An approach to mathematical statements
based on the Maxwell model and illustrated by the Lavrent'ev
problem on the wave formation caused by explosion welding is
presented. The global existence and uniqueness of a solution to
the initial boundary-value problem for the equations arising in
the modelling of the tension-driven Marangoni convection and the
existence of a minimal global attractor are established. The
existence results, regularity properties, and pointwise estimates
for solutions to the Cauchy problem for linear and nonlinear
Kolmogorov-type operators arising in diffusion theory,
probability, and finance, are proved. The existence of minimizers
for the energy functional in the Skyrme model for the low-energy
interaction of pions which describes elementary particles as
spatially localized solutions of nonlinear partial differential
equations is also proved.
Several papers are devoted to the study of nonlinear elliptic and
parabolic operators. Versions of the mean value theorems and
Harnack inequalities are studied for the heat equation, and
connections with the so-called growth theorems for more general
second-order elliptic and parabolic equations in the divergence
or nondivergence form are investigated. Additionally, qualitative
properties of viscosity solutions of fully nonlinear partial
differential inequalities of elliptic and degenerate elliptic
type are clarified. Some uniqueness results for identification of
quasilinear elliptic and parabolic equations are presented and
the existence of smooth solutions of a class of Hessian equations
on a compact Riemannian manifold without imposing any curvature
restrictions on the manifold is established.
Description
The Handbook of the Economics of Finance, edited by George
Constantinides, Milton Harris, and Rene Stulz, surveys recent
developments in the three main branches of finance research:
corporate finance and banking, asset pricing, and the structure
of financial markets. Each essay is written by world renowned
leaders in the surveyed field of research. Authors include
Franklin Allen, Patrick Bolton, Michael Brennan, John Campbell,
Darrell Duffie, Michael Jensen, Stewart Myers, Edward Prescott,
Raghuram Rajan, Stephen Ross, Jeremy Stein, Rene Stulz, Richard
Thaler, and Luigi Zingales. The Handbook will provide readers
with a comprehensive picture of the state of the art of finance
research
Contents
Preliminary Contents. Part 1: Corporate Finance.
Introduction (M. Harris, R. Stulz).
Theory of the Firm.
Boundaries and organization of the firm (R. Rajan, Luigi Zingales).
Agency and the theory of the firm (M. Jensen).
Agency, information and corporate investment (J. Stein).
Corporate investment policy (M. Brennan).
Corporate governance and control (M. Becht, P. Bolton and A.
Roell).
Capital Structure and Finance Policies.
Payout policies (F. Allen, R. Michaely).
Financing policies (S. Myers).
Financial Intermediaries.
Banking (G. Gorton, A. Winton).
Investment banking and security issuance (J. Ritter).
Financial intermediaries and financial innovation (P. Tufano).
Market microstructure (H. Stoll).
Part 2: Financial Markets and Asset Pricing.
Introduction (G.M. Constantinides, R. Stulz).
Arbitrage, state prices and portfolio theory (S. Ross, P.H.
Dybvig).
Intertemporal asset pricing models (D. Duffie).
Tests of multi-factor pricing models, volatility, and portfolio
performance (W. Ferson).
The equity premium puzzle (R. Mehr, E.C. Prescott).
Anomalies and market efficiency (G.W. Schwert).
Surveys of behavioral science (N.C. Barberis, R.H. Thaler).
Consumption-based asset pricing (J.Y. Campbell).
Asset prices and market microstructure (D. Easley, M. O'Hara).
Empirical analysis of fixed income pricing models (Q. Dai, K.
Singleton).
Derivatives (R.E. Whaley).
Issues in international asset pricing (R. Stulz, A. Karolyi).
Year 2003 Hardbound
ISBN: 0-444-50298-X
approx. 1200 pages
Description
The book presents surveys describing recent developments in most
of the primary subfields of General Topology and its applications
to Algebra and Analysis during the last decade. It follows freely
the previous edition (North Holland, 1992), Open Problems in
Topology (North Holland, 1990) and Handbook of Set-Theoretic
Topology (North Holland, 1984). The book was prepared in
connection with the Prague Topological Symposium, held in 2001.
During the last 10 years the focus in General Topology changed
and therefore the selection of topics differs slightly from those
chosen in 1992. The following areas experienced significant
developments: Topological Groups, Function Spaces, Dimension
Theory, Hyperspaces, Selections, Geometric Topology (including
Infinite-Dimensional Topology and the Geometry of Banach Spaces).
Of course, not every important topic could be included in this
book.
Except surveys, the book contains several historical essays
written by such eminent topologists as:
R.D. Anderson, W.W. Comfort, M. Henriksen, S. Mardesic, J.
Nagata, M.E. Rudin, J.M. Smirnov (several reminiscences of L.
Vietoris are added). In addition to extensive author and subject
indexes, a list of all problems and questions posed in this book
are added.
List of all authors of surveys:
A. Arhangel'skii, J. Baker and K. Kunen, H. Bennett and D.
Lutzer, J. Dijkstra and J. van Mill, A. Dow, E. Glasner, G.
Godefroy, G. Gruenhage, N. Hindman and D. Strauss, L. Hola and J.
Pelant, K. Kawamura, H.-P. Kuenzi, W. Marciszewski, K. Martin and
M. Mislove and M. Reed, R. Pol and H. Torunczyk, D. Repovs and P.
Semenov, D. Shakhmatov, S. Solecki, M. Tkachenko.
Audience
University libraries. Libraries of scientific institutions.
Topologists.
Contents
Topological invariants in algebraic environment (A.V.
Arhangel'skii). Matrices and ultrafilters (J. Baker, K. Kunen).
Recent developments in the topology of ordered spaces (H.R.
Bennett, D.J. Lutzer). Infinite-dimensional topology (J.J.
Dijkstra, J. van Mill). Recent results in set-theoretical
topology (A. Dow). Topics in topological dynamics, 1991 to 2001 (E.
Glasner). Banach spaces of continuous functions on compact spaces
(G. Godefroy). Metrizable spaces and generalizations (G.
Gruenhage). Recent progress in the topological theory of
semigroups and the algebra of S (N. Hindman, D. Strauss). Recent
progress in hyperspace topologies (L'. Hola, J. Pelant). Some
topics in geometric topology (K. Kawamura). Quasi-uniform spaces
in the year 2001 (H.-P. Kunzi). Function spaces (W. Marciszewski).
Topology and domain theory (K. Martin, M.W. Mislove, G.M. Reed).
Topics in dimension theory (R. Pol, H. Torunczyk). Continuous
selections of multivalued mappings (D. Repovs, P.V. Semenov).
Convergence in the presence of algebraic structure (D. Shakhmatov).
Descriptive set theory in topology (S. Solecki). Topological
groups: between compactness and o-boundedness (M. Tkachenko).
Essays (R.D. Anderson, W.W. Comfort, M. Henriksen, S. Mardesic, J.
Nagata, M.E. Rudin, Yu.M. Smirnov, reminiscences of L. Vietoris).
List of open problems and questions.
Author index Special symbols Subject index
Year 2002 Hardbound
ISBN: 0-444-50980-1
v+xii + 638 pages
Sarvadaman Chowla (1907 - 1995) was an extremely talented
mathematician who earned an international reputation for his
research in number theory and related areas. His output was
impressive and reflected his special gift for expressing complex
ideas simply. Several important theorems (the Bruck-Chowla-Ryser
theorem, the Ankeny-Artin-Chowla congruence, the Chowla-Mordell
theorem and the Chowla-Selberg formula) are named after him. One
of the best-known number theorists from India following in the
tradition of Ramanujan, Chowla's fertile and creative imagination
justified the title "poet of mathematics" given him by
his associates. Chowla wrote over 350 mathematical papers during
the period 1926 - 1986. These papers have been collected together
and arranged chronologically in three volumes. In addition, the
first volume contains a biography of Chowla by James G. Huard, an
overview of Chowla's work by M. Ram Murty, V. Kumar Murty and
Kenneth S. Williams, recollections of Chowla by a number of
famous mathematicians, copies of letters to Chowla by such
mathematicians as G. H. Hardy and A. Weil, several photographs,
as well as other material.
These volumes provide a valuable source of problems, conjectures,
and new ideas for all mathematicians with an interest in number
theory.
Le present texte de reference s'adresse aux etudiants du
baccalaureat en mathematiques qui ont une bonne connaissance de
l'analyse reelle; ainsi, ce manuel peut etre considere comme une
suite de l'ouvrage Introduction a l'analyse reelle [6]. Dans le
present texte on etudie, entre autres, les concepts de fonctions
scalaires et vectorielles, la continuite de ces fonctions, les
derivees partielles, les fonctions differentiables, la notion de
fonctions inverses, les fonctions implicites et les points
extremums avec ou sans contraintes. Ces themes sont abordes de
facon theorique et ainsi certaines notions sur la topologie de Rn
seront necessaires pour aborder de facon correcte ces nouvelles
notions. De nombreux exemples sont faits en detail dans le but
d'ameliorer la comprehension de certains resultats abstraits et
aussi pour developper de nouvelles techniques necessaires pour
solutionner un certain type de problemes. Notons qu'une
connaissance elementaire de l'algebre lineaire sera aussi
supposee connue. Finalement le materiel du present texte est
suffisant pour un semestre.
184 pages
ISBN 2-921120-36-4
2002