Conte, R., Gif-sur-Yvette, France
(Ed.)
One Century Later
1999. Approx. 600 pp. 12 figs.
0-387-98888-2
The subject this volume is explicit integration, that is, the
analytical as opposed to the numerical solution, of all kinds of
nonlinear
differential equations (ordinary differential, partial
differential, finite difference). Such equations describe many
physical phenomena,
their analytic solutions (particular solutions, first integral,
and so forth) are in many cases preferable to numerical
computation, which
may be long, costly and, worst, subject to numerical errors. In
addition, the analytic approach can provide a global knowledge of
the
solution, while the numerical approach is always local. Explicit
integration is based on the powerful methods based on an in-depth
study
of singularities, that were first used by Poincar? and
subsequently developed by Painlev? in his famous Le?ons de
Stockholm of 1895.
The recent interest in the subject and in the equations
investigated by Painlev? dates back about thirty years ago,
arising from three,
apparently disjoint, fields: the Ising model of statistical
physics and field theory, propagation of solitons, and dynamical
systems. The
chapters in this volume, based on courses given at Carg?se 1998,
alternate mathematics and physics; they are intended to bring
researchers entering the field to the level of present research.
Contents: Singularities of Ordinary Linear Differential
Equations.- Introduction to the Theory of Isomonodronic
Deformations.-
Painlev? Approach to Nonlinear Ordinary Differential Equations.-
Asymptotic Studies of the Painlev? Equations.- 2D Quantum and
Topological Gravities.- Painlev? Transcendents in Two Dimensional
Topological Field.- Discrete Painlev? Equations.- Painlev?
Analysis
for Partial Differential Equations.- On Painlev? and Darboux
Halpen Type Equations.- Symmetry Reduction and Exact Solutions.-
Painlev? Equations in Terms of Entire Functions.- Backlund
Transformations of Painlev? Equations.- The Hamiltonians
Associated to
Painleve Equations.- Completeness of the Painlev? Test.
Series: CRM Series in Mathematical Physics.
Coombes, K.R., University of Maryland, College Park, MD, USA
Lipsman, R.L., University of Maryland, College Park, MD, USA
Rosenberg, J.M., University of Maryland, College Park, MD, USA
With Applications to Geometry and Physics
1998. XIII, 283 pp. Diskette.
0-387-98360-0
Aiming to "modernise" the course through the
integration of Mathematica, this publication introduces students
to its multivariable
uses, instructs them on its use as a tool in simplifying
calculations, and presents introductions to geometry,
mathematical physics, and
kinematics. The authors make it clear that Mathematica is not
algorithms, but at the same time, they clearly see the ways in
which
Mathematica can make things cleaner, clearer and simpler. The
sets of problems give students an opportunity to practice their
newly
learned skills, covering simple calculations, simple plots, a
review of one-variable calculus using Mathematica for symbolic
differentiation,
integration and numerical integration, and also cover the
practice of incorporating text and headings into a Mathematica
notebook.
The accompanying diskette contains both Mathematica 2.2 and 3.0
version notebooks, as well as sample examination problems for
students, which can be used with any standard multivariable
calculus textbook. It is assumed that students will also have
access to an
introductory primer for Mathematica.
Contents: Introduction.- Vectors and Graphics.- Geometry of
Curves. - Kinematics - Directional Derivative.- Geometry of
Surfaces.- Optimization in Several Variables.- Multiple
Integrals.- Physical Applications of Vector Calculus.-
Mathematica Tips.
Engel, A., Johann-Wolfgang Goethe Universit?t, Frankfurt,
Germany
1st ed. 1998. Corr. 2nd printing 1999. X, 403 pp. 223 figs.
0-387-98219-1
A unique collection of competition problems from over twenty
major national and international mathematical competitions for
high
school students. Written for trainers and participants of
contests of all levels up to the highest level, this will appeal
to high school
teachers conducting a mathematics club who need a range of simple
to complex problems and to those instructors wishing to pose a
"problem of the week", thus bringing a creative
atmosphere into the classrooms. Equally, this is a must-have for
individuals interested
in solving difficult and challenging problems. Each chapter
starts with typical examples illustrating the central concepts
and is followed
by a number of carefully selected problems and their solutions.
Most of the solutions are complete, but some merely point to the
road
leading to the final solution. In addition to being a valuable
resource of mathematical problems and solution strategies, this
is the most
complete training book on the market.
Contents: The Invariance Principle.- Coloring Proofs.- The
Extremal Principle.- The Box Principle.- Enumerative
Combinatorics.-
Number Theory.- Inequalities.- The Induction Principle.-
Sequences.- Polynomials.- Functional Equations.- Geometry.-
Games.-
Further Strategies.- References.- Index.
Series: Problem Books in Mathematics.
Ebbinghaus, H.-D., University of Freiburg, Germany
Flum, J., University of Freiburg, Germany
2nd rev. and enlarged ed. 1999. XIV, 360 pp.
3-540-65758-4
The book presents the main results of descriptive complexity
theory, that is, the connections between axiomatizability of
classes of
finite structures and their complexity with respect to time and
space bounds. The logics that are important in this context
include
fixed-point logics, transitive closure logics, and also certain
infinitary languages; their model theory is studied in full
detail. Other topics
include DATALOG languages, quantifiers and oracles, 0-1 laws, and
optimization and approximation problems. The book is written in
such a way that the respective parts on model theory and
descriptive complexity theory may be read independently. This
second
edition is a thoroughly revised and enlarged version of the
original text.
Keywords: Finite model theory, descriptive complexity theory,
fixed - point logics, 0 - 1 - laws
Series: Perspectives in Mathematical Logic.
Nissanke, N., University of Reading, UK
Techniques and Applications
1999. XX, 296 pp. 7 figs.
1-85233-002-3
Formal Specification is a textbook for 2nd/3rd year undergraduate
and postgraduate courses in Formal Methods which offers a
practical and versatile approach to constructing specifications.
It covers both model-based and algebraic approaches and
emphasises
the range of languages and approaches which are available.
Mathematical principles are explained using examples from
everyday life
(like card games), in order to "demystify" them and
make them more comprehensible. It includes: unrivalled coverage
of the topic
including all important, recent advances lots of exercises with
model answers case studies to guide students through the main
principles
margin notes to identify key points. Readers of this book do not
have to be fully competent in formal specification - it is
written to be
accessible to any student who wants to learn about the topic.
Contents: Introduction.- Schema Language.- An Approach to
Specification.- Specification for Fun.- A Specifiction for
Clocks.-
Reasoning About Specifications.- Specification of a Network
Protocal.- Object Oriented Specification.- Specification of
Safety.- An
Overview of VDM.- Algebraic Approach to Specification.- Algebraic
Specification in CLEAR.- A. Exercises on Reading Formal
Specifications.- B. Exercises on Writing Formal Specifications.-
C. The Mathematical Notation.- References.- Index.
Ganzha, V.G., Technische Universit?t M?nchen, Germany
Mayr, E., Technische Universit?t M?nchen, Germany
Vorozhtsov, E.V., Russian Academy of Sciences, Novosibirsk,
Russia
(Eds.)
CASC '99
1999. XI, 511 pp.
3-540-66047-X
This book contains papers submitted by the participants of the
workshop on Computer Algebra in Scientific Computing CASC '99, as
well as two invited papers. The collection of papers included in
the proceedings covers various topics of computer algebra
methods,
algorithms and software applied to scientific computing.
Moreover, applications of computer algebra methods for the
solution of current
problems in group theory are treated, which mostly arise in
mathematical physics. Another important trend which may be seen
from the
present collection of papers is the application of computer
algebra methods to the development of new efficient analytic and
numerical
solvers, both for ordinary and partial differential equations.
Some papers deal with algorithmic and software aspects associated
with the
implementation of computer algebra methods, or study the
stability of satellite and mechanical systems, or the application
of computer
algebra to the solution of problems in technology.
Keywords: Symbolic computation, computer algebra, scientific
computing
Saito, M., Hokkaido University, Sapporo, Japan
Sturmfels, B., University of California, Berkeley, CA, USA
Takayama, N., University of Kobe, Japan
1999. VIII, 254 pp. 14 figs.
3-540-66065-8
In recent years, new algorithms for dealing with rings of
differential operators have been discovered and implemented. A
main tool is the
theory of Gr?bner bases, which is reexamined here from the point
of view of geometric deformations. Perturbation techniques have a
long tradition in analysis; Gr?bner deformations of left ideals
in the Weyl algebra are the algebraic analogue to classical
perturbation
techniques. The algorithmic methods introduced here are
particularly useful for studying the systems of multidimensional
hypergeometric PDEs introduced by Gelfand, Kapranov and
Zelevinsky. The Gr?bner deformation of these GKZ hypergeometric
systems reduces problems concerning hypergeometric functions to
questions about commutative monomial ideals, and leads to an
unexpected interplay between analysis and combinatorics. This
book contains a number of original research results on holonomic
systems and hypergeometric functions, and raises many open
problems for future research in this area.
Keywords: hypergeometric functions, Gr?bner bases, holonomic
systems, Weyl algebra, combinatorial
commutative algebra
Contents: Chapter 1. Basic Notions.- Chapter 2. Gr?bner
Deformations of Regular Holonomic Systems.- Chapter 3.
Hypergeometric
Series.- Chapter 4. Rank versus volume.- Chapter 5. Integration
of D-modules
Series: Algorithms and Computation in Mathematics.VOL. 6
Tamanoi, H., University of California, Santa Cruz, CA, USA
1999. VI, 390 pp.
3-540-66006-2
This monograph deals with two aspects of the theory of elliptic
genus: its topological aspect involving elliptic functions, and
its
representation theoretic aspect involving vertex operator
super-algebras. For the second aspect, elliptic genera are shown
to have
the structure of modules over certain vertex operator
super-algebras. The vertex operators corresponding to parallel
tensor fields on
closed Riemannian Spin K?hler manifolds such as Riemannian
tensors and K?hler forms are shown to give rise to Virasoro
algebras and
affine Lie algebras. This monograph is chiefly intended for
topologists and it includes accounts on topics outside of
topology such as
vertex operator algebras.
Keywords: vertex operator super - algebras Virasoro algebras
affine Lie algebras K?hler manifolds
modular functions
Series: Lecture Notes in Mathematics.VOL. 1704
Zong, C., Chinese Academy of Sciences, Beijng, China
1999. Approx. 250 pp. 31 figs.
0-387-98794-0
Preliminary Text. Do not use. Sphere Packings is one of the most
attractive and challenging subjects in mathematics. Almost 4
centuries ago, Kepler studied the densities of sphere packings
and made his famous conjecture. In the course of centuries, many
exciting results have been obtained, ingenious methods created,
related challenging problems proposed, and many surprising
connections with othe subjects found. Thus, though some of its
original problems are still open, sphere packings has been
developed into
an important discipline. This book tries to give a full account
of this fascinating subject, especially its local aspects,
discrete aspects and
its proof methods.
Keywords: Shere packing Kabatjanski - Levenstein method lattice
packings sausage conjecture
Contents: The Gregory-Newton Problem and Kepler's Conjecture.-
Positive Definite Quadratic Forms and Lattice Sphere Packings.-
Lower Bounds for the Packing Densities of Spheres.- Lower Bounds
for the Blocking Numbers and the Kissing Numbers of Spheres.-
Sphere Packings Constructed from Codes.- Upper Bounds for the
Packing Densities and the Kissing Numbers of Spheres I.- Upper
Bounds for the Packing Densities and the Kissing Numbers of
Spheres II.- Upper Bounds for the Packing Densities and the
Kissing
Numbers of Spheres III.- The Kissing Numbers of Spheres in Eight
and Twenty Four Dimensions.- Multiple Sphere Packings.- Holes in
Sphere Packings.- Problems of Blocking Light Rays.- Finite Sphere
Packings.
Series: Universitext.
Hsieh, P.-F., Western Michigan University Kalamazoo, MI, USA
Sibuya, Y., University of Minnesota, Minneapolis, MN, USA
(Eds.)
1999. Approx. 500 pp. 120 figs.
0-387-98699-5
Preliminary Text. Do not use. The authors' aim is to provide the
reader with the very basic knowledge necessary to begin research
on
differential equations with professional ability. The selection
of topics should provide the reader with methods and results
which are
applicable in a variety of different fields. The book is divided
into four parts. The first covers fundamental existence,
uniqueness,
smoothness with respect to data, and nonuniqueness. The second
part describes the basic results concerning linear differential
equations, the third deals with nonlinear equations. In the last
part the authors write about the basic results concerning power
series
solutions. Each chapter begins with a brief discussion of its
contents and history and ends with a number of problems and
exercises.
Keywords: Ordinary Differential Euquations
Contents: Fundamental Theorems of Ordinary Differential
Equations.- Dependence of Data.- Nonuniqueness.- General Theory
of
Linear Systems.- Singularities of the First Kind.- Boundary-value
Problems of Linear Differential Equations of the Second Order.-
Asymptotic Behavior of Solutions of Linear Systems.- Stabiblity.-
Autonomous Systems.- Second Order Differential Equations.-
Asymptotic Expansions.- Asymptotic Expansions in a Parameter.-
Singularities of the Second Kind.
Series: Universitext.
Lee, J.M., University of Washington, Seattle, WA, USA
1999. Approx. 250 pp. 100 figs.
0-387-98759-2
Preliminary Text. DO NOT USE. A course on manifolds differs from
most other introductory mathematics graduate courses in that the
subject matter is often completely unfamiliar. It is possible to
get through an entire undergraduate mathematics education without
ever
hearing the word "manifold." One reason for this
anomaly is that even the definition of manifolds involves rather
a lot of technical
details. In his beautifully conceived Introduction the author
motivates what is to follow in the book by explaining the roles
manifolds play
in topology, geometry, complex analysis, algebra and classical
mechanics with a final pass at general relativity. The book
begins with the
basics of general topology and gently moves to manifolds, the
fundamental group, and covering spaces. The pace is leisurely;
the book is
aimed at beginning graduate students.
Contents: Introduction * General Topology * New Spaces From Old *
Compactness and Connectedness * Surfaces * Homotopy and
the Fundamental Group * The Circle * Some Group Theory *
Fundamental Groups of Surfaces * Covering Spaces * Classification
of
Covering Spaces
Series: Graduate Texts in Mathematics.
Canestrelli, E., University of Venice, Italy
(Ed.)
1999. VIII, 139 pp. 14 figs., 23 tabs.
(Recommended Retail Price)
The volume collects a selection of papers of the 21st EURO
Working Group on Financial Modelling. The papers in this book
provide a
representative, though not complete, sample of the current
scientific activity in the field of quantitative finance. Such
activity is not
only theoretical but also practical, because it tries to combine
theoretic analyses with empirical evidence.
The topics deal with corporate finance, asset price analysis,
portfolio management, decision theory, international exchange
markets and
financial derivatives. It is important to note the presence of
algorithms, methods and models, helpful in the real activities of
a decision
maker such as performance evaluations and scenarios
identifications in portfolio models, how to measure bank
efficiency, and how to
realize an efficient diversification of international
investments.
Keywords: Finance, Corporate Finance, Asset Pricing, Portfolio
Management, Decision Theory, Financial
Derivates
Contents: J. Abaffy, M. Bertocchi, J. Dupaov?, V. Moriggia:
Performance Evaluation of Algorithms for Black-Derman-Toy
Lattice.-
M. Bonilla, A. Medal: Efficient Diversification of International
Investment: The Spanish Point of View.- E. Canestrelli, S. Giove:
Scenarios Identification for Financial Modelling.- M. Corazza:
Merton-like Theoretical Frame for Fractional Brownian Motion in
Finance.- A. Gamba: Portfolio Analysis With Symmetric Stable
Paretian Returns.- T. Pinvanichkul, J.P. Gupta: Dynamics of Bond
Returns in the Emerging Markets: A Study of the Thai Bond
Market.- W.G. Hallerbach: Modelling Option-Implied Return
Distributions:
A Generalized Log-Logistic Approximation.- M. Ko?k: Dichotomous
Rate in Stock-Price Process.- A. Resti: How Should We Measure
Bank Efficiency? A Comparison of Classic and Recent Techniques
Based on Simulated Data.- M.R. Simonelli: The Scheme of Fuzzy
Dominance.
Series: Contributions to Management Science.
Everitt, B.S., Institute of Psychiatry, London, UK
An Informal Guide to Probability, Risk and Statistics
1999. Approx. 225 pp. 20 figs.
0-387-98768-1
An entertaining exploration of aspects of chance, risk and
probability, ranging from the toss of a coin to the use of
clinical trials in
medicine and the evaluation of alternative therapies. Aimed at
all those who would like to discover more about chance and the
way it
operates in a variety of settings, the book is written by the
prolific author, Professor Brian S. Everitt, Head of the
Biostatistics and
Computing Department at Kings College, London.
Contents: A Brief History of Chance.- Tossing Coins and Having
Babies.- Rolling Dice.- Gambling for Fun: Lotteries and Football
Pools.- Serious Gambling: Roulette, Cards and Horse Racing.-
Birthdays and Coincidences.- Conditional Probability and the
Reverend
Thomas Bayes.- Puzzling Probabilities.- Taking Risks.-
Statistics, Statisticians and Medicine.- Alternative
Therapies-Paneceas of
Placebos?- Chance in Nature.- What is Chance?
Ottaviani, G., Rome, Italy
(Ed.)
1st ed. 1995. 2nd printing 1999. XII, 112 pp. 20 figs.
3-540-66143-3
This book, published with the contribution of the Italian
insurance company INA, contains the invited contributions
presented at the 3rd
International AFIR Colloquium, held in Rome in 1993. The
colloquium was aimed at encouraging research on the theoretical
bases of
actuarial sciences, its interaction with the theory of finance
and of corporate finance, together with mathematical methods,
such as
probability and the theory of stochastic processes. In the spirit
of actuarial tradition, attention was given to the link between
the
theoretical approach and the operative problems of financial
markets and institutions, and insurance companies in particular.
The book
is an important reference work for students and researchers of
actuarial sciences and finance. It could also be recommended to
practitioners with theoretical interests.
Keywords: Actuarial Mathematics, stochastics, finance, corporate
finance, asset / liability management
Contents: Hans B?hlmann: Life Insurance with Stochastic Interest
Rates.- Franco Moriconi: Analyzing Default-Free Bond Markets by
Diffusion Models.- Phelim P. Boyle: Risk-based Capital for
Financial Institutions.- Massimo de Felice: Immunization Theory:
An
Actuarial Perspective on Asset-Liability Management.- Flavio
Pressacco: Financial Risk, Financial Intermediaries and Game
Theory.
Singpurwalla, N., George Washington University, Washington,
DC, USA
Wilson, S.P., Trinity College, Dublin, Ireland
Reliability and Risk
1999. Approx. 310 pp. 55 figs.
0-387-98823-8
In establishing a framework for dealing with uncertainties in
software engineering, and for using quantitative measures in
related
decision-making, this text puts into perspective the large body
of work having statistical content that is relevant to software
engineering. Aimed at computer scientists, software engineers,
and reliability analysts who have some exposure to probability
and
statistics, the content is pitched at a level appropriate for
research workers in software reliability, and for graduate level
courses in
applied statistics computer science, operations research, and
software engineering.
Series: Springer Series in Statistics.
Yong, J., Fudan University, Shanghai, China
Zhou, X.Y., The Chinese University of Hong Kong, Shatin, China
Hamiltonian Systems and HJB Equations
1999. Approx. 400 pp.
0-387-98723-1
The maximum principle and dynamic programming are the two most
commonly used approaches in solving optimal control problems.
These approaches have been developed independently. The theme of
this book is to unify these two approaches, and to demonstrate
that the viscosity solution theory provides the framework to
unify them.
Contents: Preliminary.- Stochastic Control Problems.- Maximum
Principle and Stochastic Hamiltonian Systems.- Dynamic
Programming and HJB Equations.- Relationship between Maximum
Principle and Dynamic Programming.- Partially Observed
Processes.- Backward Stochastic Differential Equations.-
References.- Index.
Series: Applications of Mathematics.VOL. 43
Ammann, M., University of St. Gallen, Switzerland
1999. XII, 228 pp.
3-540-65753-3
This book presents new approaches to valuing derivative
securities with credit risk, focussing on options and forward
contracts subject
to counterparty default risk, but also treating options on
credit-risky bonds and credit derivatives. The text provides
detailed
descriptions of the state-of-the-art martingale methods and
advanced numerical implementations based on multi-variate trees
used to
price derivative credit risk. Numerical examples illustrate the
effects of credit risk on the prices of financial derivatives.
Keywords: Credit risk, derivative securities, pricing /
valuation, martingale theory, multi - dimensional
tree structures
Contents: Acknowledgements.- Preface.- Introduction.- Contingent
Claim Valuation.- Review of Credit Risk Models.- Firm Value
Model.- Hybrid Model.- Credit Derivatives.- Conclusion.- Proofs.-
Stochastic Utilities.- References.- Index.- List of Figures.-
List of
Tables
Series: Lecture Notes in Economics and Mathematical Systems.VOL.
470
Bianchi, G., Milano, Italy
(Ed.)
Proceedings of CISM 30th Anniversary Conference, Udine, May
29, 1999
1999. VI, 135 pp. 68 figs.
3-211-83152-5
In 1999 the International Centre for Mechanical Sciences
celebrates thirty years of activity. For this celebration CISM
has organized a
series of courses and meetings on environmental problems, one of
the leading subjects today of theoretical and applied research
all over
the world. The results obtained directly influence our daily
life, particularly in applications for protection from pollution
and natural
hazards. The most significant of the events was the Conference on
"Environmental Applications of Mechanics and Computer
Science",
where prominent scientists in the field presented significant
examples of the scientific approach to large scale phenomena
involved in
environmental problems.
Contents: Long-Term Morphodynamics of Alluvial Rivers and Coasts
(H. de Vriend).- Conflict Resolution in Water Resources
Management: the Case of Lake Como (S. Rinaldi).- Mechanics
Applied to the Underground Storage of Radioactive Waste Materials
(K.S. Chan, S.R. Bodner, and D.E. Munson).- Environmental Fluid
Mechanics: its Role in Solving Problems of Pollution in Lakes,
Rivers
and Coastal Waters (G.H. Jirka).- Computational Environmental
Geomechanics (B.A. Schrefler).
Series: CISM International Centre for Mechanical Sciences.NR. 409