This book brings together many important recent developments in the analysis of singular perturbation and hysteresis phenomena in an accessible and reasonably comprehensive fashion. To bridge a gap between practitioners of these phenomena, the editors conducted a workshop in April 2002 at University College Cork to provide a forum for experts in both fields to share their interests and knowledge. For this book, the editors have compiled research from those practitioners in areas such as reacting systems, semiconductor lasers, shock phenomena in economic modeling, and fluid mechanics, all with an emphasis on hysteresis and singular perturbations.
The book begins with a basic introduction to hysteresis and
singular perturbations theory, including simple examples from
both physics and mathematics. Later chapters address
applications of hysteresis to economics,
various aspects of the asymptotic theory of singularly perturbed
systems,
typical problems of the asymptotic theory of contrast structures,
and
the geometrical approach to an investigation of models with
singular perturbations and hysteresis.
The editors intend for this text not only to be a useful and
accessible introduction to techniques and the research literature
but also to generate new ideas for researchers and to attract new
researchers into this vibrant and dynamic field.
Audience
This is a book for applied mathematicians, engineers, and
physicists curious about the important nonlinear phenomena of
singular perturbations and hysteresis.
Contents
List of Contributors; Preface; Chapter 1: A Na・e View of Time
Relaxation and Hysteresis, A. Pokrovskii, V. Sobolev; Chapter 2:
Frustration Minimization, Hysteresis and the El Farol Problem, R.
Cross, M. Grinfeld, H. Lamba, A. Pittock; Chapter 3: Hysteresis
in Singularly Perturbed Problems, P. Krej?・ Chapter 4: Combined
Asymptotic Expansions, E. Beno, A. Fruchard, A. El Hamidi;
Chapter 5: Contrast Structures of Alternating Type, A. Vasilieva;
Chapter 6: Multi-Dimensional Internal Layers, N. Nefedov; Chapter
7: Geometry of Singular Perturbations: Critical Cases, V.
Sobolev; Chapter 8: Black Swans and Canards in Laser and
Combustion Models, E. Shchepakina, V. Sobolev; Chapter 9: Multi-Scale
Analysis of Pressure Driven Flames, V. Bykov, I. Goldfarb, V.
Golshtein; Chapter 10: Split-Hyperbolicity, Hysteresis and Lang-Kobayashi
Equations, A. Pokrovskii, O. Rasskazov, R. Studdert; Index.
Available June 2005 / Approx. 360 pages / Softcover / ISBN 0-89871-597-0
MPS-SIAM Book Series on Optimization 5
Research on algorithms and applications of stochastic
programming, the study of procedures for decision making under
uncertainty over time, has been very active in recent years and
deserves to be more widely known. This is the first book devoted
to the full scale of applications of stochastic programming and
also the first to provide access to publicly available
algorithmic systems. The 32 contributed papers in this volume are
written by leading stochastic programming specialists and reflect
the high level of activity in recent years in research on
algorithms and applications. The book introduces the power of
stochastic programming to a wider audience and demonstrates the
application areas where this approach is superior to other
modeling approaches.
Applications of Stochastic Programming consists of two parts. The
first part presents papers describing publicly available
stochastic programming systems that are currently operational.
All the codes have been extensively tested and developed and will
appeal to researchers and developers who want to make models
without extensive programming and other implementation costs. The
codes are a synopsis of the best systems available, with the
requirement that they be user-friendly, ready to go, and publicly
available.
The second part of the book is a diverse collection of
application papers in areas such as production, supply chain and
scheduling, gaming, environmental and pollution control,
financial modeling, telecommunications, and electricity. It
contains the most complete collection of real applications using
stochastic programming available in the literature. The papers
show how leading researchers choose to treat randomness when
making planning models, with an emphasis on modeling, data, and
solution approaches.
Audience
Researchers in stochastic programming will find this book an
excellent source of publicly available codes. Those interested in
creating their own applications, and those looking for real
applications to introduce stochastic programming in the
classroom, will find the book a valuable resource.
Contents
Preface: Part I: Stochastic Programming Codes; Chapter 1:
Stochastic Programming Computer Implementations, Horand I.
Gassmann, SteinW.Wallace, and William T. Ziemba; Chapter 2: The
SMPS Format for Stochastic Linear Programs, Horand I. Gassmann;
Chapter 3: The IBM Stochastic Programming System, Alan J. King,
Stephen E.Wright, Gyana R. Parija, and Robert Entriken; Chapter 4:
SQG: Software for Solving Stochastic Programming Problems with
Stochastic Quasi-Gradient Methods, Alexei A. Gaivoronski; Chapter
5: Computational Grids for Stochastic Programming, Jeff Linderoth
and Stephen J.Wright; Chapter 6: Building and Solving Stochastic
Linear Programming Models with SLP-IOR, Peter Kall and Janos
Mayer; Chapter 7: Stochastic Programming from Modeling Languages,
Emmanuel Fragniere and Jacek Gondzio; Chapter 8: A Stochastic
Programming Integrated Environment (SPInE), P. Valente, G. Mitra,
and C. A. Poojari; Chapter 9: Stochastic Modelling and
Optimization Using Stochastics? , M. A. H. Dempster, J. E. Scott,
and G.W. P. Thompson; Chapter 10: An Integrated Modelling
Environment for Stochastic Programming, Horand I. Gassmann and
David M. Gay; Part II: Stochastic Programming Applications;
Chapter 11: Introduction to Stochastic Programming Applications
Horand I. Gassmann, Sandra L. Schwartz, SteinW.Wallace, and
William T. Ziemba Chapter 12: Fleet Management, Warren B. Powell
and Huseyin Topaloglu; Chapter 13: Modeling Production Planning
and Scheduling under Uncertainty, A. Alonso-Ayuso, L. F.
Escudero, and M. T. Ortuno; Chapter 14: A Supply Chain
Optimization Model for the Norwegian Meat Cooperative, A.
Tomasgard and E. Hoeg; Chapter 15: Melt Control: Charge
Optimization via Stochastic Programming, Jitka Dupa?cova and
Pavel Popela; Chapter 16: A Stochastic Programming Model for
Network Resource Utilization in the Presence of Multiclass Demand
Uncertainty, Julia L. Higle and Suvrajeet Sen; Chapter 17:
Stochastic Optimization and Yacht Racing, A. B. Philpott; Chapter
18: Stochastic Approximation, Momentum, and Nash Play, H.
Berglann and S. D. Flam; Chapter 19: Stochastic Optimization for
Lake Eutrophication Management, Alan J. King, Laszlo Somlyody,
and Roger J.-B.Wets; Chapter 20: Mitigating Anthropogenic Climate
Change, GaryW. Yohe; Chapter 21: Groundwater Pollution Control,
David W.Watkins, Jr., Daene C. McKinney, and David P. Morton;
Chapter 22: Catastrophic Risk Management: Flood and Seismic Risks
Case Studies, Tatiana Ermolieva and Yuri Ermoliev; Chapter 23:
Refinancing Mortgages in Switzerland, Karl Frauendorfer and
Michael Schurle; Chapter 24. Optimization Models for Structuring
Index Funds, Stavros A. Zenios; Chapter 25: Decentralized Risk
Management for Global P/C Insurance Companies, John M. Mulvey and
Hafize Gaye Erkan; Chapter 26: Wealth Goals Investing, Leonard C.
MacLean, Yonggan Zhao, and William T. Ziemba; Chapter 27:
Scenario-Based Risk Management Tools, Helmut Mausser and Dan
Rosen; Chapter 28: Price Protection Strategies for an Oil
Company, E. A. Medova and A. Sembos; Chapter 29: Numerical
Comparison of CVaR and CDaR Approaches: Application to Hedge
Funds, P. Krokhma, S. Uryasev, and G. Zrazhevsky; Chapter 30:
Stochastic Unit Commitment in Hydro-Thermal Power Production
Planning, Nicole Growe-Kuska and Werner Romisch; Chapter 31:
Valuation of Electricity Generation Capacity, Shi-Jie Deng and
Shmuel S. Oren; Chapter 32: Stochastic Optimization Problems in
Telecommunications, Alexei A. Gaivoronski; Index
Available June 2005 / xvi + 704 pages / Softcover / ISBN 0-89871-555-5
Advances in Design and Control 9
Based on the results of over 10 years of research and development
by the authors, this book presents a broad cross section of
dynamic programming (DP) techniques applied to the optimization
of dynamical systems. The main goal of the research effort was to
develop a robust path planning/trajectory optimization tool that
did not require an initial guess. The goal was partially met with
a combination of DP and homotopy algorithms. DP algorithms are
presented here with a theoretical development, and their
successful application to variety of practical engineering
problems is emphasized.
Applied Dynamic Programming for Optimization of Dynamical Systems
presents applications of DP algorithms that are easily adapted to
the reader’s own interests and problems. The book is organized
in such a way that it is possible for readers to use DP
algorithms before thoroughly comprehending the full theoretical
development. A general architecture is introduced for DP
algorithms emphasizing the solution to nonlinear problems. DP
algorithm development is introduced gradually with illustrative
examples that surround linear systems applications. Many examples
and explicit design steps applied to case studies illustrate the
ideas and principles behind DP algorithms.
DP algorithms potentially address a wide class of applications
composed of many different physical systems described by
dynamical equations of motion that require optimized trajectories
for effective maneuverability. The DP algorithms determine
control inputs and corresponding state histories of dynamic
systems for a specified time while minimizing a performance index.
Constraints may be applied to the final states of the dynamic
system or to the states and control inputs during the transient
portion of the maneuver.
Audience
Physicists and mechanical, electrical, aerospace, and industrial
engineers will find this book enormously useful. It will also
appeal to research scientists and engineering students who have a
background in dynamics and control and are able to develop and
apply the DP algorithms to their particular problems. This book
is suitable as a reference or supplemental textbook for graduate
courses in optimization of dynamical and control systems.
Contents
List of Figures; Preface; List of Tables; Chapter 1:
Introduction; Chapter 2: Constrained Optimization; Chapter 3:
Introduction to Dynamic Programming; Chapter 4: Advanced Dynamic
Programming; Chapter 5: Applied Case Studies; Appendix A:
Mathematical Supplement; Appendix B: Applied Case Studies -
MATLAB Software Addendum; Bibliography; Index.
Available July 2005 / xviii + 259 pages / Hardcover / ISBN 0-89871-586-5
Series: Monographs in Computer Science
2005, XII, 420 p. 54 illus., Hardcover
ISBN: 0-387-23759-3
About this book
This monograph details several important advances in the area
known as the proofs-as-programs paradigm, a set of approaches to
developing programs from proofs in constructive logic. It serves
the dual purpose of providing a state-of-the-art overview of the
field and detailing tools and techniques to stimulate further
research.
One of the book’s central themes is a general, abstract
framework for developing new systems of program synthesis by
adapting proofs-as-programs to new contexts, which the authors
call the Curry--Howard Protocol. This protocol is used to provide
two novel applications for industrial-scale, complex software
engineering: contractual imperative program synthesis and
structured software synthesis. These applications constitute an
exemplary justification for the applicability of the protocol to
different contexts.
The book is intended for graduate students in computer science or
mathematics who wish to extend their background in logic and type
theory as well as gain experience working with logical frameworks
and practical proof systems. In addition, the proofs-as-programs
research community, and the wider computational logic, formal
methods and software engineering communities will benefit. The
applications given in the book should be of interest for
researchers working in the target problem domains.
Table of contents
Part I. Prologue.- Introduction.- Part II. Generalizing Proofs-as-Programs.-
Functional Program Synthesis.- The Curry--Howard protocol.- Part
III. Imperative Proofs-as-Programs.- Intuitionistic Hoare Logic.-
Properties of Intuitionistic Hoare Logic.- Proofs-as-Imperative-Programs.-
Part IV. Structured Proofs-as-Programs.- Reasoning about
Structured Specifications.- Proof-theoretic Properties of SSL.-
Structured Proofs-as-Programs.- Generic Specifications.-
Structured Program Synthesis.- Part V. Epilogue.- Conclusions:
Toward Constructive Logic as a Practical 4GL.- Part VI. Appendix.-
A: Constructive Logic.- References.- Index.
Series: Graduate Texts in Mathematics, Vol. 173
2005, Approx. 430 p., Hardcover
ISBN: 3-540-26182-6
About this textbook
The third edition of this standard textbook of modern graph
theory has been carefully revised, updated, and substantially
extended. Covering all its major recent developments it can be
used both as a reliable textbook for an introductory course and
as a graduate text: on each topic it covers all the basic
material in full detail, and adds one or two deeper results (again
with detailed proofs) to illustrate the more advanced methods of
that field.
From the reviews of the first two editions (1997, 2000):
"This outstanding book cannot be substituted with any other
book on the present textbook market. It has every chance of
becoming the standard textbook for graph theory."
Acta Scientiarum Mathematiciarum
"The book has received a very enthusiastic reception, which
it amply deserves. A masterly elucidation of modern graph theory."
Bulletin of the Institute of Combinatorics and its Applications
"A highlight of the book is what is by far the best account
in print of the Seymour-Robertson theory of graph minors."
Mathematika
". . . like listening to someone explain mathematics."
Bulletin of the AMS
Table of contents
The Basics.- Matching, Covering and Packing.- Connectivity.-
Planar Graphs.- Colouring.- Flows.- External Graph Theory.-
Infinite Graphs.- Ramsey Theory for Graphs.- Hamilton Cycles.-
Random Graphs.- Minors, Trees, and WQO.- A: Infinite Sets.- B:
Surfaces.
2005, X, 392 p. 180 illus., 3 in colour., Softcover
ISBN: 0-387-25827-2
About this book
Of all of Martin Gardners writings, none gained him a wider
audience or was more central to his reputation than his
Mathematical Recreations column in Scientific American - which
virtually defined the genre of popular mathematics writing for a
generation. Flatland, Hydras and Eggs: Mathematical
Mystifications is the final collection of these columns, covering
the period roughly from 1979 to Gardners retirement in 1986. As
always in his published collections, Gardner includes letters
commenting on the ideas presented in his articles. These columns
show him at the top of his form and should not be missed by
anyone with an interest in mathematics.
Table of contents
Wonders of the Planiverse.- Bulgarian Solitaire and Other
Seemingly Endless Tasks.- Fun with Eggs.- Fun with Eggs.-The
Topology of Knots. M-Pire Maps.- Directed Graphs and Cannibals.-
Dinner Guests, Schoolgirls, and Handcuffed Prisoners.- The
Monster and Other Sporadic Groups.- Taxicab Geometry.- The Power
of the Pigeonhole.- Strong Laws of Small Primes.- Checker
Recreations.- Checker Recreations.- Modulo Arithmetic and
Hummer's Witch.- Lavinia's Room and Other Problems.- The Symmetry
Art of Scott Kim.- Parabolas.- Non-Euclidian Geometry.- Voting
Mathematics.- A Toroidal Paradox and Other Problems.- Minimal
Steiner Trees.- Trivalent Graphs, Snarks, and Boojums.