This is the first volume of a comprehensive
and up-to-date two-volume treatment of quadratic
optimal control theory for partial differential
equations over a finite or infinite time
horizon, and related differential (integral)
and algebraic Riccati equations. Both
continuous theory and numerical approximation
theory are included. The authors use an abstract
space, operator theoretic approach, which
is based on semigroups methods, and which
is unifying across a few basic classes of
evolution. The various abstract frameworks
are motivated by, and ultimately directed
to, partial differential equations with bdundary/point
control. Volume 1 includes the abstract parabolic
theory
(continuous theory and numerical approximation
theory) for the finite and infinite cases
and corresponding PDE illustrations as well
as various abstract hyperbolic settings in
the finite case. lt presents numerous new
results. These volumes will appeal to graduate
students and researchers in pure and applied
mathematics and theoretical engineering with
an interest in optimal control problems.
Contents: Introduction; Part A. Analytic Semigroups:
1. The optimal quadratic cost problem over
a preassigned finite time interval: the differential
Riccati equation; 2. The optimal quadratic cost problem over
a preassigned finite time interval: the algebraic
Riccati equation;
3. IIlustrations of the abstract theory of
chapters 1 and 2 to PDEs with boundary/point
controls; 4. Numerical approximations of algebraic Riccati
equations; 5. lllustrations of the numerical theory of
chapter 4 to parabolic-like boundary/point
control PDE problems; 6. Min-max game theory over an infinite time
interval and algebraic Riccati equations.
,
Subject areas : control theory, mathematical
analysis, applied mathematics, engineering
Series: Encyclopedia of Mathematics and its Applications,
74- I
0521 434084 Hardback 600pp c February2000
This book covers most of the known results
on reducibility of polynomials over arbitrary
fields, algebraically closed fields and fnitely
generated fields. Included also are results
based on recent work of E. Bombieri and U.
Zannier (presented here by Zannier in an
appendix). The book also treats other subjects
like Ritt's theory of composition of polynomials,
and properties of the Mahler measure, This
unique work will be a necessary resource
for all number theorists and researchers
in related fields.
Contents: 1. Arbitrary polynomials over an
arbitrary field; 2. Lacunary polynomials
over an arbitrary field; 3. Polynomials over
an algebraically closed field; 4. Polynomials
over a finitely generated field; 5. Polynomials
over a number field; 6. Polynomials over
a Kroneckerian field;
Appendices; Bibliography.
Subject areas : mathematics (number theory)
Series: Encyclopedia of Mathematics and its Applications,
77 ,
0521 662257 Hardback 500pp c February2000
Several Complex Variables is a central area
of mathematics with strong interactions with
partial differential equations, algebraic
geometry, number theory, and differential
geometry. The 199516 MSRl program on Several
Complex Variables emphasized these interactions
and concentrated on developments and problems
of current interest. This collection provides
a clear and complete picture of the status
of research in these overlapping areas. Several
of the articles are expository, making this
an excellent introduction for students to
the use of techniques from these other areas
in several complex variables.
Contents: 1. Local holomorphic equivalence of real analytic
submanifolds in CN M. S. BaouendI' and Linda
PJneiss Rothschild; 2. How to use cycle space in complex geometry
DanI'el Badet,. 3. Resolution of singularities Edwald Bierstone
and PI'enle D. Milman; 4. Global regularity of the
partial-Neuman problem: a survey of the L2-Sobolev
theory Harold P. Boas and EmiaI J. Straube;
5. Recent developments in the classification
theory of compact Kaehler manifolds Fnederic
Campana and Thomas PeterneII; 6. Remarks on global irregularity in the partial-Neumann
problem Michael Christ,I 7. Subelliptic estimates and finite-type John
P. D'Angelo and Joseph J, Kohn,I 8. Pseudoconvex-concave duality and regularization
of currents Jean-Pienle DemaI'Ily,I 9. Complex dynamics in higher dimension John
Erik Fornaess and Nessim Sibony,I 10. Attractors in P2 John Erik Fornaess and
Brendan Weickert,. 11. Varieties of minimal rational tangents
on uniruled projective manifolds Jun-Muk
Hwang and Ngaiming Mok; 12. Recent developments in Seiberg-Witten theory
and complex geometry Christian Okonek andAndllei
Teleman; 13. Recent techniques in hyperbolicity problems
Yum-Tong Siu; 14. Rigidity theorems in Kaehler geometry and
fundamental groups of varieties DomI'ngO
Toledo; 15.Nevanlinna theory and diophantine approximation
Paul Voj'ta.
Subject areas : analysis, geometry, algebra,
number theory
Series: Mathematical Sciences Research Institute
Publications, 37
0521 770866 Hardback 550pp c February2000
c i:40.00C
This book provides an accessible and up-to-date
introduction to how knot theory and Feynman
diagrams can be used to illuminate problems
in quantum field theory. The emphasis in
the book is to show how conventional calculational
methods for perturbative quantum field theory
lead to more elegant and potentially more
powerful methods inspired by new mathematical
discoveries. Dealing with material at perhaps
the most productive interface betwehen mathematics
and physics, the book will be of interest
to theoretical and particle physicists, and
mathematicians.
Contents: 1. Introduction; 2. Perturbative quantum field theory; 3. The Hopf algebra structure of renormalization;
4. Rationality: no knots, no transcendentals;
5. The simplest link diagrams; 6. Necessary topics from knot theory; 7. Knots to numbers; 8. One-loop words; 9. EulerTZagier
sums; 10. Knots and transcendentals; 11. The 4-teml relation; 12. Hopf algebras, non-commutative geometry,
and what else?
Subject areasiheoretical physics, particle
physics, applied mathematics
Market: graduate students, academic researchers
Series: Cambridge Lecture Notes in Physics
0521 58761 1 Paperback 260pp c February2000
97 line diagrams 8 tables
This is a textbook for advanced undergraduate
and graduate students in the field of mobile
robotics. Emphasising computation and algorithms,
the authors address a range of strategies
for enabling robots to perform'tasks involving
motion and behavior.
The book is divided into three sections:
focomotion, sensing, and reasoning. Concentrating
on wheeled and legged robots, it discusses
a variety of other propulsion systems. 1t
presents algorithms for various sensor technologies,
including sonar, vision, and laser scanners.
Addressing reasoning, the authors emphasize
the problems of navigation, pose estimation,
and autonomous exploration.
Contents: 1. Overview and motivation; Part l. Locomotion
and Perception: 2. Mobile robot hardware; 3. Non-visual sensors and algorithms; 4. Visual sensors and algorithms; Part ll.
Representation and Planning: 5. Representing and reasoning about space;
6. Operating environment; 7. Pose maintenance; 8. Maps and related tasks; 9, Practical mobile robot tasks; 10. The future of mobile robotics.
Subject areas :Robotics, engineering, artificial
intelligence, cognitive science
0 521 56021 7 Hardback 288pp c February2000
0 521 56876 5 Paperback 288pp c February2000
79 line diagrams 60 half-tones 41 exercises
This book shows how computer-aided mathematics
has reached a level where it can support
effectively many of the computations in science
and engineering. ln addition to treating
traditional computer science topics, this
introductory course shows scientists and
engineers how these computer-based tools
can be used to do scientific computations,
A valuable text for computer science courses
for scientists and engineers, this book should
also prove useful to Mathematica users at
all levels. Covering the latest release of
Mathematica, the book includes useful tips
and
techniques to help even seasoned users.
Contents: Preface; 1. About this book; 2. Computers and science; 3, Mathematica's programming language; 4. lteration and recursion;
5. Structure of programs; 6. Abstract data types; 7. Algorithms for searching and sorting; 8. Complexity of algorithms; 9. Operations on vectors and matrices; 10. List processing and recursion; 11. Rule-based programming; 12. Functions; 13. Theory of computation; 14. Databases;
15. Object-oriented programming; Appendix A. Further reading; Appendix B. More information about Mathematica; Index.
Subject areas : Electrical and mechanical
engineering, physics, chemistry
0521 631726 Hardback 400pp c February2000
0521 663954 Paperback 400pp c February2000