edited by P M Pardalos (University of Florida, USA), A Migdalas (Technical University of Crete, Greece) & R E Burkard (Technical University of Graz, Austria)

COMBINATORIAL AND GLOBAL OPTIMIZATION

Combinatorial and global optimization problems appear in a wide range of applications in operations research, engineering, biological science, and computer science. In combinatorial optimization and graph theory, many approaches have been developed that link the discrete universe to the continuous universe through geometric, analytic, and algebraic techniques. Such techniques include global optimization formulations, semidefinite programming, and spectral theory. Recent major successes based on these approaches include interior point algorithms for linear and discrete problems, the celebrated Goemans妨illiamson relaxation of the maximum cut problem, and the Du蓬wang solution of the Gilbert鳳ollak conjecture. Since integer constraints are equivalent to nonconvex constraints, the fundamental difference between classes of optimization problems is not between discrete and continuous problems but between convex and nonconvex optimization problems. This volume is a selection of refereed papers based on talks presented at a conference on "Combinatorial and Global Optimization" held at Crete, Greece.

Contents:

A Forest Exterior Point Algorithm for Assignment Problems (H Achatz et al.)
Location/Allocation of Queuing Facilities in Continuous Space Using Minsum and Minmax Criteria (J Brimberg et al.)
Algorithms for the Consistency Analysis in Scenario Projects (R Feldmann et al.)
Solving Quadratic Knapsack Problems by Reformulation and Tabu Search (F Glover & G Kochenberger)
Global Optimization Using Dynamic Search Trajectories (A A Groenwold & J A Snyman)
On Pareto Efficiency. A General Constructive Existence Principle (G Isac)
Piecewise Linear Network Flow Problems (D Kim & P M Pardalos)
Semidefinite Programming Approaches for MAX-2-SAT and MAX-3-SAT: Computational Perspectives (E de Klerk & J P Warners)
Heuristic Solutions of Vehicle Routing Problems in Supply Chain Management (Y Marinakis & A Migdalas)
A New Finite Cone Covering Algorithm for Concave Minimization (C Meyer & B Jaumard)
Frequency Assignment for Very Large, Sparse Networks (R Murphy)
GPS Network Design: An Application of the Simulated Annealing Heuristic Technique (H A Saleh & P J Dare)
Normal Branch and Bound Algorithms for General Nonconvex Quadratic Programming (H Tuy)
and other papers

Readership: Researchers in numerical & computational mathematics, optimization, combinatorics & graph theory, networking and materials engineering.

370pp (approx.) Pub. date: Scheduled Winter 2001
ISBN 981-02-4802-4

edited by Wolfgang Tutschke, H Florian (Graz University of Technology, Austria), N Ortner (University of Innsbruck, Austria) & F J Schnitzer (Mining University Leoben, Austria)

FUNCTIONAL-ANALYTIC AND COMPLEX METHODS, THEIR INTERACTIONS, AND APPLICATIONS TO PARTIAL DIFFERENTIAL EQUATIONS:Proceedings of the International Graz Workshop
Graz, Austria 12 - 16 February 2001

Functional analysis is not only a tool for unifying mathematical analysis, but it also provides the background for today's rapid development of the theory of partial differential equations. Using concepts of functional analysis, the field of complex analysis has developed methods (such as the theory of generalized analytic functions) for solving very general classes of partial differential equations.
This book is aimed at promoting further interactions of functional analysis, partial differential equations, and complex analysis including its generalizations such as Clifford analysis. New interesting problems in the field of partial differential equations concern, for instance, the Dirichlet problem for hyperbolic equations. Applications to mathematical physics address mainly Maxwell's equations, crystal optics, dynamical problems for cusped bars, and conservation laws.

Contents:

Boundary Value Problems and Initial Value Problems for Partial Differential Equations
Applications of Functional-Analytic and Complex Methods to Mathematical Physics
Partial Complex Differential Equations in the Plane
Complex Methods in Higher Dimensions

Readership: Researchers, lecturers and graduate students in the fields of analysis & differential equations, applied mathematics and mathematical physics.

460pp (approx.) Pub. date: Scheduled Winter 2001
ISBN 981-02-4764-8

by Christian Beck (University of London, UK)

SPATIO-TEMPORAL CHAOS
AND VACUUM FLUCTUATIONS OF QUANTIZED FIELDS

Advanced Series in Nonlinear Dynamics

This book describes new applications for spatio-temporal chaotic dynamical systems in elementary particle physics and quantum field theories. The stochastic quantization approach of Parisi and Wu is extended to more general deterministic chaotic processes as generated by coupled map lattices. In particular, so-called chaotic strings are introduced as a suitable small-scale dynamics of vacuum fluctuations. This more general approach to second quantization reduces to the ordinary stochastic quantization scheme on large scales, but it also opens up interesting new perspectives: chaotic strings appear to minimize their vacuum energy for the observed numerical values of the free standard model parameters.

Contents:

Chaotic Quantization
Coupled Map Lattices as Models of Vacuum Fluctuations on a Small Scale
Chaotic Strings
Phase Transitions and Spontaneous Symmetry Breaking
Generalized Statistical Mechanics Approach
Vacuum Energy of Chaotic Strings
Standard Model Parameters
Towards Quantum Gravity

Readership: Graduate students, researchers and academics involved in dynamical systems.

300pp (approx.) Pub. date: Scheduled Spring 2002
ISBN 981-02-4798-2

edited by Pawel Walczak (Uniwersytet Lodzki, Poland), Lawrence Conlon (Washington University, USA), Remi Langevin (Universite de Bourgogne, France) & Takashi Tsuboi (University of Tokyo)

FOLIATIONS: GEOMETRY AND DYNAMICS
Proceedings of the Euroworkshop Warsaw, Poland 29 May - 9 June 2000

This volume contains surveys and research articles regarding different aspects of the theory of foliation. The main aspects concern the topology of foliations of low-dimensional manifolds, the geometry of foliated Riemannian manifolds and the dynamical properties of foliations. Among the surveys are lecture notes devoted to the analysis of some operator algebras on foliated manifolds and the theory of confoliations (objects defined recently by W Thurston and Y Eliashberg, situated between foliations and contact structures). Among the research articles one can find a detailed proof of an unpublished theorem (due to Duminy) concerning ends of leaves in exceptional minimal sets.

Contents:

Surveys: Recent Results on Secondary Characteristic Classes of Transversely Holomorphic Foliations (T Asuke)
LS-Categories for Foliated Manifolds (H Colman)
Dynamics and the Godbillon坊ey Class: A History and Survey (S Hurder)
Similarity and Conformal Geometry of Foliations (R Langevin)
Foliations and Contact Structures (Y Mitsumatsu)
Operator Algebras and the Index Theorem on Foliated Manifolds (H Moriyoshi)
Research Articles: Distributional Betti Numbers of Transitive Foliations of Codimension 1 (J Alvarez-Lopez & Y Kordyukov)
Tautly Foliated 3-Manifolds (M Brittenham)
Endsets of Exceptional Leaves (J Cantwell & L Conlon)
Foliations and Compactly Generated Pseudogroups (A Haefliger)
Transverse Lusternik亡chnirelmann Category and Non-Proper Leaves (R Langevin & P Walczak)
On Exact Poisson Manifolds of Dimension 3 (T Mizutani)
On the Perfectness of Groups of Diffeomorphisms of the Interval Tangent to the Identity at the End Points (T Tsuboi)
and other papers

Readership: Researchers interested in mathematics, especially in fields related to differential geometry and topology, and the theory of dynamical systems.

350pp (approx.) Pub. date: Scheduled Spring 2002
ISBN 981-02-4796-6