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This book presents in a unified way the mathematical theory of well-posedness in optimization. The book is addressed to mathematicians interested in optimization and related topics, and also to engineers, control theorists, economists and applied scientists who can find here a mathematical justification of practical procedures they encounter.

The theory of explicit formulas for regularized products and series forms a natural continuation of the analytic theory developed in LNM 1564. Their wide range of applications includes the spectral theory of a broad class of manifolds and also the theory of zeta functions in number theory and representation theory.

Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM.

The present edition of this text summarizes the research results that have been achieved since the first edition was published 30 years ago. It also incorporates new material and an updated bibliography.

Variational methods are applied to prove the existence of weak solutions for boundary value problems from the deformation theory of plasticity as well as for the slow, steady state flow of generalized Newtonian fluids including the Bingham and Prandtl-Eyring model.

Functionals involving both volume and surface energies have a number of applications ranging from computer vision to fracture mechanics. The purpose of this text is to present a global approach to approximations using the theory of gamma-convergence and of special functions of bounded variation.

While optimality conditions for optimal control problems with state constraints have been extensively investigated in the literature the results pertaining to numerical methods are relatively scarce. This approach enables the author to provide global convergence analysis of first order and superlinearly convergent second order methods.

This book based on lectures given by James Arthur discussesthe trace formula of Selberg and Arthur. The emphasis islaid on Arthur's trace formula for GL(r), with severalexamples in order to illustrate the basic concepts. Orbital integrals andSelberg's trace formula, 2.3.Three examples, 2.4.

In recent years, the classical theory of stochastic integration and stochastic differential equations has been extended to a non-commutative set-up to develop models for quantum noises.

This work is a research-level monograph whose goal is to develop a general combination, decomposition, and structure theory for branched coverings of the two-sphere to itself, regarded as the combinatorial and topological objects which arise in the classification of certain holomorphic dynamical systems on the Riemann sphere.

The book systematically develops the nonlinear potential theory connected with the weighted Sobolev spaces, where the weight usually belongs to Muckenhoupt's class of Ap weights. Applications of potential theory to weighted Sobolev spaces include quasi continuity of Sobolev functions, Poincare inequalities, and spectral synthesis theorems.

This new edition of LNM 1693 aims to reduce questions on monotone multifunctions to questions on convex functions. The journey begins with the Hahn-Banach theorem and culminates in a survey of current results on monotone multifunctions on a Banach space.

This volume covers the stability of nonautonomous differential equations in Banach spaces in the presence of nonuniform hyperbolicity. The exposition is directed to researchers as well as graduate students interested in differential equations and dynamical systems, particularly in stability theory.

The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained.

The 13 chapters of this book centre around the proof ofTheorem 1 of Faltings' paper "Diophantine approximation onabelian varieties", Ann. Eachchapter is based on an instructional lecture given by itsauthor ata special conference for graduate students, on thetopic of Faltings' paper.

This book provides mathematical proof of several existence, structure and regularity properties, empirically observed in transportation networks.

The Bayreuth meeting on "Complex Algebraic Varieties"focussed on the classification of algebraic varieties andtopics such as vector bundles, Hodge theory and hermitiandifferential geometry. Tyurin: Thegeometry of the special components of moduli space of vectorbundles over algebraic surfaces of general type.

Lectures given at the Banach Center and C.I.M.E. Joint Summer School held in Bedlewo, PolandSeptember 4-9, 2006