Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators
Uniqueness and Non-Uniqueness of Semigroups Generated by Singular Diffusion Operators

Author: Andreas Eberle

Publisher: Springer

Published: 2007-01-05

Total Pages: 265

ISBN-13: 3540480765

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This book addresses both probabilists working on diffusion processes and analysts interested in linear parabolic partial differential equations with singular coefficients. The central question discussed is whether a given diffusion operator, i.e., a second order linear differential operator without zeroth order term, which is a priori defined on test functions over some (finite or infinite dimensional) state space only, uniquely determines a strongly continuous semigroup on a corresponding weighted Lp space. Particular emphasis is placed on phenomena causing non-uniqueness, as well as on the relation between different notions of uniqueness appearing in analytic and probabilistic contexts.

Matrix Inequalities
Matrix Inequalities

Author: Xingzhi Zhan

Publisher: Springer

Published: 2004-10-19

Total Pages: 127

ISBN-13: 3540454217

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The main purpose of this monograph is to report on recent developments in the field of matrix inequalities, with emphasis on useful techniques and ingenious ideas. Among other results this book contains the affirmative solutions of eight conjectures. Many theorems unify or sharpen previous inequalities. The author's aim is to streamline the ideas in the literature. The book can be read by research workers, graduate students and advanced undergraduates.

Monomialization of Morphisms from 3-Folds to Surfaces
Monomialization of Morphisms from 3-Folds to Surfaces

Author: Steven D. Cutkosky

Publisher: Springer

Published: 2004-10-13

Total Pages: 245

ISBN-13: 3540480307

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A morphism of algebraic varieties (over a field characteristic 0) is monomial if it can locally be represented in e'tale neighborhoods by a pure monomial mappings. The book gives proof that a dominant morphism from a nonsingular 3-fold X to a surface S can be monomialized by performing sequences of blowups of nonsingular subvarieties of X and S. The construction is very explicit and uses techniques from resolution of singularities. A research monograph in algebraic geometry, it addresses researchers and graduate students.

Moduli of Families of Curves for Conformal and Quasiconformal Mappings
Moduli of Families of Curves for Conformal and Quasiconformal Mappings

Author: Alexander Vasilʹev

Publisher: Springer Science & Business Media

Published: 2002-07-23

Total Pages: 228

ISBN-13: 9783540438465

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The monograph is concerned with the modulus of families of curves on Riemann surfaces and its applications to extremal problems for conformal, quasiconformal mappings, and the extension of the modulus onto Teichmller spaces. The main part of the monograph deals with extremal problems for compact classes of univalent conformal and quasiconformal mappings. Many of them are grouped around two-point distortion theorems. Montel's functions and functions with fixed angular derivatives are also considered. The last portion of problems is directed to the extension of the modulus varying the complex structure of the underlying Riemann surface that sheds some new light on the metric problems of Teichmller spaces.

Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids
Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids

Author: Martin Fuchs

Publisher: Springer Science & Business Media

Published: 2000-12-12

Total Pages: 284

ISBN-13: 9783540413974

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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. For perfect plasticity the role of the stress tensor is emphasized by studying the dual variational problem in appropriate function spaces. The main results describe the analytic properties of weak solutions, e.g. differentiability of velocity fields and continuity of stresses. The monograph addresses researchers and graduate students interested in applications of variational and PDE methods in the mechanics of solids and fluids.

Big Queues
Big Queues

Author: Ayalvadi J. Ganesh

Publisher: Springer

Published: 2004-01-28

Total Pages: 263

ISBN-13: 3540398899

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Big Queues aims to give a simple and elegant account of how large deviations theory can be applied to queueing problems. Large deviations theory is a collection of powerful results and general techniques for studying rare events, and has been applied to queueing problems in a variety of ways. The strengths of large deviations theory are these: it is powerful enough that one can answer many questions which are hard to answer otherwise, and it is general enough that one can draw broad conclusions without relying on special case calculations.

Manis Valuations and Prüfer Extensions I
Manis Valuations and Prüfer Extensions I

Author: Manfred Knebusch

Publisher: Springer

Published: 2004-10-19

Total Pages: 276

ISBN-13: 3540456252

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The present book is devoted to a study of relative Prüfer rings and Manis valuations, with an eye to application in real and p-adic geometry. If one wants to expand on the usual algebraic geometry over a non-algebraically closed base field, e.g. a real closed field or p-adically closed field, one typically meets lots of valuation domains. Usually they are not discrete and hence not noetherian. Thus, for a further develomemt of real algebraic and real analytic geometry in particular, and certainly also rigid analytic and p-adic geometry, new chapters of commutative algebra are needed, often of a non-noetherian nature. The present volume presents one such chapter.

Noncommutative Geometry
Noncommutative Geometry

Author: Alain Connes

Publisher: Springer Science & Business Media

Published: 2003-12-08

Total Pages: 372

ISBN-13: 9783540203575

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Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.

Loeb Measures in Practice: Recent Advances
Loeb Measures in Practice: Recent Advances

Author: Nigel J. Cutland

Publisher: Springer

Published: 2004-10-11

Total Pages: 118

ISBN-13: 3540445315

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This expanded version of the 1997 European Mathematical Society Lectures given by the author in Helsinki, begins with a self-contained introduction to nonstandard analysis (NSA) and the construction of Loeb Measures, which are rich measures discovered in 1975 by Peter Loeb, using techniques from NSA. Subsequent chapters sketch a range of recent applications of Loeb measures due to the author and his collaborators, in such diverse fields as (stochastic) fluid mechanics, stochastic calculus of variations ("Malliavin" calculus) and the mathematical finance theory. The exposition is designed for a general audience, and no previous knowledge of either NSA or the various fields of applications is assumed.