From Divergent Power Series to Analytic Functions

From Divergent Power Series to Analytic Functions
Author: Werner Balser
Publisher: Springer
Total Pages: 117
Release: 2006-11-15
Genre: Mathematics
ISBN: 3540485945

Multisummability is a method which, for certain formal power series with radius of convergence equal to zero, produces an analytic function having the formal series as its asymptotic expansion. This book presents the theory of multisummabi- lity, and as an application, contains a proof of the fact that all formal power series solutions of non-linear meromorphic ODE are multisummable. It will be of use to graduate students and researchers in mathematics and theoretical physics, and especially to those who encounter formal power series to (physical) equations with rapidly, but regularly, growing coefficients.

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
Total Pages: 284
Release: 2000-12-12
Genre: Mathematics
ISBN: 9783540413974

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.

Loeb Measures in Practice: Recent Advances

Loeb Measures in Practice: Recent Advances
Author: Nigel J. Cutland
Publisher: Springer
Total Pages: 118
Release: 2004-10-11
Genre: Mathematics
ISBN: 3540445315

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.

Superconvergence in Galerkin Finite Element Methods

Superconvergence in Galerkin Finite Element Methods
Author: Lars Wahlbin
Publisher: Springer
Total Pages: 179
Release: 2006-11-14
Genre: Mathematics
ISBN: 3540494014

This book is essentially a set of lecture notes from a graduate seminar given at Cornell in Spring 1994. It treats basic mathematical theory for superconvergence in the context of second order elliptic problems. It is aimed at graduate students and researchers. The necessary technical tools are developed in the text although sometimes long proofs are merely referenced. The book gives a rather complete overview of the field of superconvergence (in time-independent problems). It is the first text with such a scope. It includes a very complete and up-to-date list of references.

Complex Differential and Difference Equations

Complex Differential and Difference Equations
Author: Galina Filipuk
Publisher: Walter de Gruyter GmbH & Co KG
Total Pages: 520
Release: 2019-11-18
Genre: Mathematics
ISBN: 3110609614

With a balanced combination of longer survey articles and shorter, peer-reviewed research-level presentations on the topic of differential and difference equations on the complex domain, this edited volume presents an up-to-date overview of areas such as WKB analysis, summability, resurgence, formal solutions, integrability, and several algebraic aspects of differential and difference equations.

The Minnesota Notes on Jordan Algebras and Their Applications

The Minnesota Notes on Jordan Algebras and Their Applications
Author: Max Koecher
Publisher: Springer Science & Business Media
Total Pages: 198
Release: 1999-09-17
Genre: Mathematics
ISBN: 9783540663607

This volume contains a re-edition of Max Koecher's famous Minnesota Notes. The main objects are homogeneous, but not necessarily convex, cones. They are described in terms of Jordan algebras. The central point is a correspondence between semisimple real Jordan algebras and so-called omega-domains. This leads to a construction of half-spaces which give an essential part of all bounded symmetric domains. The theory is presented in a concise manner, with only elementary prerequisites. The editors have added notes on each chapter containing an account of the relevant developments of the theory since these notes were first written.

The Red Book of Varieties and Schemes

The Red Book of Varieties and Schemes
Author: David Mumford
Publisher: Springer
Total Pages: 316
Release: 2004-02-21
Genre: Mathematics
ISBN: 3540460217

Mumford's famous "Red Book" gives a simple, readable account of the basic objects of algebraic geometry, preserving as much as possible their geometric flavor and integrating this with the tools of commutative algebra. It is aimed at graduates or mathematicians in other fields wishing to quickly learn aboutalgebraic geometry. This new edition includes an appendix that gives an overview of the theory of curves, their moduli spaces and their Jacobians -- one of the most exciting fields within algebraic geometry.

Flows on 2-dimensional Manifolds

Flows on 2-dimensional Manifolds
Author: Igor Nikolaev
Publisher: Springer Science & Business Media
Total Pages: 324
Release: 1999-07-15
Genre: Mathematics
ISBN: 9783540660804

Time-evolution in low-dimensional topological spaces is a subject of puzzling vitality. This book is a state-of-the-art account, covering classical and new results. The volume comprises Poincaré-Bendixson, local and Morse-Smale theories, as well as a carefully written chapter on the invariants of surface flows. Of particular interest are chapters on the Anosov-Weil problem, C*-algebras and non-compact surfaces. The book invites graduate students and non-specialists to a fascinating realm of research. It is a valuable source of reference to the specialists.

Seminaire de Probabilites XXXI

Seminaire de Probabilites XXXI
Author: Jacques Azema
Publisher: Springer
Total Pages: 342
Release: 2008-05-01
Genre: Mathematics
ISBN: 3540683526

The 31 papers collected here present original research results obtained in 1995-96, on Brownian motion and, more generally, diffusion processes, martingales, Wiener spaces, polymer measures.