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Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.

This book provides an accessible yet comprehensive description of the application methods of group analysis to integro-differential equations. It offers both fundamental theoretical and algorithmic aspects of these methods and includes instructive examples.

This book provides an accessible yet comprehensive description of the application methods of group analysis to integro-differential equations. It offers both fundamental theoretical and algorithmic aspects of these methods and includes instructive examples.

This volume contains detailed expositions of talks given during an instructional conference held at Luminy in December 1998, which was devoted to classical and recent results concerning the fundamental group of algebraic curves, especially over finite and local fields. The scientific guidance of the conference was supplied by M. Raynaud, a leading expert in the field. The purpose of this volume is twofold. Firstly, it gives an account of basic results concerning rigid geometry, stable curves, and algebraic fundamental groups, in a form which should make them largely accessible to graduate students mastering a basic course in modern algebraic geometry. However classic, most of this material has not appeared in book form yet. In particular, the semi-stable reduction theorem for curves is covered with special care, including various detailed proofs. Secondly, it presents self-contained expositions of important recent developments, including the work of Tamagawa on Grothendieck's anabelian conjecture for curves over finite fields, and the solution by Raynaud and Harbater of Abhyankar's conjecture about coverings of affine curves in positive characteristic. These expositions should be...

Bioinformatics is growing by leaps and bounds; theories/algorithms/statistical techniques are constantly evolving. Nevertheless, a core body of algorithmic ideas have emerged and researchers are beginning to adopt a "problem solving" approach to bioinformatics, wherein they use solutions to well-abstracted problems as building blocks to solve larger scope problems. Problem Solving Handbook for Computational Biology and Bioinformatics is an edited volume contributed by world renowned leaders in this field. This comprehensive handbook with problem solving emphasis, covers all relevant areas of computational biology and bioinformatics. Web resources and related themes are highlighted at every opportunity in this central easy-to-read reference. Designed for advanced-level students, researchers and professors in computer science and bioengineering as a reference or secondary text, this handbook is also suitable for professionals working in this industry.

M. Brelot: Historical introduction.- H. Bauer: Harmonic spaces and associated Markov processes.- J.M. Bony: Opérateurs elliptiques dégénérés associés aux axiomatiques de la theorie du potentiel.- J. Deny: Méthodes hilbertiennes en theory du potentiel.- J.L. Doob: Martingale theory – Potential theory.- G. Mokobodzki: Cônes de potentiels et noyaux subordonnés.

This book is part of a tri-lingual dictionary of production engineering compiled under the auspices of the International Institution of Production Engineering Research (C.I.R.P.) headquartered in Paris. The first two volumes contain about 3400 terms for metal forming. This volume contains the terminology related to the following chapters: Rolling; Drawing and Extrusion. Definitions are provided for nearly all terms, and illustrations are included where needed. In addition, reference is made to national and international standards. Alphabetical indices in each of the three languages provide easy access to the entries.