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Book Description
Dans ce travail, on s'intéresse aux relations entre les méthodes de type volumes finis et les méthodes éléments finis mixtes pour la discrétisation des problèmes elliptiques. L'intérêt est d'utiliser un cadre théorique de type variationnel permettant d'obtenir pour une classe de schémas de type volumes finis, des résultats de majoration d'erreurs, à priori et à posteriori. Un estimateur d'erreur à posteriori, asymptotiquement exact, est obtenu en exploitant les liens existant entre méthodes volumes finis, éléments finis mixtes et éléments finis non conformes, et une méthode adaptative de décomposition de domaines est développée pour des méthodes volumes finis.
Book Description
Dans ce travail, on s'intéresse aux relations entre les méthodes de type volumes finis et les méthodes éléments finis mixtes pour la discrétisation des problèmes elliptiques. L'intérêt est d'utiliser un cadre théorique de type variationnel permettant d'obtenir pour une classe de schémas de type volumes finis, des résultats de majoration d'erreurs, à priori et à posteriori. Un estimateur d'erreur à posteriori, asymptotiquement exact, est obtenu en exploitant les liens existant entre méthodes volumes finis, éléments finis mixtes et éléments finis non conformes, et une méthode adaptative de décomposition de domaines est développée pour des méthodes volumes finis.
Author: Fayssal Benkhaldoun Publisher: Wiley-ISTE ISBN: Category : Mathematics Languages : en Pages : 866
Book Description
This volume contains contributions from speakers at the 4th International Symposium on Finite Volumes for Complex Applications, held in Marrakech, Morocco, in July 2005. The subject of these papers ranges from theoretical and numerical results to physical applications. Topics covered include: Theoretical and numerical results • theoretical foundation • convergence • new finite volume schemes • adaptivity • higher order discretization and parallelization Physical applications • multiphase flow and flows through porous media • turbulent flows • shallow water problems • stiff source terms • cryogenic applications • medical and biological applications • image processing Papers on Industrial codes, as well as interdisciplinary approaches are also included in these proceedings.
Author: S. Lang Publisher: Springer Science & Business Media ISBN: 3662070103 Category : Mathematics Languages : en Pages : 270
Book Description
It is possible to write endlessly on elliptic curves. (This is not a threat.) We deal here with diophantine problems, and we lay the foundations, especially for the theory of integral points. We review briefly the analytic theory of the Weierstrass function, and then deal with the arithmetic aspects of the addition formula, over complete fields and over number fields, giving rise to the theory of the height and its quadraticity. We apply this to integral points, covering the inequalities of diophantine approximation both on the multiplicative group and on the elliptic curve directly. Thus the book splits naturally in two parts. The first part deals with the ordinary arithmetic of the elliptic curve: The transcendental parametrization, the p-adic parametrization, points of finite order and the group of rational points, and the reduction of certain diophantine problems by the theory of heights to diophantine inequalities involving logarithms. The second part deals with the proofs of selected inequalities, at least strong enough to obtain the finiteness of integral points.
Author: Goro Shimura Publisher: Springer Science & Business Media ISBN: 1441917322 Category : Mathematics Languages : en Pages : 245
Book Description
This book is divided into two parts. The first part is preliminary and consists of algebraic number theory and the theory of semisimple algebras. There are two principal topics: classification of quadratic forms and quadratic Diophantine equations. The second topic is a new framework which contains the investigation of Gauss on the sums of three squares as a special case. To make the book concise, the author proves some basic theorems in number theory only in some special cases. However, the book is self-contained when the base field is the rational number field, and the main theorems are stated with an arbitrary number field as the base field. So the reader familiar with class field theory will be able to learn the arithmetic theory of quadratic forms with no further references.
Author: Yulia Zinova Publisher: Language Science Press ISBN: 3961102988 Category : Language Arts & Disciplines Languages : en Pages : 396
Book Description
This book addresses the complexity of Russian verbal prefixation system that has been extensively studied but yet not explained. Traditionally, different meanings have been investigated and listed in the dictionaries and grammars and more recently linguists attempted to unify various prefix usages under more general descriptions. The existent semantic approaches, however, do not aim to use semantic representations in order to account for the problems of prefix stacking and aspect determination. This task has been so far undertaken by syntactic approaches to prefixation, that divide verbal prefixes in classes and limit complex verb formation by restricting structural positions available for the members of each class. I show that these approaches have two major drawbacks: the implicit prediction of the non-existence of complex biaspectual verbs and the absence of uniformly accepted formal criteria for the underlying prefix classification. In this book the reader can find an implementable formal semantic approach to prefixation that covers five prefixes: za-, na-, po-, pere-, and do-. It is shown how to predict the existence, semantics, and aspect of a given complex verb with the help of the combination of an LTAG and frame semantics. The task of identifying the possible affix combinations is distributed between three modules: syntax, which is kept simple (only basic structural assumptions), frame semantics, which ensures that the constraints are respected, and pragmatics, which rules out some prefixed verbs and restricts the range of available interpretations. For the purpose of the evaluation of the theory, an implementation of the proposed analysis for a grammar fragment using a metagrammar description is provided. It is shown that the proposed analysis delivers more accurate and complete predictions with respect to the existence of complex verbs than the most precise syntactic account.
Author: Franco Brezzi Publisher: Springer Science & Business Media ISBN: 8847025923 Category : Mathematics Languages : en Pages : 394
Book Description
This volume is a selection of contributions offered by friends, collaborators, past students in memory of Enrico Magenes. The first part gives a wide historical perspective of Magenes' work in his 50-year mathematical career; the second part contains original research papers, and shows how ideas, methods, and techniques introduced by Magenes and his collaborators still have an impact on the current research in Mathematics.
Author: Gary Cornell Publisher: Springer Science & Business Media ISBN: 1461219744 Category : Mathematics Languages : en Pages : 592
Book Description
This volume contains the expanded lectures given at a conference on number theory and arithmetic geometry held at Boston University. It introduces and explains the many ideas and techniques used by Wiles, and to explain how his result can be combined with Ribets theorem and ideas of Frey and Serre to prove Fermats Last Theorem. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions and curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of the proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serres conjectures, Galois deformations, universal deformation rings, Hecke algebras, and complete intersections. The book concludes by looking both forward and backward, reflecting on the history of the problem, while placing Wiles'theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this an indispensable resource.
Author: Fabienne Oudin
Author: Fabienne Oudin
Author: Fayssal Benkhaldoun
Author: Philippe G. Ciarlet
Author: S. Lang
Author: Goro Shimura
Author: Yulia Zinova
Author: Franco Brezzi
Author: 
Author: 
Author: Gary Cornell