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Algèbre commutative, Chapitre 10 = Commutative Algebra, Chapter 10
Depth, Regularity, Duality The Mathematics Elements of Nicolas BOURBAKI aim to provide a rigorous, systematic presentation without prerequisites of mathematics from their foundations. This volume of the Book of Commutative Algebra, Book 7 of the treatise, is a continuation of the earlier chapters. It introduces in particular the notions of depth and smoothness, fundamental in algebraic geometry. It ends with the introduction of the dualizing modules and the Grothendieck duality.
Algèbre commutative : Chapitres 5 à 7 = Commutative algebra : Chapters 5 to 7
The Mathematics Elements of Nicolas BOURBAKI aim to provide a rigorous, systematic presentation without prerequisites of mathematics from their foundations.This second volume of the Book of Commutative Algebra, Seventh Book of the treatise, introduces two fundamental notions in commutative algebra, that of algebraic integer and that of valuation, which have many applications in number theory and algebraic geometry.
Algebraic Theory of Locally Nilpotent Derivations
This book explores the theory and application of locally nilpotent derivations, which is a subject of growing interest and importance not only among those in commutative algebra and algebraic geometry, but also in fields such as Lie algebras and differential equations. The author provides a unified treatment of the subject, beginning with 16 First Principles on which the entire theory is based. These are used to establish classical results, such as Rentschler’s Theorem for the plane, right up to the most recent results, such as Makar-Limanov’s Theorem for locally nilpotent derivations of polynomial rings.
Algebraic Methods for Nonlinear Control Systems
A self-contained introduction to algebraic control for nonlinear systems suitable for researchers and graduate students.The most popular treatment of control for nonlinear systems is from the viewpoint of differential geometry yet this approach proves not to be the most natural when considering problems like dynamic feedback and realization. Professors Conte, Moog and Perdon develop an alternative linear-algebraic strategy based on the use of vector spaces over suitable fields of nonlinear functions. This algebraic perspective is complementary to, and parallel in concept with, its more celebrated differential-geometric counterpart.Algebraic Methods for Nonlinear Control Systems describes a wide range of results, some of which can be derived using differential geometry but many of which cannot.
Algebraic Geometry and Number Theory : In Honor of Vladimir Drinfeld's 50th Birthday
One of the most creative mathematicians of our times, Vladimir Drinfeld received the Fields Medal in 1990 for his groundbreaking contributions to the Langlands program and to the theory of quantum groups.These ten original articles by prominent mathematicians, dedicated to Drinfeld on the occasion of his 50th birthday, broadly reflect the range of Drinfeld's own interests in algebra, algebraic geometry, and number theory.
Algebraic Geometry and Geometric Modeling
Algebraic Geometry provides an impressive theory targeting the understanding of geometric objects defined algebraically. Geometric Modeling uses every day, in order to solve practical and difficult problems, digital shapes based on algebraic models. In this book, we have collected articles bridging these two areas. The confrontation of the different points of view results in a better analysis of what the key challenges are and how they can be met. We focus on the following important classes of problems: implicitization, classification, and intersection. The combination of illustrative pictures, explicit computations and review articles will help the reader to handle these subjects.
Algebraic Geometry : An Introduction
The book starts with easily-formulated problems with non-trivial solutions – for example, Bézout’s theorem and the problem of rational curves – and uses these problems to introduce the fundamental tools of modern algebraic geometry: dimension; singularities; sheaves; varieties; and cohomology. The treatment uses as little commutative algebra as possible by quoting without proof (or proving only in special cases) theorems whose proof is not necessary in practice, the priority being to develop an understanding of the phenomena rather than a mastery of the technique. A range of exercises is provided for each topic discussed, and a selection of problems and exam papers are collected in an appendix to provide material for further study.
Algebraic Cycles, Sheaves, Shtukas, and Moduli : Impanga Lecture Notes
The articles in this volume are devoted to: - moduli of coherent sheaves. - principal bundles and sheaves and their moduli. - new insights into Geometric Invariant Theory. - stacks of shtukas and their compactifications. - algebraic cycles vs. commutative algebra. - Thom polynomials of singularities. - zero schemes of sections of vector bundles.
Algebraic and Proof-theoretic Aspects of Non-classical Logics : Papers in Honor of Daniele Mundici on the Occasion of His 60th Birthday
It profound connections between logic and such diverse fields of research as functional analysis, probability and measure theory, the geometry of toric varieties, piecewise linear geometry, and error-correcting codes. Several prominent logicians, mathematicians, and computer scientists
Algebra 3 : Homological Algebra and Its Applications
Includes algebra, deals with important topics in homological algebra, including abstract theory of derived functors, sheaf co-homology, and an introduction to etale and l-adic co-homology. It contains four chapters which discuss homology theory in an abelian category together with some important and fundamental applications in geometry, topology, algebraic geometry (including basics in abstract algebraic geometry), and group theory.
Algebra ; Vol. I : Fields and Galois Theory
The present textbook is a lively, problem-oriented and carefully written introduction to classical modern algebra. The first volume focuses on field extensions. Galois theory and its applications are treated more thoroughly than in most texts. It also covers basic applications to number theory, ring extensions and algebraic geometry.The main focus of the second volume is on additional structure of fields and related topics. Much material not usually covered in textbooks appears here, including real fields and quadratic forms, diophantine dimensions of a field, the calculus of Witt vectors, the Schur group of a field, and local class field theory.
Algebra : Fields with structure, algebras and advanced topics
The present textbook is a lively, problem-oriented and carefully written introduction to classical modern algebra. The author leads the reader through interesting subject matter, while assuming only the background provided by a first course in linear algebra. The first volume focuses on field extensions. Galois theory and its applications are treated more thoroughly than in most texts. It also covers basic applications to number theory, ring extensions and algebraic geometry. The main focus of the second volume is on additional structure of fields and related topics. Much material not usually covered in textbooks appears here, including real fields and quadratic forms, the Tsen rank of a field, the calculus of Witt vectors, the Schur group of a field, and local class field theory.
Affine Density in Wavelet Analysis
Provides the first thorough and comprehensive treatment of irregular wavelet frames by introducing and employing a new notion of affine density as a highly effective tool for examining the geometry of sequences of time-scale indices.
Advances on mechanics, design engineering and manufacturing III ; Proceedings of the international joint conference on mechanics, design engineering & advanced manufacturing, JCM 2020, June 2-4, 2020
This open access book gathers contributions presented at the International Joint Conference on Mechanics, Design Engineering and Advanced Manufacturing (JCM 2020), held as a web conference on June 2–4, 2020.
Advances in visual computing ; Vol. 4292 ; 2nd International symposium, ISVC 2006, Lake Tahoe, NV, USA, November 6-8, 2006, Proceedings, Part II
This year, the program consisted of 13 oral sessions, one poster session, ten special tracks, and six keynote presentations. The response to the call for - pers was very strong. We received more than twice the papers received last year. Specifcally, we received over 280 submissions for the main symposium from which we accepted 65 papers for oral presentation (23% acceptance) and 56 papers for poster presentation (20% acceptance). Special track papers were solicited separately through the Organizing and Program Committees of each track. A total of 57 papers were accepted for presentation in the special tracks. All papers were reviewed with an emphasis on potential to contribute to the state of the art in the ?eld. Selection criteria included accuracy and originality of ideas, clarity and signi?cance of results, and presentation quality. The review process was quite rigorous, involving two to three independent blind reviews followed by several days of discussion.
Advances in Visual Computing ; Vol. 4291 ; 2nd International Symposium, ISVC 2006, Lake Tahoe, NV, USA, November 6-8, 2006, Proceedings, Part I
This year, the program consisted of 13 oral sessions, one poster session, ten special tracks, and six keynote presentations. The response to the call for - pers was very strong. We received more than twice the papers received last year. Specifcally, we received over 280 submissions for the main symposium from which we accepted 65 papers for oral presentation (23% acceptance) and 56 papers for poster presentation (20% acceptance). Special track papers were solicited separately through the Organizing and Program Committees of each track. A total of 57 papers were accepted for presentation in the special tracks. All papers were reviewed with an emphasis on potential to contribute to the state of the art in the ?eld. Selection criteria included accuracy and originality of ideas, clarity and signi?cance of results, and presentation quality. The review process was quite rigorous, involving two to three independent blind reviews followed by several days of discussion. During the discussion period we tried to correct anomalies and errors that might have existed in the initial reviews.
Advances in visual computing ; 4th International symposium, ISVC 2008, Las Vegas, NV, USA, December 1-3, 2008. Proceedings, Part II
The two volume set LNCS 5358 and LNCS 5359 constitutes the refereed proceedings of the 4th International Symposium on Visual Computing, ISVC 2008, held in Las Vegas, NV, USA, in December 2008.
Advances in visual computing ; 4th International Symposium, ISVC 2008, Las Vegas, NV, USA, December 1-3, 2008. Proceedings, Part I
The two volume set LNCS 5358 and LNCS 5359 constitutes the refereed proceedings of the 4th International Symposium on Visual Computing, ISVC 2008, held in Las Vegas, NV, USA, in December 2008.
Advances in Multiresolution for Geometric Modelling
Multiresolution methods in geometric modelling are concerned with the generation, representation, and manipulation of geometric objects at several levels of detail. Applications include fast visualization and rendering as well as coding, compression, and digital transmission of 3D geometric objects.The book contains seven survey papers, providing a detailed overview of recent advances in the various fields within multiresolution modelling, and sixteen additional research papers. Each of the seven parts of the book starts with a survey paper, followed by the associated research papers in that area.
Advances in Image and Video Technology ; 1st Pacific Rim Symposium, PSIVT 2006, Hsinchu, Taiwan, December 10-13, 2006, Proceedings
The conference of the 1st IEEE Pacisc-Rim Symposium on Image and Video Technology (PSIVT 2006) was held at Hsinchu, Taiwan, Republic of China, on December 11–13, 2006. This volume contains papers selected for presentation at this conference. The aim of this conference was to bring together theoretical advances and practical implementations contributing to, or being involved in, image and video technology. PSIVT 2006 featured a comprehensive program including tutorials, keynote and invited talks, oral paper presentations, and posters. We received 450 s- missions from 22 countries and accepted 141 papers among those (i.e., de?ning an acceptance rate of 31.3%). The intention was to establish PSIVT as a t- quality series of symposia. Decisions were discult sometimes, but we hope that the ?nal result is acceptable to all involved.
