Cubic Action of a Rank One Group, Matthias Gruninger
Автор: Wood Название: The Twisted Cubic ISBN: 1107493722 ISBN-13(EAN): 9781107493728 Издательство: Cambridge Academ Рейтинг: Цена: 3008.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Originally published in 1913 as number fourteen in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book provides a concise account regarding the properties of the twisted cubic. A bibliography and appendix section are also included.
Автор: Henderson Название: The Twenty-Seven Lines upon the Cubic Surface ISBN: 110749351X ISBN-13(EAN): 9781107493513 Издательство: Cambridge Academ Рейтинг: Цена: 3643.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Originally published in 1911 as number thirteen in the Cambridge Tracts in Mathematics and Mathematical Physics series, this book presents a general survey of the problem of the 27 lines upon the cubic surface. Illustrative figures and a bibliography are also included.
This second edition covers essentially the same topics as the first. However, the presentation of the material has been extensively revised and improved. In addition, there are two new chapters, one dealing with the fundamental theorem of finitely generated abelian groups and the other a brief introduction to semigroup theory and automata.
This book is appropriate for second to fourth year undergraduates. In addition to the material traditionally taught at this level, the book contains several applications: Polya-Burnside Enumeration, Mutually Orthogonal Latin Squares, Error-Correcting Codes, and a classification of the finite groups of isometries of the plane and the finite rotation groups in Euclidean 3-space, semigroups and automata. It is hoped that these applications will help the reader achieve a better grasp of the rather abstract ideas presented and convince him/her that pure mathematics, in addition to having an austere beauty of its own, can be applied to solving practical problems.
Considerable emphasis is placed on the algebraic system consisting of the congruence classes mod n under the usual operations of addition and multiplication. The reader is thus introduced -- via congruence classes -- to the idea of cosets and factor groups. This enables the transition to cosets and factor objects to be relatively painless.
In this book, cosets, factor objects and homomorphisms are introduced early on so that the reader has at his/her disposal the tools required to give elegant proofs of the fundamental theorems. Moreover, homomorphisms play such a prominent role in algebra that they are used in this text wherever possible.
Автор: Hambleton Samuel A., Williams Hugh C. Название: Cubic Fields with Geometry ISBN: 3030014029 ISBN-13(EAN): 9783030014025 Издательство: Springer Рейтинг: Цена: 19564.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The objective of this book is to provide tools for solving problems which involve cubic number fields. Many such problems can be considered geometrically; both in terms of the geometry of numbers and geometry of the associated cubic Diophantine equations that are similar in many ways to the Pell equation. With over 50 geometric diagrams, this book includes illustrations of many of these topics. The book may be thought of as a companion reference for those students of algebraic number theory who wish to find more examples, a collection of recent research results on cubic fields, an easy-to-understand source for learning about Voronoi’s unit algorithm and several classical results which are still relevant to the field, and a book which helps bridge a gap in understanding connections between algebraic geometry and number theory.
The exposition includes numerous discussions on calculating with cubic fields including simple continued fractions of cubic irrational numbers, arithmetic using integer matrices, ideal class group computations, lattices over cubic fields, construction of cubic fields with a given discriminant, the search for elements of norm 1 of a cubic field with rational parametrization, and Voronoi's algorithm for finding a system of fundamental units. Throughout, the discussions are framed in terms of a binary cubic form that may be used to describe a given cubic field. This unifies the chapters of this book despite the diversity of their number theoretic topics.
Автор: Browning Tim Название: Cubic Forms and the Circle Method ISBN: 3030868710 ISBN-13(EAN): 9783030868710 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The Hardy-Littlewood circle method was invented over a century ago to study integer solutions to special Diophantine equations, but it has since proven to be one of the most successful all-purpose tools available to number theorists.
Описание: Sara Confalonieri presents an overview of Cardano`s mathematical treatises and, in particular, discusses the writings that deal with cubic equations. The author gives an insight into the latest of Cardano`s algebraic works, the De Regula Aliza (1570), which displays the attempts to overcome the difficulties entailed by the casus irreducibilis.
Описание: This handbook provides a complete overview of the concepts, theories, algorithms, and applications related to robust low-rank and sparse matrix decompositions. It offers a framework for computer vision applications, including image processing and video surveillance, and describes many methods and algorithms to tackle different formulation proble
Автор: Helmut Strade Название: Classifying the Absolute Toral Rank Two Case ISBN: 3110516764 ISBN-13(EAN): 9783110516760 Издательство: Walter de Gruyter Цена: 22305.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
The problem of classifying the finite dimensional simple Lie algebras over fields of characteristic p > 0 is a long standing one. Work on this question has been directed by the Kostrikin Shafarevich Conjecture of 1966, which states that over an algebraically closed field of characteristic p > 5 a finite dimensional restricted simple Lie algebra is classical or of Cartan type. This conjecture was proved for p > 7 by Block and Wilson in 1988. The generalization of the Kostrikin-Shafarevich Conjecture for the general case of not necessarily restricted Lie algebras and p > 7 was announced in 1991 by Strade and Wilson and eventually proved by Strade in 1998. The final Block-Wilson-Strade-Premet Classification Theorem is a landmark result of modern mathematics and can be formulated as follows: Every simple finite dimensional simple Lie algebra over an algebraically closed field of characteristic p > 3 is of classical, Cartan, or Melikian type.
This is the second part of a three-volume book about the classifi cation of the simple Lie algebras over algebraically closed fi elds of characteristic > 3. The first volume contains the methods, examples and a first classification result. This second volume presents insight in the structure of tori of Hamiltonian and Melikian algebras. Based on sandwich element methods due to A. I. Kostrikin and A. A. Premet and the investigations of filtered and graded Lie algebras, a complete proof for the classification of absolute toral rank 2 simple Lie algebras over algebraically closed fields of characteristic > 3 is given.
Contents
Tori in Hamiltonian and Melikian algebras
1-sections
Sandwich elements and rigid tori
Towards graded algebras
The toral rank 2 case
Автор: Hiroshi Konno; Phan Thien Thach; Hoang Tuy Название: Optimization on Low Rank Nonconvex Structures ISBN: 1461368359 ISBN-13(EAN): 9781461368359 Издательство: Springer Рейтинг: Цена: 27950.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This text is an introduction to harmonic analysis on symmetric spaces, focusing on advanced topics such as higher rank spaces, positive definite matrix space and generalizations.
Автор: Viktoria Heu, Frank Loray Название: Flat Rank Two Vector Bundles on Genus Two Curves ISBN: 1470435667 ISBN-13(EAN): 9781470435660 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 12474.00 р. Наличие на складе: Поставка под заказ.
Описание: Examines the moduli space of trace-free irreducible rank 2 connections over a curve of genus 2 and the forgetful map towards the moduli space of underlying vector bundles (including unstable bundles), for which they compute a natural Lagrangian rational section.
This book studies the interplay between the geometry and topology of locally symmetric spaces, and the arithmetic aspects of the special values of L-functions.
The authors study the cohomology of locally symmetric spaces for GL(N) where the cohomology groups are with coefficients in a local system attached to a finite-dimensional algebraic representation of GL(N). The image of the global cohomology in the cohomology of the Borel-Serre boundary is called Eisenstein cohomology, since at a transcendental level the cohomology classes may be described in terms of Eisenstein series and induced representations. However, because the groups are sheaf-theoretically defined, one can control their rationality and even integrality properties. A celebrated theorem by Langlands describes the constant term of an Eisenstein series in terms of automorphic L-functions. A cohomological interpretation of this theorem in terms of maps in Eisenstein cohomology allows the authors to study the rationality properties of the special values of Rankin-Selberg L-functions for GL(n) x GL(m), where n + m = N. The authors carry through the entire program with an eye toward generalizations.
This book should be of interest to advanced graduate students and researchers interested in number theory, automorphic forms, representation theory, and the cohomology of arithmetic groups.
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