Polynomial Identities in Algebras, Di Vincenzo Onofrio Mario, Giambruno Antonio
Автор: Anjos Название: Handbook on Semidefinite, Conic and Polynomial Optimization ISBN: 1461407680 ISBN-13(EAN): 9781461407683 Издательство: Springer Рейтинг: Цена: 163040.00 T Наличие на складе: Есть Описание: Semidefinite and conic optimization is a major and thriving research area within the optimization community. Although semidefinite optimization has been studied (under different names) since at least the 1940s, its importance grew immensely during the 1990s after polynomial-time interior-point methods for linear optimization were extended to solve semidefinite optimization problems. Since the beginning of the 21st century, not only has research into semidefinite and conic optimization continued unabated, but also a fruitful interaction has developed with algebraic geometry through the close connections between semidefinite matrices and polynomial optimization. This has brought about important new results and led to an even higher level of research activity. This Handbook on Semidefinite, Conic and Polynomial Optimization provides the reader with a snapshot of the state-of-the-art in the growing and mutually enriching areas of semidefinite optimization, conic optimization, and polynomial optimization. It contains a compendium of the recent research activity that has taken place in these thrilling areas, and will appeal to doctoral students, young graduates, and experienced researchers alike. The Handbook’s thirty-one chapters are organized into four parts:Theory, covering significant theoretical developments as well as the interactions between conic optimization and polynomial optimization;Algorithms, documenting the directions of current algorithmic development;Software, providing an overview of the state-of-the-art;Applications, dealing with the application areas where semidefinite and conic optimization has made a significant impact in recent years.
Автор: Smith, Larry Название: Polynomial Invariants of Finite Groups ISBN: 0367449137 ISBN-13(EAN): 9780367449131 Издательство: Taylor&Francis Рейтинг: Цена: 65320.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This is a book about the invariant theory of finite groups, written by an algebraic topologist. It illustrates the theorems by applying them to concrete cases, and examines several basic ideas and problems of invariant theory in the context of some elementary examples.
Автор: Peter Borwein; Tamas Erdelyi Название: Polynomials and Polynomial Inequalities ISBN: 1461269024 ISBN-13(EAN): 9781461269021 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Polynomials pervade mathematics, virtually every branch of mathematics from algebraic number theory and algebraic geometry to applied analysis and computer science, has a corpus of theory arising from polynomials. The material explored in this book primarily concerns polynomials as they arise in analysis; it focuses on polynomials and rational functions of a single variable. The book is self-contained and assumes at most a senior-undergraduate familiarity with real and complex analysis. After an introduction to the geometry of polynomials and a discussion of refinements of the Fundamental Theorem of Algebra, the book turns to a consideration of various special polynomials. Chebyshev and Descartes systems are then introduced, and Muntz systems and rational systems are examined in detail. Subsequent chapters discuss denseness questions and the inequalities satisfied by polynomials and rational functions. Appendices on algorithms and computational concerns, on the interpolation theorem, and on orthogonality and irrationality conclude the book.
Автор: Amitai Regev, Antonio Giambruno, Claudio Procesi, Eli Aljadeff Название: Rings with Polynomial Identities and Finite Dimensional Representations of Algebras ISBN: 1470451743 ISBN-13(EAN): 9781470451745 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 82770.00 T Наличие на складе: Поставка под заказ. Описание: A polynomial identity for an algebra (or a ring) $A$ is a polynomial in noncommutative variables that vanishes under any evaluation in $A$. An algebra satisfying a nontrivial polynomial identity is called a PI algebra, and this is the main object of study in this book, which can be used by graduate students and researchers alike. The book is divided into four parts. Part 1 contains foundational material on representation theory and noncommutative algebra. In addition to setting the stage for the rest of the book, this part can be used for an introductory course in noncommutative algebra. An expert reader may use Part 1 as reference and start with the main topics in the remaining parts. Part 2 discusses the combinatorial aspects of the theory, the growth theorem, and Shirshov's bases. Here methods of representation theory of the symmetric group play a major role. Part 3 contains the main body of structure theorems for PI algebras, theorems of Kaplansky and Posner, the theory of central polynomials, M. Artin's theorem on Azumaya algebras, and the geometric part on the variety of semisimple representations, including the foundations of the theory of Cayley-Hamilton algebras. Part 4 is devoted first to the proof of the theorem of Razmyslov, Kemer, and Braun on the nilpotency of the nil radical for finitely generated PI algebras over Noetherian rings, then to the theory of Kemer and the Specht problem. Finally, the authors discuss PI exponent and codimension growth. This part uses some nontrivial analytic tools coming from probability theory. The appendix presents the counterexamples of Golod and Shafarevich to the Burnside problem.
Автор: Kanel-Belov, Alexei , Karasik, Yakov , Rowen, Lo Название: Computational Aspects of Polynomial Identities ISBN: 0367445808 ISBN-13(EAN): 9780367445805 Издательство: Taylor&Francis Рейтинг: Цена: 65320.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This edition presents the underlying ideas in recent polynomial identity (PI)-theory and demonstrates the validity of the proofs of PI-theorems. It gives all the details involved in Kemer`s proof of Specht`s conjecture for affine PI-algebras in characteristic 0. This edition presents a tighter formulation of Zubrilin`s theory and contains a more
Автор: Kanel-Belov, Alexei , Rowen, Louis Halle Название: Computational Aspects of Polynomial Identities ISBN: 0367446502 ISBN-13(EAN): 9780367446505 Издательство: Taylor&Francis Рейтинг: Цена: 63280.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book introduces polynomial identity (PI)-algebras and reviews some well-known results and techniques, most of which are associated with the structure theory. It presents a full proof of Kemer`s solution to Specht`s conjecture.
Автор: Teo Mora Название: Solving Polynomial Equation Systems I ISBN: 0521811546 ISBN-13(EAN): 9780521811545 Издательство: Cambridge Academ Рейтинг: Цена: 183750.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Mora covers the classical theory of finding roots of a univariate polynomial, emphasising computational aspects. He shows that solving a polynomial equation really means finding algorithms that help one manipulate roots rather than simply computing them; to that end he also surveys algorithms for factorizing univariate polynomials.
Автор: Ronald de Haan Название: Parameterized Complexity in the Polynomial Hierarchy ISBN: 3662606690 ISBN-13(EAN): 9783662606698 Издательство: Springer Рейтинг: Цена: 68930.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: For problems at higher levels of the PH, a promising solving approach is to develop fixed-parameter tractable reductions to SAT, and to subsequently use a SAT solving algorithm to solve the problem.
Автор: Peter Stefanidis; Andrzej P. Paplinski; Michael J. Название: Numerical Operations with Polynomial Matrices ISBN: 3540549927 ISBN-13(EAN): 9783540549925 Издательство: Springer Рейтинг: Цена: 104480.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The purpose of this monograph is to describe a class of com-putational methods, based on polynomial matrices, for thedesign of dynamic compensators for linear multi-variablecontrol systems.
Автор: Dhananjay Singh; Madhusudan Singh; Zaynidinov Haki Название: Signal Processing Applications Using Multidimensional Polynomial Splines ISBN: 9811322384 ISBN-13(EAN): 9789811322389 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book highlights new methods, algorithms and software for the digital processing and recovery of signals. In addition, it describes a new method for modeling one dimensional and multidimensional signals as successions of local polynomial splines and their spectral characteristics. It provides examples of how the proposed methods can be applied in specific cases, together with signal processing software examples in the MATLAB environment, and models of special processes in the Simulink environment. The book’s goal is to make it easier for beginners to understand the subject matter; it is intended for engineers, undergraduate and graduate students engaged in research or the evaluation and design of hardware and software for the digital processing and recovery of signals.
Автор: Lucian Trifina; Daniela Tarniceriu Название: Permutation Polynomial Interleavers for Turbo Codes ISBN: 9811347980 ISBN-13(EAN): 9789811347986 Издательство: Springer Рейтинг: Цена: 139750.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book investigates the permutation polynomial (PP) based interleavers for turbo codes, including all the main theoretical and practical findings related to topics such as full coefficient conditions for PPs up to fifth; the number of all true different PPs up to fifth degree; the number of true different PPs under Zhao and Fan sufficient conditions, for any degree (with direct formulas or with a simple algorithm); parallel decoding of turbo codes using PP interleavers by butterfly networks; upper bounds of the minimum distance for turbo codes with PP interleavers; specific methods to design and find PP interleavers with good bit/frame error rate (BER/FER) performance. The theoretical results are explained in great detail to enhance readers’ understanding. The book is intended for engineers in the telecommunications field, but the chapters dealing with the PP coefficient conditions and with the number of PP are of interest to mathematicians working in the field.
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