Noncommutative Polynomial Algebras Of Solvable Type And Their Modules

Author : Huishi Li
Publisher : CRC Press
Page : 177 pages
File Size : 41,7 Mb
Release : 2021-11-08
Category : Mathematics
ISBN : 9781000471120

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Noncommutative Polynomial Algebras of Solvable Type and Their Modules by Huishi Li Pdf

Noncommutative Polynomial Algebras of Solvable Type and Their Modules is the first book to systematically introduce the basic constructive-computational theory and methods developed for investigating solvable polynomial algebras and their modules. In doing so, this book covers: A constructive introduction to solvable polynomial algebras and Gröbner basis theory for left ideals of solvable polynomial algebras and submodules of free modules The new filtered-graded techniques combined with the determination of the existence of graded monomial orderings The elimination theory and methods (for left ideals and submodules of free modules) combining the Gröbner basis techniques with the use of Gelfand-Kirillov dimension, and the construction of different kinds of elimination orderings The computational construction of finite free resolutions (including computation of syzygies, construction of different kinds of finite minimal free resolutions based on computation of different kinds of minimal generating sets), etc. This book is perfectly suited to researchers and postgraduates researching noncommutative computational algebra and would also be an ideal resource for teaching an advanced lecture course.

Author : Pham Loi Vu
Publisher : CRC Press
Page : 453 pages
File Size : 47,9 Mb
Release : 2023-05-15
Category : Mathematics
ISBN : 9781000872057

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Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations by Pham Loi Vu Pdf

Inverse Scattering Problems and Their Applications to Nonlinear Integrable Equations, Second Edition is devoted to inverse scattering problems (ISPs) for differential equations and their applications to nonlinear evolution equations (NLEEs). The book is suitable for anyone who has a mathematical background and interest in functional analysis, differential equations, and equations of mathematical physics. This book is intended for a wide community working with ISPs and their applications. There is an especially strong traditional community in mathematical physics. In this monograph, the problems are presented step-by-step, and detailed proofs are given for considered problems to make the topics more accessible for students who are approaching them for the first time. New to the Second Edition All new chapter dealing with the Bäcklund transformations between a common solution of both linear equations in the Lax pair and the solution of the associated IBVP for NLEEs on the half-line Updated references and concluding remarks Features Solving the direct and ISP, then solving the associated initial value problem (IVP) or initial-boundary value problem (IBVP) for NLEEs are carried out step-by-step. The unknown boundary values are calculated with the help of the Lax (generalized) equations, then the time-dependent scattering data (SD) are expressed in terms of preassigned initial and boundary conditions. Thereby, the potential functions are recovered uniquely in terms of the given initial and calculated boundary conditions. The unique solvability of the ISP is proved and the SD of the scattering problem is described completely. The considered ISPs are well-solved. The ISPs are set up appropriately for constructing the Bӓckhund transformations (BTs) for solutions of associated IBVPs or IVPs for NLEEs. The procedure for finding a BT for the IBVP for NLEEs on the half-line differs from the one used for obtaining a BT for non-linear differential equations defined in the whole space. The interrelations between the ISPs and the constructed BTs are established to become new powerful unified transformations (UTs) for solving IBVPs or IVPs for NLEEs, that can be used in different areas of physics and mechanics. The application of the UTs is consistent and efficiently embedded in the scheme of the associated ISP.

Author : Candace M. Kent,David M. Chan
Publisher : CRC Press
Page : 261 pages
File Size : 40,8 Mb
Release : 2022-06-07
Category : Mathematics
ISBN : 9781000594430

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Analysis of a Model for Epilepsy by Candace M. Kent,David M. Chan Pdf

In the 1960s and 1970s, mathematical biologists Sir Robert M. May, E.C. Pielou, and others utilized difference equations as models of ecological and epidemiological phenomena. Since then, with or without applications, the mathematics of difference equations has evolved into a field unto itself. Difference equations with the maximum (or the minimum or the "rank-type") function were rigorously investigated from the mid-1990s into the 2000s, without any applications in mind. These equations often involved arguments varying from reciprocal terms with parameters in the numerators to other special functions. Recently, the authors of Analysis of a Model for Epilepsy: Application of a Max-Type Difference Equation to Mesial Temporal Lobe Epilepsy and their colleagues investigated the first known application of a "max-type" difference equation. Their equation is a phenomenological model of epileptic seizures. In this book, the authors expand on that research and present a more comprehensive development of mathematical, numerical, and biological results. Additionally, they describe the first documented instance of a novel dynamical behavior that they call rippled almost periodic behavior, which can be described as an unpredictable pseudo-periodic behavior. Features: Suitable for researchers in mathematical neuroscience and potentially as supplementary reading for postgraduate students Thoroughly researched and replete with references

Author : Ilwoo Cho
Publisher : CRC Press
Page : 228 pages
File Size : 46,7 Mb
Release : 2022-07-04
Category : Mathematics
ISBN : 9781000600698

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Banach-Space Operators On C*-Probability Spaces Generated by Multi Semicircular Elements by Ilwoo Cho Pdf

Banach-Space Operators On C*-Probability Spaces Generated by Multi Semicircular Elements introduces new areas in operator theory and operator algebra, in connection with free probability theory. In particular, the book considers projections and partial isometries distorting original free-distributional data on the C∗-probability spaces. Features Suitable for graduate students and professional researchers in operator theory and/or analysis. Numerous applications in related scientific fields and areas

Author : Vsevolod K. Malinovskii
Publisher : CRC Press
Page : 453 pages
File Size : 44,7 Mb
Release : 2021-07-25
Category : Mathematics
ISBN : 9781000392920

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Level-Crossing Problems and Inverse Gaussian Distributions by Vsevolod K. Malinovskii Pdf

Primarily aimed at researchers and postgraduates, but may be of interest to some professionals working in related fields, such as the insurance industry Suitable as supplementary reading for a standard course in applied probability Requires minimal prerequisites in mathematical analysis and probability theory

Author : Vladimir Rakočević
Publisher : CRC Press
Page : 195 pages
File Size : 53,9 Mb
Release : 2021-12-30
Category : Mathematics
ISBN : 9781000496161

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Fixed Point Results in W-Distance Spaces by Vladimir Rakočević Pdf

Fixed Point Results in W-Distance Spaces is a self-contained and comprehensive reference for advanced fixed-point theory and can serve as a useful guide for related research. The book can be used as a teaching resource for advanced courses on fixed-point theory, which is a modern and important field in mathematics. It would be especially valuable for graduate and postgraduate courses and seminars. Features Written in a concise and fluent style, covers a broad range of topics and includes related topics from research. Suitable for researchers and postgraduates. Contains brand new results not published elsewhere.

Author : Freddy Van Oystaeyen,Manolo Saorin
Publisher : CRC Press
Page : 470 pages
File Size : 42,9 Mb
Release : 2000-04-05
Category : Mathematics
ISBN : 0824703677

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Interactions Between Ring Theory and Representations of Algebras by Freddy Van Oystaeyen,Manolo Saorin Pdf

This work is based on a set of lectures and invited papers presented at a meeting in Murcia, Spain, organized by the European Commission's Training and Mobility of Researchers (TMR) Programme. It contains information on the structure of representation theory of groups and algebras and on general ring theoretic methods related to the theory.

Author : Svetlana Cojocaru,Gerhard Pfister,Victor Ufnarovski
Publisher : IOS Press
Page : 336 pages
File Size : 50,6 Mb
Release : 2005
Category : Electronic books
ISBN : 9781586035051

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Computational Commutative and Non-commutative Algebraic Geometry by Svetlana Cojocaru,Gerhard Pfister,Victor Ufnarovski Pdf

Author : Achim Ilchmann,Timo Reis
Publisher : Springer
Page : 343 pages
File Size : 47,6 Mb
Release : 2014-12-04
Category : Mathematics
ISBN : 9783319110509

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Surveys in Differential-Algebraic Equations II by Achim Ilchmann,Timo Reis Pdf

The present volume comprises survey articles on various fields of Differential-Algebraic Equations (DAEs), which have widespread applications in controlled dynamical systems, especially in mechanical and electrical engineering and a strong relation to (ordinary) differential equations. The individual chapters provide reviews, presentations of the current state of research and new concepts in - Observers for DAEs - DAEs in chemical processes - Optimal control of DAEs - DAEs from a functional-analytic viewpoint - Algebraic methods for DAEs The results are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study.

Author : Andres Iglesias,Nobuki Takayama
Publisher : Springer
Page : 467 pages
File Size : 47,6 Mb
Release : 2006-08-31
Category : Computers
ISBN : 9783540380863

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Mathematical Software - ICMS 2006 by Andres Iglesias,Nobuki Takayama Pdf

This book constitutes the refereed proceedings of the Second International Congress on Mathematical Software, ICMS 2006. The book presents 45 revised full papers, carefully reviewed and selected for presentation. The papers are organized in topical sections on new developments in computer algebra packages, interfacing computer algebra in mathematical visualization, software for algebraic geometry and related topics, number-theoretical software, methods in computational number theory, free software for computer algebra, and general issues.

Author : Teo Mora
Publisher : Cambridge University Press
Page : 833 pages
File Size : 51,8 Mb
Release : 2003
Category : Mathematics
ISBN : 9781107109636

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Solving Polynomial Equation Systems by Teo Mora Pdf

Covers extensions of Buchberger's Theory and Algorithm, and promising recent alternatives to Gröbner bases.

Author : Moulay Barkatou,Thomas Cluzeau,Georg Regensburger,Markus Rosenkranz
Publisher : Springer
Page : 210 pages
File Size : 49,5 Mb
Release : 2014-02-25
Category : Computers
ISBN : 9783642544798

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Algebraic and Algorithmic Aspects of Differential and Integral Operators by Moulay Barkatou,Thomas Cluzeau,Georg Regensburger,Markus Rosenkranz Pdf

This book constitutes the proceedings of the 5th International Meeting on Algebraic and Algorithmic Aspects of Differential and Integral Operators, AADIOS 2012, held at the Applications of Computer Algebra Conference in Sofia, Bulgaria, on June 25-28, 2012. The total of 9 papers presented in this volume consists of 2 invited papers and 7 regular papers which were carefully reviewed and selected from 13 submissions. The topics of interest are: symbolic computation for operator algebras, factorization of differential/integral operators, linear boundary problems and green's operators, initial value problems for differential equations, symbolic integration and differential galois theory, symbolic operator calculi, algorithmic D-module theory, rota-baxter algebra, differential algebra, as well as discrete analogs and software aspects of the above.

Author : André Leroy,Christian Lomp,Sergio López-Permouth,Frédérique Oggier
Publisher : American Mathematical Soc.
Page : 355 pages
File Size : 40,7 Mb
Release : 2019-04-12
Category : Modules (Algebra)
ISBN : 9781470441043

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Rings, Modules and Codes by André Leroy,Christian Lomp,Sergio López-Permouth,Frédérique Oggier Pdf

This book contains the proceedings of the Fifth International Conference on Noncommutative Rings and their Applications, held from June 12–15, 2017, at the University of Artois, Lens, France. The papers are related to noncommutative rings, covering topics such as: ring theory, with both the elementwise and more structural approaches developed; module theory with popular topics such as automorphism invariance, almost injectivity, ADS, and extending modules; and coding theory, both the theoretical aspects such as the extension theorem and the more applied ones such as Construction A or Reed–Muller codes. Classical topics like enveloping skewfields, weak Hopf algebras, and tropical algebras are also presented.

Author : Manuel Bronstein,Johannes Grabmeier,Volker Weispfenning
Publisher : Birkhäuser
Page : 291 pages
File Size : 43,7 Mb
Release : 2013-03-11
Category : Computers
ISBN : 9783034888004

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Symbolic Rewriting Techniques by Manuel Bronstein,Johannes Grabmeier,Volker Weispfenning Pdf

Symbolic rewriting techniques are methods for deriving consequences from systems of equations, and are of great use when investigating the structure of the solutions. Such techniques appear in many important areas of research within computer algebra: • the Knuth-Bendix completion for groups, monoids and general term-rewriting systems, • the Buchberger algorithm for Gröbner bases, • the Ritt-Wu characteristic set method for ordinary differential equations, and • the Riquier-Janet method for partial differential equations. This volume contains invited and contributed papers to the Symbolic Rewriting Techniques workshop, which was held at the Centro Stefano Franscini in Ascona, Switzerland, from April 30 to May 4, 1995. That workshop brought together 40 researchers from various areas of rewriting techniques, the main goal being the investigation of common threads and methods. Following the workshops, each contribution was formally refereed and 14 papers were selected for publication.

Author : Oleksandr Motsak
Publisher : Sudwestdeutscher Verlag Fur Hochschulschriften AG
Page : 168 pages
File Size : 47,6 Mb
Release : 2011
Category : Electronic
ISBN : 3838127528

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Non-commutative Computer Algebra with applications by Oleksandr Motsak Pdf

This book that represents the author's Ph.D. thesis is devoted to constructive module theory of polynomial graded commutative algebras over a field. It treats the theory of Grobner bases, standard bases (SB) and syzygies as well as algorithms and their implementations over graded commutative algebras, which naturally unify exterior and commutative polynomial algebras. They are graded non-commutative, associative unital algebras over fields and may contain zero-divisors. In this book we try to make the most use out of a-priori knowledge about their characteristic (super-commutative) structure in developing direct symbolic methods, algorithms and implementations, which are intrinsic to these algebras and practically efficient. We also tackle their central localizations by generalizing a variation of Mora algorithm. In this setting we prove a generalized Buchberger's criterion, which shows that syzygies of leading terms play the utmost important role in SB and syzygy computations. We develop a variation of the La Scala-Stillman free resolution algorithm. Benchmarks show that our new algorithms and implementation are efficient. We give some applications of the developed framework.