Noncommutative Polynomial Algebras Of Solvable Type And Their Modules
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Noncommutative Polynomial Algebras Of Solvable Type And Their Modules
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Author : Huishi Li
language : en
Publisher: CRC Press
Release Date : 2021-11-08
Noncommutative Polynomial Algebras Of Solvable Type And Their Modules written by Huishi Li and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-08 with Mathematics categories.
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.
Noncommutative Polynomial Algebras Of Solvable Type And Their Modules
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Author : Huishi Li
language : en
Publisher: CRC Press
Release Date : 2021-11-07
Noncommutative Polynomial Algebras Of Solvable Type And Their Modules written by Huishi Li and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-07 with Mathematics categories.
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.
Inverse Scattering Problems And Their Application To Nonlinear Integrable Equations
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Author : Pham Loi Vu
language : en
Publisher: CRC Press
Release Date : 2023-05-15
Inverse Scattering Problems And Their Application To Nonlinear Integrable Equations written by Pham Loi Vu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-15 with Mathematics categories.
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.
Analysis Of A Model For Epilepsy
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Author : Candace M. Kent
language : en
Publisher: CRC Press
Release Date : 2022-06-07
Analysis Of A Model For Epilepsy written by Candace M. Kent and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-07 with Mathematics categories.
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
Banach Space Operators On C Probability Spaces Generated By Multi Semicircular Elements
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Author : Ilwoo Cho
language : en
Publisher: CRC Press
Release Date : 2022-07-04
Banach Space Operators On C Probability Spaces Generated By Multi Semicircular Elements written by Ilwoo Cho and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-04 with Mathematics categories.
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
Fixed Point Results In W Distance Spaces
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Author : Vladimir Rakočević
language : en
Publisher: CRC Press
Release Date : 2021-12-30
Fixed Point Results In W Distance Spaces written by Vladimir Rakočević and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-12-30 with Mathematics categories.
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.
Level Crossing Problems And Inverse Gaussian Distributions
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Author : Vsevolod K. Malinovskii
language : en
Publisher: CRC Press
Release Date : 2021-07-25
Level Crossing Problems And Inverse Gaussian Distributions written by Vsevolod K. Malinovskii and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-25 with Mathematics categories.
Level-Crossing Problems and Inverse Gaussian Distributions: Closed-Form Results and Approximations focusses on the inverse Gaussian approximation for the distribution of the first level-crossing time in a shifted compound renewal process framework. This approximation, whose name was coined by the author, is a successful competitor of the normal (or Cramér's), diffusion, and Teugels’ approximations, being a breakthrough in its conditions and accuracy. Since such approximations underlie numerous applications in risk theory, queueing theory, reliability theory, and mathematical theory of dams and inventories, this book is of interest not only to professional mathematicians, but also to physicists, engineers, and economists. People from industry with a theoretical background in level-crossing problems, e.g., from the insurance industry, can also benefit from reading this book. Features: Primarily aimed at researchers and postgraduates, but may be of interest to some professionals working in related fields, such as the insurance industry Suitable for advanced courses in Applied Probability and, as a supplementary reading, for basic courses in Applied Probability
Interactions Between Ring Theory And Representations Of Algebras
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Author : Freddy Van Oystaeyen
language : en
Publisher: CRC Press
Release Date : 2000-04-05
Interactions Between Ring Theory And Representations Of Algebras written by Freddy Van Oystaeyen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-05 with Mathematics categories.
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.
Computational Commutative And Non Commutative Algebraic Geometry
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Author : Svetlana Cojocaru
language : en
Publisher: IOS Press
Release Date : 2005
Computational Commutative And Non Commutative Algebraic Geometry written by Svetlana Cojocaru and has been published by IOS Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Electronic books categories.
Surveys In Differential Algebraic Equations Ii
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Author : Achim Ilchmann
language : en
Publisher: Springer
Release Date : 2014-12-04
Surveys In Differential Algebraic Equations Ii written by Achim Ilchmann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-04 with Mathematics categories.
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.