Noncommutative Polynomial Algebras of Solvable Type and Their Modules

Noncommutative Polynomial Algebras of Solvable Type and Their Modules

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: Huishi Li

Publisher: CRC Press

ISBN: 9781000471120

Category: Mathematics

Page: 177

View: 209

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.
Categories: Mathematics

Analysis of a Model for Epilepsy

Analysis of a Model for Epilepsy

The Center and Focus Problem Algebraic Solutions and Hypotheses M.N. Popa & V.V. Pricop Abstract Calculus A Categorical Approach Francisco Javier Garcia-Pacheco Noncommutative Polynomial Algebras of Solvable Type and Their Modules Basic ...

Author: Candace M. Kent

Publisher: CRC Press

ISBN: 9781000594430

Category: Mathematics

Page: 172

View: 560

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
Categories: Mathematics

Banach Space Operators On C Probability Spaces Generated by Multi Semicircular Elements

Banach Space Operators On C  Probability Spaces Generated by Multi Semicircular Elements

The Center and Focus Problem Algebraic Solutions and Hypotheses M.N. Popa & V.V. Pricop Abstract Calculus A Categorical Approach Francisco Javier Garcia-Pacheco Noncommutative Polynomial Algebras of Solvable Type and Their Modules Basic ...

Author: Ilwoo Cho

Publisher: CRC Press

ISBN: 9781000600698

Category: Mathematics

Page: 228

View: 760

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
Categories: Mathematics

Level Crossing Problems and Inverse Gaussian Distributions

Level Crossing Problems and Inverse Gaussian Distributions

... Pricop Abstract Calculus A Categorical Approach Francisco Javier Garcia-Pacheco Noncommutative Polynomial Algebras of Solvable Type and Their Modules Basic Constructive-Computational Theory and Methods Huishi Li For more information ...

Author: Vsevolod K. Malinovskii

Publisher: CRC Press

ISBN: 9781000392920

Category: Mathematics

Page: 452

View: 162

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
Categories: Mathematics

Fixed Point Results in W Distance Spaces

Fixed Point Results in W Distance Spaces

... Pricop Abstract Calculus A Categorical Approach Francisco Javier Garcia-Pacheco Noncommutative Polynomial Algebras of Solvable Type and Their Modules Basic Constructive-Computational Theory and Methods Huishi Li Fixed Point Results ...

Author: Vladimir Rakočević

Publisher: CRC Press

ISBN: 9781000489477

Category: Mathematics

Page: 193

View: 409

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.
Categories: Mathematics

Interactions Between Ring Theory and Representations of Algebras

Interactions Between Ring Theory and Representations of Algebras

[ K - RW ] A. Kandri - Rody and V. Weispfenning , Non - commutative Groebner bases in algebras of solvable type , J. Symbolic Computation , 9 ( 1990 ) , 1–26 . [ Li ] Li Huishi , Hilbert polynomial of modules over the homogeneous ...

Author: Freddy Van Oystaeyen

Publisher: CRC Press

ISBN: 0824703677

Category: Mathematics

Page: 470

View: 966

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.
Categories: Mathematics

Computational Commutative and Non commutative Algebraic Geometry

Computational Commutative and Non commutative Algebraic Geometry

[3] Bueso, J.; Gomez Torrecillas, J.; Verschoren, A. Algorithmic methods in noncommutative algebra. ... A.; Ovsienko, S.A.; Futornyj, V.M. On Gelfand-Zetlin modules. ... Non—commutative grobner bases in algebras of solvable type.

Author: Svetlana Cojocaru

Publisher: IOS Press

ISBN: 9781586035051

Category: Electronic books

Page: 337

View: 630

Categories: Electronic books

Solving Polynomial Equation Systems

Solving Polynomial Equation Systems

Hermiller, S. M., McCammond, J., Noncommutative Gröbner Bases for the Commutator Ideal, Int. J. Algebra Comp. ... Kandri-Rody, A., Weispfenning, W., Non-commutative Gröbner Bases in Algebras of Solvable Type, J. Symb. Comp.

Author: Teo Mora

Publisher: Cambridge University Press

ISBN: 9781107109636

Category: Mathematics

Page: 833

View: 318

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

Mathematical Software ICMS 2006

Mathematical Software   ICMS 2006

Available from http://servus.math.su.se/bergman/. Kandri-Rody, A. and Weispfenning, V. Non–commutative Gröbner bases in algebras of solvable type. J. of Symbolic Computation, 9(1):1–26, 1990. Kredel, H. Solvable polynomial rings.

Author: Andres Iglesias

Publisher: Springer

ISBN: 9783540380863

Category: Computers

Page: 452

View: 927

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.
Categories: Computers

Surveys in Differential Algebraic Equations II

Surveys in Differential Algebraic Equations II

16, 319–376 (2005) Cohn, P.: Free Rings and Their Relations. ... Involutive bases of polynomial ideals. Math. ... USA 54, 1503–1508 (1965) Kandry-Rody, A., Weispfenning, V.: Non-commutative Gröbner bases in algebras of solvable type.

Author: Achim Ilchmann

Publisher: Springer

ISBN: 9783319110509

Category: Mathematics

Page: 339

View: 168

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.
Categories: Mathematics