Computer Algebra Methods For Equivariant Dynamical Systems
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Computer Algebra Methods For Equivariant Dynamical Systems
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Author : Karin Gatermann
language : en
Publisher: Springer
Release Date : 2007-05-06
Computer Algebra Methods For Equivariant Dynamical Systems written by Karin Gatermann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-06 with Mathematics categories.
This book starts with an overview of the research of Gröbner bases which have many applications in various areas of mathematics since they are a general tool for the investigation of polynomial systems. The next chapter describes algorithms in invariant theory including many examples and time tables. These techniques are applied in the chapters on symmetric bifurcation theory and equivariant dynamics. This combination of different areas of mathematics will be interesting to researchers in computational algebra and/or dynamics.
Computer Algebra Handbook
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Author : Johannes Grabmeier
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Computer Algebra Handbook written by Johannes Grabmeier and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
Two ideas lie gleaming on the jeweler's velvet. The first is the calculus, the sec ond, the algorithm. The calculus and the rich body of mathematical analysis to which it gave rise made modern science possible; but it has been the algorithm that has made possible the modern world. -David Berlinski, The Advent of the Algorithm First there was the concept of integers, then there were symbols for integers: I, II, III, 1111, fttt (what might be called a sticks and stones representation); I, II, III, IV, V (Roman numerals); 1, 2, 3, 4, 5 (Arabic numerals), etc. Then there were other concepts with symbols for them and algorithms (sometimes) for ma nipulating the new symbols. Then came collections of mathematical knowledge (tables of mathematical computations, theorems of general results). Soon after algorithms came devices that provided assistancefor carryingout computations. Then mathematical knowledge was organized and structured into several related concepts (and symbols): logic, algebra, analysis, topology, algebraic geometry, number theory, combinatorics, etc. This organization and abstraction lead to new algorithms and new fields like universal algebra. But always our symbol systems reflected and influenced our thinking, our concepts, and our algorithms.
Normal Forms And Unfoldings For Local Dynamical Systems
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Author : James Murdock
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-10
Normal Forms And Unfoldings For Local Dynamical Systems written by James Murdock and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-10 with Mathematics categories.
The subject of local dynamical systems is concerned with the following two questions: 1. Given an n×n matrix A, describe the behavior, in a neighborhood of the origin, of the solutions of all systems of di?erential equations having a rest point at the origin with linear part Ax, that is, all systems of the form x ? = Ax+··· , n where x? R and the dots denote terms of quadratic and higher order. 2. Describethebehavior(neartheorigin)ofallsystemsclosetoasystem of the type just described. To answer these questions, the following steps are employed: 1. A normal form is obtained for the general system with linear part Ax. The normal form is intended to be the simplest form into which any system of the intended type can be transformed by changing the coordinates in a prescribed manner. 2. An unfolding of the normal form is obtained. This is intended to be the simplest form into which all systems close to the original s- tem can be transformed. It will contain parameters, called unfolding parameters, that are not present in the normal form found in step 1. vi Preface 3. The normal form, or its unfolding, is truncated at some degree k, and the behavior of the truncated system is studied.
Ergodic Theory Analysis And Efficient Simulation Of Dynamical Systems
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Author : Bernold Fiedler
language : en
Publisher: Springer Science & Business Media
Release Date : 2001
Ergodic Theory Analysis And Efficient Simulation Of Dynamical Systems written by Bernold Fiedler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
This book summarizes and highlights progress in Dynamical Systems achieved during six years of the German Priority Research Program "Ergotic Theory, Analysis, and Efficient Simulation of Dynamical Systems", funded by the Deutsche Forschungsgemeinschaft (DFG). The three fundamental topics of large time behavior, dimension, and measure are tackled with by a rich circle of uncompromisingly rigorous mathematical concepts. The range of applied issues comprises such diverse areas as crystallization and dendrite growth, the dynamo effect, efficient simulation of biomolecules, fluid dynamics and reacting flows, mechanical problems involving friction, population biology, the spread of infectious diseases, and quantum chaos. The surveys in the book are addressed to experts and non-experts in the mathematical community alike. In addition they intend to convey the significance of the results for applications fair into the neighboring disciplines of Science.
Gorenstein Dimensions
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Author : Lars W. Christensen
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-11-06
Gorenstein Dimensions written by Lars W. Christensen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-11-06 with Mathematics categories.
This book is intended as a reference for mathematicians working with homological dimensions in commutative algebra and as an introduction to Gorenstein dimensions for graduate students with an interest in the same. Any admirer of classics like the Auslander-Buchsbaum-Serre characterization of regular rings, and the Bass and Auslander-Buchsbaum formulas for injective and projective dimension of f.g. modules will be intrigued by this book's content. Readers should be well-versed in commutative algebra and standard applications of homological methods. The framework is that of complexes, but all major results are restated for modules in traditional notation, and an appendix makes the proofs accessible for even the casual user of hyperhomological methods.
Forward Backward Stochastic Differential Equations And Their Applications
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Author : Jin Ma
language : en
Publisher: Springer
Release Date : 2007-04-24
Forward Backward Stochastic Differential Equations And Their Applications written by Jin Ma and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-24 with Mathematics categories.
This volume is a survey/monograph on the recently developed theory of forward-backward stochastic differential equations (FBSDEs). Basic techniques such as the method of optimal control, the 'Four Step Scheme', and the method of continuation are presented in full. Related topics such as backward stochastic PDEs and many applications of FBSDEs are also discussed in detail. The volume is suitable for readers with basic knowledge of stochastic differential equations, and some exposure to the stochastic control theory and PDEs. It can be used for researchers and/or senior graduate students in the areas of probability, control theory, mathematical finance, and other related fields.
Yetter Drinfel D Hopf Algebras Over Groups Of Prime Order
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Author : Yorck Sommerhäuser
language : en
Publisher: Springer
Release Date : 2004-10-19
Yetter Drinfel D Hopf Algebras Over Groups Of Prime Order written by Yorck Sommerhäuser and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-19 with Mathematics categories.
Being the first monograph devoted to this subject, the book addresses the classification problem for semisimple Hopf algebras, a field that has attracted considerable attention in the last years. The special approach to this problem taken here is via semidirect product decompositions into Yetter-Drinfel'd Hopf algebras and group rings of cyclic groups of prime order. One of the main features of the book is a complete treatment of the structure theory for such Yetter-Drinfel'd Hopf algebras.
Bifurcations In Hamiltonian Systems
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Author : Henk Broer
language : en
Publisher: Springer
Release Date : 2003-01-01
Bifurcations In Hamiltonian Systems written by Henk Broer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-01-01 with Mathematics categories.
The authors consider applications of singularity theory and computer algebra to bifurcations of Hamiltonian dynamical systems. They restrict themselves to the case were the following simplification is possible. Near the equilibrium or (quasi-) periodic solution under consideration the linear part allows approximation by a normalized Hamiltonian system with a torus symmetry. It is assumed that reduction by this symmetry leads to a system with one degree of freedom. The volume focuses on two such reduction methods, the planar reduction (or polar coordinates) method and the reduction by the energy momentum mapping. The one-degree-of-freedom system then is tackled by singularity theory, where computer algebra, in particular, Gröbner basis techniques, are applied. The readership addressed consists of advanced graduate students and researchers in dynamical systems.
Noncommutative Gr Bner Bases And Filtered Graded Transfer
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Author : Huishi Li
language : en
Publisher: Springer
Release Date : 2004-10-19
Noncommutative Gr Bner Bases And Filtered Graded Transfer written by Huishi Li and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-19 with Mathematics categories.
This self-contained monograph is the first to feature the intersection of the structure theory of noncommutative associative algebras and the algorithmic aspect of Groebner basis theory. A double filtered-graded transfer of data in using noncommutative Groebner bases leads to effective exploitation of the solutions to several structural-computational problems, e.g., an algorithmic recognition of quadric solvable polynomial algebras, computation of GK-dimension and multiplicity for modules, and elimination of variables in noncommutative setting. All topics included deal with algebras of (q-)differential operators as well as some other operator algebras, enveloping algebras of Lie algebras, typical quantum algebras, and many of their deformations.
Characters And Cyclotomic Fields In Finite Geometry
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Author : Bernhard Schmidt
language : en
Publisher: Springer
Release Date : 2004-10-13
Characters And Cyclotomic Fields In Finite Geometry written by Bernhard Schmidt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-13 with Mathematics categories.
This monograph contributes to the existence theory of difference sets, cyclic irreducible codes and similar objects. The new method of field descent for cyclotomic integers of presribed absolute value is developed. Applications include the first substantial progress towards the Circulant Hadamard Matrix Conjecture and Ryser`s conjecture since decades. It is shown that there is no Barker sequence of length l with 13