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Algebraic And Algorithmic Aspects Of Differential And Integral Operators
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Book Synopsis Algebraic and Algorithmic Aspects of Differential and Integral Operators by : Moulay Barkatou
Download or read book Algebraic and Algorithmic Aspects of Differential and Integral Operators written by Moulay Barkatou and published by Springer. This book was released on 2014-02-25 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Surveys in Differential-Algebraic Equations II by : Achim Ilchmann
Download or read book Surveys in Differential-Algebraic Equations II written by Achim Ilchmann and published by Springer. This book was released on 2014-12-04 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Algebraic and Symbolic Computation Methods in Dynamical Systems by : Alban Quadrat
Download or read book Algebraic and Symbolic Computation Methods in Dynamical Systems written by Alban Quadrat and published by Springer Nature. This book was released on 2020-05-30 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims at reviewing recent progress in the direction of algebraic and symbolic computation methods for functional systems, e.g. ODE systems, differential time-delay equations, difference equations and integro-differential equations. In the nineties, modern algebraic theories were introduced in mathematical systems theory and in control theory. Combined with real algebraic geometry, which was previously introduced in control theory, the past years have seen a flourishing development of algebraic methods in control theory. One of the strengths of algebraic methods lies in their close connections to computations. The use of the above-mentioned algebraic theories in control theory has been an important source of motivation to develop effective versions of these theories (when possible). With the development of computer algebra and computer algebra systems, symbolic methods for control theory have been developed over the past years. The goal of this book is to propose a partial state of the art in this direction. To make recent results more easily accessible to a large audience, the chapters include materials which survey the main mathematical methods and results and which are illustrated with explicit examples.
Book Synopsis D-Finite Functions by : Manuel Kauers
Download or read book D-Finite Functions written by Manuel Kauers and published by Springer Nature. This book was released on 2023-11-08 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: Defined as solutions of linear differential or difference equations with polynomial coefficients, D-finite functions play an important role in various areas of mathematics. This book is a comprehensive introduction to the theory of these functions with a special emphasis on computer algebra algorithms for computing with them: algorithms for detecting relations from given data, for evaluating D-finite functions, for executing closure properties, for obtaining various kinds of “explicit” expressions, for factoring operators, and for definite and indefinite symbolic summation and integration are explained in detail. The book comes “with batteries included” in the sense that it requires no background in computer algebra as the relevant facts from this area are summarized in the beginning. This makes the book accessible to a wide range of readers, from mathematics students who plan to work themselves on D-finite functions to researchers who want to apply the theory to their own work. Hundreds of exercises invite the reader to apply the techniques in the book and explore further aspects of the theory on their own. Solutions to all exercises are given in the appendix. When algorithms for D-finite functions came up in the early 1990s, computer proofs were met with a certain skepticism. Fortunately, these times are over and computer algebra has become a standard tool for many mathematicians. Yet, this powerful machinery is still not as widely known as it deserves. This book helps to spread the word that certain tasks can be safely delegated to a computer algebra system, and also what the limitations of these techniques are.
Book Synopsis Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers by : Kenji Iohara
Download or read book Two Algebraic Byways from Differential Equations: Gröbner Bases and Quivers written by Kenji Iohara and published by Springer Nature. This book was released on 2020-02-20 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edited volume presents a fascinating collection of lecture notes focusing on differential equations from two viewpoints: formal calculus (through the theory of Gröbner bases) and geometry (via quiver theory). Gröbner bases serve as effective models for computation in algebras of various types. Although the theory of Gröbner bases was developed in the second half of the 20th century, many works on computational methods in algebra were published well before the introduction of the modern algebraic language. Since then, new algorithms have been developed and the theory itself has greatly expanded. In comparison, diagrammatic methods in representation theory are relatively new, with the quiver varieties only being introduced – with big impact – in the 1990s. Divided into two parts, the book first discusses the theory of Gröbner bases in their commutative and noncommutative contexts, with a focus on algorithmic aspects and applications of Gröbner bases to analysis on systems of partial differential equations, effective analysis on rings of differential operators, and homological algebra. It then introduces representations of quivers, quiver varieties and their applications to the moduli spaces of meromorphic connections on the complex projective line. While no particular reader background is assumed, the book is intended for graduate students in mathematics, engineering and related fields, as well as researchers and scholars.
Book Synopsis Skew PBW Extensions by : William Fajardo
Download or read book Skew PBW Extensions written by William Fajardo and published by Springer Nature. This book was released on 2020-12-11 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to a new class of non-commutative rings, skew Poincaré–Birkhoff–Witt (PBW) extensions. Beginning with the basic definitions and ring-module theoretic/homological properties, it goes on to investigate finitely generated projective modules over skew PBW extensions from a matrix point of view. To make this theory constructive, the theory of Gröbner bases of left (right) ideals and modules for bijective skew PBW extensions is developed. For example, syzygies and the Ext and Tor modules over these rings are computed. Finally, applications to some key topics in the noncommutative algebraic geometry of quantum algebras are given, including an investigation of semi-graded Koszul algebras and semi-graded Artin–Schelter regular algebras, and the noncommutative Zariski cancellation problem. The book is addressed to researchers in noncommutative algebra and algebraic geometry as well as to graduate students and advanced undergraduate students.
Book Synopsis Rings, Modules and Codes by : André Leroy
Download or read book Rings, Modules and Codes written by André Leroy and published by American Mathematical Soc.. This book was released on 2019-04-12 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Orthogonal Polynomials by : Mama Foupouagnigni
Download or read book Orthogonal Polynomials written by Mama Foupouagnigni and published by Springer Nature. This book was released on 2020-03-11 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents contributions of international and local experts from the African Institute for Mathematical Sciences (AIMS-Cameroon) and also from other local universities in the domain of orthogonal polynomials and applications. The topics addressed range from univariate to multivariate orthogonal polynomials, from multiple orthogonal polynomials and random matrices to orthogonal polynomials and Painlevé equations. The contributions are based on lectures given at the AIMS-Volkswagen Stiftung Workshop on Introduction of Orthogonal Polynomials and Applications held on October 5–12, 2018 in Douala, Cameroon. This workshop, funded within the framework of the Volkswagen Foundation Initiative "Symposia and Summer Schools", was aimed globally at promoting capacity building in terms of research and training in orthogonal polynomials and applications, discussions and development of new ideas as well as development and enhancement of networking including south-south cooperation.
Book Synopsis Geometric Methods in Physics by : Piotr Kielanowski
Download or read book Geometric Methods in Physics written by Piotr Kielanowski and published by Birkhäuser. This book was released on 2015-09-21 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a selection of papers based on the XXXIII Białowieża Workshop on Geometric Methods in Physics, 2014. The Białowieża Workshops are among the most important meetings in the field and attract researchers from both mathematics and physics. The articles gathered here are mathematically rigorous and have important physical implications, addressing the application of geometry in classical and quantum physics. Despite their long tradition, the workshops remain at the cutting edge of ongoing research. For the last several years, each Białowieża Workshop has been followed by a School on Geometry and Physics, where advanced lectures for graduate students and young researchers are presented; some of the lectures are reproduced here. The unique atmosphere of the workshop and school is enhanced by its venue, framed by the natural beauty of the Białowieża forest in eastern Poland. The volume will be of interest to researchers and graduate students in mathematical physics, theoretical physics and mathematmtics.
Book Synopsis Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory by : Gebhard Böckle
Download or read book Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory written by Gebhard Böckle and published by Springer. This book was released on 2018-03-22 with total page 753 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents state-of-the-art research and survey articles that highlight work done within the Priority Program SPP 1489 “Algorithmic and Experimental Methods in Algebra, Geometry and Number Theory”, which was established and generously supported by the German Research Foundation (DFG) from 2010 to 2016. The goal of the program was to substantially advance algorithmic and experimental methods in the aforementioned disciplines, to combine the different methods where necessary, and to apply them to central questions in theory and practice. Of particular concern was the further development of freely available open source computer algebra systems and their interaction in order to create powerful new computational tools that transcend the boundaries of the individual disciplines involved. The book covers a broad range of topics addressing the design and theoretical foundations, implementation and the successful application of algebraic algorithms in order to solve mathematical research problems. It offers a valuable resource for all researchers, from graduate students through established experts, who are interested in the computational aspects of algebra, geometry, and/or number theory.
Book Synopsis Pseudodifferential Operators and Applications by : Francois Treves
Download or read book Pseudodifferential Operators and Applications written by Francois Treves and published by American Mathematical Soc.. This book was released on 1985 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Proceedings of the Symposium on Pseudodifferential Operators and Fourier Integral Operators with Applications to Partial Differential Equations held at the University of Notre Dame, Notre Dame, Indiana, April 2-5, 1984"--T.p. verso.
Book Synopsis Applications of Computer Algebra by : Ilias S. Kotsireas
Download or read book Applications of Computer Algebra written by Ilias S. Kotsireas and published by Springer. This book was released on 2017-07-26 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Applications of Computer Algebra (ACA) conference covers a wide range of topics from Coding Theory to Differential Algebra to Quantam Computing, focusing on the interactions of these and other areas with the discipline of Computer Algebra. This volume provides the latest developments in the field as well as its applications in various domains, including communications, modelling, and theoretical physics. The book will appeal to researchers and professors of computer algebra, applied mathematics, and computer science, as well as to engineers and computer scientists engaged in research and development.
Book Synopsis Aspects of Algorithmic Algebra by : Raimundas Vidūnas
Download or read book Aspects of Algorithmic Algebra written by Raimundas Vidūnas and published by . This book was released on 1999 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computer Algebra in Scientific Computing by : Vladimir P. Gerdt
Download or read book Computer Algebra in Scientific Computing written by Vladimir P. Gerdt and published by Springer. This book was released on 2009-09-30 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing, CASC 2009, held in Kobe, Japan, in September 2009. The 28 revised full papers presented together with 2 invited lectures were carefully reviewed and selected from numerous submissions. The topics addressed are all basic areas of scientific computing as they benefit from the application of computer algebra methods and software. The papers cover computer algebra methods and algorithms, application of symbolic and algebraic manipulation, and CA methods and results for the numerical integration of the partial differential equations of the mathematical physics.
Book Synopsis Anti-Differentiation and the Calculation of Feynman Amplitudes by : Johannes Blümlein
Download or read book Anti-Differentiation and the Calculation of Feynman Amplitudes written by Johannes Blümlein and published by Springer Nature. This book was released on 2021-11-26 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises review papers presented at the Conference on Antidifferentiation and the Calculation of Feynman Amplitudes, held in Zeuthen, Germany, in October 2020, and a few additional invited reviews. The book aims at comprehensive surveys and new innovative results of the analytic integration methods of Feynman integrals in quantum field theory. These methods are closely related to the field of special functions and their function spaces, the theory of differential equations and summation theory. Almost all of these algorithms have a strong basis in computer algebra. The solution of the corresponding problems are connected to the analytic management of large data in the range of Giga- to Terabytes. The methods are widely applicable to quite a series of other branches of mathematics and theoretical physics.
Book Synopsis A Treatise on Differential Equations by : George Boole
Download or read book A Treatise on Differential Equations written by George Boole and published by . This book was released on 1859 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is an aspect of Boole's work that is not closely related to his treatises in logic or the theory of sets but which is familiar to every student of differential equations. This is the algorithm of differential operators, which he introduced to facilitate the treatment of linear differential equations. If, for example, we wish to solve the differential equation ay + by + cy = 0, the equation is written in the notation (aD2 + bD + c)y = 0. Then, regarding D as an unknown quantity rather than an operator, we solve the algebraic quadratic equation aD2 + bD + c = 0. There are many other situations in which Boole, in his Treatise on Differential Equations of 1859, pointed out parallels between the properties of the differential operator (and its inverse) and the rules of algebra. British mathematicians in the second half of the nineteenth century were thus again becoming leaders in algorithmic analysis, a field in which, fifty years earlier, they had been badly deficient.
Book Synopsis Pseudo-Differential Operators and Generalized Functions by : Stevan Pilipović
Download or read book Pseudo-Differential Operators and Generalized Functions written by Stevan Pilipović and published by Birkhäuser. This book was released on 2015-04-27 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers peer-reviewed contributions representing modern trends in the theory of generalized functions and pseudo-differential operators. It is dedicated to Professor Michael Oberguggenberger (Innsbruck University, Austria) in honour of his 60th birthday. The topics covered were suggested by the ISAAC Group in Generalized Functions (GF) and the ISAAC Group in Pseudo-Differential Operators (IGPDO), which met at the 9th ISAAC congress in Krakow, Poland in August 2013. Topics include Columbeau algebras, ultra-distributions, partial differential equations, micro-local analysis, harmonic analysis, global analysis, geometry, quantization, mathematical physics, and time-frequency analysis. Featuring both essays and research articles, the book will be of great interest to graduate students and researchers working in analysis, PDE and mathematical physics, while also offering a valuable complement to the volumes on this topic previously published in the OT series.
