Computational Noncommutative Algebra And Applications

Author : Jim Byrnes
Publisher : Springer Science & Business Media
ISBN 13 : 1402023073
Total Pages : 435 pages
Book Rating : 4.71/5 ( download)

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Download or read book Computational Noncommutative Algebra and Applications written by Jim Byrnes and published by Springer Science & Business Media. This book was released on 2006-01-28 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fusion of algebra, analysis and geometry, and their application to real world problems, have been dominant themes underlying mathematics for over a century. Geometric algebras, introduced and classified by Clifford in the late 19th century, have played a prominent role in this effort, as seen in the mathematical work of Cartan, Brauer, Weyl, Chevelley, Atiyah, and Bott, and in applications to physics in the work of Pauli, Dirac and others. One of the most important applications of geometric algebras to geometry is to the representation of groups of Euclidean and Minkowski rotations. This aspect and its direct relation to robotics and vision will be discussed in several chapters of this multi-authored textbook, which resulted from the ASI meeting. Moreover, group theory, beginning with the work of Burnside, Frobenius and Schur, has been influenced by even more general problems. As a result, general group actions have provided the setting for powerful methods within group theory and for the use of groups in applications to physics, chemistry, molecular biology, and signal processing. These aspects, too, will be covered in detail. With the rapidly growing importance of, and ever expanding conceptual and computational demands on signal and image processing in remote sensing, computer vision, medical image processing, and biological signal processing, and on neural and quantum computing, geometric algebras, and computational group harmonic analysis, the topics of the book have emerged as key tools. The list of authors includes many of the world's leading experts in the development of new algebraic modeling and signal representation methodologies, novel Fourier-based and geometrictransforms, and computational algorithms required for realizing the potential of these new application fields. The intention of this textbook is share their profound wisdom with the many future stars of pure and computational noncommutative algebra. A key feature of both the meeting and the book will be their presentation of problems and applications that will shape the twenty-first century computational technology base.

Author : Martin Kreuzer
Publisher : Springer Science & Business Media
ISBN 13 : 3540706283
Total Pages : 326 pages
Book Rating : 4.81/5 ( download)

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Download or read book Computational Commutative Algebra 1 written by Martin Kreuzer and published by Springer Science & Business Media. This book was released on 2008-07-05 with total page 326 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to polynomial rings, Gröbner bases and applications bridges the gap in the literature between theory and actual computation. It details numerous applications, covering fields as disparate as algebraic geometry and financial markets. To aid in a full understanding of these applications, more than 40 tutorials illustrate how the theory can be used. The book also includes many exercises, both theoretical and practical.

Author : Huishi Li
Publisher : CRC Press
ISBN 13 : 1000471128
Total Pages : 177 pages
Book Rating : 4.20/5 ( download)

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Download or read book Noncommutative Polynomial Algebras of Solvable Type and Their Modules written by Huishi Li and published by CRC Press. This book was released on 2021-11-08 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Svetlana Cojocaru
Publisher : IOS Press
ISBN 13 : 1586035053
Total Pages : 336 pages
Book Rating : 4.51/5 ( download)

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Download or read book Computational Commutative and Non-commutative Algebraic Geometry written by Svetlana Cojocaru and published by IOS Press. This book was released on 2005 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : S. Cojocaru
Publisher :
ISBN 13 : 9781607501121
Total Pages : 336 pages
Book Rating : 4.20/5 ( download)

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Download or read book Computational Commutative and Non-Commutative Algebraic Geometry written by S. Cojocaru and published by . This book was released on 2005 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: This publication gives a good insight in the interplay between commutative and non-commutative algebraic geometry. The theoretical and computational aspects are the central theme in this study. The topic is looked at from different perspectives in over 20 lecture reports. It emphasizes the current trends in commutative and non-commutative algebraic geometry and algebra. The contributors to this publication present the most recent and state-of-the-art progresses which reflect the topic discussed in this publication. Both researchers and graduate students will find this book a good source of information on commutative and non-commutative algebraic geometry.

Author : Sergey I. Kumkov
Publisher : Springer Nature
ISBN 13 : 3030375145
Total Pages : 195 pages
Book Rating : 4.40/5 ( download)

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Download or read book Advances in Information Technologies, Telecommunication, and Radioelectronics written by Sergey I. Kumkov and published by Springer Nature. This book was released on 2020-02-04 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to problems of information technologies (description and processing signals, especially ones corrupted by noises and disturbances) and to problems of telecommunications and production of advanced equipment in radio-electronics developed at the Ural Federal University, Ekaterinburg, Russia. It describes the contemporary state of the art and the development of methods for solving problems of signal processing and building equipment for practical solutions. The volume is mainly a collection of ideas, techniques and results in the field of video information technologies and various related applications of numerical methods. It comprises 18 chapters grouped under four main topics: image processing and computer vision, signal processing and navigation, simulation of some practical processes and computations for antennas, and applications of microwaves. The research described in this volume is addressed to a wide audience of scientists, engineers and mathematicians involved in the above mentioned four scientific topics.

Author : Emil Prodan
Publisher : Springer
ISBN 13 : 3319550233
Total Pages : 118 pages
Book Rating : 4.37/5 ( download)

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Download or read book A Computational Non-commutative Geometry Program for Disordered Topological Insulators written by Emil Prodan and published by Springer. This book was released on 2017-03-17 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents a computational program based on the principles of non-commutative geometry and showcases several applications to topological insulators. Noncommutative geometry has been originally proposed by Jean Bellissard as a theoretical framework for the investigation of homogeneous condensed matter systems. Recently, this approach has been successfully applied to topological insulators, where it facilitated many rigorous results concerning the stability of the topological invariants against disorder.In the first part of the book the notion of a homogeneous material is introduced and the class of disordered crystals defined together with the classification table, which conjectures all topological phases from this class. The manuscript continues with a discussion of electrons’ dynamics in disordered crystals and the theory of topological invariants in the presence of strong disorder is briefly reviewed. It is shown how all this can be captured in the language of noncommutative geometry using the concept of non-commutative Brillouin torus, and a list of known formulas for various physical response functions is presented. In the second part, auxiliary algebras are introduced and a canonical finite-volume approximation of the non-commutative Brillouin torus is developed. Explicit numerical algorithms for computing generic correlation functions are discussed. In the third part upper bounds on the numerical errors are derived and it is proved that the canonical-finite volume approximation converges extremely fast to the thermodynamic limit. Convergence tests and various applications concludes the presentation.The book is intended for graduate students and researchers in numerical and mathematical physics.

Author : Dmitry I. Ignatov
Publisher : Springer
ISBN 13 : 331952920X
Total Pages : 386 pages
Book Rating : 4.02/5 ( download)

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Download or read book Analysis of Images, Social Networks and Texts written by Dmitry I. Ignatov and published by Springer. This book was released on 2017-02-15 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 5th International Conference on Analysis of Images, Social Networks and Texts, AIST 2016, held in Yekaterinburg, Russia, in April 2016. The 23 full papers, 7 short papers, and 3 industrial papers were carefully reviewed and selected from 142 submissions. The papers are organized in topical sections on machine learning and data analysis; social networks; natural language processing; analysis of images and video.

Author : Mihai Putinar
Publisher : Springer Science & Business Media
ISBN 13 : 0387096868
Total Pages : 382 pages
Book Rating : 4.65/5 ( download)

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Download or read book Emerging Applications of Algebraic Geometry written by Mihai Putinar and published by Springer Science & Business Media. This book was released on 2008-12-10 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent advances in both the theory and implementation of computational algebraic geometry have led to new, striking applications to a variety of fields of research. The articles in this volume highlight a range of these applications and provide introductory material for topics covered in the IMA workshops on "Optimization and Control" and "Applications in Biology, Dynamics, and Statistics" held during the IMA year on Applications of Algebraic Geometry. The articles related to optimization and control focus on burgeoning use of semidefinite programming and moment matrix techniques in computational real algebraic geometry. The new direction towards a systematic study of non-commutative real algebraic geometry is well represented in the volume. Other articles provide an overview of the way computational algebra is useful for analysis of contingency tables, reconstruction of phylogenetic trees, and in systems biology. The contributions collected in this volume are accessible to non-experts, self-contained and informative; they quickly move towards cutting edge research in these areas, and provide a wealth of open problems for future research.

Author : Klaus G. Fischer
Publisher : Routledge
ISBN 13 : 135145899X
Total Pages : 272 pages
Book Rating : 4.93/5 ( download)

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Download or read book Computational Algebra written by Klaus G. Fischer and published by Routledge. This book was released on 2018-02-19 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the fifth Mid-Atlantic Algebra Conference held recently at George Mason University, Fairfax, Virginia. Focuses on both the practical and theoretical aspects of computational algebra. Demonstrates specific computer packages, including the use of CREP to study the representation of theory for finite dimensional algebras and Axiom to study algebras of finite rank.