Commutation Relations Normal Ordering And Stirling Numbers
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Commutation Relations Normal Ordering And Stirling Numbers
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Author : Toufik Mansour
language : en
Publisher: CRC Press
Release Date : 2015-09-18
Commutation Relations Normal Ordering And Stirling Numbers written by Toufik Mansour and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-18 with Mathematics categories.
Commutation Relations, Normal Ordering, and Stirling Numbers provides an introduction to the combinatorial aspects of normal ordering in the Weyl algebra and some of its close relatives. The Weyl algebra is the algebra generated by two letters U and V subject to the commutation relation UV - VU = I. It is a classical result that normal ordering pow
Algebraic Structures And Applications
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Author : Sergei Silvestrov
language : en
Publisher: Springer Nature
Release Date : 2020-06-18
Algebraic Structures And Applications written by Sergei Silvestrov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-18 with Mathematics categories.
This book explores the latest advances in algebraic structures and applications, and focuses on mathematical concepts, methods, structures, problems, algorithms and computational methods important in the natural sciences, engineering and modern technologies. In particular, it features mathematical methods and models of non-commutative and non-associative algebras, hom-algebra structures, generalizations of differential calculus, quantum deformations of algebras, Lie algebras and their generalizations, semi-groups and groups, constructive algebra, matrix analysis and its interplay with topology, knot theory, dynamical systems, functional analysis, stochastic processes, perturbation analysis of Markov chains, and applications in network analysis, financial mathematics and engineering mathematics. The book addresses both theory and applications, which are illustrated with a wealth of ideas, proofs and examples to help readers understand the material and develop new mathematical methods and concepts of their own. The high-quality chapters share a wealth of new methods and results, review cutting-edge research and discuss open problems and directions for future research. Taken together, they offer a source of inspiration for a broad range of researchers and research students whose work involves algebraic structures and their applications, probability theory and mathematical statistics, applied mathematics, engineering mathematics and related areas.
Combinatorics And Number Theory Of Counting Sequences
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Author : Istvan Mezo
language : en
Publisher: CRC Press
Release Date : 2019-08-19
Combinatorics And Number Theory Of Counting Sequences written by Istvan Mezo and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-19 with Computers categories.
Combinatorics and Number Theory of Counting Sequences is an introduction to the theory of finite set partitions and to the enumeration of cycle decompositions of permutations. The presentation prioritizes elementary enumerative proofs. Therefore, parts of the book are designed so that even those high school students and teachers who are interested in combinatorics can have the benefit of them. Still, the book collects vast, up-to-date information for many counting sequences (especially, related to set partitions and permutations), so it is a must-have piece for those mathematicians who do research on enumerative combinatorics. In addition, the book contains number theoretical results on counting sequences of set partitions and permutations, so number theorists who would like to see nice applications of their area of interest in combinatorics will enjoy the book, too. Features The Outlook sections at the end of each chapter guide the reader towards topics not covered in the book, and many of the Outlook items point towards new research problems. An extensive bibliography and tables at the end make the book usable as a standard reference. Citations to results which were scattered in the literature now become easy, because huge parts of the book (especially in parts II and III) appear in book form for the first time.
Mathematical Analysis And Applications Ii
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Author : Hari M. Srivastava
language : en
Publisher: MDPI
Release Date : 2020-03-19
Mathematical Analysis And Applications Ii written by Hari M. Srivastava and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-19 with Mathematics categories.
This issue is a continuation of the previous successful Special Issue “Mathematical Analysis and Applications”
Non Commutative And Non Associative Algebra And Analysis Structures
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Author : Sergei Silvestrov
language : en
Publisher: Springer Nature
Release Date : 2023-09-25
Non Commutative And Non Associative Algebra And Analysis Structures written by Sergei Silvestrov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-25 with Mathematics categories.
The goal of the 2019 conference on Stochastic Processes and Algebraic Structures held in SPAS2019, Västerås, Sweden, from September 30th to October 2nd 2019 was to showcase the frontiers of research in several important topics of mathematics, mathematical statistics, and its applications. The conference has been organized along the following tracks: 1. Stochastic processes and modern statistical methods in theory and practice, 2. Engineering Mathematics, 3. Algebraic Structures and applications. This book highlights the latest advances in algebraic structures and applications focused on mathematical notions, methods, structures, concepts, problems, algorithms, and computational methods for the natural sciences, engineering, and modern technology. In particular, the book features mathematical methods and models from non-commutative and non-associative algebras and rings associated to generalizations of differential calculus, quantum deformations of algebras, Lie algebras, Lie superalgebras, color Lie algebras, Hom-algebras and their n-ary generalizations, semi-groups and group algebras, non-commutative and non-associative algebras and computational algebra interplay with q-special functions and q-analysis, topology, dynamical systems, representation theory, operator theory and functional analysis, applications of algebraic structures in coding theory, information analysis, geometry and probability theory. The book gathers selected, high-quality contributed chapters from several large research communities working on modern algebraic structures and their applications. The chapters cover both theory and applications, and are illustrated with a wealth of ideas, theorems, notions, proofs, examples, open problems, and results on the interplay of algebraic structures with other parts of Mathematics. The applications help readers grasp the material, and encourage them to develop new mathematical methods and concepts in their future research. Presenting new methods and results, reviews of cutting-edge research, open problems, and directions for future research, will serve as a source of inspiration for a broad range of researchers and students.
Stirling Polynomials In Several Indeterminates
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Author : Alfred Schreiber
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2021-02-10
Stirling Polynomials In Several Indeterminates written by Alfred Schreiber and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-10 with Mathematics categories.
The classical exponential polynomials, today commonly named after E.,T. Bell, have a wide range of remarkable applications in Combinatorics, Algebra, Analysis, and Mathematical Physics. Within the algebraic framework presented in this book they appear as structural coefficients in finite expansions of certain higher-order derivative operators. In this way, a correspondence between polynomials and functions is established, which leads (via compositional inversion) to the specification and the effective computation of orthogonal companions of the Bell polynomials. Together with the latter, one obtains the larger class of multivariate `Stirling polynomials'. Their fundamental recurrences and inverse relations are examined in detail and shown to be directly related to corresponding identities for the Stirling numbers. The following topics are also covered: polynomial families that can be represented by Bell polynomials; inversion formulas, in particular of Schlömilch-Schläfli type; applications to binomial sequences; new aspects of the Lagrange inversion, and, as a highlight, reciprocity laws, which unite a polynomial family and that of orthogonal companions. Besides a Mathematica(R) package and an extensive bibliography, additional material is compiled in a number of notes and supplements.
Crossing Numbers Of Graphs
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Author : Marcus Schaefer
language : en
Publisher: CRC Press
Release Date : 2018-01-02
Crossing Numbers Of Graphs written by Marcus Schaefer and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-02 with Mathematics categories.
Crossing Numbers of Graphs is the first book devoted to the crossing number, an increasingly popular object of study with surprising connections. The field has matured into a large body of work, which includes identifiable core results and techniques. The book presents a wide variety of ideas and techniques in topological graph theory, discrete geometry, and computer science. The first part of the text deals with traditional crossing number, crossing number values, crossing lemma, related parameters, computational complexity, and algorithms. The second part includes the rich history of alternative crossing numbers, the rectilinear crossing number, the pair crossing number, and the independent odd crossing number.It also includes applications of the crossing number outside topological graph theory. Aimed at graduate students and professionals in both mathematics and computer science The first book of its kind devoted to the topic Authored by a noted authority in crossing numbers
Stochastic Processes Statistical Methods And Engineering Mathematics
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Author : Anatoliy Malyarenko
language : en
Publisher: Springer Nature
Release Date : 2023-01-26
Stochastic Processes Statistical Methods And Engineering Mathematics written by Anatoliy Malyarenko and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-26 with Mathematics categories.
The goal of the 2019 conference on Stochastic Processes and Algebraic Structures held in SPAS2019, Västerås, Sweden, from September 30th to October 2nd 2019, was to showcase the frontiers of research in several important areas of mathematics, mathematical statistics, and its applications. The conference was organized around the following topics 1. Stochastic processes and modern statistical methods,2. Engineering mathematics,3. Algebraic structures and their applications. The conference brought together a select group of scientists, researchers, and practitioners from the industry who are actively contributing to the theory and applications of stochastic, and algebraic structures, methods, and models. The conference provided early stage researchers with the opportunity to learn from leaders in the field, to present their research, as well as to establish valuable research contacts in order to initiate collaborations in Sweden and abroad. New methods for pricing sophisticated financial derivatives, limit theorems for stochastic processes, advanced methods for statistical analysis of financial data, and modern computational methods in various areas of applied science can be found in this book. The principal reason for the growing interest in these questions comes from the fact that we are living in an extremely rapidly changing and challenging environment. This requires the quick introduction of new methods, coming from different areas of applied science. Advanced concepts in the book are illustrated in simple form with the help of tables and figures. Most of the papers are self-contained, and thus ideally suitable for self-study. Solutions to sophisticated problems located at the intersection of various theoretical and applied areas of the natural sciences are presented in these proceedings.
Proceedings Of The 3rd International Symposium Quantum Theory And Symmetries
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Author : Philip C. Argyres
language : en
Publisher: World Scientific
Release Date : 2004
Proceedings Of The 3rd International Symposium Quantum Theory And Symmetries written by Philip C. Argyres and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Science categories.
The book contains the text of lectures given at the third of a series of biennial symposia in mathematical physics held in odd-numbered years. The subject of the symposium is the frontiers of mathematical physics. It deals with quantum phenomena and includes topics such as string theory and quantum gravity, particle physics and field theory, non-communative geometry, integrable models and infinite dimensional symmetry groups, quantum computing and information processing, and quantum chaos.The proceedings have been selected for coverage in: ? Index to Scientific & Technical Proceedings? (ISTP? / ISI Proceedings)? Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)? CC Proceedings ? Engineering & Physical Sciences
Introduction To Combinatorics
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Author : Walter D. Wallis
language : en
Publisher: CRC Press
Release Date : 2016-12-12
Introduction To Combinatorics written by Walter D. Wallis and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-12 with Mathematics categories.
What Is Combinatorics Anyway? Broadly speaking, combinatorics is the branch of mathematics dealing with different ways of selecting objects from a set or arranging objects. It tries to answer two major kinds of questions, namely, counting questions: how many ways can a selection or arrangement be chosen with a particular set of properties; and structural questions: does there exist a selection or arrangement of objects with a particular set of properties? The authors have presented a text for students at all levels of preparation. For some, this will be the first course where the students see several real proofs. Others will have a good background in linear algebra, will have completed the calculus stream, and will have started abstract algebra. The text starts by briefly discussing several examples of typical combinatorial problems to give the reader a better idea of what the subject covers. The next chapters explore enumerative ideas and also probability. It then moves on to enumerative functions and the relations between them, and generating functions and recurrences., Important families of functions, or numbers and then theorems are presented. Brief introductions to computer algebra and group theory come next. Structures of particular interest in combinatorics: posets, graphs, codes, Latin squares, and experimental designs follow. The authors conclude with further discussion of the interaction between linear algebra and combinatorics. Features Two new chapters on probability and posets. Numerous new illustrations, exercises, and problems. More examples on current technology use A thorough focus on accuracy Three appendices: sets, induction and proof techniques, vectors and matrices, and biographies with historical notes, Flexible use of MapleTM and MathematicaTM