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Hypernumbers And Extrafunctions
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Book Synopsis Hypernumbers and Extrafunctions by : Mark Burgin
Download or read book Hypernumbers and Extrafunctions written by Mark Burgin and published by Springer Science & Business Media. This book was released on 2012-05-16 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: “Hypernumbers and Extrafunctions” presents a rigorous mathematical approach to operate with infinite values. First, concepts of real and complex numbers are expanded to include a new universe of numbers called hypernumbers which includes infinite quantities. This brief extends classical calculus based on real functions by introducing extrafunctions, which generalize not only the concept of a conventional function but also the concept of a distribution. Extrafucntions have been also efficiently used for a rigorous mathematical definition of the Feynman path integral, as well as for solving some problems in probability theory, which is also important for contemporary physics. This book introduces a new theory that includes the theory of distributions as a subtheory, providing more powerful tools for mathematics and its applications. Specifically, it makes it possible to solve PDE for which it is proved that they do not have solutions in distributions. Also illustrated in this text is how this new theory allows the differentiation and integration of any real function. This text can be used for enhancing traditional courses of calculus for undergraduates, as well as for teaching a separate course for graduate students.
Book Synopsis Semitopological Vector Spaces by : Mark Burgin
Download or read book Semitopological Vector Spaces written by Mark Burgin and published by CRC Press. This book was released on 2017-06-26 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new volume shows how it is possible to further develop and essentially extend the theory of operators in infinite-dimensional vector spaces, which plays an important role in mathematics, physics, information theory, and control theory. The book describes new mathematical structures, such as hypernorms, hyperseminorms, hypermetrics, semitopological vector spaces, hypernormed vector spaces, and hyperseminormed vector spaces. It develops mathematical tools for the further development of functional analysis and broadening of its applications. Exploration of semitopological vector spaces, hypernormed vector spaces, hyperseminormed vector spaces, and hypermetric vector spaces is the main topic of this book. A new direction in functional analysis, called quantum functional analysis, has been developed based on polinormed and multinormed vector spaces and linear algebras. At the same time, normed vector spaces and topological vector spaces play an important role in physics and in control theory. To make this book comprehendible for the reader and more suitable for students with some basic knowledge in mathematics, denotations and definitions of the main mathematical concepts and structures used in the book are included in the appendix, making the book useful for enhancing traditional courses of calculus for undergraduates, as well as for separate courses for graduate students. The material of Semitopological Vector Spaces: Hypernorms, Hyperseminorms and Operators is closely related to what is taught at colleges and universities. It is possible to use a definite number of statements from the book as exercises for students because their proofs are not given in the book but left for the reader.
Book Synopsis Advances in Inequalities for Series by : Sever Silvestru Dragomir
Download or read book Advances in Inequalities for Series written by Sever Silvestru Dragomir and published by Nova Publishers. This book was released on 2008 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research monograph, deals with identities and inequalities relating to series and their application. This is the first volume of research monographs on advances in inequalities for series. All of the papers in this volume have been fully peer reviewed. Some papers in this volume appear in print for the first time, detailing many technical results and some other papers offer a review of a number of recently published results. The papers appear in author alphabetical order and not in mathematics subject classification. There are fifteen diverse papers in this volume each with its own speciality. An important issue in many applications of Probability Theory is finding an approximate measure of distance, or discrimination, between two probability distributions. A number of divergence measures for this purpose have been proposed.
Book Synopsis Stochastic Processes and Functional Analysis by : Alan C. Krinik
Download or read book Stochastic Processes and Functional Analysis written by Alan C. Krinik and published by CRC Press. This book was released on 2004-03-23 with total page 526 pages. Available in PDF, EPUB and Kindle. Book excerpt: This extraordinary compilation is an expansion of the recent American Mathematical Society Special Session celebrating M. M. Rao's distinguished career and includes most of the presented papers as well as ancillary contributions from session invitees. This book shows the effectiveness of abstract analysis for solving fundamental problems of stochas
Book Synopsis Trilogy Of Numbers And Arithmetic - Book 1: History Of Numbers And Arithmetic: An Information Perspective by : Mark Burgin
Download or read book Trilogy Of Numbers And Arithmetic - Book 1: History Of Numbers And Arithmetic: An Information Perspective written by Mark Burgin and published by World Scientific. This book was released on 2022-04-22 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is the first in the trilogy which will bring you to the fascinating world of numbers and operations with them. Numbers provide information about myriads of things. Together with operations, numbers constitute arithmetic forming in basic intellectual instruments of theoretical and practical activity of people and offering powerful tools for representation, acquisition, transmission, processing, storage, and management of information about the world.The history of numbers and arithmetic is the topic of a variety of books and at the same time, it is extensively presented in many books on the history of mathematics. However, all of them, at best, bring the reader to the end of the 19th century without including the developments in these areas in the 20th century and later. Besides, such books consider and describe only the most popular classes of numbers, such as whole numbers or real numbers. At the same time, a diversity of new classes of numbers and arithmetic were introduced in the 20th century.This book looks into the chronicle of numbers and arithmetic from ancient times all the way to 21st century. It also includes the developments in these areas in the 20th century and later. A unique aspect of this book is its information orientation of the exposition of the history of numbers and arithmetic.
Book Synopsis Theory of Information by : Mark Burgin
Download or read book Theory of Information written by Mark Burgin and published by World Scientific. This book was released on 2010 with total page 689 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a fresh approach to scientific understanding of information phenomena. Based on an analysis of information processes in nature, technology, and society, as well as on the main directions in information theory, this book offers a theory that synthesizes various directions into a unified system.
Book Synopsis Theory Of Knowledge: Structures And Processes by : Mark Burgin
Download or read book Theory Of Knowledge: Structures And Processes written by Mark Burgin and published by World Scientific. This book was released on 2016-10-27 with total page 965 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to synthesize different directions in knowledge studies into a unified theory of knowledge and knowledge processes. It explicates important relations between knowledge and information. It provides the readers with understanding of the essence and structure of knowledge, explicating operations and process that are based on knowledge and vital for society.The book also highlights how the theory of knowledge paves the way for more advanced design and utilization of computers and networks.
Book Synopsis Non-diophantine Arithmetics In Mathematics, Physics And Psychology by : Mark Burgin
Download or read book Non-diophantine Arithmetics In Mathematics, Physics And Psychology written by Mark Burgin and published by World Scientific. This book was released on 2020-11-04 with total page 960 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a long time, all thought there was only one geometry — Euclidean geometry. Nevertheless, in the 19th century, many non-Euclidean geometries were discovered. It took almost two millennia to do this. This was the major mathematical discovery and advancement of the 19th century, which changed understanding of mathematics and the work of mathematicians providing innovative insights and tools for mathematical research and applications of mathematics.A similar event happened in arithmetic in the 20th century. Even longer than with geometry, all thought there was only one conventional arithmetic of natural numbers — the Diophantine arithmetic, in which 2+2=4 and 1+1=2. It is natural to call the conventional arithmetic by the name Diophantine arithmetic due to the important contributions to arithmetic by Diophantus. Nevertheless, in the 20th century, many non-Diophantine arithmetics were discovered, in some of which 2+2=5 or 1+1=3. It took more than two millennia to do this. This discovery has even more implications than the discovery of new geometries because all people use arithmetic.This book provides a detailed exposition of the theory of non-Diophantine arithmetics and its various applications. Reading this book, the reader will see that on the one hand, non-Diophantine arithmetics continue the ancient tradition of operating with numbers while on the other hand, they introduce extremely original and innovative ideas.
Book Synopsis Abstracts of Papers Presented to the American Mathematical Society by : American Mathematical Society
Download or read book Abstracts of Papers Presented to the American Mathematical Society written by American Mathematical Society and published by . This book was released on 2008 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Reviews written by and published by . This book was released on 2006 with total page 900 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Neoclassical Analysis by : Mark Semenovich Burgin
Download or read book Neoclassical Analysis written by Mark Semenovich Burgin and published by . This book was released on 2007 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neoclassical analysis extends methods of classical calculus to reflect uncertainties that arise in computations and measurements. In it, ordinary structures of analysis, that is, functions, sequences, series, and operators, are studied by means of fuzzy concepts: fuzzy limits, fuzzy continuity, and fuzzy derivatives. For example, continuous functions, which are studied in the classical analysis, become a part of the set of the fuzzy continuous functions studied in neoclassical analysis. Aiming at representation of uncertainties and imprecision and extending the scope of the classical calculus and analysis, neoclassical analysis makes, at the same time, methods of the classical calculus more precise with respect to real life applications. Consequently, new results are obtained extending and even completing classical theorems. In addition, facilities of analytical methods for various applications also become more broad and efficient.
Book Synopsis An Introduction to the Theory of Surreal Numbers by : Harry Gonshor
Download or read book An Introduction to the Theory of Surreal Numbers written by Harry Gonshor and published by Cambridge University Press. This book was released on 1986-09-18 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes provide a formal introduction to the theory of surreal numbers in a clear and lucid style.
Book Synopsis Semitopological Vector Spaces by : Mark Burgin
Download or read book Semitopological Vector Spaces written by Mark Burgin and published by CRC Press. This book was released on 2017-06-26 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new volume shows how it is possible to further develop and essentially extend the theory of operators in infinite-dimensional vector spaces, which plays an important role in mathematics, physics, information theory, and control theory. The book describes new mathematical structures, such as hypernorms, hyperseminorms, hypermetrics, semitopological vector spaces, hypernormed vector spaces, and hyperseminormed vector spaces. It develops mathematical tools for the further development of functional analysis and broadening of its applications. Exploration of semitopological vector spaces, hypernormed vector spaces, hyperseminormed vector spaces, and hypermetric vector spaces is the main topic of this book. A new direction in functional analysis, called quantum functional analysis, has been developed based on polinormed and multinormed vector spaces and linear algebras. At the same time, normed vector spaces and topological vector spaces play an important role in physics and in control theory. To make this book comprehendible for the reader and more suitable for students with some basic knowledge in mathematics, denotations and definitions of the main mathematical concepts and structures used in the book are included in the appendix, making the book useful for enhancing traditional courses of calculus for undergraduates, as well as for separate courses for graduate students. The material of Semitopological Vector Spaces: Hypernorms, Hyperseminorms and Operators is closely related to what is taught at colleges and universities. It is possible to use a definite number of statements from the book as exercises for students because their proofs are not given in the book but left for the reader.
Book Synopsis Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems by : Jingrui Sun
Download or read book Stochastic Linear-Quadratic Optimal Control Theory: Differential Games and Mean-Field Problems written by Jingrui Sun and published by Springer Nature. This book was released on 2020-06-29 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers the most essential results, including recent ones, on linear-quadratic optimal control problems, which represent an important aspect of stochastic control. It presents results for two-player differential games and mean-field optimal control problems in the context of finite and infinite horizon problems, and discusses a number of new and interesting issues. Further, the book identifies, for the first time, the interconnections between the existence of open-loop and closed-loop Nash equilibria, solvability of the optimality system, and solvability of the associated Riccati equation, and also explores the open-loop solvability of mean-filed linear-quadratic optimal control problems. Although the content is largely self-contained, readers should have a basic grasp of linear algebra, functional analysis and stochastic ordinary differential equations. The book is mainly intended for senior undergraduate and graduate students majoring in applied mathematics who are interested in stochastic control theory. However, it will also appeal to researchers in other related areas, such as engineering, management, finance/economics and the social sciences.
Book Synopsis Mean Field Games and Mean Field Type Control Theory by : Alain Bensoussan
Download or read book Mean Field Games and Mean Field Type Control Theory written by Alain Bensoussan and published by Springer Science & Business Media. This book was released on 2013-10-16 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mean field games and Mean field type control introduce new problems in Control Theory. The terminology “games” may be confusing. In fact they are control problems, in the sense that one is interested in a single decision maker, whom we can call the representative agent. However, these problems are not standard, since both the evolution of the state and the objective functional is influenced but terms which are not directly related to the state or the control of the decision maker. They are however, indirectly related to him, in the sense that they model a very large community of agents similar to the representative agent. All the agents behave similarly and impact the representative agent. However, because of the large number an aggregation effect takes place. The interesting consequence is that the impact of the community can be modeled by a mean field term, but when this is done, the problem is reduced to a control problem.
Book Synopsis Mathematical Physics with Partial Differential Equations by : James Kirkwood
Download or read book Mathematical Physics with Partial Differential Equations written by James Kirkwood and published by Academic Press. This book was released on 2012-01-20 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for advanced undergraduate and beginning graduate students taking a course on mathematical physics, this title presents some of the most important topics and methods of mathematical physics. It contains mathematical derivations and solutions - reinforcing the material through repetition of both the equations and the techniques.
Book Synopsis Non-Diophantine Arithmetics in Mathematics, Physics and Psychology by : Mark Burgin
Download or read book Non-Diophantine Arithmetics in Mathematics, Physics and Psychology written by Mark Burgin and published by World Scientific Publishing Company. This book was released on 2020-09-11 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a long time, all thought there was only one geometry -- Euclidean geometry. Nevertheless, in the 19th century, many non-Euclidean geometries were discovered. It took almost two millennia to do this. This was the major mathematical discovery and advancement of the 19th century, which changed understanding of mathematics and the work of mathematicians providing innovative insights and tools for mathematical research and applications of mathematics.A similar event happened in arithmetic in the 20th century. Even longer than with geometry, all thought there was only one conventional arithmetic of natural numbers -- the Diophantine arithmetic, in which 2+2=4 and 1+1=2. It is natural to call the conventional arithmetic by the name Diophantine arithmetic due to the important contributions to arithmetic by Diophantus. Nevertheless, in the 20th century, many non-Diophantine arithmetics were discovered, in some of which 2+2=5 or 1+1=3. It took more than two millennia to do this. This discovery has even more implications than the discovery of new geometries because all people use arithmetic.This book provides a detailed exposition of the theory of non-Diophantine arithmetics and its various applications. Reading this book, the reader will see that on the one hand, non-Diophantine arithmetics continue the ancient tradition of operating with numbers while on the other hand, they introduce extremely original and innovative ideas.
