Download or read book Functional Equations in Probability Theory written by Ramachandran Balasubrahmanyan and published by Elsevier. This book was released on 2014-05-12 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional Equations in Probability Theory deals with functional equations in probability theory and covers topics ranging from the integrated Cauchy functional equation (ICFE) to stable and semistable laws. The problem of identical distribution of two linear forms in independent and identically distributed random variables is also considered, with particular reference to the context of the common distribution of these random variables being normal. Comprised of nine chapters, this volume begins with an introduction to Cauchy functional equations as well as distribution functions and characteristic functions. The discussion then turns to the nonnegative solutions of ICFE on R+; ICFE with a signed measure; and application of ICFE to the characterization of probability distributions. Subsequent chapters focus on stable and semistable laws; ICFE with error terms on R+; independent/identically distributed linear forms and the normal laws; and distribution problems relating to the arc-sine, the normal, and the chi-square laws. The final chapter is devoted to ICFE on semigroups of Rd. This book should be of interest to mathematicians and statisticians.

Download or read book Functional Equations and How to Solve Them written by Christopher G. Small and published by Springer Science & Business Media. This book was released on 2007-04-03 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many books have been written on the theory of functional equations, but very few help readers solve functional equations in mathematics competitions and mathematical problem solving. This book fills that gap. Each chapter includes a list of problems associated with the covered material. These vary in difficulty, with the easiest being accessible to any high school student who has read the chapter carefully. The most difficult will challenge students studying for the International Mathematical Olympiad or the Putnam Competition. An appendix provides a springboard for further investigation of the concepts of limits, infinite series and continuity.

Download or read book Entropy and Diversity written by Tom Leinster and published by Cambridge University Press. This book was released on 2021-04-22 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discover the mathematical riches of 'what is diversity?' in a book that adds mathematical rigour to a vital ecological debate.

Download or read book Functional Equations History Applications and Theory written by J. Aczél and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from It isn't that they can't see the right end and begin with the solution. It is that they the answers. Then one day, can't see the problem. perhaps you will find the G.K. Chesterton. The Scandal of final question. Father Brown 'The Point of a Pin' . 'The Hermit Clad ~n Crane Feathers' in R. van Gulik's The Chinese Haze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathe matics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) ~n re gional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical pro gramming profit from homotopy theory; Lie algebras are rele vant to filtering; and prediction and electrical en~ineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existinf, classifi~ation schemes. They draw upon widely different sections of mathematics.

Download or read book Lectures on Functional Equations and Their Applications written by J. Aczel and published by Courier Corporation. This book was released on 2006-02-01 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerous detailed proofs highlight this treatment of functional equations. Starting with equations that can be solved by simple substitutions, the book then moves to equations with several unknown functions and methods of reduction to differential and integral equations. Also includes composite equations, equations with several unknown functions of several variables, vector and matrix equations, more. 1966 edition.

Download or read book An Introduction to the Theory of Functional Equations and Inequalities written by Marek Kuczma and published by Springer Science & Business Media. This book was released on 2009-03-12 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: Marek Kuczma was born in 1935 in Katowice, Poland, and died there in 1991. After finishing high school in his home town, he studied at the Jagiellonian University in Kraków. He defended his doctoral dissertation under the supervision of Stanislaw Golab. In the year of his habilitation, in 1963, he obtained a position at the Katowice branch of the Jagiellonian University (now University of Silesia, Katowice), and worked there till his death. Besides his several administrative positions and his outstanding teaching activity, he accomplished excellent and rich scientific work publishing three monographs and 180 scientific papers. He is considered to be the founder of the celebrated Polish school of functional equations and inequalities. "The second half of the title of this book describes its contents adequately. Probably even the most devoted specialist would not have thought that about 300 pages can be written just about the Cauchy equation (and on some closely related equations and inequalities). And the book is by no means chatty, and does not even claim completeness. Part I lists the required preliminary knowledge in set and measure theory, topology and algebra. Part II gives details on solutions of the Cauchy equation and of the Jensen inequality [...], in particular on continuous convex functions, Hamel bases, on inequalities following from the Jensen inequality [...]. Part III deals with related equations and inequalities (in particular, Pexider, Hosszú, and conditional equations, derivations, convex functions of higher order, subadditive functions and stability theorems). It concludes with an excursion into the field of extensions of homomorphisms in general." (Janos Aczel, Mathematical Reviews) "This book is a real holiday for all the mathematicians independently of their strict speciality. One can imagine what deliciousness represents this book for functional equationists." (B. Crstici, Zentralblatt für Mathematik)

Download or read book Functional Integration and Partial Differential Equations AM 109 Volume 109 written by Mark Iosifovich Freidlin and published by Princeton University Press. This book was released on 2016-03-02 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses some aspects of the theory of partial differential equations from the viewpoint of probability theory. It is intended not only for specialists in partial differential equations or probability theory but also for specialists in asymptotic methods and in functional analysis. It is also of interest to physicists who use functional integrals in their research. The work contains results that have not previously appeared in book form, including research contributions of the author.

Download or read book Functional Equations and Inequalities written by B. Forte and published by Springer Science & Business Media. This book was released on 2011-06-02 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: J. Aczél: Some applications of functional equations and inequalities to information measures.- J.A. Baker: Functional equations in vector space, part II.- I Fenyo: Sur les équations distributionnelles.- B. Forte: Applications of functional equations and inequalities to information theory.- S. Golab: Sur l’équation fonctionnelle des brigade.- E. Hille: Mean-values and functional equations.- J. Kampé de Feriet: Applications of functional equations and inequalities to information theory. Measure of information by a set of observers: a functional equation.- M. Kuczma: Convex functions.- S. Kurepa: Functional equations on vector spaces.- E. Lukacs: Inequalities and functional equations in probability theory.- M.A. McKiernan: Difference and mean-value type functional equations.- T.S. Motzkin: Solutions of differential and functional inequalities.- C.T. Ng: Uniqueness theorems in the theory of functional equations and related homotopy.- A.M. Ostrowski: Integral inequalities.- H. Schwerdtfeger: Remark on an inequality for monotonic functions.

Download or read book Iterative Functional Equations written by Marek Kuczma and published by Cambridge University Press. This book was released on 1990-07-27 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: A cohesive and comprehensive account of the modern theory of iterative functional equations. Many of the results included have appeared before only in research literature, making this an essential volume for all those working in functional equations and in such areas as dynamical systems and chaos, to which the theory is closely related. The authors introduce the reader to the theory and then explore the most recent developments and general results. Fundamental notions such as the existence and uniqueness of solutions to the equations are stressed throughout, as are applications of the theory to such areas as branching processes, differential equations, ergodic theory, functional analysis and geometry. Other topics covered include systems of linear and nonlinear equations of finite and infinite ORD various function classes, conjugate and commutable functions, linearization, iterative roots of functions, and special functional equations.

Download or read book Functional Equations and Inequalities with Applications written by Palaniappan Kannappan and published by Springer Science & Business Media. This book was released on 2009-06-10 with total page 817 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional Equations and Inequalities with Applications presents a comprehensive, nearly encyclopedic, study of the classical topic of functional equations. This self-contained monograph explores all aspects of functional equations and their applications to related topics, such as differential equations, integral equations, the Laplace transformation, the calculus of finite differences, and many other basic tools in analysis. Each chapter examines a particular family of equations and gives an in-depth study of its applications as well as examples and exercises to support the material.

Download or read book Functional Equations written by David Leigh-Lancaster and published by Aust Council for Ed Research. This book was released on 2006 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Functional equations provides mathematics teachers with an introduction to elementary aspects of functional equations. These equations are linked to function in various topics of the senior secondary mathematics curriculum including transformations, identities difference equations and mathematical modelling.

Download or read book Handbook of Functional Equations written by Themistocles M. Rassias and published by Springer. This book was released on 2014-11-21 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook consists of seventeen chapters written by eminent scientists from the international mathematical community, who present important research works in the field of mathematical analysis and related subjects, particularly in the Ulam stability theory of functional equations. The book provides an insight into a large domain of research with emphasis to the discussion of several theories, methods and problems in approximation theory, analytic inequalities, functional analysis, computational algebra and applications. The notion of stability of functional equations has its origins with S. M. Ulam, who posed the fundamental problem for approximate homomorphisms in 1940 and with D. H. Hyers, Th. M. Rassias, who provided the first significant solutions for additive and linear mappings in 1941 and 1978, respectively. During the last decade the notion of stability of functional equations has evolved into a very active domain of mathematical research with several applications of interdisciplinary nature. The chapters of this handbook focus mainly on both old and recent developments on the equation of homomorphism for square symmetric groupoids, the linear and polynomial functional equations in a single variable, the Drygas functional equation on amenable semigroups, monomial functional equation, the Cauchy–Jensen type mappings, differential equations and differential operators, operational equations and inclusions, generalized module left higher derivations, selections of set-valued mappings, D’Alembert’s functional equation, characterizations of information measures, functional equations in restricted domains, as well as generalized functional stability and fixed point theory.

Download or read book Functional Equations and Inequalities written by Themistocles RASSIAS and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an extensive study of some of the most important topics of current interest in functional equations and inequalities. Subjects dealt with include: a Pythagorean functional equation, a functional definition of trigonometric functions, the functional equation of the square root spiral, a conditional Cauchy functional equation, an iterative functional equation, the Hille-type functional equation, the polynomial-like iterative functional equation, distribution of zeros and inequalities for zeros of algebraic polynomials, a qualitative study of Lobachevsky's complex functional equation, functional inequalities in special classes of functions, replicativity and function spaces, normal distributions, some difference equations, finite sums, decompositions of functions, harmonic functions, set-valued quasiconvex functions, the problems of expressibility in some extensions of free groups, Aleksandrov problem and mappings which preserve distances, Ulam's problem, stability of some functional equation for generalized trigonometric functions, Hyers-Ulam stability of Hosszú's equation, superstability of a functional equation, and some demand functions in a duopoly market with advertising. Audience: This book will be of interest to mathematicians and graduate students whose work involves real functions, functions of a complex variable, functional analysis, integral transforms, and operational calculus.

Download or read book Developments in Functional Equations and Related Topics written by Janusz Brzdęk and published by Springer. This book was released on 2017-08-14 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents current research on Ulam stability for functional equations and inequalities. Contributions from renowned scientists emphasize fundamental and new results, methods and techniques. Detailed examples are given to theories to further understanding at the graduate level for students in mathematics, physics, and engineering. Key topics covered in this book include: Quasi means Approximate isometries Functional equations in hypergroups Stability of functional equations Fischer-Muszély equation Haar meager sets and Haar null sets Dynamical systems Functional equations in probability theory Stochastic convex ordering Dhombres functional equation Nonstandard analysis and Ulam stability This book is dedicated in memory of Staniłsaw Marcin Ulam, who posed the fundamental problem concerning approximate homomorphisms of groups in 1940; which has provided the stimulus for studies in the stability of functional equations and inequalities.

Download or read book Proceedings of the St Petersburg Mathematical Society written by N.N. Uraltseva (Mathematikerin, Russland) and published by American Mathematical Soc.. This book was released on with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection presents new results in algebra, functional analysis, and mathematical physics. In particular, evolution and spectral problems related to small motions of viscoelastic fluid are considered. Specific areas covered in the book include functional equations and functional operator equations from the point of view of the $C*$-algebraic approach, the existence of an isomorphism between certain ideals regarded as Galois modules, spectral problems in singularly perturbed domains, scattering theory, the existence of bounded solutions to the equation $\operatorname{div} u = f$ in a plane domain, and a compactification of a locally compact group. Also given is an historic overview of the mathematical seminars held at St. Petersburg State University. The results, ideas, and methods given in the book will be of interest to a broad range of specialists.

Download or read book Functional Equations And Inequalities Solutions And Stability Results written by John Michael Rassias and published by World Scientific Publishing Company. This book was released on 2017-03-20 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers the topic in functional equations in a broad sense and is written by authors who are in this field for the past 50 years. It contains the basic notions of functional equations, the methods of solving functional equations, the growth of functional equations in the last four decades and an extensive reference list on fundamental research papers that investigate the stability results of different types of functional equations and functional inequalities. This volume starts by taking the reader from the fundamental ideas to higher levels of results that appear in recent research papers. Its step-by-step expositions are easy for the reader to understand and admire the elegant results and findings on the stability of functional equations.

Download or read book Air Force Research Resum s written by and published by . This book was released on with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: