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Author: Anatoly A. Kilbas
Publisher: CRC Press
ISBN: 0203487370
Category : Mathematics
Languages : en
Pages : 399
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Book Description
Along with more than 2100 integral equations and their solutions, this handbook outlines exact analytical methods for solving linear and nonlinear integral equations and provides an evaluation of approximate methods. Each section provides examples that show how methods can be applied to specific equations.
Author: Anatoly A. Kilbas
Publisher: CRC Press
ISBN: 0203487370
Category : Mathematics
Languages : en
Pages : 399
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Book Description
Along with more than 2100 integral equations and their solutions, this handbook outlines exact analytical methods for solving linear and nonlinear integral equations and provides an evaluation of approximate methods. Each section provides examples that show how methods can be applied to specific equations.
Author: A.M. Mathai
Publisher: Springer Science & Business Media
ISBN: 1441909168
Category : Science
Languages : en
Pages : 276
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Book Description
TheH-function or popularly known in the literature as Fox’sH-function has recently found applications in a large variety of problems connected with reaction, diffusion, reaction–diffusion, engineering and communication, fractional differ- tial and integral equations, many areas of theoretical physics, statistical distribution theory, etc. One of the standard books and most cited book on the topic is the 1978 book of Mathai and Saxena. Since then, the subject has grown a lot, mainly in the elds of applications. Due to popular demand, the authors were requested to - grade and bring out a revised edition of the 1978 book. It was decided to bring out a new book, mostly dealing with recent applications in statistical distributions, pa- way models, nonextensive statistical mechanics, astrophysics problems, fractional calculus, etc. and to make use of the expertise of Hans J. Haubold in astrophysics area also. It was decided to con ne the discussion toH-function of one scalar variable only. Matrix variable cases and many variable cases are not discussed in detail, but an insight into these areas is given. When going from one variable to many variables, there is nothing called a unique bivariate or multivariate analogue of a givenfunction. Whatever be the criteria used, there may be manydifferentfunctions quali ed to be bivariate or multivariate analogues of a given univariate function. Some of the bivariate and multivariateH-functions, currently in the literature, are also questioned by many authors.
Author: S.B. Yakubovich
Publisher: Springer Science & Business Media
ISBN: 9401111960
Category : Mathematics
Languages : en
Pages : 335
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Book Description
The aim of this book is to develop a new approach which we called the hyper geometric one to the theory of various integral transforms, convolutions, and their applications to solutions of integro-differential equations, operational calculus, and evaluation of integrals. We hope that this simple approach, which will be explained below, allows students, post graduates in mathematics, physicists and technicians, and serious mathematicians and researchers to find in this book new interesting results in the theory of integral transforms, special functions, and convolutions. The idea of this approach can be found in various papers of many authors, but systematic discussion and development is realized in this book for the first time. Let us explain briefly the basic points of this approach. As it is known, in the theory of special functions and its applications, the hypergeometric functions play the main role. Besides known elementary functions, this class includes the Gauss's, Bessel's, Kummer's, functions et c. In general case, the hypergeometric functions are defined as a linear combinations of the Mellin-Barnes integrals. These ques tions are extensively discussed in Chapter 1. Moreover, the Mellin-Barnes type integrals can be understood as an inversion Mellin transform from the quotient of products of Euler's gamma-functions. Thus we are led to the general construc tions like the Meijer's G-function and the Fox's H-function.
Author: Alexander D. Poularikas
Publisher: CRC Press
ISBN: 1420066536
Category : Mathematics
Languages : en
Pages : 914
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Book Description
Updating the original, Transforms and Applications Handbook, Third Edition solidifies its place as the complete resource on those mathematical transforms most frequently used by engineers, scientists, and mathematicians. Highlighting the use of transforms and their properties, this latest edition of the bestseller begins with a solid introduction to signals and systems, including properties of the delta function and some classical orthogonal functions. It then goes on to detail different transforms, including lapped, Mellin, wavelet, and Hartley varieties. Written by top experts, each chapter provides numerous examples and applications that clearly demonstrate the unique purpose and properties of each type. The material is presented in a way that makes it easy for readers from different backgrounds to familiarize themselves with the wide range of transform applications. Revisiting transforms previously covered, this book adds information on other important ones, including: Finite Hankel, Legendre, Jacobi, Gengenbauer, Laguerre, and Hermite Fraction Fourier Zak Continuous and discrete Chirp-Fourier Multidimensional discrete unitary Hilbert-Huang Most comparable books cover only a few of the transforms addressed here, making this text by far the most useful for anyone involved in signal processing—including electrical and communication engineers, mathematicians, and any other scientist working in this field.
Author: L. C. G. Rogers
Publisher: Cambridge University Press
ISBN: 9780521775939
Category : Mathematics
Languages : en
Pages : 498
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Book Description
This celebrated volume gives an accessible introduction to stochastic integrals, stochastic differential equations, excursion theory and the general theory of processes.
Author: Semyon B Yakubovich
Publisher: World Scientific
ISBN: 9814506141
Category : Mathematics
Languages : en
Pages : 308
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Book Description
This book presents new results in the theory of the double Mellin-Barnes integrals popularly known as the general H-function of two variables.A general integral convolution is constructed by the authors and it contains Laplace convolution as a particular case and possesses a factorization property for one-dimensional H-transform. Many examples of convolutions for classical integral transforms are obtained and they can be applied for the evaluation of series and integrals.
Author: P.K. Banerjee
Publisher: Scientific Publishers
ISBN: 9387741605
Category : Mathematics
Languages : en
Pages : 181
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Book Description
The present Learned Research Work is an exhaustive survey and researches carried out by the authors, which led to the theories of distributions, generalized functions and transforms involving them, which includes interesting results and the fundamental concepts of the youngest generalization of Schwartz theory of distributions, the Boehmians. The tempered distribution and utilizations have been described, which provide suitable platforms for the generalizations of Fourier transforms, Stieltjes and Mellin transforms. To overcome the Fourier series this work includes wavelet transform, for which meticulous extensive study of the existing literature has been produced including recent researches carried out by the authors. This compilation, in the form of the present book, is believed to be of help to researchers in the field of distribution and transform analysis and, may even be treated as the reference book to post graduate students.
Author: Catherine Donati-Martin
Publisher: Springer
ISBN: 3319185853
Category : Mathematics
Languages : en
Pages : 657
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Book Description
This volume is dedicated to the memory of Marc Yor, who passed away in 2014. The invited contributions by his collaborators and former students bear testament to the value and diversity of his work and of his research focus, which covered broad areas of probability theory. The volume also provides personal recollections about him, and an article on his essential role concerning the Doeblin documents. With contributions by P. Salminen, J-Y. Yen & M. Yor; J. Warren; T. Funaki; J. Pitman& W. Tang; J-F. Le Gall; L. Alili, P. Graczyk & T. Zak; K. Yano & Y. Yano; D. Bakry & O. Zribi; A. Aksamit, T. Choulli & M. Jeanblanc; J. Pitman; J. Obloj, P. Spoida & N. Touzi; P. Biane; J. Najnudel; P. Fitzsimmons, Y. Le Jan & J. Rosen; L.C.G. Rogers & M. Duembgen; E. Azmoodeh, G. Peccati & G. Poly, timP-L Méliot, A. Nikeghbali; P. Baldi; N. Demni, A. Rouault & M. Zani; N. O'Connell; N. Ikeda & H. Matsumoto; A. Comtet & Y. Tourigny; P. Bougerol; L. Chaumont; L. Devroye & G. Letac; D. Stroock and M. Emery.
Author: Donald Andrew Dawson
Publisher: American Mathematical Soc.
ISBN: 9780821870440
Category : Mathematics
Languages : en
Pages : 260
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Book Description
The papers in this collection explore the connections between the rapidly developing fields of measure-valued processes, stochastic partial differential equations, and interacting particle systems, each of which has undergone profound development in recent years. Bringing together ideas and tools arising from these different sources, the papers include contributions to major directions of research in these fields, explore the interface between them, and describe newly developing research problems and methodologies. Several papers are devoted to different aspects of measure-valued branching processes (also called superprocesses). Some new classes of these processes are described, including branching in catalytic media, branching with change of mass, and multilevel branching. Sample path and spatial clumping properties of superprocesses are also studied. The papers on Fleming-Viot processes arising in population genetics include discussions of the role of genealogical structures and the application of the Dirichlet form methodology. Several papers are devoted to particle systems studied in statistical physics and to stochastic partial differential equations which arise as hydrodynamic limits of such systems. With overview articles on some of the important new developments in these areas, this book would be an ideal source for an advanced graduate course on superprocesses.
Author: Hans-Dieter Alber
Publisher: Springer
ISBN: 354069689X
Category : Mathematics
Languages : en
Pages : 172
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Book Description
This book contributes to the mathematical theory of systems of differential equations consisting of the partial differential equations resulting from conservation of mass and momentum, and of constitutive equations with internal variables. The investigations are guided by the objective of proving existence and uniqueness, and are based on the idea of transforming the internal variables and the constitutive equations. A larger number of constitutive equations from the engineering sciences are presented. The book is therefore suitable not only for specialists, but also for mathematicians seeking for an introduction in the field, and for engineers with a sound mathematical background.
