The Double Mellin-Barnes Type Integrals and Their Applications to Convolution Theory PDF Download
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Author: Thanh Hai Nguyen
Publisher: World Scientific
ISBN: 9789810206901
Category : Mathematics
Languages : en
Pages : 318
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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: Thanh Hai Nguyen
Publisher: World Scientific
ISBN: 9789810206901
Category : Mathematics
Languages : en
Pages : 318
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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: 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: Anthony Roberts
Publisher: Oxford University Press
ISBN: 0192598325
Category : Science
Languages : en
Pages : 750
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Book Description
Customarily, much of traditional mathematics curricula was predicated on 'by hand' calculation. However, ubiquitous computing requires us to refresh what we teach and how it is taught. This is especially true in the rapidly broadening fields of Data Mining and Artificial Intelligence, and also in fields such as Bioinformatics, which all require the use of Singular Value Decomposition (SVD). Indeed, SVD is sometimes called the jewel in the crown of linear algebra. Linear Algebra for 21st Century Applications adapts linear algebra to best suit modern teaching and application, and it places the SVD as central to the text early on to empower science and engineering students to learn and use potent practical and theoretical techniques. No rigour is lost in this new route as the text demonstrates that most theory is better proved with an SVD. In addition to this, there is earlier introduction, development, and emphasis on orthogonality that is vital in so many applied disciplines throughout science, engineering, computing and increasingly within the social sciences. To assimilate the so-called third arm of science, namely computing, Matlab/Octave computation is explicitly integrated into developing the mathematical concepts and applications. A strong graphical emphasis takes advantage of the power of visualisation in the human brain and examples are included to exhibit modern applications of linear algebra, such as GPS, text mining, and image processing. Active learning is encouraged with exercises throughout that are aimed to enhance ectures, quizzes, or 'flipped' teaching.
Author: Iryna Fedotova
Publisher: World Scientific
ISBN: 9814492817
Category : Mathematics
Languages : en
Pages : 217
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Book Description
The various types of special functions have become essential tools for scientists and engineers. One of the important classes of special functions is of the hypergeometric type. It includes all classical hypergeometric functions such as the well-known Gaussian hypergeometric functions, the Bessel, Macdonald, Legendre, Whittaker, Kummer, Tricomi and Wright functions, the generalized hypergeometric functions ρFq, Meijer's G-function, Fox's H-function, etc.Application of the new special functions allows one to increase considerably the number of problems whose solutions are found in a closed form, to examine these solutions, and to investigate the relationships between different classes of the special functions.This book deals with the theory and applications of generalized associated Legendre functions of the first and the second kind, Pm,nκ(z) and Qm,nκ(z), which are important representatives of the hypergeometric functions. They occur as generalizations of classical Legendre functions of the first and the second kind respectively. The authors use various methods of contour integration to obtain important properties of the generalized associated Legnedre functions as their series representations, asymptotic formulas in a neighborhood of singular points, zero properties, connection with Jacobi functions, Bessel functions, elliptic integrals and incomplete beta functions.The book also presents the theory of factorization and composition structure of integral operators associated with the generalized associated Legendre function, the fractional integro-differential properties of the functions Pm,nκ(z) and Qm,nκ(z), the classes of dual and triple integral equations associated with the function Pm,n-1/2+iς(chα) etc.
Author: Rúben Sousa
Publisher: Springer Nature
ISBN: 303105296X
Category : Mathematics
Languages : en
Pages : 269
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Book Description
This book provides an introduction to recent developments in the theory of generalized harmonic analysis and its applications. It is well known that convolutions, differential operators and diffusion processes are interconnected: the ordinary convolution commutes with the Laplacian, and the law of Brownian motion has a convolution semigroup property with respect to the ordinary convolution. Seeking to generalize this useful connection, and also motivated by its probabilistic applications, the book focuses on the following question: given a diffusion process Xt on a metric space E, can we construct a convolution-like operator * on the space of probability measures on E with respect to which the law of Xt has the *-convolution semigroup property? A detailed analysis highlights the connection between the construction of convolution-like structures and disciplines such as stochastic processes, ordinary and partial differential equations, spectral theory, special functions and integral transforms. The book will be valuable for graduate students and researchers interested in the intersections between harmonic analysis, probability theory and differential equations.
Author: Virginia S Kiryakova
Publisher: CRC Press
ISBN: 9780582219779
Category : Mathematics
Languages : en
Pages : 412
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Book Description
In this volume various applications are discussed, in particular to the hyper-Bessel differential operators and equations, Dzrbashjan-Gelfond-Leontiev operators and Borel type transforms, convolutions, new representations of hypergeometric functions, solutions to classes of differential and integral equations, transmutation method, and generalized integral transforms. Some open problems are also posed. This book is intended for graduate and post-graduate students, lecturers, researchers and others working in applied mathematical analysis, mathematical physics and related disciplines.
Author: Semen B. Yakubovich
Publisher: World Scientific
ISBN: 9789810222161
Category : Mathematics
Languages : en
Pages : 272
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Book Description
This book deals with the theory and some applications of integral transforms that involve integration with respect to an index or parameter of a special function of hypergeometric type as the kernel (index transforms). The basic index transforms are considered, such as the Kontorovich-Lebedev transform, the Mehler-Fock transform, the Olevskii Transform and the Lebedev-Skalskaya transforms. The p theory of index transforms is discussed, and new index transforms and convolution constructions are demonstrated. For the first time, the essentially multidimensional Kontorovich-Lebedev transform is announced. General index transform formulae are obtained. The connection between the multidimensional index kernels and G and H functions of several variables is presented. The book is self-contained, and includes a list of symbols with definitions, author and subject indices, and an up-to-date bibliography.This work will be of interest to researchers and graudate students in the mathematical and physical sciences whose work involves integral transforms and special functions.
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: Soumen Chakrabarti
Publisher: Morgan Kaufmann
ISBN: 1558607544
Category : Computers
Languages : en
Pages : 366
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Book Description
The definitive book on mining the Web from the preeminent authority.
Author: Mark Weichold
Publisher: Springer
ISBN: 3319245406
Category : Computers
Languages : en
Pages : 808
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Book Description
This book constitutes the thoroughly refereed post-conference proceedings of the 10th International Conference on Cognitive Radio Oriented Wireless Networks, CROWNCOM 2015, held in Doha, Qatar, in April 2015. The 66 revised full papers presented were carefully reviewed and selected from 110 submissions and cover the evolution of cognitive radio technology pertaining to 5G networks. The papers are clustered to topics on dynamic spectrum access/management, networking protocols for CR, modeling and theory, HW architecture and implementations, next generation of cognitive networks, standards and business models, and emerging applications for cognitive networks.
