Index Transforms

Index Transforms
Author: Semen B. Yakubovich
Publisher: World Scientific
Total Pages: 272
Release: 1996
Genre: Mathematics
ISBN: 9789810222161
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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.

The Hypergeometric Approach to Integral Transforms and Convolutions

The Hypergeometric Approach to Integral Transforms and Convolutions
Author: S.B. Yakubovich
Publisher: Springer Science & Business Media
Total Pages: 335
Release: 2012-12-06
Genre: Mathematics
ISBN: 9401111960
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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.

Generalized Integral Transforms In Mathematical Finance

Generalized Integral Transforms In Mathematical Finance
Author: Andrey Itkin
Publisher: World Scientific
Total Pages: 508
Release: 2021-10-12
Genre: Business & Economics
ISBN: 9811231753
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This book describes several techniques, first invented in physics for solving problems of heat and mass transfer, and applies them to various problems of mathematical finance defined in domains with moving boundaries. These problems include: (a) semi-closed form pricing of options in the one-factor models with time-dependent barriers (Bachelier, Hull-White, CIR, CEV); (b) analyzing an interconnected banking system in the structural credit risk model with default contagion; (c) finding first hitting time density for a reducible diffusion process; (d) describing the exercise boundary of American options; (e) calculating default boundary for the structured default problem; (f) deriving a semi-closed form solution for optimal mean-reverting trading strategies; to mention but some.The main methods used in this book are generalized integral transforms and heat potentials. To find a semi-closed form solution, we need to solve a linear or nonlinear Volterra equation of the second kind and then represent the option price as a one-dimensional integral. Our analysis shows that these methods are computationally more efficient than the corresponding finite-difference methods for the backward or forward Kolmogorov PDEs (partial differential equations) while providing better accuracy and stability.We extend a large number of known results by either providing solutions on complementary or extended domains where the solution is not known yet or modifying these techniques and applying them to new types of equations, such as the Bessel process. The book contains several novel results broadly applicable in physics, mathematics, and engineering.

Advanced Database Indexing

Advanced Database Indexing
Author: Yannis Manolopoulos
Publisher: Springer Science & Business Media
Total Pages: 297
Release: 2012-09-07
Genre: Computers
ISBN: 1441985905
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Advanced Database Indexing begins by introducing basic material on storage media, including magnetic disks, RAID systems and tertiary storage such as optical disk and tapes. Typical access methods (e.g. B+ trees, dynamic hash files and secondary key retrieval) are also introduced. The remainder of the book discusses recent advances in indexing and access methods for particular database applications. More specifically, issues such as external sorting, file structures for intervals, temporal access methods, spatial and spatio-temporal indexing, image and multimedia indexing, perfect external hashing methods, parallel access methods, concurrency issues in indexing and parallel external sorting are presented for the first time in a single book. Advanced Database Indexing is an excellent reference for database professionals and may be used as a text for advanced courses on the topic.

Egyptian Coastal Lakes and Wetlands: Part I

Egyptian Coastal Lakes and Wetlands: Part I
Author: Abdelazim M. Negm
Publisher: Springer
Total Pages: 304
Release: 2018-12-12
Genre: Science
ISBN: 3319935909
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Egyptian coastal lakes and wetlands are among the most productive wetland ecosystems in the world. This volume explores their current status and how it can be maintained and improved. It describes the five Northern coastal lakes, their origin, physical and chemical properties and current development activities, and discusses the challenges facing these lakes, such as shrinking, pollution, degradation, and adaptive management. Further topics include hydrodynamics and modeling techniques, as well as strategies for the sustainable development of these valuable resources. The book closes with a concise summary of the conclusions and recommendations presented in the chapters. As such, it offers an invaluable resource for the academic community and postgraduate students, as well as for environmental managers and policymakers.

Physics from Symmetry

Physics from Symmetry
Author: Jakob Schwichtenberg
Publisher: Springer
Total Pages: 282
Release: 2015-06-04
Genre: Science
ISBN: 3319192019
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This is a textbook that derives the fundamental theories of physics from symmetry. It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived. As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations.

Einstein Gravity in a Nutshell

Einstein Gravity in a Nutshell
Author: A. Zee
Publisher: Princeton University Press
Total Pages: 888
Release: 2013-05-05
Genre: Science
ISBN: 069114558X
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An ideal introduction to Einstein's general theory of relativity This unique textbook provides an accessible introduction to Einstein's general theory of relativity, a subject of breathtaking beauty and supreme importance in physics. With his trademark blend of wit and incisiveness, A. Zee guides readers from the fundamentals of Newtonian mechanics to the most exciting frontiers of research today, including de Sitter and anti-de Sitter spacetimes, Kaluza-Klein theory, and brane worlds. Unlike other books on Einstein gravity, this book emphasizes the action principle and group theory as guides in constructing physical theories. Zee treats various topics in a spiral style that is easy on beginners, and includes anecdotes from the history of physics that will appeal to students and experts alike. He takes a friendly approach to the required mathematics, yet does not shy away from more advanced mathematical topics such as differential forms. The extensive discussion of black holes includes rotating and extremal black holes and Hawking radiation. The ideal textbook for undergraduate and graduate students, Einstein Gravity in a Nutshell also provides an essential resource for professional physicists and is accessible to anyone familiar with classical mechanics and electromagnetism. It features numerous exercises as well as detailed appendices covering a multitude of topics not readily found elsewhere. Provides an accessible introduction to Einstein's general theory of relativity Guides readers from Newtonian mechanics to the frontiers of modern research Emphasizes symmetry and the Einstein-Hilbert action Covers topics not found in standard textbooks on Einstein gravity Includes interesting historical asides Features numerous exercises and detailed appendices Ideal for students, physicists, and scientifically minded lay readers Solutions manual (available only to teachers)

Game Development for iOS with Unity3D

Game Development for iOS with Unity3D
Author: Jeff W. Murray
Publisher: CRC Press
Total Pages: 282
Release: 2012-07-26
Genre: Computers
ISBN: 1040055362
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This hands-on guide takes you through the complete process of Unity iOS game development. A game developer for over 12 years, the author presents production-proven techniques and valuable tips and tricks needed to plan, build, test, and launch games for the iPhone, iPod, and iPad. He walks you through all the necessary procedures, including how to publish your game to the App Store.

Index Transforms

Index Transforms
Author: Semyon B Yakubovich
Publisher: World Scientific
Total Pages: 265
Release: 1996-02-29
Genre: Mathematics
ISBN: 9814500607
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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 Lp 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.

Circuit Theory and Design 85

Circuit Theory and Design 85
Author: Václav Zima
Publisher: North Holland
Total Pages: 820
Release: 1985
Genre: Technology & Engineering
ISBN:
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Hardbound. The organizers of ECCTD'85 have prepared a comprehensive program covering the broadest possible area of circuit theory and design. Due to the close connection between circuit theory and signal theory, speech processing and communication systems have also been included.The papers have been selected on the basis of evaluation by three reviewers, and are topically arranged as follows: - Analysis and design (large network analysis, layout, statistical circuit design, VLSI circuits, CAD) - General network and system theory (mathematical methods in system theory, system theory, biological system modelling, nonlinear networks, power microelectronics) - Communications (radio and optical fibre communications systems, electronic circuits for communications) - Discrete signal processing (digital filters, digital signal processing, multidimensional filters and systems, speech processing, image processing) - Filters