Index Transforms
Index Transforms

Author: Semen B. Yakubovich

Publisher: World Scientific

Published: 1996

Total Pages: 272

ISBN-13: 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

Published: 2012-12-06

Total Pages: 335

ISBN-13: 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.

Encyclopaedia of Mathematics
Encyclopaedia of Mathematics

Author: Michiel Hazewinkel

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 639

ISBN-13: 9401512795

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This is the second supplementary volume to Kluwer's highly acclaimed eleven-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing eleven volumes, and together these twelve volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.

Generalized Integral Transforms In Mathematical Finance
Generalized Integral Transforms In Mathematical Finance

Author: Andrey Itkin

Publisher: World Scientific

Published: 2021-10-12

Total Pages: 508

ISBN-13: 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.

C# Game Programming Cookbook for Unity 3D
C# Game Programming Cookbook for Unity 3D

Author: Jeff W. Murray

Publisher: CRC Press

Published: 2014-06-24

Total Pages: 462

ISBN-13: 1466581409

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An Accessible, Modular Style of Game Building—Easily Start Making Games with Unity 3D C# Game Programming Cookbook for Unity 3D presents a highly flexible core framework to create just about any type of game by plugging in different script components. Most scripts function within the game framework or in your own structures. The techniques and concepts discussed in the book give you a solid foundation in game development. The first ten chapters set up the flexible, reusable framework based in C# and suitable for all game types. The book also explains scripting of generic, reusable, and common functionality. The remainder of the text adds game-specific code to the framework to create four example games: a top-down arena shooter, a futuristic racing combat game, a tank arena deathmatch game, and a classic arcade-style vertical scrolling shoot ’em up. The games encompass artificial intelligence (path following, target chasing, and line-of-sight patrolling behaviors), game state control, wheel colliders, and weapon inventory management. The example files are available for download on the book’s CRC Press web page. Reducing your recoding, repurposing, or adaptation time, this book provides script-based components that you can use to jump start your own projects. The book’s modular components can be mixed and matched to build various kinds of video games for the Unity game engine.

Multivariate Approximation Theory IV
Multivariate Approximation Theory IV

Author: CHUI

Publisher: Birkhäuser

Published: 2013-03-08

Total Pages: 348

ISBN-13: 3034872984

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Multivariate Approximation Theory forms a rapidly evolving field in Applied Mathematics. The reason for its particular current interest lies in its impact on Computer Aided Geometric Design (CAGD), Image Processing, Pattern Recogni tion, and Mult idimensional Signal Processing. Mul ti var iate Bernstein polynomials and box splines, for example, play an important role in CAGD. Conversely, the highly important filter bank design problem of signal processing, for instance, gives rise to a new family of multivariate approximating functions, the Gabor wavelets, with interesting technological and biological applications. The conferences on Multivariate Approximation Theory held at the Mathematical Research Institute at Oberwolfach, Black Forest, in 1976, 1979, 1982, 1985 and 1989 ref lect the progress made in this area and related fie Ids. The present volume which is a continuation of the preceding volumes Constructive Theory of Functions of Several Variables, Lecture Notes in Mathematics 571 (1977) Multivariate Approximation Theory, ISNM 51 (1979) Multivariate Approximation Theory II, ISNM 61 (1982) Multivariate Approximation Theory III, ISNM 75 (1985) is based on the conference held on February 12-18, 1989. It includes most of the lectures presented at the Oberwolfach meeting and reveals the wide spectrum of activities in the field of multivariate approximation. The organizers are grateful to the Director of the Oberwolfach Mathematical Research Institute, Professor Dr. M. Barner, and his staff for providing the facili ties, and to Dr. G. Baszenski, Professor Dr. F. J. Delvos, Dr. H.

Einstein Gravity in a Nutshell
Einstein Gravity in a Nutshell

Author: A. Zee

Publisher: Princeton University Press

Published: 2013-05-05

Total Pages: 888

ISBN-13: 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)

Special Relativity and Classical Field Theory
Special Relativity and Classical Field Theory

Author: Leonard Susskind

Publisher: Basic Books

Published: 2017-09-26

Total Pages: 295

ISBN-13: 0465093353

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The third volume in the bestselling physics series cracks open Einstein's special relativity and field theory Physicist Leonard Susskind and data engineer Art Friedman are back. This time, they introduce readers to Einstein's special relativity and Maxwell's classical field theory. Using their typical brand of real math, enlightening drawings, and humor, Susskind and Friedman walk us through the complexities of waves, forces, and particles by exploring special relativity and electromagnetism. It's a must-read for both devotees of the series and any armchair physicist who wants to improve their knowledge of physics' deepest truths.

Advanced Database Indexing
Advanced Database Indexing

Author: Yannis Manolopoulos

Publisher: Springer Science & Business Media

Published: 2012-09-07

Total Pages: 297

ISBN-13: 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.

Quantum Field Theory
Quantum Field Theory

Author: Anthony G. Williams

Publisher: Cambridge University Press

Published: 2022-08-04

Total Pages: 793

ISBN-13: 1108470904

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This textbook offers a detailed and self-contained presentation of quantum field theory, suitable for advanced undergraduate and graduate level courses. The author provides full derivations wherever possible and adopts a pedagogical tone without sacrificing rigour. A fully worked solutions manual is available online for instructors.