Trigonometric And Hyperbolic Generated Approximation Theory
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Trigonometric And Hyperbolic Generated Approximation Theory
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Author : George A Anastassiou
language : en
Publisher: World Scientific
Release Date : 2024-11-28
Trigonometric And Hyperbolic Generated Approximation Theory written by George A Anastassiou and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-28 with Mathematics categories.
This monograph is a testimony of the impact over Computational Analysis of some new trigonometric and hyperbolic types of Taylor's formulae with integral remainders producing a rich collection of approximations of a very wide spectrum.This volume covers perturbed neural network approximations by themselves and with their connections to Brownian motion and stochastic processes, univariate and multivariate analytical inequalities (both ordinary and fractional), Korovkin theory, and approximations by singular integrals (both univariate and multivariate cases). These results are expected to find applications in the many areas of Pure and Applied Mathematics, Computer Science, Engineering, Artificial Intelligence, Machine Learning, Deep Learning, Analytical Inequalities, Approximation Theory, Statistics, Economics, amongst others. Thus, this treatise is suitable for researchers, graduate students, practitioners and seminars of related disciplines, and serves well as an invaluable resource for all Science and Engineering libraries.
Advanced Topics On Semilinear Evolution Equations
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Author : Mouffak Benchohra
language : en
Publisher: World Scientific
Release Date : 2025-01-07
Advanced Topics On Semilinear Evolution Equations written by Mouffak Benchohra and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-07 with Mathematics categories.
Differential evolution equations serve as mathematical representations that capture the progression or transformation of functions or systems as time passes. Currently, differential equations continue to be an active and thriving area of study, with continuous advancements in mathematical methodologies and their practical applications spanning diverse fields such as physics, engineering, and economics. In the late 20th century, the notion of 'Differential Evolution Equations' emerged as a distinct field applied to optimization and machine learning challenges. Evolution equations hold immense importance in numerous realms of applied mathematics and have experienced notable prominence in recent times.This book delves into the study of several classes of equations, aiming to investigate the existence of mild and periodic mild solutions and their properties such as approximate controllability, complete controllability and attractivity, under various conditions. By examining diverse problems involving second-order semilinear evolution equations, differential and integro-differential equations with state-dependent delay, random effects, and functional differential equations with delay and random effects, we hope to contribute to the advancement of mathematical knowledge and provide researchers, academicians, and students with a solid foundation for further exploration in this field. Throughout this book, we explore different mathematical frameworks, employing Fréchet spaces and Banach spaces to provide a comprehensive analysis. Our investigation extends beyond traditional solutions, encompassing the study of asymptotically almost automorphic mild solutions, periodic mild solutions, and impulsive integro-differential equations. These topics shed light on the behavior of equations in both bounded and unbounded domains, offering valuable insights into the dynamics of functional evolution equations.
Approximation Theory Wavelets And Applications
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Author : S.P. Singh
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Approximation Theory Wavelets And Applications written by S.P. Singh and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Approximation Theory, Wavelets and Applications draws together the latest developments in the subject, provides directions for future research, and paves the way for collaborative research. The main topics covered include constructive multivariate approximation, theory of splines, spline wavelets, polynomial and trigonometric wavelets, interpolation theory, polynomial and rational approximation. Among the scientific applications were de-noising using wavelets, including the de-noising of speech and images, and signal and digital image processing. In the area of the approximation of functions the main topics include multivariate interpolation, quasi-interpolation, polynomial approximation with weights, knot removal for scattered data, convergence theorems in Padé theory, Lyapunov theory in approximation, Neville elimination as applied to shape preserving presentation of curves, interpolating positive linear operators, interpolation from a convex subset of Hilbert space, and interpolation on the triangle and simplex. Wavelet theory is growing extremely rapidly and has applications which will interest readers in the physical, medical, engineering and social sciences.
Generalized Trigonometric And Hyperbolic Functions
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Author : Ronald E. Mickens
language : en
Publisher: CRC Press
Release Date : 2019-01-15
Generalized Trigonometric And Hyperbolic Functions written by Ronald E. Mickens and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-15 with Mathematics categories.
Generalized Trigonometric and Hyperbolic Functions highlights, to those in the area of generalized trigonometric functions, an alternative path to the creation and analysis of these classes of functions. Previous efforts have started with integral representations for the inverse generalized sine functions, followed by the construction of the associated cosine functions, and from this, various properties of the generalized trigonometric functions are derived. However, the results contained in this book are based on the application of both geometrical phase space and dynamical systems methodologies. Features Clear, direct construction of a new set of generalized trigonometric and hyperbolic functions Presentation of why x2+y2 = 1, and related expressions, may be interpreted in three distinct ways All the constructions, proofs, and derivations can be readily followed and understood by students, researchers, and professionals in the natural and mathematical sciences
Frontiers In Approximation Theory
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Author : George A Anastassiou
language : en
Publisher: World Scientific
Release Date : 2015-06-23
Frontiers In Approximation Theory written by George A Anastassiou and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-23 with Mathematics categories.
This monograph presents the author's work of the last five years in approximation theory. The chapters are self-contained and can be read independently. Readers will find the topics covered are diverse and advanced courses can be taught out of this book.The first part of the book is dedicated to fractional monotone approximation theory introduced for the first time by the author, taking the related ordinary theory of usual differentiation at the fractional differentiation level with polynomials and splines as approximators. The second part deals with the approximation by discrete singular operators of the Favard style, for example, of the Picard and Gauss-Weierstrass types. Then, it continues in a very detailed and extensive chapter on approximation by interpolating operators induced by neural networks, a connection to computer science. This book ends with the approximation theory and functional analysis on time scales, a very modern topic, detailing all the pros and cons of this method.The results in this book are expected to find applications in many areas of pure and applied mathematics. So far, very little is written about fractional approximation theory which is at its infancy. As such, it is suitable for researchers, graduate students, and performing seminars as well as an invaluable resource for all science libraries.
An Introduction To Hypergeometric Supertrigonometric And Superhyperbolic Functions
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Author : Xiao-Jun Yang
language : en
Publisher: Academic Press
Release Date : 2021-01-23
An Introduction To Hypergeometric Supertrigonometric And Superhyperbolic Functions written by Xiao-Jun Yang and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-23 with Mathematics categories.
An Introduction to Hypergeometric, Supertigonometric, and Superhyperbolic Functions gives a basic introduction to the newly established hypergeometric, supertrigonometric, and superhyperbolic functions from the special functions viewpoint. The special functions, such as the Euler Gamma function, the Euler Beta function, the Clausen hypergeometric series, and the Gauss hypergeometric have been successfully applied to describe the real-world phenomena that involve complex behaviors arising in mathematics, physics, chemistry, and engineering. - Provides a historical overview for a family of the special polynomials - Presents a logical investigation of a family of the hypergeometric series - Proposes a new family of the hypergeometric supertrigonometric functions - Presents a new family of the hypergeometric superhyperbolic functions
Hyperbolic Cross Approximation
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Author : Dinh Dũng
language : en
Publisher: Springer
Release Date : 2018-11-02
Hyperbolic Cross Approximation written by Dinh Dũng and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-02 with Mathematics categories.
This book provides a systematic survey of classical and recent results on hyperbolic cross approximation. Motivated by numerous applications, the last two decades have seen great success in studying multivariate approximation. Multivariate problems have proven to be considerably more difficult than their univariate counterparts, and recent findings have established that multivariate mixed smoothness classes play a fundamental role in high-dimensional approximation. The book presents essential findings on and discussions of linear and nonlinear approximations of the mixed smoothness classes. Many of the important open problems explored here will provide both students and professionals with inspirations for further research.
Approximation Theory Viii Volume 2 Wavelets And Multilevel Approximation
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Author : Charles K Chui
language : en
Publisher: World Scientific
Release Date : 1995-11-07
Approximation Theory Viii Volume 2 Wavelets And Multilevel Approximation written by Charles K Chui and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-11-07 with Mathematics categories.
This is the collection of the refereed and edited papers presented at the 8th Texas International Conference on Approximation Theory. It is interdisciplinary in nature and consists of two volumes. The central theme of Vol. I is the core of approximation theory. It includes such important areas as qualitative approximations, interpolation theory, rational approximations, radial-basis functions, and splines. The second volume focuses on topics related to wavelet analysis, including multiresolution and multi-level approximation, subdivision schemes in CAGD, and applications.
Approximation Theory Xiv San Antonio 2013
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Author : Gregory E. Fasshauer
language : en
Publisher: Springer
Release Date : 2014-06-02
Approximation Theory Xiv San Antonio 2013 written by Gregory E. Fasshauer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-02 with Mathematics categories.
These proceedings were prepared in connection with the 14th International Conference on Approximation Theory, which was held April 7-10, 2013 in San Antonio, Texas. The conference was the fourteenth in a series of meetings in Approximation Theory held at various locations in the United States. The included invited and contributed papers cover diverse areas of approximation theory with a special emphasis on the most current and active areas such as compressed sensing, isogeometric analysis, anisotropic spaces, radial basis functions and splines. Classical and abstract approximation is also included. The book will be of interest to mathematicians, engineers\ and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis and related application areas.
Trigonometric Sums And Their Applications
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Author : Andrei Raigorodskii
language : en
Publisher: Springer Nature
Release Date : 2020-03-11
Trigonometric Sums And Their Applications written by Andrei Raigorodskii and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-11 with Mathematics categories.
This volume presents in a unified manner both classic as well as modern research results devoted to trigonometric sums. Such sums play an integral role in the formulation and understanding of a broad spectrum of problems which range over surprisingly many and different research areas. Fundamental and new developments are presented to discern solutions to problems across several scientific disciplines. Graduate students and researchers will find within this book numerous examples and a plethora of results related to trigonometric sums through pure and applied research along with open problems and new directions for future research.