Dyadic Walsh Analysis From 1924 Onwards Walsh Gibbs Butzer Dyadic Differentiation In Science Volume 1 Foundations
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Dyadic Walsh Analysis From 1924 Onwards Walsh Gibbs Butzer Dyadic Differentiation In Science Volume 1 Foundations
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Author : Radomir Stankovic
language : en
Publisher: Springer
Release Date : 2015-12-29
Dyadic Walsh Analysis From 1924 Onwards Walsh Gibbs Butzer Dyadic Differentiation In Science Volume 1 Foundations written by Radomir Stankovic and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-29 with Mathematics categories.
Dyadic (Walsh) analysis emerged as a new research area in applied mathematics and engineering in early seventies within attempts to provide answers to demands from practice related to application of spectral analysis of different classes of signals, including audio, video, sonar, and radar signals. In the meantime, it evolved in a mature mathematical discipline with fundamental results and important features providing basis for various applications. The book will provide fundamentals of the area through reprinting carefully selected earlier publications followed by overview of recent results concerning particular subjects in the area written by experts, most of them being founders of the field, and some of their followers. In this way, this first volume of the two volume book offers a rather complete coverage of the development of dyadic Walsh analysis, and provides a deep insight into its mathematical foundations necessary for consideration of generalizations and applications that are the subject of the second volume. The presented theory is quite sufficient to be a basis for further research in the subject area as well as to be applied in solving certain new problems or improving existing solutions for tasks in the areas which motivated development of the dyadic analysis.
Dyadic Walsh Analysis From 1924 Onwards Walsh Gibbs Butzer Dyadic Differentiation In Science Volume 2 Extensions And Generalizations
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Author : Radomir Stankovic
language : en
Publisher: Springer
Release Date : 2015-12-29
Dyadic Walsh Analysis From 1924 Onwards Walsh Gibbs Butzer Dyadic Differentiation In Science Volume 2 Extensions And Generalizations written by Radomir Stankovic and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-29 with Mathematics categories.
The second volume of the two volumes book is dedicated to various extensions and generalizations of Dyadic (Walsh) analysis and related applications. Considered are dyadic derivatives on Vilenkin groups and various other Abelian and finite non-Abelian groups. Since some important results were developed in former Soviet Union and China, we provide overviews of former work in these countries. Further, we present translations of three papers that were initially published in Chinese. The presentation continues with chapters written by experts in the area presenting discussions of applications of these results in specific tasks in the area of signal processing and system theory. Efficient computing of related differential operators on contemporary hardware, including graphics processing units, is also considered, which makes the methods and techniques of dyadic analysis and generalizations computationally feasible. The volume 2 of the book ends with a chapter presenting open problems pointed out by several experts in the area.
Bent Functions And Permutation Methods
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Author : Radomir S. Stanković
language : en
Publisher: Springer Nature
Release Date : 2024-02-20
Bent Functions And Permutation Methods written by Radomir S. Stanković and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-20 with Technology & Engineering categories.
This book discusses in a uniform way binary, ternary, and quaternary bent functions, while most of the existing books on bent functions refer to just binary bent functions. The authors describe the differences between binary and multiple-valued cases and the construction methods for bent functions are focused on the application of two types of permutation matrices. These matrices are derived from a class of differential operators on finite groups and Fast Fourier transform algorithms, respectively. The approach presented is based on the observation that given certain bent functions, many other bent functions can be constructed by manipulating them. Permutations are possible manipulations that are easy to implement. These permutations perform spectral invariant operations which ensure that they preserve bentness.
Further Improvements In The Boolean Domain
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Author : Bernd Steinbach
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2019-01-18
Further Improvements In The Boolean Domain written by Bernd Steinbach and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-18 with Computers categories.
The amount of digital systems supporting our daily life is increasing continuously. Improved technical facilities for their production have led to growing challenges for engineers and scientists working in the Boolean domain. A Boolean variable can only carry two different Boolean values: FALSE or TRUE (0 or 1), and has the best interference resistance in technical systems. However, a Boolean function exponentially depends on the number of its variables. This exponential complexity is the reason for major problems in the process of design and realization of circuits. According to Moore’s Law, the complexity of digital systems approximately doubles every 18 months. This requires comprehensive knowledge and techniques to solve very complex Boolean problems. This volume represents the third book in a series that provides further insights into the Boolean domain. Part 1 explores powerful models, methods and techniques which improve the efficiency in solving Boolean problems of extreme complexity. The universality of Boolean equations as a model to solve Non-deterministic Polynomial-time (NP) hard problems, as well as special properties of index generation functions, spectral techniques, or relational approaches, is discussed here. Both hardware devices, such as Field Programmable Gate Arrays (FPGAs) or Graphics Processing Units (GPUs), and optimized algorithms realized in software contribute to the acceleration of Boolean calculations. Part 2 contributes to the synthesis and visualization of digital circuits, and provides interesting new solutions for several types of circuits. A comprehensive collection of benchmarks supports the evolution of both existing and new synthesis approaches. The continuous reduction of the size of the transistors increases the challenges with regard to the reliability of the circuits. Part 3 describes several new approaches for the synthesis of reversible circuits. These approaches, as well as a classification of reversible functions, extend the basis of future quantum computers.
Claudio Moraga A Passion For Multi Valued Logic And Soft Computing
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Author : Rudolf Seising
language : en
Publisher: Springer
Release Date : 2016-10-20
Claudio Moraga A Passion For Multi Valued Logic And Soft Computing written by Rudolf Seising and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-20 with Computers categories.
The book is an authoritative collection of contributions by leading experts on the topics of fuzzy logic, multi-valued logic and neural network. Originally written as an homage to Claudio Moraga, seen by his colleagues as an example of concentration, discipline and passion for science, the book also represents a timely reference guide for advance students and researchers in the field of soft computing, and multiple-valued logic.
Dyadic Walsh Analysis From 1924 Onwards Walsh Gibbs Butzer Dyadic Differentiation In Science Volume 1 Foundations
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Author : Radomir Stankovic
language : en
Publisher: Atlantis Press
Release Date : 2016-01-08
Dyadic Walsh Analysis From 1924 Onwards Walsh Gibbs Butzer Dyadic Differentiation In Science Volume 1 Foundations written by Radomir Stankovic and has been published by Atlantis Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-08 with Mathematics categories.
Dyadic (Walsh) analysis emerged as a new research area in applied mathematics and engineering in early seventies within attempts to provide answers to demands from practice related to application of spectral analysis of different classes of signals, including audio, video, sonar, and radar signals. In the meantime, it evolved in a mature mathematical discipline with fundamental results and important features providing basis for various applications. The book will provide fundamentals of the area through reprinting carefully selected earlier publications followed by overview of recent results concerning particular subjects in the area written by experts, most of them being founders of the field, and some of their followers. In this way, this first volume of the two volume book offers a rather complete coverage of the development of dyadic Walsh analysis, and provides a deep insight into its mathematical foundations necessary for consideration of generalizations and applications that are the subject of the second volume. The presented theory is quite sufficient to be a basis for further research in the subject area as well as to be applied in solving certain new problems or improving existing solutions for tasks in the areas which motivated development of the dyadic analysis.
Functional Analysis And Approximation
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Author : B. Szökefalvi-Nagy
language : en
Publisher: Springer Science & Business Media
Release Date : 1981
Functional Analysis And Approximation written by B. Szökefalvi-Nagy 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 1981 with Juvenile Nonfiction categories.
These Proceedings form a record of the lectures presented at the interna tional Conference on Functional Analysis and Approximation held at the Ober wolfach Mathematical Research Institute, August 9-16, 1980. They include 33 of the 38 invited conference papers, as well as three papers subsequently submitted in writing. Further, there is a report devoted to new and unsolved problems, based on two special sessions of the conference. The present volume is the sixth Oberwolfach Conference in Birkhauser's ISNM series to be edited at Aachen *. It is once again devoted to more significant results obtained in the wide areas of approximation theory, harmonic analysis, functional analysis, and operator theory during the past three years. Many of the papers solicited not only outline fundamental advances in their fields but also focus on interconnections between the various research areas. The papers in the present volume have been grouped into nine chapters. Chapter I, on operator theory, deals with maps on positive semidefinite opera tors, spectral bounds of semigroup operators, evolution equations of diffusion type, the spectral theory of propagators, and generalized inverses. Chapter II, on functional analysis, contains papers on modular approximation, interpolation spaces, and unconditional bases.
Harmonic Analysis And Fractal Analysis Over Local Fields And Applications
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Author : Weiyi Su
language : en
Publisher: World Scientific
Release Date : 2017-08-17
Harmonic Analysis And Fractal Analysis Over Local Fields And Applications written by Weiyi Su and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-17 with Mathematics categories.
This book is a monograph on harmonic analysis and fractal analysis over local fields. It can also be used as lecture notes/textbook or as recommended reading for courses on modern harmonic and fractal analysis. It is as reliable as Fourier Analysis on Local Fields published in 1975 which is regarded as the first monograph in this research field.The book is self-contained, with wide scope and deep knowledge, taking modern mathematics (such as modern algebra, point set topology, functional analysis, distribution theory, and so on) as bases. Specially, fractal analysis is studied in the viewpoint of local fields, and fractal calculus is established by pseudo-differential operators over local fields. A frame of fractal PDE is constructed based on fractal calculus instead of classical calculus. On the other hand, the author does his best to make those difficult concepts accessible to readers, illustrate clear comparison between harmonic analysis on Euclidean spaces and that on local fields, and at the same time provide motivations underlying the new concepts and techniques. Overall, it is a high quality, up to date and valuable book for interested readers.
Fourier Analysis And Approximation
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Author : P.L. Butzer
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Fourier Analysis And Approximation written by P.L. Butzer and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
At the international conference on 'Harmonic Analysis and Integral Transforms', conducted by one of the authors at the Mathematical Research Institute in Oberwolfach (Black Forest) in August 1965, it was felt that there was a real need for a book on Fourier analysis stressing (i) parallel treatment of Fourier series and Fourier trans forms from a transform point of view, (ii) treatment of Fourier transforms in LP(lRn)_ space not only for p = 1 and p = 2, (iii) classical solution of partial differential equations with completely rigorous proofs, (iv) theory of singular integrals of convolu tion type, (v) applications to approximation theory including saturation theory, (vi) multiplier theory, (vii) Hilbert transforms, Riesz fractional integrals, Bessel potentials, (viii) Fourier transform methods on locally compact groups. This study aims to consider these aspects, presenting a systematic treatment of Fourier analysis on the circle as well as on the infinite line, and of those areas of approximation theory which are in some way or other related thereto. A second volume is in preparation which goes beyond the one-dimensional theory presented here to cover the subject for functions of several variables. Approximately a half of this first volume deals with the theories of Fourier series and of Fourier integrals from a transform point of view.
Eigenfunction Expansions Associated With Second Order Differential Equations
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Author : Edward Charles Titchmarsh
language : en
Publisher:
Release Date : 1958
Eigenfunction Expansions Associated With Second Order Differential Equations written by Edward Charles Titchmarsh and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1958 with Boundary value problems categories.