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Dyadic Walsh Analysis From 1924 Onwards Walsh Gibbs Butzer Dyadic Differentiation In Science Volume 2 Extensions And Generalizations
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Book Synopsis Dyadic Walsh Analysis from 1924 Onwards Walsh-Gibbs-Butzer Dyadic Differentiation in Science Volume 2 Extensions and Generalizations by : Radomir Stankovic
Download or read book Dyadic Walsh Analysis from 1924 Onwards Walsh-Gibbs-Butzer Dyadic Differentiation in Science Volume 2 Extensions and Generalizations written by Radomir Stankovic and published by Springer. This book was released on 2015-12-29 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Dyadic Walsh Analysis from 1924 Onwards Walsh-Gibbs-Butzer Dyadic Differentiation in Science Volume 1 Foundations by : Radomir Stankovic
Download or read book Dyadic Walsh Analysis from 1924 Onwards Walsh-Gibbs-Butzer Dyadic Differentiation in Science Volume 1 Foundations written by Radomir Stankovic and published by Springer. This book was released on 2015-12-29 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Further Improvements in the Boolean Domain by : Bernd Steinbach
Download or read book Further Improvements in the Boolean Domain written by Bernd Steinbach and published by Cambridge Scholars Publishing. This book was released on 2019-01-18 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis BENT FUNCTIONS AND PERMUTATION METHODS by : Radomir S. Stanković
Download or read book BENT FUNCTIONS AND PERMUTATION METHODS written by Radomir S. Stanković and published by Springer Nature. This book was released on 2024 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Models for Physics of the Very Small and Very Large by : Thomas J. Buckholtz
Download or read book Models for Physics of the Very Small and Very Large written by Thomas J. Buckholtz and published by Springer. This book was released on 2016-05-20 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph tackles three challenges. First, show a mathematics-based meta-model that matches known elementary particles. Second, apply models, based on the meta-model, to match other known physics data. Third, predict future physics data. The math features solutions to isotropic pairs of isotropic quantum harmonic oscillators. This monograph matches some solutions to known elementary particles. Matched properties include spin, types of interactions in which the particles partake, and (for elementary bosons) approximate masses. Other solutions point to possible elementary particles. This monograph applies the models and the extended particle list. Results narrow gaps between physics data and theory. Results pertain to elementary particles, astrophysics, and cosmology. For example, this monograph predicts properties for beyond-the-Standard-Model elementary particles, proposes descriptions of dark matter and dark energy, provides new relationships between known physics constants (including masses of some elementary particles), includes theory that dovetails with the ratio of dark matter to ordinary matter, includes math that dovetails with the number of elementary-fermion generations, suggests forces that govern the rate of expansion of the universe, and suggests additions to and details for the cosmology timeline.
Book Synopsis THEORY OF CAUSAL DIFFERENTIAL EQUATIONS by : S. Leela
Download or read book THEORY OF CAUSAL DIFFERENTIAL EQUATIONS written by S. Leela and published by Springer Science & Business Media. This book was released on 2010-01-01 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problems of modern society are both complex and inter-disciplinary. Despite the - parent diversity of problems, however, often tools developed in one context are adaptable to an entirely different situation. For example, consider the well known Lyapunov’s second method. This interesting and fruitful technique has gained increasing signi?cance and has given decisive impetus for modern development of stability theory of discrete and dynamic system. It is now recognized that the concept of Lyapunov function and theory of diff- ential inequalities can be utilized to investigate qualitative and quantitative properties of a variety of nonlinear problems. Lyapunov function serves as a vehicle to transform a given complicated system into a simpler comparison system. Therefore, it is enough to study the properties of the simpler system to analyze the properties of the complicated system via an appropriate Lyapunov function and the comparison principle. It is in this perspective, the present monograph is dedicated to the investigation of the theory of causal differential equations or differential equations with causal operators, which are nonanticipative or abstract Volterra operators. As we shall see in the ?rst chapter, causal differential equations include a variety of dynamic systems and consequently, the theory developed for CDEs (Causal Differential Equations) in general, covers the theory of several dynamic systems in a single framework.
Book Synopsis THE HYBRID GRAND UNIFIED THEORY by : E. Escultura
Download or read book THE HYBRID GRAND UNIFIED THEORY written by E. Escultura and published by Springer Science & Business Media. This book was released on 2009-03-01 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, an attempt is made to provide a hybrid grand unified theory to understand the universe, both in its micro/quantum aspects as well as macro/galactic aspects. The book describes a truly hybrid theory as it encompasses both the modern and ancient theories of the universe, together with its functioning at all levels of human comprehension. One of its authors, Dr Escultura, was nominated in 2005 for a Nobel Prize for his flux theory of gravitation. From then on this theory has been improved, clarified and is now known as the hybrid grand unified theory. This book deals with this new bold theory, unifying mathematics and physics, and answering some open fundamental questions and paradoxes in these disciplines. The book also describes what the ancient scientists knew about these matters.
Book Synopsis Functional Analysis and Approximation by : P.L. Butzer
Download or read book Functional Analysis and Approximation written by P.L. Butzer and published by Birkhäuser. This book was released on 2013-03-07 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Harmonic Analysis And Fractal Analysis Over Local Fields And Applications by : Su Weiyi
Download or read book Harmonic Analysis And Fractal Analysis Over Local Fields And Applications written by Su Weiyi and published by World Scientific. This book was released on 2017-08-17 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis MEAN FIELD THEORIES AND DUAL VARIATION by : Takashi Suzuki
Download or read book MEAN FIELD THEORIES AND DUAL VARIATION written by Takashi Suzuki and published by Springer Science & Business Media. This book was released on 2009-01-01 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: A mathematical theory is introduced in this book to unify a large class of nonlinear partial differential equation (PDE) models for better understanding and analysis of the physical and biological phenomena they represent. The so-called mean field approximation approach is adopted to describe the macroscopic phenomena from certain microscopic principles for this unified mathematical formulation. Two key ingredients for this approach are the notions of “duality” according to the PDE weak solutions and “hierarchy” for revealing the details of the otherwise hidden secrets, such as physical mystery hidden between particle density and field concentration, quantized blow up biological mechanism sealed in chemotaxis systems, as well as multi-scale mathematical explanations of the Smoluchowski–Poisson model in non-equilibrium thermodynamics, two-dimensional turbulence theory, self-dual gauge theory, and so forth. This book shows how and why many different nonlinear problems are inter-connected in terms of the properties of duality and scaling, and the way to analyze them mathematically.
Book Synopsis Multidimensional Integral Equations and Inequalities by : B.G. Pachpatte
Download or read book Multidimensional Integral Equations and Inequalities written by B.G. Pachpatte and published by Springer Science & Business Media. This book was released on 2011-07-26 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since from more than a century, the study of various types of integral equations and inequalities has been focus of great attention by many researchers, interested both in theory and its applications. In particular, there exists a very rich literature related to the integral equations and inequalities and their applications. The present monograph is an attempt to organize recent progress related to the Multidimensional integral equations and inequalities, which we hope will widen the scope of their new applications. The field to be covered is extremely wide and it is nearly impossible to treat all of them here. The material included in the monograph is recent and hard to find in other books. It is accessible to any reader with reasonable background in real analysis and acquaintance with its related areas. All results are presented in an elementary way and the book could also serve as a textbook for an advanced graduate course. The book deserves a warm welcome to those who wish to learn the subject and it will also be most valuable as a source of reference in the field. It will be an invaluable reading for mathematicians, physicists and engineers and also for graduate students, scientists and scholars wishing to keep abreast of this important area of research.
Book Synopsis P-adic Analysis and Mathematical Physics by : Vasili? Sergeevich Vladimirov
Download or read book P-adic Analysis and Mathematical Physics written by Vasili? Sergeevich Vladimirov and published by World Scientific. This book was released on 1994 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: p-adic numbers play a very important role in modern number theory, algebraic geometry and representation theory. Lately p-adic numbers have attracted a great deal of attention in modern theoretical physics as a promising new approach for describing the non-Archimedean geometry of space-time at small distances.This is the first book to deal with applications of p-adic numbers in theoretical and mathematical physics. It gives an elementary and thoroughly written introduction to p-adic numbers and p-adic analysis with great numbers of examples as well as applications of p-adic numbers in classical mechanics, dynamical systems, quantum mechanics, statistical physics, quantum field theory and string theory.
Book Synopsis CONTINUED FRACTIONS by : Haakon Waadeland
Download or read book CONTINUED FRACTIONS written by Haakon Waadeland and published by Springer Science & Business Media. This book was released on 2008-04-01 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Continued Fractions consists of two volumes — Volume 1: Convergence Theory; and Volume 2: Representation of Functions (tentative title), which is expected in 2011. Volume 1 is dedicated to the convergence and computation of continued fractions, while Volume 2 will treat representations of meromorphic functions by continued fractions. Taken together, the two volumes will present the basic continued fractions theory without requiring too much previous knowledge; some basic knowledge of complex functions will suffice. Both new and advanced graduate students of continued fractions shall get a comprehensive understanding of how these infinite structures work in a number of applications, and why they work so well. A varied buffet of possible applications to whet the appetite is presented first, before the more basic but modernized theory is given. This new edition is the result of an increasing interest in computing special functions by means of continued fractions. The methods described in detail are, in many cases, very simple, yet reliable and efficient.
Book Synopsis Boundary Element Methods by : Goong Chen
Download or read book Boundary Element Methods written by Goong Chen and published by . This book was released on 1992 with total page 680 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Pseudo-Differential Equations And Stochastics Over Non-Archimedean Fields by : Anatoly Kochubei
Download or read book Pseudo-Differential Equations And Stochastics Over Non-Archimedean Fields written by Anatoly Kochubei and published by CRC Press. This book was released on 2001-08-03 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides comprehensive coverage of the most recent developments in the theory of non-Archimedean pseudo-differential equations and its application to stochastics and mathematical physics--offering current methods of construction for stochastic processes in the field of p-adic numbers and related structures. Develops a new theory for parabolic equat
Book Synopsis Computer Aided Systems Theory - Eurocast '89 by : Franz Pichler
Download or read book Computer Aided Systems Theory - Eurocast '89 written by Franz Pichler and published by . This book was released on 2014-01-15 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Hybrid Continuous/Discrete-Time Models by : Marat Akhmet
Download or read book Nonlinear Hybrid Continuous/Discrete-Time Models written by Marat Akhmet and published by Springer Science & Business Media. This book was released on 2011-05-03 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is mainly about hybrid systems with continuous/discrete-time dynamics. The major part of the book consists of the theory of equations with piece-wise constant argument of generalized type. The systems as well as technique of investigation were introduced by the author very recently. They both generalized known theory about differential equations with piece-wise constant argument, introduced by K. Cook and J. Wiener in the 1980s. Moreover, differential equations with fixed and variable moments of impulses are used to model real world problems. We consider models of neural networks, blood pressure distribution and a generalized model of the cardiac pacemaker. All the results of the manuscript have not been published in any book, yet. They are very recent and united with the presence of the continuous/discrete dynamics of time. It is of big interest for specialists in biology, medicine, engineering sciences, electronics. Theoretical aspects of the book meet very strong expectations of mathematicians who investigate differential equations with discontinuities of any type.
