Dyadic Walsh Analysis From 1924 Onwards Walsh Gibbs Butzer Dyadic Differentiation In Science Volume 2 Extensions And Generalizations

Author : Radomir Stankovic,Paul Leo Butzer,Ferenc Schipp,William R. Wade,Weiyi Su,Yasushi Endow,Sandor Fridli,Boris I. Golubov,Franz Pichler
Publisher : Springer
Page : 360 pages
File Size : 44,5 Mb
Release : 2015-12-29
Category : Mathematics
ISBN : 9789462391635

Get Book

Dyadic Walsh Analysis from 1924 Onwards Walsh-Gibbs-Butzer Dyadic Differentiation in Science Volume 2 Extensions and Generalizations by Radomir Stankovic,Paul Leo Butzer,Ferenc Schipp,William R. Wade,Weiyi Su,Yasushi Endow,Sandor Fridli,Boris I. Golubov,Franz Pichler Pdf

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.

Author : Radomir Stankovic,Paul Leo Butzer,Ferenc Schipp,William R. Wade,Weiyi Su,Yasushi Endow,Sandor Fridli,Boris I. Golubov,Franz Pichler
Publisher : Springer
Page : 455 pages
File Size : 43,6 Mb
Release : 2015-12-29
Category : Mathematics
ISBN : 9789462391604

Get Book

Dyadic Walsh Analysis from 1924 Onwards Walsh-Gibbs-Butzer Dyadic Differentiation in Science Volume 1 Foundations by Radomir Stankovic,Paul Leo Butzer,Ferenc Schipp,William R. Wade,Weiyi Su,Yasushi Endow,Sandor Fridli,Boris I. Golubov,Franz Pichler Pdf

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.

Author : Bernd Steinbach
Publisher : Cambridge Scholars Publishing
Page : 536 pages
File Size : 44,8 Mb
Release : 2019-01-18
Category : Computers
ISBN : 9781527526389

Get Book

Further Improvements in the Boolean Domain by Bernd Steinbach Pdf

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.

Author : Radomir S. Stanković
Publisher : Springer Nature
Page : 287 pages
File Size : 54,8 Mb
Release : 2024
Category : Electronic
ISBN : 9783031506505

Get Book

BENT FUNCTIONS AND PERMUTATION METHODS by Radomir S. Stanković Pdf

Author : Thomas J. Buckholtz
Publisher : Springer
Page : 382 pages
File Size : 53,7 Mb
Release : 2016-05-20
Category : Science
ISBN : 9789462391666

Get Book

Models for Physics of the Very Small and Very Large by Thomas J. Buckholtz Pdf

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.

Author : William Wade
Publisher : Unknown
Page : 0 pages
File Size : 47,9 Mb
Release : 2017-03-08
Category : Mathematical analysis
ISBN : 0134707621

Get Book

Introduction to Analysis, an (Classic Version) by William Wade Pdf

For one- or two-semester junior or senior level courses in Advanced Calculus, Analysis I, or Real Analysis. This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics-series for a complete list of titles. This text prepares students for future courses that use analytic ideas, such as real and complex analysis, partial and ordinary differential equations, numerical analysis, fluid mechanics, and differential geometry. This book is designed to challenge advanced students while encouraging and helping weaker students. Offering readability, practicality and flexibility, Wade presents fundamental theorems and ideas from a practical viewpoint, showing students the motivation behind the mathematics and enabling them to construct their own proofs.

Author : S. Leela,V. Lakshmikantham
Publisher : Springer Science & Business Media
Page : 208 pages
File Size : 45,8 Mb
Release : 2010-01-01
Category : Mathematics
ISBN : 9789491216251

Get Book

THEORY OF CAUSAL DIFFERENTIAL EQUATIONS by S. Leela,V. Lakshmikantham Pdf

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.

Author : E. Escultura,V. Lakshmikantham
Publisher : Springer Science & Business Media
Page : 132 pages
File Size : 53,9 Mb
Release : 2009-03-01
Category : Science
ISBN : 9789491216237

Get Book

THE HYBRID GRAND UNIFIED THEORY by E. Escultura,V. Lakshmikantham Pdf

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.

Author : P.L. Butzer,E. Gärlich,B. Szökefalvi-Nagy
Publisher : Birkhäuser
Page : 461 pages
File Size : 40,9 Mb
Release : 2013-03-07
Category : Mathematics
ISBN : 9783034893695

Get Book

Functional Analysis and Approximation by P.L. Butzer,E. Gärlich,B. Szökefalvi-Nagy Pdf

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.

Author : Takashi Suzuki
Publisher : Springer Science & Business Media
Page : 299 pages
File Size : 52,7 Mb
Release : 2009-01-01
Category : Mathematics
ISBN : 9789491216220

Get Book

MEAN FIELD THEORIES AND DUAL VARIATION by Takashi Suzuki Pdf

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.

Author : B.G. Pachpatte
Publisher : Springer Science & Business Media
Page : 248 pages
File Size : 45,7 Mb
Release : 2011-07-26
Category : Mathematics
ISBN : 9789491216176

Get Book

Multidimensional Integral Equations and Inequalities by B.G. Pachpatte Pdf

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.

Author : Haakon Waadeland,Lisa Lorentzen
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 55,5 Mb
Release : 2008-04-01
Category : Mathematics
ISBN : 9789491216374

Get Book

CONTINUED FRACTIONS by Haakon Waadeland,Lisa Lorentzen Pdf

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.

Author : Goong Chen
Publisher : Unknown
Page : 680 pages
File Size : 49,8 Mb
Release : 1992
Category : Boundary element methods
ISBN : UOM:39015020880251

Get Book

Boundary Element Methods by Goong Chen Pdf

Author : Tsutomu Sasao
Publisher : Springer Nature
Page : 165 pages
File Size : 54,9 Mb
Release : 2022-05-31
Category : Technology & Engineering
ISBN : 9783031799112

Get Book

Index Generation Functions by Tsutomu Sasao Pdf

Index generation functions are binary-input integer valued functions. They represent functions of content addressable memories (CAMs). Applications include: IP address tables; terminal controllers; URL lists; computer virus scanning circuits; memory patch circuits; list of English words; code converters; and pattern matching circuits. This book shows memory-based realization of index generation functions. It shows: 1. methods to implement index generation functions by look-up table (LUT) cascades and index generation units (IGU), 2. methods to reduce the number of variables using linear transformations, and 3. methods to estimate the sizes of memories, with many illustrations, tables, examples, exercises, and their solutions.

Author : Su Weiyi
Publisher : World Scientific
Page : 332 pages
File Size : 49,9 Mb
Release : 2017-08-17
Category : Mathematics
ISBN : 9789813200524

Get Book

Harmonic Analysis And Fractal Analysis Over Local Fields And Applications by Su Weiyi Pdf

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.