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Computational Noncommutative Algebra and Applications
The fusion of algebra, analysis and geometry, and their application to real world problems, have been dominant themes underlying mathematics for over a century. Geometric algebras, introduced and classified by Clifford in the late 19th century, have played a prominent role in this effort, as seen in the mathematical work of Cartan, Brauer, Weyl, Chevelley, Atiyah, and Bott, and in applications to physics in the work of Pauli, Dirac and others. One of the most important applications of geometric algebras to geometry is to the representation of groups of Euclidean and Minkowski rotations. This aspect and its direct relation to robotics and vision will be discussed in several chapters of this m...
Signal and Image Representation in Combined Spaces
This volume explains how the recent advances in wavelet analysis provide new means for multiresolution analysis and describes its wide array of powerful tools. The book covers variations of the windowed Fourier transform, constructions of special waveforms suitable for specific tasks, the use of redundant representations in reconstruction and enhancement, applications of efficient numerical compression as a tool for fast numerical analysis, and approximation properties of various waveforms in different contexts.
Wavelets
Wavelets: A Tutorial in Theory and Applications is the second volume in the new series WAVELET ANALYSIS AND ITS APPLICATIONS. As a companion to the first volume in this series, this volume covers several of the most important areas in wavelets, ranging from the development of the basic theory such as construction and analysis of wavelet bases to an introduction of some of the key applications, including Mallat's local wavelet maxima technique in second generation image coding. A fairly extensive bibliography is also included in this volume. - Covers several of the most important areas in wavelets, ranging from the development of the basic theory, such as: Construction and analysis of wavelet bases - Introduction of some of the key applications, including Mallat's local wavelet maxima technique in second generation image coding - Extensive bibliography is also included in this volume - Companion to the first volume in this series, An Introduction to Wavelets, and can be used as supplementary instructional material for a two-semester course on wavelet analysis
Computational Excursions in Analysis and Number Theory
This introduction to computational number theory is centered on a number of problems that live at the interface of analytic, computational and Diophantine number theory, and provides a diverse collection of techniques for solving number- theoretic problems. There are many exercises and open research problems included.
Looking Beyond the Highway
Looking beyond the Highway is an examination of road history and roadside attractions specific to the South. Focused in part on numerous aspects of thematerial culture landscape of the Dixie Highway, the essays consider the politics of roadbuilding, roadside entertainment, the buildings and businesses one might encounter along the road, and regional adaptations to the needs and desires of northern tourists. Following the Dixie Highway from southern Illinois to Florida with sidetrips down other southern roads, the essays cover a wide variety of subjects, many of which will resonate with anyone who has ever lived in or vacationed in the South: Harrison Mayes's “Get Right With God” signs; t...
Adaptive High-Resolution Sensor Waveform Design for Tracking
Recent innovations in modern radar for designing transmitted waveforms, coupled with new algorithms for adaptively selecting the waveform parameters at each time step, have resulted in improvements in tracking performance. Of particular interest are waveforms that can be mathematically designed to have reduced ambiguity function sidelobes, as their use can lead to an increase in the target state estimation accuracy. Moreover, adaptively positioning the sidelobes can reveal weak target returns by reducing interference from stronger targets. The manuscript provides an overview of recent advances in the design of multicarrier phase-coded waveforms based on Bjorck constant-amplitude zero-autocor...
Applications of Algebraic Geometry to Coding Theory, Physics and Computation
An up-to-date report on the current status of important research topics in algebraic geometry and its applications, such as computational algebra and geometry, singularity theory algorithms, numerical solutions of polynomial systems, coding theory, communication networks, and computer vision. Contributions on more fundamental aspects of algebraic geometry include expositions related to counting points on varieties over finite fields, Mori theory, linear systems, Abelian varieties, vector bundles on singular curves, degenerations of surfaces, and mirror symmetry of Calabi-Yau manifolds.
New Directions in Rough Sets, Data Mining, and Granular-Soft Computing
This book constitutes the refereed proceedings of the 7th International Workshop on Rough Sets, Fuzzy Sets, Data Mining, and Granular-Soft Computing, RSFDGrC'99, held in Yamaguchi, Japan, in November 1999. The 45 revised regular papers and 15 revised short papers presented together with four invited contributions were carefully reviewed and selected from 89 submissions. The book is divided into sections on rough computing: foundations and applications, rough set theory and applications, fuzzy set theory and applications, nonclassical logic and approximate reasoning, information granulation and granular computing, data mining and knowledge discovery, machine learning, and intelligent agents and systems.
Integrative Problem-Solving in a Time of Decadence
Presents a unique study of Integrative Problem-Solving (IPS). The consideration of 'Decadence' is essential in the scientific study of environmental and other problems and their rigorous solution, because the broad context within which the problems emerge can affect their solution. Stochastic reasoning underlines the conceptual and methodological framework of IPS, and its formulation has a mathematical life of its own that accounts for the multidisciplinarity of real world problems, the multisourced uncertainties characterizing their solution, and the different thinking modes of the people involved. Only by interpolating between the full range of disciplines (including stochastic mathematics, physical science, neuropsychology, philosophy, and sociology) and the associated thinking modes can scientists arrive at a satisfactory account of problem-solving, and be able to distinguish between a technically complete problem-solution, and a solution that has social impact.
Modern Sampling Theory
A state-of-the-art edited survey covering all aspects of sampling theory. Theory, methods and applications are discussed in authoritative expositions ranging from multi-dimensional signal analysis to wavelet transforms. The book is an essential up-to-date resource.
