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Advances in Hypercomplex Analysis

Advances in Hypercomplex Analysis Author Graziano Gentili
ISBN-10 9788847024458
Release 2012-11-14
Pages 148
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This volume is intended to collect important research results to the lectures and discussions which took Place in Rome, at the INdAM Workshop on Different Notions of Regularity for Functions of Quaternionic Variables in September 2010. This volume will collect recent and new results, which are connected to the topic covered during the workshop. The work aims at bringing together international leading specialists in the field of Quaternionic and Clifford Analysis, as well as young researchers interested in the subject, with the idea of presenting and discussing recent results, analyzing new trends and techniques in the area and, in general, of promoting scientific collaboration. Particular attention is paid to the presentation of different notions of regularity for functions of hypercomplex variables, and to the study of the main features of the theories that they originate.



Hypercomplex Analysis New Perspectives and Applications

Hypercomplex Analysis  New Perspectives and Applications Author Swanhild Bernstein
ISBN-10 9783319087719
Release 2014-10-10
Pages 227
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Hypercomplex analysis is the extension of complex analysis to higher dimensions where the concept of a holomorphic function is substituted by the concept of a monogenic function. In recent decades this theory has come to the forefront of higher dimensional analysis. There are several approaches to this: quaternionic analysis which merely uses quaternions, Clifford analysis which relies on Clifford algebras, and generalizations of complex variables to higher dimensions such as split-complex variables. This book includes a selection of papers presented at the session on quaternionic and hypercomplex analysis at the ISAAC conference 2013 in Krakow, Poland. The topics covered represent new perspectives and current trends in hypercomplex analysis and applications to mathematical physics, image analysis and processing, and mechanics.



Regular Functions of a Quaternionic Variable

Regular Functions of a Quaternionic Variable Author Graziano Gentili
ISBN-10 9783642338717
Release 2013-01-11
Pages 185
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The theory of slice regular functions over quaternions is the central subject of the present volume. This recent theory has expanded rapidly, producing a variety of new results that have caught the attention of the international research community. At the same time, the theory has already developed sturdy foundations. The richness of the theory of the holomorphic functions of one complex variable and its wide variety of applications are a strong motivation for the study of its analogs in higher dimensions. In this respect, the four-dimensional case is particularly interesting due to its relevance in physics and its algebraic properties, as the quaternion forms the only associative real division algebra with a finite dimension n>2. Among other interesting function theories introduced in the quaternionic setting, that of (slice) regular functions shows particularly appealing features. For instance, this class of functions naturally includes polynomials and power series. The zero set of a slice regular function has an interesting structure, strictly linked to a multiplicative operation, and it allows the study of singularities. Integral representation formulas enrich the theory and they are a fundamental tool for one of the applications, the construction of a noncommutative functional calculus. The volume presents a state-of-the-art survey of the theory and a brief overview of its generalizations and applications. It is intended for graduate students and researchers in complex or hypercomplex analysis and geometry, function theory, and functional analysis in general. ​



Basics of Functional Analysis with Bicomplex Scalars and Bicomplex Schur Analysis

Basics of Functional Analysis with Bicomplex Scalars  and Bicomplex Schur Analysis Author Daniel Alpay
ISBN-10 9783319051109
Release 2014-03-19
Pages 95
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This book provides the foundations for a rigorous theory of functional analysis with bicomplex scalars. It begins with a detailed study of bicomplex and hyperbolic numbers and then defines the notion of bicomplex modules. After introducing a number of norms and inner products on such modules (some of which appear in this volume for the first time), the authors develop the theory of linear functionals and linear operators on bicomplex modules. All of this may serve for many different developments, just like the usual functional analysis with complex scalars and in this book it serves as the foundational material for the construction and study of a bicomplex version of the well known Schur analysis.



Slice Hyperholomorphic Schur Analysis

Slice Hyperholomorphic Schur Analysis Author Daniel Alpay
ISBN-10 9783319425146
Release 2016-12-09
Pages 362
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This book defines and examines the counterpart of Schur functions and Schur analysis in the slice hyperholomorphic setting. It is organized into three parts: the first introduces readers to classical Schur analysis, while the second offers background material on quaternions, slice hyperholomorphic functions, and quaternionic functional analysis. The third part represents the core of the book and explores quaternionic Schur analysis and its various applications. The book includes previously unpublished results and provides the basis for new directions of research.



Hypercomplex Analysis

Hypercomplex Analysis Author Irene Sabadini
ISBN-10 9783764398934
Release 2009-04-21
Pages 289
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This volume contains some papers written by the participants to the Session “Quaternionic and Cli?ord Analysis” of the 6th ISAAC Conference (held in Ankara, Turkey, in August 2007) and some invited contributions. The contents cover several di?erent aspects of the hypercomplex analysis. All contributed - pers represent the most recent achievements in the area as well as “state-of-the art” expositions. The Editors are grateful to the contributors to this volume, as their works show how the topic of hypercomplex analysis is lively and fertile, and to the r- erees, for their painstaking and careful work. The Editors also thank professor M.W. Wong, President of the ISAAC, for his support which made this volume possible. October 2008, Irene Sabadini Michael Shapiro Frank Sommen Quaternionic and Cli?ord Analysis Trends in Mathematics, 1–9 c 2008 Birkh ̈ auser Verlag Basel/Switzerland An Extension Theorem for Biregular Functions in Cli?ord Analysis Ricardo Abreu Blaya and Juan Bory Reyes Abstract. In this contribution we are interested in ?nding necessary and s- ?cient conditions for thetwo-sided biregular extendibility of functions de?ned 2n on a surface of R , but the latter without imposing any smoothness requi- ment. Mathematics Subject Classi?cation (2000). Primary 30E20, 30E25; Secondary 30G20. Keywords.Cli?ord analysis, biregular functions, Bochner-Martinelli formulae, extension theorems.



Proceedings of 2nd International Conference on Computer Vision Image Processing

Proceedings of 2nd International Conference on Computer Vision   Image Processing Author Bidyut B. Chaudhuri
ISBN-10 9789811078958
Release 2018-04-11
Pages 424
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The book provides insights into the Second International Conference on Computer Vision & Image Processing (CVIP-2017) organized by Department of Computer Science and Engineering of Indian Institute of Technology Roorkee. The book presents technological progress and research outcomes in the area of image processing and computer vision. The topics covered in this book are image/video processing and analysis; image/video formation and display; image/video filtering, restoration, enhancement and super-resolution; image/video coding and transmission; image/video storage, retrieval and authentication; image/video quality; transform-based and multi-resolution image/video analysis; biological and perceptual models for image/video processing; machine learning in image/video analysis; probability and uncertainty handling for image/video processing; motion and tracking; segmentation and recognition; shape, structure and stereo.



Mathematics and Its History

Mathematics and Its History Author John Stillwell
ISBN-10 9781441960528
Release 2010-08-02
Pages 662
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From a review of the second edition: "This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here." (David Parrott, Australian Mathematical Society) This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it’s accessible to a broad audience. This third edition includes new chapters on simple groups and new sections on alternating groups and the Poincare conjecture. Many more exercises have been added as well as commentary that helps place the exercises in context.



Linear Operators and Linear Systems

Linear Operators and Linear Systems Author Jonathan R. Partington
ISBN-10 0521546192
Release 2004-03-15
Pages 166
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Linear systems can be regarded as a causal shift-invariant operator on a Hilbert space of signals, and by doing so this book presents an introduction to the common ground between operator theory and linear systems theory. The book therefore includes material on pure mathematical topics such as Hardy spaces, closed operators, the gap metric, semigroups, shift-invariant subspaces, the commutant lifting theorem and almost-periodic functions, which would be entirely suitable for a course in functional analysis; at the same time, the book includes applications to partial differential equations, to the stability and stabilization of linear systems, to power signal spaces (including some recent material not previously available in books), and to delay systems, treated from an input/output point of view. Suitable for students of analysis, this book also acts as an introduction to a mathematical approach to systems and control for graduate students in departments of applied mathematics or engineering.



Noncommutative Functional Calculus

Noncommutative Functional Calculus Author Fabrizio Colombo
ISBN-10 9783034801102
Release 2011-03-18
Pages 222
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This book presents a functional calculus for n-tuples of not necessarily commuting linear operators. In particular, a functional calculus for quaternionic linear operators is developed. These calculi are based on a new theory of hyperholomorphicity for functions with values in a Clifford algebra: the so-called slice monogenic functions which are carefully described in the book. In the case of functions with values in the algebra of quaternions these functions are named slice regular functions. Except for the appendix and the introduction all results are new and appear for the first time organized in a monograph. The material has been carefully prepared to be as self-contained as possible. The intended audience consists of researchers, graduate and postgraduate students interested in operator theory, spectral theory, hypercomplex analysis, and mathematical physics.



Fourier Analysis in Several Complex Variables

Fourier Analysis in Several Complex Variables Author Leon Ehrenpreis
ISBN-10 9780486153032
Release 2011-11-30
Pages 528
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Suitable for advanced undergraduates and graduate students, this text develops comparison theorems to establish the fundamentals of Fourier analysis and to illustrate their applications to partial differential equations. 1970 edition.



Handbook of Iris Recognition

Handbook of Iris Recognition Author Kevin W. Bowyer
ISBN-10 9781447167846
Release 2016-07-28
Pages 568
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The definitive work on iris recognition technology, this comprehensive handbook presents a broad overview of the state of the art in this exciting and rapidly evolving field. Revised and updated from the highly-successful original, this second edition has also been considerably expanded in scope and content, featuring four completely new chapters. Features: provides authoritative insights from an international selection of preeminent researchers from government, industry, and academia; reviews issues covering the full spectrum of the iris recognition process, from acquisition to encoding; presents surveys of topical areas, and discusses the frontiers of iris research, including cross-wavelength matching, iris template aging, and anti-spoofing; describes open source software for the iris recognition pipeline and datasets of iris images; includes new content on liveness detection, correcting off-angle iris images, subjects with eye conditions, and implementing software systems for iris recognition.



An Imaginary Tale

An Imaginary Tale Author Paul J. Nahin
ISBN-10 1400833892
Release 2010-02-22
Pages 296
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Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them. In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times. Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics. Some images inside the book are unavailable due to digital copyright restrictions.



Intelligent Human Computer Interaction

Intelligent Human Computer Interaction Author Anupam Basu
ISBN-10 9783319525037
Release 2017-03-02
Pages 290
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This book constitutes the proceedings of the 8th International Conference on Intelligent Human Computer Interaction, IHCI 2016, held in Pilani, India, in December 2016. The 22 regular papers and 3 abstracts of invited talks included in this volume were carefully reviewed and selected from 115 initial submissions. They deal with intelligent interfaces; brain machine interaction; HCI applications and technology; and interface and systems.



Topological Vector Spaces Distributions and Kernels

Topological Vector Spaces  Distributions and Kernels Author François Treves
ISBN-10 9781483223629
Release 2016-06-03
Pages 582
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Topological Vector Spaces, Distributions and Kernels discusses partial differential equations involving spaces of functions and space distributions. The book reviews the definitions of a vector space, of a topological space, and of the completion of a topological vector space. The text gives examples of Frechet spaces, Normable spaces, Banach spaces, or Hilbert spaces. The theory of Hilbert space is similar to finite dimensional Euclidean spaces in which they are complete and carry an inner product that can determine their properties. The text also explains the Hahn-Banach theorem, as well as the applications of the Banach-Steinhaus theorem and the Hilbert spaces. The book discusses topologies compatible with a duality, the theorem of Mackey, and reflexivity. The text describes nuclear spaces, the Kernels theorem and the nuclear operators in Hilbert spaces. Kernels and topological tensor products theory can be applied to linear partial differential equations where kernels, in this connection, as inverses (or as approximations of inverses), of differential operators. The book is suitable for vector mathematicians, for students in advanced mathematics and physics.



Computer Vision

Computer Vision Author David A. Forsyth
ISBN-10 0273764144
Release 2012
Pages 791
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Appropriate for upper-division undergraduate and graduate level courses in computer vision found in departments of computer science, computer engineering and electrical engineering, this book offers a treatment of modern computer vision methods.



The Semantic Sphere 1

The Semantic Sphere 1 Author Pierre Lévy
ISBN-10 9781118601518
Release 2013-01-22
Pages 381
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The new digital media offers us an unprecedented memory capacity, an ubiquitous communication channel and a growing computing power. How can we exploit this medium to augment our personal and social cognitive processes at the service of human development? Combining a deep knowledge of humanities and social sciences as well as a real familiarity with computer science issues, this book explains the collaborative construction of a global hypercortex coordinated by a computable metalanguage. By recognizing fully the symbolic and social nature of human cognition, we could transform our current opaque global brain into a reflexive collective intelligence.