Quaternion And Clifford Fourier Transforms And Wavelets

Quaternion And Clifford Fourier Transforms And Wavelets Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Quaternion And Clifford Fourier Transforms And Wavelets book. This book definitely worth reading, it is an incredibly well-written.

Quaternion and Clifford Fourier Transforms and Wavelets

Eckhard Hitzer,Stephen J. Sangwine
Quaternion and Clifford Fourier Transforms and Wavelets Book PDF

Author : Eckhard Hitzer,Stephen J. Sangwine
Publisher : Springer Science & Business Media
Page : 338 pages
File Size : 44,5 Mb
Release : 2013-06-24
Category : Mathematics
ISBN : 9783034806039

Get Book

Quaternion and Clifford Fourier Transforms and Wavelets by Eckhard Hitzer,Stephen J. Sangwine Pdf

Quaternion and Clifford Fourier and wavelet transformations generalize the classical theory to higher dimensions and are becoming increasingly important in diverse areas of mathematics, physics, computer science and engineering. This edited volume presents the state of the art in these hypercomplex transformations. The Clifford algebras unify Hamilton’s quaternions with Grassmann algebra. A Clifford algebra is a complete algebra of a vector space and all its subspaces including the measurement of volumes and dihedral angles between any pair of subspaces. Quaternion and Clifford algebras permit the systematic generalization of many known concepts. This book provides comprehensive insights into current developments and applications including their performance and evaluation. Mathematically, it indicates where further investigation is required. For instance, attention is drawn to the matrix isomorphisms for hypercomplex algebras, which will help readers to see that software implementations are within our grasp. It also contributes to a growing unification of ideas and notation across the expanding field of hypercomplex transforms and wavelets. The first chapter provides a historical background and an overview of the relevant literature, and shows how the contributions that follow relate to each other and to prior work. The book will be a valuable resource for graduate students as well as for scientists and engineers.

Quaternion and Clifford Fourier Transforms

Eckhard Hitzer
Quaternion and Clifford Fourier Transforms Book PDF

Author : Eckhard Hitzer
Publisher : CRC Press
Page : 475 pages
File Size : 53,6 Mb
Release : 2021-09-21
Category : Mathematics
ISBN : 9781000429343

Get Book

Quaternion and Clifford Fourier Transforms by Eckhard Hitzer Pdf

Quaternion and Clifford Fourier Transforms describes the development of quaternion and Clifford Fourier transforms in Clifford (geometric) algebra over the last 30 years. It is the first comprehensive, self-contained book covering this vibrant new area of pure and applied mathematics in depth. The book begins with a historic overview, followed by chapters on Clifford and quaternion algebra and geometric (vector) differential calculus (part of Clifford analysis). The core of the book consists of one chapter on quaternion Fourier transforms and one on Clifford Fourier transforms. These core chapters and their sections on more special topics are reasonably self-contained, so that readers already somewhat familiar with quaternions and Clifford algebra will hopefully be able to begin reading directly in the chapter and section of their particular interest, without frequently needing to skip back and forth. The topics covered are of fundamental interest to pure and applied mathematicians, physicists, and engineers (signal and color image processing, electrical engineering, computer science, computer graphics, artificial intelligence, geographic information science, aero-space engineering, navigation, etc.). Features Intuitive real geometric approach to higher-dimensional Fourier transformations A comprehensive reference, suitable for graduate students and researchers Includes detailed definitions, properties, and many full step-by-step proofs Many figures and tables, a comprehensive biography, and a detailed index make it easy to locate information

Quaternion Fourier Transforms for Signal and Image Processing

Todd A. Ell,Nicolas Le Bihan,Stephen J. Sangwine
Quaternion Fourier Transforms for Signal and Image Processing Book PDF

Author : Todd A. Ell,Nicolas Le Bihan,Stephen J. Sangwine
Publisher : John Wiley & Sons
Page : 168 pages
File Size : 48,7 Mb
Release : 2014-06-23
Category : Technology & Engineering
ISBN : 9781848214781

Get Book

Quaternion Fourier Transforms for Signal and Image Processing by Todd A. Ell,Nicolas Le Bihan,Stephen J. Sangwine Pdf

Based on updates to signal and image processing technology made in the last two decades, this text examines the most recent research results pertaining to Quaternion Fourier Transforms. QFT is a central component of processing color images and complex valued signals. The book’s attention to mathematical concepts, imaging applications, and Matlab compatibility render it an irreplaceable resource for students, scientists, researchers, and engineers.

Quaternionic Integral Transforms

Eckhard Hitzer
Quaternionic Integral Transforms Book PDF

Author : Eckhard Hitzer
Publisher : Springer Nature
Page : 187 pages
File Size : 41,6 Mb
Release : 2023-09-09
Category : Mathematics
ISBN : 9783031283758

Get Book

Quaternionic Integral Transforms by Eckhard Hitzer Pdf

This book presents a machine-generated literature overview of quaternion integral transforms from select papers published by Springer Nature, which have been organized and introduced by the book’s editor. Each chapter presents summaries of predefined themes and provides the reader with a basis for further exploration of the topic. As one of the experimental projects initiated by Springer Nature for AI book content generation, this book shows the latest developments in the field. It will be a useful reference for students and researchers who are interested in exploring the latest developments in quaternion integral transforms.

Wavelet Analysis

Sabrine Arfaoui,Anouar Ben Mabrouk,Carlo Cattani
Wavelet Analysis Book PDF

Author : Sabrine Arfaoui,Anouar Ben Mabrouk,Carlo Cattani
Publisher : CRC Press
Page : 255 pages
File Size : 47,6 Mb
Release : 2021-04-20
Category : Mathematics
ISBN : 9781000369540

Get Book

Wavelet Analysis by Sabrine Arfaoui,Anouar Ben Mabrouk,Carlo Cattani Pdf

Wavelet Analysis: Basic Concepts and Applications provides a basic and self-contained introduction to the ideas underpinning wavelet theory and its diverse applications. This book is suitable for master’s or PhD students, senior researchers, or scientists working in industrial settings, where wavelets are used to model real-world phenomena and data needs (such as finance, medicine, engineering, transport, images, signals, etc.). Features: Offers a self-contained discussion of wavelet theory Suitable for a wide audience of post-graduate students, researchers, practitioners, and theorists Provides researchers with detailed proofs Provides guides for readers to help them understand and practice wavelet analysis in different areas

Mathematics and Computation

Dia Zeidan,Juan C. Cortés,Aliaa Burqan,Ahmad Qazza,Jochen Merker,Gharib Gharib
Mathematics and Computation Book PDF

Author : Dia Zeidan,Juan C. Cortés,Aliaa Burqan,Ahmad Qazza,Jochen Merker,Gharib Gharib
Publisher : Springer Nature
Page : 476 pages
File Size : 48,7 Mb
Release : 2023-05-29
Category : Mathematics
ISBN : 9789819904471

Get Book

Mathematics and Computation by Dia Zeidan,Juan C. Cortés,Aliaa Burqan,Ahmad Qazza,Jochen Merker,Gharib Gharib Pdf

This book collects select papers presented at the 7th International Arab Conference on Mathematics and Computations (IACMC 2022), held from 11–13 May 2022, at Zarqa University, Zarqa, Jordan. These papers discuss a new direction for mathematical sciences. Researchers, professionals and educators will be exposed to research results contributed by worldwide scholars in fundamental and advanced interdisciplinary mathematical research such as differential equations, dynamical systems, matrix analysis, numerical methods and mathematical modelling. The vision of this book is to establish prototypes in completed, current and future mathematical and applied sciences research from advanced and developing countries. The book is intended to make an intellectual contribution to the theory and practice of mathematics. This proceedings would connect scientists in this part of the world to the international level.

Empowering Novel Geometric Algebra for Graphics and Engineering

Eckhard Hitzer,George Papagiannakis,Petr Vasik
Empowering Novel Geometric Algebra for Graphics and Engineering Book PDF

Author : Eckhard Hitzer,George Papagiannakis,Petr Vasik
Publisher : Springer Nature
Page : 138 pages
File Size : 45,6 Mb
Release : 2023-04-26
Category : Mathematics
ISBN : 9783031309236

Get Book

Empowering Novel Geometric Algebra for Graphics and Engineering by Eckhard Hitzer,George Papagiannakis,Petr Vasik Pdf

This book constitutes the proceedings of the Workshop Empowering Novel Geometric Algebra for Graphics and Engineering, ENGAGE 2022, held in conjunction with Computer Graphics International conference, CGI 2022, which took place virtually, in September 2022. The 10 full papers included in this volume were carefully reviewed and selected from 12 submissions. The workshop focused specifically on important aspects of geometric algebra including algebraic foundations, digitized transformations, orientation, conic fitting, protein modelling, digital twinning, and multidimensional signal processing.

Towards Intelligent Systems Modeling and Simulation

Samsul Ariffin Abdul Karim,Afza Shafie
Towards Intelligent Systems Modeling and Simulation Book PDF

Author : Samsul Ariffin Abdul Karim,Afza Shafie
Publisher : Springer Nature
Page : 439 pages
File Size : 52,6 Mb
Release : 2021-09-17
Category : Technology & Engineering
ISBN : 9783030796068

Get Book

Towards Intelligent Systems Modeling and Simulation by Samsul Ariffin Abdul Karim,Afza Shafie Pdf

This book creates the emergence of disruptive technologies that have led to a significant change in the role of mathematics and statistics for problem solving, with the use of sophisticated software and hardware in solving complex systems and process. In the era of digital technology, mathematics and statistics need to be highly relevant to be able to cater for the needs of IR4.0 such as big data analytics, simulation, autonomous system, and cloud computing. Motivated by this development, a total of 26 chapters are contributed by respectable experts for this book. The main scope of the book is to conduct a new system of modeling and simulations on solving differential equations, nonlinear equations, energy, epidemiology, and risk assessment. This book is of interest for postgraduate students, researchers as well as other scientists who are working in numerical modeling and simulations based on efficient mathematical and statistical techniques.

Geometric Algebra Applications Vol. I

Eduardo Bayro-Corrochano
Geometric Algebra Applications Vol I Book PDF

Author : Eduardo Bayro-Corrochano
Publisher : Springer
Page : 742 pages
File Size : 51,5 Mb
Release : 2018-06-20
Category : Technology & Engineering
ISBN : 9783319748306

Get Book

Geometric Algebra Applications Vol. I by Eduardo Bayro-Corrochano Pdf

The goal of the Volume I Geometric Algebra for Computer Vision, Graphics and Neural Computing is to present a unified mathematical treatment of diverse problems in the general domain of artificial intelligence and associated fields using Clifford, or geometric, algebra. Geometric algebra provides a rich and general mathematical framework for Geometric Cybernetics in order to develop solutions, concepts and computer algorithms without losing geometric insight of the problem in question. Current mathematical subjects can be treated in an unified manner without abandoning the mathematical system of geometric algebra for instance: multilinear algebra, projective and affine geometry, calculus on manifolds, Riemann geometry, the representation of Lie algebras and Lie groups using bivector algebras and conformal geometry. By treating a wide spectrum of problems in a common language, this Volume I offers both new insights and new solutions that should be useful to scientists, and engineers working in different areas related with the development and building of intelligent machines. Each chapter is written in accessible terms accompanied by numerous examples, figures and a complementary appendix on Clifford algebras, all to clarify the theory and the crucial aspects of the application of geometric algebra to problems in graphics engineering, image processing, pattern recognition, computer vision, machine learning, neural computing and cognitive systems.

Scientific Legacy Of Professor Zbigniew Oziewicz: Selected Papers From The International Conference "Applied Category Theory Graph-operad-logic"

Hilda Maria Colin Garcia,Jose De Jesus Cruz Guzman,Louis H Kauffman,Hanna Makaruk
Scientific Legacy Of Professor Zbigniew Oziewicz Selected Papers From The International Conference Applied Category Theory Graph operad logic Book PDF

Author : Hilda Maria Colin Garcia,Jose De Jesus Cruz Guzman,Louis H Kauffman,Hanna Makaruk
Publisher : World Scientific
Page : 771 pages
File Size : 55,9 Mb
Release : 2023-09-27
Category : Mathematics
ISBN : 9789811271168

Get Book

Scientific Legacy Of Professor Zbigniew Oziewicz: Selected Papers From The International Conference "Applied Category Theory Graph-operad-logic" by Hilda Maria Colin Garcia,Jose De Jesus Cruz Guzman,Louis H Kauffman,Hanna Makaruk Pdf

Dedicated to the memory of the late Professor Zbigniew Oziewicz from Universidad Nacional Autónoma de México, the book consists of papers on a wide variety of topics related to the work of Professor Oziewicz, which were presented at the special conference on Graph-Operads-Logic (GOL 2021), selected through peer review to promote his scientific legacy.Professor Oziewicz was a great enthusiast and supporter of category theory and its applications in physics, as well as in various areas of mathematics (topology, noncommutative geometry, etc.). In particular, he made significant contributions to the theory of Frobenius algebras, which now are becoming more important due to their connection with topological quantum field theories that are used in mathematical physics and in quantum topology. Professor Oziewicz was a great and very generous teacher, who immersed his students in the beautiful ideas of category theory as well as mathematical physics and computation. It was his idea to start a series of conferences under the title Graphs-Operads-Logic, most of them held in Mexico, with some of them in the USA, which were a great platform to discuss various ideas connected with category theory and its various applications, and to make friends with other scientists. Despite his passing, the GOL 2021 conference is included in this series to pay tribute to his many contributions to diverse areas of science.The book is laid out in twelve main topics where we can find relevant works from distinguished experts.

Advances in Computer Graphics

Bin Sheng,Lei Bi,Jinman Kim,Nadia Magnenat-Thalmann,Daniel Thalmann
Advances in Computer Graphics Book PDF

Author : Bin Sheng,Lei Bi,Jinman Kim,Nadia Magnenat-Thalmann,Daniel Thalmann
Publisher : Springer Nature
Page : 409 pages
File Size : 43,6 Mb
Release : 2024-01-24
Category : Computers
ISBN : 9783031500787

Get Book

Advances in Computer Graphics by Bin Sheng,Lei Bi,Jinman Kim,Nadia Magnenat-Thalmann,Daniel Thalmann Pdf

This 4-volume set of LNCS 14495-14498 constitutes the proceedings of the 40th Computer Graphics International Conference, CGI 2023, held in Shanghai, China, August 28 – September 1, 2023. The 149 papers in this set were carefully reviewed and selected from 385 submissions. They are organized in topical sections as follows: Detection and Recognition; Image Analysis and Processing; Image Restoration and Enhancement; Image Attention and Perception; Reconstruction; Rendering and Animation; Synthesis and Generation; Visual Analytics and Modeling; Graphics and AR/VR; Medical Imaging and Robotics; Theoretical Analysis; Image Analysis and Visualization in Advanced Medical Imaging Technology; Empowering Novel Geometric Algebra for Graphics and Engineering.

Wavelet Analysis on the Sphere

Sabrine Arfaoui,Imen Rezgui,Anouar Ben Mabrouk
Wavelet Analysis on the Sphere Book PDF

Author : Sabrine Arfaoui,Imen Rezgui,Anouar Ben Mabrouk
Publisher : Walter de Gruyter GmbH & Co KG
Page : 156 pages
File Size : 47,9 Mb
Release : 2017-03-20
Category : Mathematics
ISBN : 9783110481242

Get Book

Wavelet Analysis on the Sphere by Sabrine Arfaoui,Imen Rezgui,Anouar Ben Mabrouk Pdf

The goal of this monograph is to develop the theory of wavelet harmonic analysis on the sphere. By starting with orthogonal polynomials and functional Hilbert spaces on the sphere, the foundations are laid for the study of spherical harmonics such as zonal functions. The book also discusses the construction of wavelet bases using special functions, especially Bessel, Hermite, Tchebychev, and Gegenbauer polynomials.

New Directions in Function Theory: From Complex to Hypercomplex to Non-Commutative

Daniel Alpay,Ronen Peretz,David Shoikhet,Mihaela B. Vajiac
New Directions in Function Theory From Complex to Hypercomplex to Non Commutative Book PDF

Author : Daniel Alpay,Ronen Peretz,David Shoikhet,Mihaela B. Vajiac
Publisher : Springer Nature
Page : 389 pages
File Size : 43,5 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9783030764739

Get Book

New Directions in Function Theory: From Complex to Hypercomplex to Non-Commutative by Daniel Alpay,Ronen Peretz,David Shoikhet,Mihaela B. Vajiac Pdf

This volume presents selected contributions from experts gathered at Chapman University for a conference held in November 2019 on new directions in function theory. The papers, written by leading researchers in the field, relate to hypercomplex analysis, Schur analysis and de Branges spaces, new aspects of classical function theory, and infinite dimensional analysis. Signal processing constitutes a strong presence in several of the papers.A second volume in this series of conferences, this book will appeal to mathematicians interested in learning about new fields of development in function theory.

Clifford Analysis and Its Applications

F. Brackx,John Stephen roy Chisholm,V. Soucek
Clifford Analysis and Its Applications Book PDF

Author : F. Brackx,John Stephen roy Chisholm,V. Soucek
Publisher : Springer Science & Business Media
Page : 440 pages
File Size : 46,5 Mb
Release : 2001-07-31
Category : Mathematics
ISBN : 0792370449

Get Book

Clifford Analysis and Its Applications by F. Brackx,John Stephen roy Chisholm,V. Soucek Pdf

In its traditional form, Clifford analysis provides the function theory for solutions of the Dirac equation. From the beginning, however, the theory was used and applied to problems in other fields of mathematics, numerical analysis, and mathematical physics. recently, the theory has enlarged its scope considerably by incorporating geometrical methods from global analysis on manifolds and methods from representation theory. New, interesting branches of the theory are based on conformally invariant, first-order systems other than the Dirac equation, or systems that are invariant with respect to a group other than the conformal group. This book represents an up-to-date review of Clifford analysis in its present form, its applications, and directions for future research. Readership: Mathematicians and theoretical physicists interested in Clifford analysis itself, or in its applications to other fields.

Quaternion Algebras

John Voight
Quaternion Algebras Book PDF

Author : John Voight
Publisher : Springer Nature
Page : 877 pages
File Size : 54,5 Mb
Release : 2021-06-28
Category : Mathematics
ISBN : 9783030566944

Get Book

Quaternion Algebras by John Voight Pdf

This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.