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| hypercomplex algebra: Hypercomplex Numbers Isaĭ Lʹvovich Kantor, Aleksandr Samuilovich Solodovnikov, 1989 |
| hypercomplex algebra: Geometric Computing with Clifford Algebras Gerald Sommer, 2013-06-29 Clifford algebra, then called geometric algebra, was introduced more than a cenetury ago by William K. Clifford, building on work by Grassmann and Hamilton. Clifford or geometric algebra shows strong unifying aspects and turned out in the 1960s to be a most adequate formalism for describing different geometry-related algebraic systems as specializations of one mother algebra in various subfields of physics and engineering. Recent work outlines that Clifford algebra provides a universal and powerfull algebraic framework for an elegant and coherent representation of various problems occuring in computer science, signal processing, neural computing, image processing, pattern recognition, computer vision, and robotics. This monograph-like anthology introduces the concepts and framework of Clifford algebra and provides computer scientists, engineers, physicists, and mathematicians with a rich source of examples of how to work with this formalism. |
| hypercomplex algebra: Harmonic Analysis in Hypercomplex Systems Yu.M. Berezansky, A.A. Kalyuzhnyi, 2013-06-29 First works related to the topics covered in this book belong to J. Delsarte and B. M. Le vitan and appeared since 1938. In these works, the families of operators that generalize usual translation operators were investigated and the corresponding harmonic analysis was constructed. Later, starting from 1950, it was noticed that, in such constructions, an important role is played by the fact that the kernels of the corresponding convolutions of functions are nonnegative and by the properties of the normed algebras generated by these convolutions. That was the way the notion of hypercomplex system with continu ous basis appeared. A hypercomplex system is a normed algebra of functions on a locally compact space Q-the basis of this hypercomplex system. Later, similar objects, hypergroups, were introduced, which have complex-valued measures on Q as elements and convolution defined to be essentially the convolution of functionals and dual to the original convolution (if measures are regarded as functionals on the space of continuous functions on Q). However, until 1991, the time when this book was written in Russian, there were no monographs containing fundamentals of the theory (with an exception of a short section in the book by Yu. M. Berezansky and Yu. G. Kondratiev [BeKo]). The authors wanted to give an introduction to the theory and cover the most important subsequent results and examples. |
| hypercomplex algebra: Clifford Algebras Rafal Ablamowicz, 2012-12-06 The invited papers in this volume provide a detailed examination of Clifford algebras and their significance to analysis, geometry, mathematical structures, physics, and applications in engineering. While the papers collected in this volume require that the reader possess a solid knowledge of appropriate background material, they lead to the most current research topics. With its wide range of topics, well-established contributors, and excellent references and index, this book will appeal to graduate students and researchers. |
| hypercomplex algebra: Clifford Algebras with Numeric and Symbolic Computations Rafal Ablamowicz, Joseph Parra, Pertti Lounesto, 2012-12-06 Clifford algebras are at a crossing point in a variety of research areas, including abstract algebra, crystallography, projective geometry, quantum mechanics, differential geometry and analysis. For many researchers working in this field in ma- thematics and physics, computer algebra software systems have become indispensable tools in theory and applications. This edited survey book consists of 20 chapters showing application of Clifford algebra in quantum mechanics, field theory, spinor calculations, projective geometry, Hypercomplex algebra, function theory and crystallography. Many examples of computations performed with a variety of readily available software programs are presented in detail, i.e., Maple, Mathematica, Axiom, etc. A key feature of the book is that it shows how scientific knowledge can advance with the use of computational tools and software. |
| hypercomplex algebra: Space-Time Algebra of Sedeons Victor L. Mironov, Sergey V. Mironov, 2025-03-31 This book is a comprehensive guide to the space-time algebra of sixteen-component values sedeons. This algebra is designed to provide a compact representation of equations that describe various physical systems. The book considers the symmetry of physical quantities concerning the operations of spatial and temporal inversion. This approach allows the formulation of a wide class of mathematical physics equations within a unified framework and enables the generalization of these equations for essential problems in electrodynamics, hydrodynamics, plasma physics, field theory, and quantum mechanics. In particular, it is shown that the broken symmetry between electricity and magnetism in electrodynamics equations is a result of choosing an asymmetric representation of these phenomena. The sedeonic algebra enables the formulation of Maxwell-like equations for the fields with a nonzero mass of quantum, which facilitates the calculation of energy for baryon-baryon interaction and the semi-classical interpretation of this interaction. It also allows one to generalize the hydrodynamics equations for the case of vortex turbulent flows and for a hydrodynamic two-fluid model of electron-ion plasma. |
| hypercomplex algebra: Hypercomplex Numbers I.L. Kantor, A.S. Solodovnikov, 1989-05-15 This book deals with various systems of numbers that can be constructed by adding imaginary units to the real numbers. The complex numbers are a classical example of such a system. One of the most important properties of the complex numbers is given by the identity (1) Izz'l = Izl·Iz'I· It says, roughly, that the absolute value of a product is equal to the product of the absolute values of the factors. If we put z = al + a2i, z' = b+ bi, 1 2 then we can rewrite (1) as The last identity states that the product of a sum of two squares by a sum of two squares is a sum of two squares. It is natural to ask if there are similar identities with more than two squares, and how all of them can be described. Already Euler had given an example of an identity with four squares. Later an identity with eight squares was found. But a complete solution of the problem was obtained only at the end of the 19th century. It is substantially true that every identity with n squares is linked to formula (1), except that z and z' no longer denote complex numbers but more general numbers where i,j, . . . , I are imaginary units. One of the main themes of this book is the establishing of the connection between identities with n squares and formula (1). |
| hypercomplex algebra: A History of Abstract Algebra Israel Kleiner, 2007-09-20 This book does nothing less than provide an account of the intellectual lineage of abstract algebra. The development of abstract algebra was propelled by the need for new tools to address certain classical problems that appeared insoluble by classical means. A major theme of the book is to show how abstract algebra has arisen in attempting to solve some of these classical problems, providing a context from which the reader may gain a deeper appreciation of the mathematics involved. Mathematics instructors, algebraists, and historians of science will find the work a valuable reference. |
| hypercomplex algebra: Quaternionic Structures in Mathematics and Physics Stefano Marchiafava, Paolo Piccinni, Massimiliano Pontecorvo, 2001 During the last five years, after the first meeting on OC Quaternionic Structures in Mathematics and PhysicsOCO, interest in quaternionic geometry and its applications has continued to increase. Progress has been made in constructing new classes of manifolds with quaternionic structures (quaternionic Knhler, hyper-Knhler, hyper-complex, etc.), studying the differential geometry of special classes of such manifolds and their submanifolds, understanding relations between the quaternionic structure and other differential-geometric structures, and also in physical applications of quaternionic geometry. Some generalizations of classical quaternion-like structures (like HKT structures and hyper-Knhler manifolds with singularities) appeared naturally and were studied. Some of those results are published in this book. Contents: Hypercomplex Structures on Special Classes of Nilpotent and Solvable Lie Groups (M L Barberis); Twistor Quotients of HyperKnhler Manifolds (R Bielawski); Quaternionic Contact Structures (O Biquard); A New Construction of Homogeneous Quaternionic Manifolds and Related Geometric Structures (V Cortes); Quaternion Knhler Flat Manifolds (I G Dotti); A Canonical HyperKnhler Metric on the Total Space of a Cotangent Bundle (D Kaledin); Special Spinors and Contact Geometry (A Moroianu); Brane Solitons and Hypercomplex Structures (G Papadopoulos); Hypercomplex Geometry (H Pedersen); Examples of HyperKnhler Connections with Torsion (Y S Poon); A New Weight System on Chord Diagrams via HyperKnhler Geometry (J Sawon); Vanishing Theorems for Quaternionic Knhler Manifolds (U Semmelmann & G Weingart); Weakening Holonomy (A Swann); Special Knhler Geometry (A Van Proeyen); Singularities in HyperKnhler Geometry (M Verbitsky); and other papers. Readership: Researchers and graduate students in geometry, topology, mathematical physics and theoretical physics. |
| hypercomplex algebra: American Journal of Mathematics , 1919 The American Journal of Mathematics publishes research papers and articles of broad appeal covering the major areas of contemporary mathematics. |
| hypercomplex algebra: Power Quality Mr. Rohit Manglik, 2024-07-25 EduGorilla Publication is a trusted name in the education sector, committed to empowering learners with high-quality study materials and resources. Specializing in competitive exams and academic support, EduGorilla provides comprehensive and well-structured content tailored to meet the needs of students across various streams and levels. |
| hypercomplex algebra: Computational Noncommutative Algebra and Applications Jim Byrnes, Gerald Ostheimer, 2006-01-28 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 multi-authored textbook, which resulted from the ASI meeting. Moreover, group theory, beginning with the work of Burnside, Frobenius and Schur, has been influenced by even more general problems. As a result, general group actions have provided the setting for powerful methods within group theory and for the use of groups in applications to physics, chemistry, molecular biology, and signal processing. These aspects, too, will be covered in detail. With the rapidly growing importance of, and ever expanding conceptual and computational demands on signal and image processing in remote sensing, computer vision, medical image processing, and biological signal processing, and on neural and quantum computing, geometric algebras, and computational group harmonic analysis, the topics of the book have emerged as key tools. The list of authors includes many of the world's leading experts in the development of new algebraic modeling and signal representation methodologies, novel Fourier-based and geometrictransforms, and computational algorithms required for realizing the potential of these new application fields. The intention of this textbook is share their profound wisdom with the many future stars of pure and computational noncommutative algebra. A key feature of both the meeting and the book will be their presentation of problems and applications that will shape the twenty-first century computational technology base. |
| hypercomplex algebra: Contemporary Geometry And Related Topics, Proceedings Of The Workshop Neda Bokan, Mirjana Djoric, Anatoly T Fomenko, Zoran Rakic, Julius Wess, 2004-03-15 This volume covers a broad range of subjects in modern geometry and related branches of mathematics, physics and computer science. Most of the papers show new, interesting results in Riemannian geometry, homotopy theory, theory of Lie groups and Lie algebras, topological analysis, integrable systems, quantum groups, and noncommutative geometry. There are also papers giving overviews of the recent achievements in some special topics, such as the Willmore conjecture, geodesic mappings, Weyl's tube formula, and integrable geodesic flows. This book provides a great chance for interchanging new results and ideas in multidisciplinary studies.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences |
| hypercomplex algebra: Proceedings of the Workshop Contemporary Geometry and Related Topics Neda Bokan, 2004 Readership: Researchers in geometry & topology, nonlinear science and dynamical systems. |
| hypercomplex algebra: Parallel Computing Technologies Viktor Ėmmanuilovich Malyshkin, 2005-08-18 This book constitutes the refereed proceedings of the 8th International Conference on Parallel Computing Technologies, PaCT 2005, held in Krasnoyarsk, Russia in September 2005. The 38 revised full papers presented together with 1 invited paper were carefully reviewed and selected from 78 submissions. The papers are organized in topical sections on theory, fine-grain parallelism, software, tools, and applications. A broad variety of parallel processing issues and distributed computing in general are addressed as well. |
| hypercomplex algebra: Applied Analysis, Optimization and Soft Computing Tanmoy Som, Debdas Ghosh, Oscar Castillo, Adrian Petrusel, Dayaram Sahu, 2023-06-10 This book contains select contributions presented at the International Conference on Nonlinear Applied Analysis and Optimization (ICNAAO-2021), held at the Department of Mathematics Sciences, Indian Institute of Technology (BHU) Varanasi, India, from 21–23 December 2021. The book discusses topics in the areas of nonlinear analysis, fixed point theory, dynamical systems, optimization, fractals, applications to differential/integral equations, signal and image processing, and soft computing, and exposes the young talents with the newer dimensions in these areas with their practical approaches and to tackle the real-life problems in engineering, medical and social sciences. Scientists from the U.S.A., Austria, France, Mexico, Romania, and India have contributed their research. All the submissions are peer reviewed by experts in their fields. |
| hypercomplex algebra: Old and New Questions in Physics, Cosmology, Philosophy, and Theoretical Biology Alwyn Van der Merwe, 2012-12-06 Simply to say that this is a collection of essays in honor of the late Wolfgang Yourgrau (1908-1979) is to explain, at least for-the obviously many-insiders, the unusually wide-ranging title of the present volume. In a Foreword to the Proceedings of the First International Colloquium (focusing on logic, physical reality, and history), held at the University of Denver in May of 1966 under their leadership, Wolfgang Y ourgrau and Allen Breck wrote, in an oblique reference to C. P. Snow: Indeed there are not two or three or four cultures: there is only one culture; our generation has lost its awareness of this . . . . Historians, logicians, physicists-all are banded in one common enterprise, namely in their des ire to weave an enlightened fabric of human knowledge. Augment, if you will, the foregoing categories of scholars with biologists, philos ophers, cosmologists, and theologians-all of whom, in addition to historians, Wolf gang Yourgrau, by dint of his inextinguishable enthusiasm and charismatic qualities, assembled in Denver for the Second and Third International Colloquia (in 1967 and 1974, respectively)-and a few other besides, and one arrives at a statement of the credo wh ich Y ourgrau not only professed, but consistently exemplified throughout his adult life. |
| hypercomplex algebra: The Mathematics of Frobenius in Context Thomas Hawkins, 2013-07-23 Frobenius made many important contributions to mathematics in the latter part of the 19th century. Hawkins here focuses on his work in linear algebra and its relationship with the work of Burnside, Cartan, and Molien, and its extension by Schur and Brauer. He also discusses the Berlin school of mathematics and the guiding force of Weierstrass in that school, as well as the fundamental work of d'Alembert, Lagrange, and Laplace, and of Gauss, Eisenstein and Cayley that laid the groundwork for Frobenius's work in linear algebra. The book concludes with a discussion of Frobenius's contribution to the theory of stochastic matrices. |
| hypercomplex algebra: Intelligent Systems João Carlos Xavier-Junior, Ricardo Araújo Rios, 2022-11-18 The two-volume set LNAI 13653 and 13654 constitutes the refereed proceedings of the 11th Brazilian Conference on Intelligent Systems, BRACIS 2022, which took place in Campinas, Brazil, in November/December 2022. The 89 papers presented in the proceedings were carefully reviewed and selected from 225 submissions. The conference deals with theoretical aspects and applications of artificial and computational intelligence. |
| hypercomplex algebra: Applications of Hypergroups and Related Measure Algebras , 1995-02-28 `The most important single thing about this conference was that it brought together for the first time representatives of all major groups of users of hypergroups. [They] talked to each other about how they were using hypergroups in fields as diverse as special functions, probability theory, representation theory, measure algebras, Hopf algebras, and Hecke algebras. This led to fireworks.' - from the Introduction. Hypergroups occur in a wide variety of contexts, and mathematicians the world over have been discovering this same mathematical structure hidden in very different applications. The diverse viewpoints on the subject have led to the need for a common perspective, if not a common theory. Presenting the proceedings of a Joint Summer Research Conference held in Seattle in the summer of 1993, this book will serve as a valuable starting point and reference tool for the wide range of users of hypergroups and make it easier for an even larger audience to use these structures in their work. |
| hypercomplex algebra: Proceedings of the London Mathematical Society London Mathematical Society, 1928 Papers presented to J. E. Littlewood on his 80th birthday issued as 3d ser., v. 14 A, 1965. |
| hypercomplex algebra: Hypercomplex Numbers I.L. Kantor, A.S. Solodovnikov, 1989-05-01 This book deals with various systems of numbers that can be constructed by adding imaginary units to the real numbers. The complex numbers are a classical example of such a system. One of the most important properties of the complex numbers is given by the identity (1) Izz'l = Izl·Iz'I· It says, roughly, that the absolute value of a product is equal to the product of the absolute values of the factors. If we put z = al + a2i, z' = b+ bi, 1 2 then we can rewrite (1) as The last identity states that the product of a sum of two squares by a sum of two squares is a sum of two squares. It is natural to ask if there are similar identities with more than two squares, and how all of them can be described. Already Euler had given an example of an identity with four squares. Later an identity with eight squares was found. But a complete solution of the problem was obtained only at the end of the 19th century. It is substantially true that every identity with n squares is linked to formula (1), except that z and z' no longer denote complex numbers but more general numbers where i,j, . . . , I are imaginary units. One of the main themes of this book is the establishing of the connection between identities with n squares and formula (1). |
| hypercomplex algebra: Hyperspace Unleashed Barrett Williams, ChatGPT, 2024-11-10 Unlock the mysteries of faster-than-light travel with Hyperspace Unleashed, a riveting journey through the warp theories and futuristic technologies that could transform our reality. This groundbreaking eBook serves as a doorway into the mind-bending world of warp fields and spacetime, offering detailed insights into one of the most fascinating scientific frontiers of our age. Begin your exploration with a solid foundation in the nature of spacetime, where the intricacies of warp fields are meticulously unfolded. Dive into the mathematical realm with sections that address the Einstein Field Equations and hypercomplex numbers, laying the groundwork for understanding the core mechanics of warp dynamics. Venture further into theoretical territories with Alcubierre's Warp Drive Concept, as mathematical implications and the formidable challenges of negative energy come to light. Discover how exotic matter, the Casimir effect, and quantum vacuum play pivotal roles in the theoretical landscape. Explore the compelling implications of hyperspace travel, from the technical demands of energy efficiency to the societal impact of interstellar exploration. As you navigate through these chapters, gain profound insights into the potential for groundbreaking technologies, including nano-engineering, quantum computing, and artificial intelligence, all poised to revolutionize warp field generation. Engage with thought-provoking discussions on quantum entanglement, multidimensional theories, and emerging experimental approaches, offering fascinating perspectives on what lies ahead. Delve into the engineering challenges that demand innovative solutions for controlling warp fields, from structural constraints to thermal and radiation hurdles. Hyperspace Unleashed doesn't just illuminate current scientific understanding but also ignites passion for future exploration and innovation. It's an invitation to envision a world where the speculative becomes tangible, where science fiction edges ever closer to science fact. Embark on this intellectual odyssey and see where the pursuit of warp mastery might take us. |
| hypercomplex algebra: New Perspectives on Approximation and Sampling Theory Ahmed I. Zayed, Gerhard Schmeisser, 2014-11-03 Paul Butzer, who is considered the academic father and grandfather of many prominent mathematicians, has established one of the best schools in approximation and sampling theory in the world. He is one of the leading figures in approximation, sampling theory, and harmonic analysis. Although on April 15, 2013, Paul Butzer turned 85 years old, remarkably, he is still an active research mathematician. In celebration of Paul Butzer’s 85th birthday, New Perspectives on Approximation and Sampling Theory is a collection of invited chapters on approximation, sampling, and harmonic analysis written by students, friends, colleagues, and prominent active mathematicians. Topics covered include approximation methods using wavelets, multi-scale analysis, frames, and special functions. New Perspectives on Approximation and Sampling Theory requires basic knowledge of mathematical analysis, but efforts were made to keep the exposition clear and the chapters self-contained. This volume will appeal to researchers and graduate students in mathematics, applied mathematics and engineering, in particular, engineers working in signal and image processing. |
| hypercomplex algebra: The Sixth International Symposium on Neural Networks (ISNN 2009) Hongwei Wang, Yi Shen, Tingwen Huang, Zhigang Zeng, 2009-05-03 This volume of Advances in Soft Computing and Lecture Notes in Computer th Science vols. 5551, 5552 and 5553, constitute the Proceedings of the 6 Inter- tional Symposium of Neural Networks (ISNN 2009) held in Wuhan, China during May 26–29, 2009. ISNN is a prestigious annual symposium on neural networks with past events held in Dalian (2004), Chongqing (2005), Chengdu (2006), N- jing (2007) and Beijing (2008). Over the past few years, ISNN has matured into a well-established series of international conference on neural networks and their applications to other fields. Following this tradition, ISNN 2009 provided an a- demic forum for the participants to disseminate their new research findings and discuss emerging areas of research. Also, it created a stimulating environment for the participants to interact and exchange information on future research challenges and opportunities of neural networks and their applications. ISNN 2009 received 1,235 submissions from about 2,459 authors in 29 co- tries and regions (Australia, Brazil, Canada, China, Democratic People's Republic of Korea, Finland, Germany, Hong Kong, Hungary, India, Islamic Republic of Iran, Japan, Jordan, Macao, Malaysia, Mexico, Norway, Qatar, Republic of Korea, Singapore, Spain, Taiwan, Thailand, Tunisia, United Kingdom, United States, Venezuela, Vietnam, and Yemen) across six continents (Asia, Europe, North America, South America, Africa, and Oceania). Based on rigorous reviews by the Program Committee members and reviewers, 95 high-quality papers were selected to be published in this volume. |
| hypercomplex algebra: Artificial Neural Networks and Machine Learning – ICANN 2021 Igor Farkaš, Paolo Masulli, Sebastian Otte, Stefan Wermter, 2021-09-10 The proceedings set LNCS 12891, LNCS 12892, LNCS 12893, LNCS 12894 and LNCS 12895 constitute the proceedings of the 30th International Conference on Artificial Neural Networks, ICANN 2021, held in Bratislava, Slovakia, in September 2021.* The total of 265 full papers presented in these proceedings was carefully reviewed and selected from 496 submissions, and organized in 5 volumes. In this volume, the papers focus on topics such as generative neural networks, graph neural networks, hierarchical and ensemble models, human pose estimation, image processing, image segmentation, knowledge distillation, and medical image processing. *The conference was held online 2021 due to the COVID-19 pandemic. |
| hypercomplex algebra: The Mathematical and Philosophical Legacy of Alexander Grothendieck Marco Panza, Daniele C. Struppa, Jean-Jacques Szczeciniarz, 2025-01-21 Alexander Grothendieck is often considered one of the greatest mathematicians of the twentieth century (if not all time), and his unique vision continues to impact and inspire many fields and researchers today. Utilizing a multidisciplinary approach, this edited volume explores the profound influence his work and ideas have had not only on mathematics, but also on logic and philosophy. Chapters are written by international scholars, and many were inspired by talks given at the conference “Grothendieck, A Multifarious Giant” at Chapman University (May 24-28, 2022). Some chapters are written from a historical perspective and discuss the development of the main themes that characterized Grothendieck's work. Others are more mathematical in nature, analyzing and extending some of his more relevant and obscure results that are still not well understood. Philosophical implications and applications in logic are the subjects of other chapters. This volume will be of interest not only to mathematicians working in algebraic geometry, category theory, and other areas to which Grothendieck contributed, but also to philosophers, logicians, and historians of science. |
| hypercomplex algebra: Quaternion Fourier Transforms for Signal and Image Processing Todd A. Ell, Nicolas Le Bihan, Stephen J. Sangwine, 2014-06-23 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. |
| hypercomplex algebra: Applications of Holomorphic Functions in Geometry Arif Salimov, 2023-05-06 This book expounds on the recent developments in applications of holomorphic functions in the theory of hypercomplex and anti-Hermitian manifolds as well as in the geometry of bundles. It provides detailed information about holomorphic functions in algebras and discusses some of the areas in geometry with applications. The book proves the existence of a one-to-one correspondence between hyper-complex anti-Kähler manifolds and anti-Hermitian manifolds with holomorphic metrics, and also a deformed lifting to bundles. Researchers and students of geometry, algebra, topology and physics may find the book useful as a self-study guide. |
| hypercomplex algebra: Advanced Electromagnetism: Foundations: Theory And Applications Terence William Barrett, Dale M Grimes, 1995-11-16 Advanced Electromagnetism: Foundations, Theory and Applications treats what is conventionally called electromagnetism or Maxwell's theory within the context of gauge theory or Yang-Mills theory. A major theme of this book is that fields are not stand-alone entities but are defined by their boundary conditions. The book has practical relevance to efficient antenna design, the understanding of forces and stresses in high energy pulses, ring laser gyros, high speed computer logic elements, efficient transfer of power, parametric conversion, and many other devices and systems. Conventional electromagnetism is shown to be an underdeveloped, rather than a completely developed, field of endeavor, with major challenges in development still to be met. |
| hypercomplex algebra: Transactions of the American Mathematical Society American Mathematical Society, 1919 Monthly journal devoted entirely to research in pure and applied mathematics, and, in general, includes longer papers than those in the Proceedings of the American Mathematical Society. |
| hypercomplex algebra: Encyclopaedia of Mathematics M. Hazewinkel, 2013-11-11 |
| hypercomplex algebra: Multi-Image Analysis Reinhard Klette, Thomas S. Huang, 2001-05-02 This book constitutes the thoroughly refereed post-proceedings of the 10th International Workshop on Theoretical Foundations of Computer Vision, held at Dagstuhl Castle, Germany, in March 2000. The 20 revised full papers presented have been through two rounds of reviewing, selection, and revision and give a representative assessment of the foundational issues in multiple-image processing. The papers are organized in topical sections on 3D data acquisition and sensor design, multi-image analysis, data fusion in 3D scene description, and applied 3D vision and virtual reality. |
| hypercomplex algebra: Applications of Geometric Algebra in Computer Science and Engineering Leo Dorst, Chris Doran, Joan Lasenby, 2012-12-06 Geometric algebra has established itself as a powerful and valuable mathematical tool for solving problems in computer science, engineering, physics, and mathematics. The articles in this volume, written by experts in various fields, reflect an interdisciplinary approach to the subject, and highlight a range of techniques and applications. Relevant ideas are introduced in a self-contained manner and only a knowledge of linear algebra and calculus is assumed. Features and Topics: * The mathematical foundations of geometric algebra are explored * Applications in computational geometry include models of reflection and ray-tracing and a new and concise characterization of the crystallographic groups * Applications in engineering include robotics, image geometry, control-pose estimation, inverse kinematics and dynamics, control and visual navigation * Applications in physics include rigid-body dynamics, elasticity, and electromagnetism * Chapters dedicated to quantum information theory dealing with multi- particle entanglement, MRI, and relativistic generalizations Practitioners, professionals, and researchers working in computer science, engineering, physics, and mathematics will find a wide range of useful applications in this state-of-the-art survey and reference book. Additionally, advanced graduate students interested in geometric algebra will find the most current applications and methods discussed. |
| hypercomplex algebra: Clifford Analysis and Its Applications F. Brackx, John Stephen roy Chisholm, V. Soucek, 2001-07-31 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. |
| hypercomplex algebra: Encyclopaedia of Mathematics Michiel Hazewinkel, 2013-12-01 This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques. |
| hypercomplex algebra: High Dimensional Neurocomputing Bipin Kumar Tripathi, 2014-11-05 The book presents a coherent understanding of computational intelligence from the perspective of what is known as intelligent computing with high-dimensional parameters. It critically discusses the central issue of high-dimensional neurocomputing, such as quantitative representation of signals, extending the dimensionality of neuron, supervised and unsupervised learning and design of higher order neurons. The strong point of the book is its clarity and ability of the underlying theory to unify our understanding of high-dimensional computing where conventional methods fail. The plenty of application oriented problems are presented for evaluating, monitoring and maintaining the stability of adaptive learning machine. Author has taken care to cover the breadth and depth of the subject, both in the qualitative as well as quantitative way. The book is intended to enlighten the scientific community, ranging from advanced undergraduates to engineers, scientists and seasoned researchers in computational intelligence. |
| hypercomplex algebra: Algebraic Frames for the Perception-Action Cycle Gerald Sommer, Yehoshua Y. Zeevi, 2006-12-30 This volume presents the proceedings of the 2nd International Workshop on - gebraic Frames for the Perception and Action Cycle. AFPAC 2000. held in Kiel, Germany, 10–11 September 2000. The presented topics cover new results in the conceptualization, design, and implementation of visual sensor-based robotics and autonomous systems. Special emphasis is placed on the role of algebraic modelling in the relevant disciplines, such as robotics, computer vision, theory of multidimensional signals, and neural computation. The aims of the workshop are twofold: ?rst, discussion of the impact of algebraic embedding of the task at hand on the emergence of new qualities of modelling and second, facing the strong relations between dominant geometric problems and algebraic modelling. The ?rst workshop in this series, AFPAC’97. inspired several groups to i- tiate new research programs, or to intensify ongoing research work in this ?eld, and the range of relevant topics was consequently broadened, The approach adopted by this workshop does not necessarily ?t the mainstream of worldwide research-granting policy. However, its search for fundamental problems in our ?eld may very well lead to new results in the relevant disciplines and contribute to their integration in studies of the perception–action cycle. |
| hypercomplex algebra: Bridging Circuits and Fields Alexander I. Petroianu, 2021-11-29 Energy and power are fundamental concepts in electromagnetism and circuit theory, as well as in optics, signal processing, power engineering, electrical machines, and power electronics. However, in crossing the disciplinary borders, we encounter understanding difficulties due to (1) the many possible mathematical representations of the same physical objects, and (2) the many possible physical interpretations of the same mathematical entities. The monograph proposes a quantum and a relativistic approach to electromagnetic power theory that is based on recent advances in physics and mathematics. The book takes a fresh look at old debates related to the significance of the Poynting theorem and the interpretation of reactive power. Reformulated in the mathematical language of geometric algebra, the new expression of electromagnetic power reflects the laws of conservation of energy-momentum in fields and circuits. The monograph offers a mathematically consistent and a physically coherent interpretation of the power concept and of the mechanism of power transmission at the subatomic (mesoscopic) level. The monograph proves (paraphrasing Heaviside) that there is no finality in the development of a vibrant discipline: power theory. |
| hypercomplex algebra: General Relativity and Gravitation M. A. H. MacCallum, 1987-09-24 |
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How to Pay Capital One Credit Card Bill - WalletHub
Jan 10, 2025 · You can pay your Capital One credit card bill in person at a Capital One branch, or at the Money Services counters in Kroger brand stores. You can also make a payment at …
Capital One Venture Rewards Credit Card Login Instructions
May 13, 2025 · Register your Capital One Venture credit card for online account access: Click “Set Up Online Access” and enter your last name, SSN or bank account number, and date of …
Can I pay my Capital One credit card bill by phone? - WalletHub
May 27, 2025 · How to Pay Your Capital One Credit Card Bill by Phone Call Capital One at the number on the back of your card. Follow the automated menu options to initiate a payment. …
How can I reach the Capital One credit card customer service?
Oct 25, 2024 · The Capital One credit card customer service hours are 24/7 for automated support and 8 a.m. to 11 p.m. EST for a human representative. You can reach Capital One …
Capital One Platinum Credit Card Login Instructions & Credentials
Feb 21, 2024 · Register your Capital One Platinum credit card for online account access. Click “Set Up Online Access” and enter your your last name, date of birth, and Social Security …
Kohl's Credit Card Login Instructions & Credentials - WalletHub
Feb 21, 2024 · To log in to your Kohl's Credit Card account, go to the login page on the Capital One website or mobile app and enter your username and password in the appropriate fields.
Capital One Credit Card Reviews (July 2025) - WalletHub
Jul 1, 2025 · In fact, Capital One has the best credit card rewards program overall, according to our latest rewards study. Negative reviews mention lower-than-average credit limits and …
Spectrum Channel Lineup Guide 2025 [With PDF] - The Channel …
Jul 4, 2025 · In this guide, you will find a complete Spectrum channel lineup, including all available channels and add-ons. Spectrum streaming app is available on the Google Play Store and …
Spectrum Channel Lineup 2025 (Updated)
Jun 20, 2025 · In this blog post, we’ll take a full look at the Spectrum channel lineup, highlight the major networks in its plans, and help you choose the right package that matches your …
TV Channel Lineup | Spectrum Support
You can learn more about your personalized TV channel lineup through the My Spectrum App, or you can get information on additional channel offerings on Spectrum.com.
Spectrum TV Channel Lineup Guide For 2025 (Detailed)
Mar 13, 2025 · In this post, I will provide a detailed guide to Spectrum’s channel lineup, highlighting different channel categories, available packages, and tips to help you understand …
Spectrum Channel Lineup Guide - CableTV.com
Jan 21, 2025 · Our channel lineup guide covers which popular, premium, educational, kids', and sports channels are in Spectrum TV plans, and which add-ons are available.
Spectrum Basic Cable Channels: Full Guide for 2025
Dec 15, 2024 · Check your local lineup or visit Spectrum’s website for more details! 🎉. What Channels Are Included? Spectrum Basic Cable typically includes 20 to 40 channels, …
How do I get a printable list for my channels? — Spectrum ...
Apr 13, 2025 · Navigate to the Manage TV/Streaming tab at the top. Scroll down to View Channel Lineup and on the right side is the option for Print Lineup. This would give you a printable copy …
