Hypercomplex Analysis and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Hypercomplex Analysis and Applications write by Irene Sabadini. This book was released on 2010-12-20. Hypercomplex Analysis and Applications available in PDF, EPUB and Kindle. The purpose of the volume is to bring forward recent trends of research in hypercomplex analysis. The list of contributors includes first rate mathematicians and young researchers working on several different aspects in quaternionic and Clifford analysis. Besides original research papers, there are papers providing the state-of-the-art of a specific topic, sometimes containing interdisciplinary fields. The intended audience includes researchers, PhD students, postgraduate students who are interested in the field and in possible connection between hypercomplex analysis and other disciplines, including mathematical analysis, mathematical physics, algebra.
Hypercomplex Analysis: New Perspectives and Applications
Hypercomplex Analysis: New Perspectives and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Hypercomplex Analysis: New Perspectives and Applications write by Swanhild Bernstein. This book was released on 2014-10-10. Hypercomplex Analysis: New Perspectives and Applications available in PDF, EPUB and Kindle. 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.
Hypercomplex Numbers
Hypercomplex Numbers - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Hypercomplex Numbers write by I.L. Kantor. This book was released on 2011-09-21. Hypercomplex Numbers available in PDF, EPUB and Kindle. 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).
Clifford Algebras and their Applications in Mathematical Physics
Clifford Algebras and their Applications in Mathematical Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Clifford Algebras and their Applications in Mathematical Physics write by Rafał Abłamowicz. This book was released on 2000. Clifford Algebras and their Applications in Mathematical Physics available in PDF, EPUB and Kindle. The first part of a two-volume set concerning the field of Clifford (geometric) algebra, this work consists of thematically organized chapters that provide a broad overview of cutting-edge topics in mathematical physics and the physical applications of Clifford algebras. algebras and their applications in physics. Algebraic geometry, cohomology, non-communicative spaces, q-deformations and the related quantum groups, and projective geometry provide the basis for algebraic topics covered. Physical applications and extensions of physical theories such as the theory of quaternionic spin, a projective theory of hadron transformation laws, and electron scattering are also presented, showing the broad applicability of Clifford geometric algebras in solving physical problems. Treatment of the structure theory of quantum Clifford algebras, the connection to logic, group representations, and computational techniques including symbolic calculations and theorem proving rounds out the presentation.
Advances in Hypercomplex Analysis
Advances in Hypercomplex Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Advances in Hypercomplex Analysis write by Graziano Gentili. This book was released on 2012-11-14. Advances in Hypercomplex Analysis available in PDF, EPUB and Kindle. 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.
