Generalizations of Complex Analysis and Their Applications in Physics PDF Download

Author: Julian Ławrynowicz
Publisher:
ISBN:
Category : Analytic functions
Languages : en
Pages : 378

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Author: Volker Dietrich
Publisher: Springer Science & Business Media
ISBN: 9401150362
Category : Mathematics
Languages : en
Pages : 458

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Book Description
Clifford Algebras continues to be a fast-growing discipline, with ever-increasing applications in many scientific fields. This volume contains the lectures given at the Fourth Conference on Clifford Algebras and their Applications in Mathematical Physics, held at RWTH Aachen in May 1996. The papers represent an excellent survey of the newest developments around Clifford Analysis and its applications to theoretical physics. Audience: This book should appeal to physicists and mathematicians working in areas involving functions of complex variables, associative rings and algebras, integral transforms, operational calculus, partial differential equations, and the mathematics of physics.

Author: J.S.R. Chisholm
Publisher: Springer Science & Business Media
ISBN: 9400947283
Category : Mathematics
Languages : en
Pages : 589

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Book Description
William Kingdon Clifford published the paper defining his "geometric algebras" in 1878, the year before his death. Clifford algebra is a generalisation to n-dimensional space of quaternions, which Hamilton used to represent scalars and vectors in real three-space: it is also a development of Grassmann's algebra, incorporating in the fundamental relations inner products defined in terms of the metric of the space. It is a strange fact that the Gibbs Heaviside vector techniques came to dominate in scientific and technical literature, while quaternions and Clifford algebras, the true associative algebras of inner-product spaces, were regarded for nearly a century simply as interesting mathematical curiosities. During this period, Pauli, Dirac and Majorana used the algebras which bear their names to describe properties of elementary particles, their spin in particular. It seems likely that none of these eminent mathematical physicists realised that they were using Clifford algebras. A few research workers such as Fueter realised the power of this algebraic scheme, but the subject only began to be appreciated more widely after the publication of Chevalley's book, 'The Algebraic Theory of Spinors' in 1954, and of Marcel Riesz' Maryland Lectures in 1959. Some of the contributors to this volume, Georges Deschamps, Erik Folke Bolinder, Albert Crumeyrolle and David Hestenes were working in this field around that time, and in their turn have persuaded others of the importance of the subject.

Author: Helmut Florian
Publisher: World Scientific
ISBN: 9812794557
Category : Mathematics
Languages : en
Pages : 473

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Book Description
Functional analysis is not only a tool for unifying mathematical analysis, but it also provides the background for today''s rapid development of the theory of partial differential equations. Using concepts of functional analysis, the field of complex analysis has developed methods (such as the theory of generalized analytic functions) for solving very general classes of partial differential equations. This book is aimed at promoting further interactions of functional analysis, partial differential equations, and complex analysis including its generalizations such as Clifford analysis. New interesting problems in the field of partial differential equations concern, for instance, the Dirichlet problem for hyperbolic equations. Applications to mathematical physics address mainly Maxwell''s equations, crystal optics, dynamical problems for cusped bars, and conservation laws. Sample Chapter(s). Hyperbolic Equations, Waves and the Singularity Theory (858 KB). Contents: Boundary Value Problems and Initial Value Problems for Partial Differential Equations; Applications of Functional-Analytic and Complex Methods to Mathematical Physics; Partial Complex Differential Equations in the Plane; Complex Methods in Higher Dimensions. Readership: Researchers, lecturers and graduate students in the fields of analysis & differential equations, applied mathematics and mathematical physics.

Author: Eberhard Lanckau
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3112707753
Category : Mathematics
Languages : en
Pages : 400

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No detailed description available for "Complex Analysis – Methods, Trends, and Applications".

Author: Tristan Needham
Publisher: Oxford University Press
ISBN: 9780198534464
Category : Mathematics
Languages : en
Pages : 620

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Book Description
This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.

Author: Kouei Sekigawa
Publisher: World Scientific Publishing Company Incorporated
ISBN: 9789814277716
Category : Mathematics
Languages : en
Pages : 273

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Book Description
A discrete model for Kähler magnetic fields on a complex hyperbolic space / T. Adachi -- Integrability condition on the boundary parameters of the asymmetric exclusion process and matrix product ansatz / B. Aneva -- Remarks on the double-complex Laplacian / L. Apostolova -- Generalizations of conjugate connections / O. Calin, H. Matsuzoe, J. Zhang -- Asymptotics of generalized value distribution for Herglotz functions / Y. T. Christodoulides -- Cyclic hyper-scalar systems / S. Dimiev, M. S. Marinov, Z. Zhelev -- Plane curves associated with integrable dynamical systems of the Frenet-Serret type / P. A. Djondjorov, V. M. Vassilev, I. M. Mladenov -- Relativistic strain and electromagnetic photon-like objects / S. Donev, M. Tashkova -- A construction of minimal surfaces in flat tori by swelling / N. Ejiri -- On NLS equations on BD.I symmetric spaces with constant boundary conditions / V. S. Gerdjikov, N. A. Kostov -- Orthogonal almost complex structures on S[symbol] x R[symbol] / H. Hashimoto, M. Ohashi -- Persistence of solutions for some integrable shallow water equations / D. Henry -- Some geometric properties and objects related to Bézier curves / M. J. Hristov -- Heisenberg relations in the general case / B. Z. Iliev -- Poisson structures of equations associated with groups of diffeomorphisms / R. I. Ivanov -- Hyperbolic Gauss maps and parallel surfaces in hyperbolic three-space / M. Kokubu -- On the lax pair for two and three wave interaction system / N. A. Kostov -- Mathematical outlook of fractals and chaos related to simple orthorhombic Ising-Onsager-Zhang lattices / J. Ławrynowicz, S. Marchiafava, M. Nowak-Kepczyk -- A characterization of Clifford minimal hypersurfaces of a sphere in terms of their geodesics / S. Maeda -- On the curvature properties of real time-like hypersurfaces of Kähler manifolds with Norden metric / M. Manev, M. Teofilova -- Some submanifolds of almost contact manifolds with Norden metric / G. Nakova -- A short note on the double-complex Laplace operator / P. Popivanov -- Monogenic, hypermonogenic and holomorphic Cliffordian functions - a survey / I. P. Ramadanoff -- On some classes of exact solutions of eikonal equation / Ł. T. Stepień -- Dirichlet property for tessellations of tiling-type 4 on a plane by congrent pentagons / Y. Takeo, T. Adachi -- Almost complex connections on almost complex manifolds with Norden metric / M. Teofilova -- Pseudo-boson coherent and Fock states / D. A. Trifonov -- New integrable equations of mKdV type / T. I. Valchev -- Integrable dynamical systems of the Frenet-Serret type / V. M. Vassilev, P. A. Djondjorov, I. M. Mladenov

Author: Guo Chun Wen
Publisher: World Scientific
ISBN: 981451831X
Category : Mathematics
Languages : en
Pages : 436

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Book Description
In this volume, we report new results about various boundary value problems for partial differential equations and functional equations, theory and methods of integral equations and integral operators including singular integral equations, applications of boundary value problems and integral equations to mechanics and physics, numerical methods of integral equations and boundary value problems, theory and methods for inverse problems of mathematical physics, Clifford analysis and related problems.Contributors include: L Baratchart, B L Chen, D C Chen, S S Ding, K Q Lan, A Farajzadeh, M G Fei, T Kosztolowicz, A Makin, T Qian, J M Rassias, J Ryan, C-Q Ru, P Schiavone, P Wang, Q S Zhang, X Y Zhang, S Y Du, H Y Gao, X Li, Y Y Qiao, G C Wen, Z T Zhang, etc.

Author: Elias M. Stein
Publisher: Princeton University Press
ISBN: 1400831156
Category : Mathematics
Languages : en
Pages : 398

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Book Description
With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

Author: Swanhild Bernstein
Publisher: Springer
ISBN: 3319087711
Category : Mathematics
Languages : en
Pages : 228

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Book Description
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.