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Trends in Differential Geometry, Complex Analysis and Mathematical Physics : Proceedings of the 9th International Workshop on Complex Structures, Integrability and Vector Fields, Sofia, Bulgaria, 25-29 August 2008 / editors, Kouei Sekigawa, Vladimir S. Gerdjikov, Stancho Dimiev.

By: (9th : International Workshop on Complex Structures, Integrability, and Vector Fields (9th : 2008 : Sofia, Bulgaria)Contributor(s): Sekigawa, Kouei | Gerdjikov, V. S. (Vladimir Stefanov) | Dimiev, Stancho | World Scientific (Firm)Material type: TextTextPublication details: Singapore ; Hackensack, N.J. : World Scientific Pub. Co., ©2009. Description: 1 online resource (xv, 273 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9789814277723; 981427772XSubject(s): Functional analysis -- Congresses | Geometry, Differential -- Congresses | Mathematical physics -- Congresses | MATHEMATICS -- Functional Analysis | Functional analysis | Geometry, Differential | Mathematical physicsGenre/Form: Electronic books. | Conference papers and proceedings. | Electronic books. Additional physical formats: No title; No titleDDC classification: 515.7 LOC classification: QA319 | .I59 2008ebOnline resources: Click here to access online
Contents:
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.
Summary: This book contains the contributions by the participants in the nine of a series of workshops. Throughout the series of workshops, the contributors are consistently aiming at higher achievements of studies of the current topics in complex analysis, differential geometry and mathematical physics and further in any intermediate areas, with expectation of discovery of new research directions. Concerning the present one, it is worthwhile to mention that, in addition to the new developments of the traditional trends, many attractive and pioneering works were presented and their results were contributed to the present volume. The contents of this volume therefore will provide not only significant and useful information for researchers in complex analysis, differential geometry and mathematical physics (including their related areas), but also interesting mathematics for non-specialists and a broad audience. The present volume contains new developments and trends in the studies on constructions of holomorphic Cliffordian functions; the swelling constructions of minimal surfaces with higher genus in flat tori; the spectral properties of soliton equations on symmetric spaces; new types of shallow water waves described by Camassa-Holm type equations, the properties of pseudo-hermitian boson and fermion coherent states; fractals and chaos on orthorhombic lattices, and even an ambitious proposal of a graph model for Kaehler manifolds with Kaehler magnetic fields.
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Includes bibliographical references and author index.

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.

This book contains the contributions by the participants in the nine of a series of workshops. Throughout the series of workshops, the contributors are consistently aiming at higher achievements of studies of the current topics in complex analysis, differential geometry and mathematical physics and further in any intermediate areas, with expectation of discovery of new research directions. Concerning the present one, it is worthwhile to mention that, in addition to the new developments of the traditional trends, many attractive and pioneering works were presented and their results were contributed to the present volume. The contents of this volume therefore will provide not only significant and useful information for researchers in complex analysis, differential geometry and mathematical physics (including their related areas), but also interesting mathematics for non-specialists and a broad audience. The present volume contains new developments and trends in the studies on constructions of holomorphic Cliffordian functions; the swelling constructions of minimal surfaces with higher genus in flat tori; the spectral properties of soliton equations on symmetric spaces; new types of shallow water waves described by Camassa-Holm type equations, the properties of pseudo-hermitian boson and fermion coherent states; fractals and chaos on orthorhombic lattices, and even an ambitious proposal of a graph model for Kaehler manifolds with Kaehler magnetic fields.

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