Trends in Differential Geometry, Complex Analysis and Mathematical Physics : Proceedings of 9th International Workshop on Complex Structures, Integrability and Vector Fields.
Title:
Trends in Differential Geometry, Complex Analysis and Mathematical Physics : Proceedings of 9th International Workshop on Complex Structures, Integrability and Vector Fields.
Author:
Sekigawa, Kouei.
ISBN:
9789814277723
Personal Author:
Physical Description:
1 online resource (290 pages)
Contents:
CONTENTS -- Preface -- Organizing Committees -- Presentations -- A discrete model for Kahler magnetic fields on a complex hyperbolic space T. Adachi -- 1. Introduction -- 2. Kahler magnetic fields on complex hyperbolic spaces -- 3. Graphs of K ahler type -- 4. Counting prime cycles -- References -- Integrability condition on the boundary parameters of the asymmetric exclusion process and matrix product ansatz B. Aneva -- 1. Introduction -- 2. Matrix Product State Ansatz (MPA) -- 3. Detailed Balance and MPA -- 4. Conclusion -- Acknowledgments -- References -- Remarks on the double-complex Laplacian L. Apostolova -- 1. Double-complex Laplace operator -- 2. Decomposition of the double-complex Laplace operator into two @-operators -- 3. D'Alamber's type formula for the initial value problem in the whole space C(1 -- j) -- 4. Real representation of the equation +u = 0 -- Acknowledgements -- References -- Generalizations of conjugate connections O. Calin, H. Matsuzoe, J. Zhang -- Introduction -- 1. Generalizations of conjugate connections -- 2. Generalized conjugate connections and gauge transformations -- 3. Local triviality of generalized conjugate connections and equia ne structures -- Acknowledgement -- References -- Asymptotics of generalized value distribution for Herglotz functions Y.T. Christodoulides -- 1. Introduction -- 2. Herglotz functions and their integral representation -- 3. Value distribution for Herglotz functions -- Acknowledgement -- References -- Cyclic hyper-scalar systems S. Dimiev, M.S. Marinov, Z. Zhelev -- 1. Hyper-real systems: K = R -- 2. Hyper-complex systems -- 3. Real double-variables or para-complex variables -- 4. Four real variables, K = R -- 5. Four-real functions of four real variables -- 6. Partial derivatives with respect to the double-real variables and -- 7. Para-complex di erentiability.
8. Hyper four-dimensional real scalar Hankel geometry [2-4] -- Acknowledgments -- References -- Plane curves associated with integrable dynamical systems of the Frenet-Serret type P.A. Djondjorov, V.M. Vassilev, I.M. Mladenov -- 1. Dynamical systems of the Frenet-Serret type -- 2. Levy's elasticae -- 3. Profile curves of Delaunay's surfaces -- Acknowledgments -- References -- Relativistic strain and electromagnetic photon-like objects S. Donev, M. Tashkova -- 1. Strain -- 2. The Concept of photon-like object(s) -- 3. The Electromagnetic strain tensors -- 4. Discussion -- 5. Conclusion -- Acknowledgment -- References -- A construction of minimal surfaces in at tori by swelling N. Ejiri -- 1. Introduction -- 2. Preliminary -- 3. Minimal surfaces in Riemannian at tori -- References -- On NLS equations on BD.I symmetric spaces with constant boundary conditions V.S. Gerdjikov, N.A. Kostov -- 1. Introduction -- 2. MNLS eqs on BD.I-symmetric spaces -- 3. MNLS with Constant Boundary Conditions -- 4. Spectral properties of BD.I-type MNLS with CBC -- 5. Discussion -- References -- Orthogonal almost complex structures on S2 R4 H. Hashimoto, M. Ohashi -- 1. Introduction -- 2. Preliminaries -- 3. Hypersurfaces in ImC -- 4. On G frame eld on S2 R4 -- 5. Orbits related to G -- References -- Persistence of solutions for some integrable shallow water equations D. Henry -- 1. Introduction -- 2. The b-equations -- 2.1. Compactly supported solutions -- 2.2. Soliton-type solutions -- References -- Some geometric properties and objects related to B ezier curves M.J. Hristov -- 1. Preliminaries -- 1.1. Barycentric coordinates and barycentric trajectories -- 1.2. Barycentric characterization of the duality in the projective plane. Projective isotomic conjugation -- 2. Bezier curves and related geometric properties and objects -- Acknowledgements -- References.
Heisenberg relations in the general case B.Z. Iliev -- 1. Introduction -- 2. The Poincar e group -- 3. Internal transformations -- 4. The general case -- 5. Fibre bundle approach -- 6. Conclusion -- Acknowledgments -- References -- Poisson structures of equations associated with groups of di eomorphisms R.I. Ivanov -- 1. Camassa-Holm equation -- 2. n-dimensional EP Diff equations -- 3. Reduction to the subgroup of volume-preserving diffeomorphisms -- Acknowledgments -- References -- Hyperbolic Gauss maps and parallel surfaces in hyperbolic three-space M. Kokubu -- 1. Introduction -- 2. Basic items -- 3. Parallel surface -- 4. Linear Weingarten surface -- References -- On the lax pair for two and three wave interaction system N.A. Kostov -- 1. Two-wave interaction system and monomer -- 2. Three-wave interaction system -- Acknowledgements -- References -- Mathematical outlook of fractals and chaos related to simple orthorhombic Ising-Onsager-Zhang lattices J. Lawrynowicz, S. Marchiafava, M. Nowak-K epczyk -- 1. Introduction and relationship with Bethe-type fractals -- 2. First, second, and third nearest neighbours of an atom in an alloy -- 3. Ising-Onsager-Zhang lattices vs. Jordan-von Neumann-Wigner approach -- 4. The use of fractals of the algebraic structure -- 5. Further perspectives -- References -- A characterization of Cli ord minimal hypersurfaces of a sphere in terms of their geodesics S. Maeda -- 1. Introduction -- 2. Geodesics on Cli ord hypersurfaces -- 3. Statements of resuls -- References -- On the curvature properties of real time-like hypersurfaces of K ahler manifolds with Norden metric M. Manev, M. Teo lova -- Introduction -- 1. Preliminaries -- 1.1. Almost complex manifolds with Norden metric -- 1.2. Almost contact manifolds with Norden metric.
2. Curvatures on the real time-like hypersurfaces of a K ahler manifold with Norden metric -- 3. Curvatures on W0's real time-like hypersurfaces, belonging to the main classes -- Acknowledgement -- References -- Some submanifolds of almost contact manifolds with Norden metric G. Nakova -- 1. Introduction -- 2. Submanifolds of codimension 2 of almost contact manifolds with Norden metric with totally real non-orthogonal to normal spaces -- 3. Submanifolds of codimension 2 of almost contact manifolds with Norden metric with totally real orthogonal to normal spaces -- 4. Examples of submanifolds of codimension 2 of almost contact manifolds with Norden metric with totally real normal spaces -- Acknowledgement -- References -- A short note on the double-complex Laplace operator P. Popivanov -- 1. Introduction and formulation of the main results -- References -- Monogenic, hypermonogenic and holomorphic Cli ordian functions
2. Almost complex connections on almost complex manifolds with Norden metric -- 3. Complex connections on conformal K ahler manifolds with Norden metric -- Acknowledgement -- References -- Pseudo-boson coherent and Fock states D.A. Trifonov -- 1. Introduction -- 2. Pseudo-boson ladder operators -- 3. Pseudo-boson Fock states -- 4. Pseudo-boson coherent states -- 5. Example -- 5.1. Pseudo-boson Fock state wave functions -- 5.2. Pseudo-boson CS wave functions -- Conclusion -- References -- New integrable equations of mKdV type T.I. Valchev -- 1. Introduction -- 2. Some facts from the theory of solitons -- 3. Multicomponent mKdV associated with symmetric spaces of BD:I series -- 4. Conclusion -- Acknowledgments -- References -- Integrable dynamical systems of the Frenet-Serret type V.M. Vassilev, P.A. Djondjorov, I.M. Mladenov -- 1. Introduction -- 2. Variational Symmetries -- 3. Conservation Laws -- 4. Group Classification -- 5. Integrable Systems -- 6. Concluding Remarks -- Acknowledgments -- References -- Author Index.
Abstract:
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. Sample Chapter(s). Chapter 1: A Discrete Model for KAhler Magnetic Fields on a Complex Hyperbolic Space (236 KB). Contents: A Discrete Model for Kähler Magnetic Fields on a Complex Hyperbolic Space (T Adachi); Generalizations of Conjugate Connections (O Calin et al.); Cyclic Hyper-Scalar Systems (S Dimiev et al.); Relativistic Strain and Electromagnetic Photon-Like Objects (S Donev & M Tashkova);
Persistence of Solutions for Some Integrable Shallow Water Equations (D Henry); 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 et al.); A Characterization of Clifford Minimal Hypersurfaces of a Sphere in Terms of Their Geodesics (S Maeda); A Short Note on the Double-Complex Laplace Operator (P Popivanov); Monogenic, Hypermonogenic and Holomorphic Cliffordian Functions - A Survey (I P Ramadanoff); New Integrable Equations of mKdV Type (T I Valchev); and other papers. Readership: Graduate students and researchers in analysis, differential geometry and mathematical physics including their intermediate fields.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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