The 21st Hilbert Problem For Linear Fuchsian Systems
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The 21st Hilbert Problem For Linear Fuchsian Systems
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Author : A. A. Bolibrukh
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
The 21st Hilbert Problem For Linear Fuchsian Systems written by A. A. Bolibrukh and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
Bolibrukh presents the negative solution of Hilbert's twenty-first problem for linear Fuchsian systems of differential equations. Methods developed by Bolibrukh in solving this problem are then applied to the study of scalar Fuchsian equations and systems with regular singular points on the Riemmann sphere.
The 21st Hilbert Problem For Linear Fuchsian Systems
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Author : A. A. Bolibruch
language : en
Publisher:
Release Date : 1995
The 21st Hilbert Problem For Linear Fuchsian Systems written by A. A. Bolibruch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Fuchsian groups categories.
The 21st Hilbert Problem For Linear Fuchsian Systems
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Author :
language : en
Publisher:
Release Date : 1998
The 21st Hilbert Problem For Linear Fuchsian Systems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with categories.
The Riemann Hilbert Problem
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Author : D. V. Anosov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
The Riemann Hilbert Problem written by D. V. Anosov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
This book is devoted to Hilbert's 21st problem (the Riemann-Hilbert problem) which belongs to the theory of linear systems of ordinary differential equations in the complex domain. The problem concems the existence of a Fuchsian system with prescribed singularities and monodromy. Hilbert was convinced that such a system always exists. However, this tumed out to be a rare case of a wrong forecast made by hirn. In 1989 the second author (A.B.) discovered a counterexample, thus 1 obtaining a negative solution to Hilbert's 21st problem. After we recognized that some "data" (singularities and monodromy) can be obtai ned from a Fuchsian system and some others cannot, we are enforced to change our point of view. To make the terminology more precise, we shaII caII the foIIowing problem the Riemann-Hilbert problem for such and such data: does there exist a Fuchsian system having these singularities and monodromy? The contemporary version of the 21 st Hilbert problem is to find conditions implying a positive or negative solution to the Riemann-Hilbert problem.
Perspectives Of Complex Analysis Differential Geometry And Mathematical Physics
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Author : Stancho Dimiev
language : en
Publisher: World Scientific
Release Date : 2001
Perspectives Of Complex Analysis Differential Geometry And Mathematical Physics written by Stancho Dimiev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
The Deligne-Simpson problem for zero index of rigidity / V.P. Rostov -- Theorems for extension on manifolds with almost complex structures / L.N. Apostolova, M.S. Marinov and K.P. Petrov -- The theorem on analytic representation on hypersurface with singularities / A.M. Kytmanov and S.G. Myslivets -- Pseudogroup structures on Spencer manifolds / S. Dimiev -- Type-changing transformations of Hurwitz pairs, quasiregular functions, and hyper Kahlerian holomorphic chains I / J. Lawrynowicz and L.M. Tovar -- Embedding of the moduli space of Riemann surfaces with Igeta structures into the Sato Grassmann manifold / Y. Hashimoto and K. Ohba -- On the quotient spaces of S2 x S2 under the natural action of subgroups of D4 / K. Kikuchi -- Existence of spin structures on cyclic branched covering spaces over four-manifolds / S. Nagami -- Length spectrum of geodesic spheres in rank one symmetric spaces / T. Adachi -- Grassmann geometry of 6-dimensional sphere, II / H. Hashimoto and K. Mashimo -- Hypersurfaces in Euclidean space which are one-parameter families of spheres / G. Ganchev and V. Mihova -- Hypersurfaces of conullity two in Euclidean space which are one-parameter systems of torses / G. Ganchev and V. Milousheva -- Real hypersurfaces of a Kaehler manifold (the sixteen classes) / G. Ganchev and M. Hristov -- Almost contact B-metric hypersurfaces of Kaehlerian manifolds with B-metric / M. Manev -- Projective formalism and some methods from algebraic geometry in the theory of gravitation / B.G. Dimitrov -- Geometry of manifolds and dark matter / I.B. Pestov -- Lagrangian fluid mechanics / S. Manoff -- Transformation of connectednesses / G. Zlatanov
Perspectives Of Complex Analysis Differential Geometry And Mathematical Physics Proceedings Of The 5th International Workshop On Complex Structures And Vector Fields
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Author : Stancho Dimiev
language : en
Publisher: World Scientific
Release Date : 2001-08-02
Perspectives Of Complex Analysis Differential Geometry And Mathematical Physics Proceedings Of The 5th International Workshop On Complex Structures And Vector Fields written by Stancho Dimiev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-08-02 with Mathematics categories.
This workshop brought together specialists in complex analysis, differential geometry, mathematical physics and applications for stimulating cross-disciplinary discussions. The lectures presented ranged over various current topics in those fields. The proceedings will be of value to graduate students and researchers in complex analysis, differential geometry and theoretical physics, and also related fields.
Hilbert G Ttingen And The Development Of Modern Mathematics
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Author : Joan Roselló
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2019-02-01
Hilbert G Ttingen And The Development Of Modern Mathematics written by Joan Roselló and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-01 with Mathematics categories.
David Hilbert is one of the outstanding mathematicians of the twentieth century and probably the most influential. This book highlights Hilbert’s contributions to mathematics, putting them in their historical, social and cultural context. In doing so, particular attention is paid to Hilbert’s axiomatic method and his proposal for the foundations of mathematics, the so-called Hilbert’s program. The book also discusses the development of algebraic number theory, the theory of integral equations, modern algebra and the structural image of mathematics. In addition, it considers the famous list of Mathematical Problems presented in Paris in 1900, the mathematical tradition of the University of Göttingen, the great debate on the foundations of mathematics in the twenties between formalists and intuitionists, and, finally, Hilbert’s work on the theory of relativity and the foundations of quantum mechanics. The book will primarily appeal to an academic audience, although it will also be of interest to general-interest science readers.
The Ball And Some Hilbert Problems
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Author : Rolf-Peter Holzapfel
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
The Ball And Some Hilbert Problems written by Rolf-Peter Holzapfel and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
As an interesting object of arithmetic, algebraic and analytic geometry the complex ball was born in a paper of the French Mathematician E. PICARD in 1883. In recent developments the ball finds great interest again in the framework of SHIMURA varieties but also in the theory of diophantine equations (asymptotic FERMAT Problem, see ch. VI). At first glance the original ideas and the advanced theories seem to be rather disconnected. With these lectures I try to build a bridge from the analytic origins to the actual research on effective problems of arithmetic algebraic geometry. The best motivation is HILBERT'S far-reaching program consisting of 23 prob lems (Paris 1900) " . . . one should succeed in finding and discussing those functions which play the part for any algebraic number field corresponding to that of the exponential function in the field of rational numbers and of the elliptic modular functions in the imaginary quadratic number field". This message can be found in the 12-th problem "Extension of KRONECKER'S Theorem on Abelian Fields to Any Algebraic Realm of Rationality" standing in the middle of HILBERTS'S pro gram. It is dedicated to the construction of number fields by means of special value of transcendental functions of several variables. The close connection with three other HILBERT problems will be explained together with corresponding advanced theories, which are necessary to find special effective solutions, namely: 7. Irrationality and Transcendence of Certain Numbers; 21.
Control Theory And Optimization I
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Author : M.I. Zelikin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Control Theory And Optimization I written by M.I. Zelikin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
This book is devoted to the development of geometrie methods for studying and revealing geometrie aspects of the theory of differential equations with quadratie right-hand sides (Riccati-type equations), which are closely related to the calculus of variations and optimal control theory. The book contains the following three parts, to each of which aseparate book could be devoted: 1. the classieal calculus of variations and the geometrie theory of the Riccati equation (Chaps. 1-5), 2. complex Riccati equations as flows on Cartan-Siegel homogeneity da mains (Chap. 6), and 3. the minimization problem for multiple integrals and Riccati partial dif ferential equations (Chaps. 7 and 8). Chapters 1-4 are mainly auxiliary. To make the presentation complete and self-contained, I here review the standard facts (needed in what folIows) from the calculus of variations, Lie groups and algebras, and the geometry of Grass mann and Lagrange-Grassmann manifolds. When choosing these facts, I pre fer to present not the most general but the simplest assertions. Moreover, I try to organize the presentation so that it is not obscured by formal and technical details and, at the same time, is sufficiently precise. Other chapters contain my results concerning the matrix double ratio, com plex Riccati equations, and also the Riccati partial differential equation, whieh the minimization problem for a multiple integral. arises in The book is based on a course of lectures given in the Department of Me and Mathematics of Moscow State University during several years.
Special Functions
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Author : Sergeĭ I︠U︡rʹevich Slavi︠a︡nov
language : en
Publisher: OUP Oxford
Release Date : 2000
Special Functions written by Sergeĭ I︠U︡rʹevich Slavi︠a︡nov and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
The subject of this book is the theory of special functions, not considered as a list of functions exhibiting a certain range of properties, but based on the unified study of singularities of second-order ordinary differential equations in the complex domain. The number and characteristics of the singularities serve as a basis for classification of each individual special function. Links between linear special functions (as solutions of linear second-order equations), and non-linear special functions (as solutions of Painlevé equations) are presented as a basic and new result. Many applications to different areas of physics are shown and discussed. The book is written from a practical point of view and will address all those scientists whose work involves applications of mathematical methods. Lecturers, graduate students and researchers will find this a valuable text and reference work.