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Kobayashi-hyperbolic manifolds are an object of active research in complex geometry. In this monograph the author presents a coherent exposition of recent results on complete characterization of Kobayashi-hyperbolic manifolds with high-dimensional groups of holomorphic automorphisms. These classification results can be viewed as complex-geometric analogues of those known for Riemannian manifolds with high-dimensional isotropy groups, that were extensively studied in the 1950s-70s. The common feature of the Kobayashi-hyperbolic and Riemannian cases is the properness of the actions of the holomorphic automorphism group and the isometry group on respective manifolds.
Automorfismen. --- Hyperbolische ruimten. --- Hyperbolic spaces. --- Automorphisms. --- Espaces hyperboliques --- Automorphismes --- Electronic books. -- local. --- Probabilities. --- Topology. --- Hyperbolic spaces --- Automorphisms --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Calculus --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Probability --- Statistical inference --- Mathematics. --- Functions of complex variables. --- Several Complex Variables and Analytic Spaces. --- Complex variables --- Elliptic functions --- Functions of real variables --- Math --- Science --- Polyhedra --- Set theory --- Algebras, Linear --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Differential equations, partial. --- Partial differential equations --- Group theory --- Symmetry (Mathematics) --- Hyperbolic complex manifolds --- Manifolds, Hyperbolic complex --- Spaces, Hyperbolic --- Geometry, Non-Euclidean
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We examine Levi non-degenerate tube hypersurfaces in complex linear space which are "spherical," that is, locally CR-equivalent to the real hyperquadric. Spherical hypersurfaces are characterized by the condition of the vanishing of the CR-curvature form, so such hypersurfaces are flat from the CR-geometric viewpoint. On the other hand, such hypersurfaces are also of interest from the point of view of affine geometry. Thus our treatment of spherical tube hypersurfaces in this book is two-fold: CR-geometric and affine-geometric. As the book shows, spherical tube hypersurfaces possess remarkable properties. For example, every such hypersurface is real-analytic and extends to a closed real-analytic spherical tube hypersurface in complex space. One of our main goals is to provide an explicit affine classification of closed spherical tube hypersurfaces whenever possible. In this book we offer a comprehensive exposition of the theory of spherical tube hypersurfaces, starting with the idea proposed in the pioneering work by P. Yang (1982) and ending with the new approach put forward by G. Fels and W. Kaup (2009).
Hypersurfaces --- Cauchy-Riemann equations --- Geometry, Affine --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Geometry --- Hypersurfaces. --- Mathematics. --- Functions of complex variables. --- Several Complex Variables and Analytic Spaces. --- Complex variables --- Elliptic functions --- Functions of real variables --- Math --- Science --- Hyperspace --- Surfaces --- Differential equations, partial. --- Partial differential equations
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Bioinformatics --- Mathematics. --- Life sciences. --- Bioinformatics. --- Applied mathematics. --- Engineering mathematics. --- Life Sciences. --- Applications of Mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Bio-informatics --- Biological informatics --- Biology --- Information science --- Computational biology --- Systems biology --- Biosciences --- Sciences, Life --- Science --- Mathematics --- Data processing --- 519.22 --- 519.22 Statistical theory. Statistical models. Mathematical statistics in general --- Statistical theory. Statistical models. Mathematical statistics in general --- Biomathematics. Biometry. Biostatistics --- Stochastic processes --- Bio-informatique --- Mathématiques --- EPUB-LIV-FT LIVBIOLO SPRINGER-B --- Math
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At its core, this concise textbook presents standard material for a first course in complex analysis at the advanced undergraduate level. This distinctive text will prove most rewarding for students who have a genuine passion for mathematics as well as certain mathematical maturity. Primarily aimed at undergraduates with working knowledge of real analysis and metric spaces, this book can also be used to instruct a graduate course. The text uses a conversational style with topics purposefully apportioned into 21 lectures, providing a suitable format for either independent study or lecture-based teaching. Instructors are invited to rearrange the order of topics according to their own vision. A clear and rigorous exposition is supported by engaging examples and exercises unique to each lecture; a large number of exercises contain useful calculation problems. Hints are given for a selection of the more difficult exercises. This text furnishes the reader with a means of learning complex analysis as well as a subtle introduction to careful mathematical reasoning. To guarantee a student’s progression, more advanced topics are spread out over several lectures. This text is based on a one-semester (12 week) undergraduate course in complex analysis that the author has taught at the Australian National University for over twenty years. Most of the principal facts are deduced from Cauchy’s Independence of Homotopy Theorem allowing us to obtain a clean derivation of Cauchy’s Integral Theorem and Cauchy’s Integral Formula. Setting the tone for the entire book, the material begins with a proof of the Fundamental Theorem of Algebra to demonstrate the power of complex numbers and concludes with a proof of another major milestone, the Riemann Mapping Theorem, which is rarely part of a one-semester undergraduate course.
Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Analysis. --- Global analysis (Mathematics). --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- 517.1 Mathematical analysis --- Mathematical analysis --- Calculus. --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Functions --- Geometry, Infinitesimal
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Mathematics --- Biomathematics. Biometry. Biostatistics --- toegepaste wiskunde --- bio-informatica --- biometrie
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Mathematics --- wiskunde
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Analytical spaces --- Mathematical analysis --- analyse (wiskunde)
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At its core, this concise textbook presents standard material for a first course in complex analysis at the advanced undergraduate level. This distinctive text will prove most rewarding for students who have a genuine passion for mathematics as well as certain mathematical maturity. Primarily aimed at undergraduates with working knowledge of real analysis and metric spaces, this book can also be used to instruct a graduate course. The text uses a conversational style with topics purposefully apportioned into 21 lectures, providing a suitable format for either independent study or lecture-based teaching. Instructors are invited to rearrange the order of topics according to their own vision. A clear and rigorous exposition is supported by engaging examples and exercises unique to each lecture; a large number of exercises contain useful calculation problems. Hints are given for a selection of the more difficult exercises. This text furnishes the reader with a means of learning complex analysis as well as a subtle introduction to careful mathematical reasoning. To guarantee a student’s progression, more advanced topics are spread out over several lectures. This text is based on a one-semester (12 week) undergraduate course in complex analysis that the author has taught at the Australian National University for over twenty years. Most of the principal facts are deduced from Cauchy’s Independence of Homotopy Theorem allowing us to obtain a clean derivation of Cauchy’s Integral Theorem and Cauchy’s Integral Formula. Setting the tone for the entire book, the material begins with a proof of the Fundamental Theorem of Algebra to demonstrate the power of complex numbers and concludes with a proof of another major milestone, the Riemann Mapping Theorem, which is rarely part of a one-semester undergraduate course.
Differential geometry. Global analysis --- Mathematical analysis --- analyse (wiskunde) --- statistiek
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toMathematical Methodsin Bioinformatics With 76 Figures and 3 Tables Alexander Isaev Australian National University Department of Mathematics Canberra, ACT 0200 Australia e-mail: alexander. isaev@maths. anu. edu. au Corrected Second Printing 2006 Mathematics Subject Classi?cation (2000 ): 91 -01 (Primary) 91 D20 (Secondary) Libraryof Congress Control Number: 2006930998 ISBN: 3-540 -21973 -0 ISBN: 9783540219736 This work is subject to copyright. All rights are reserved, whether the whole or part of the mat- ial is concerned, speci?cally the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on micro?lm or in any other way, and storage in data banks. Dup- cation of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9 , 1965 , in its current version, and permission for use must always beobtainedfromSpringer. ViolationsareliableforprosecutionundertheGermanCopyrightLaw. Springer is a part of Springer Science+Business Media springer. com Springer-Verlag Berlin Heidelberg 2006 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a speci?c statement, that such names are exempt from the re- vant protective laws and regulations and therefore free for general use. Cover design: Erich Kirchner, Heidelberg A Typesetting by the author and SPi using a Springer LT X macro package E Printed on acid-free paper: SPIN:11809142 41 /2141 /SPi-543210 To Esya and Masha Preface Broadly speaking, Bioinformatics can be de?ned as a collection of mathema- cal, statistical and computational methods for analyzing biological sequences, thatis,DNA,RNAandaminoacid(protein)sequences.
Mathematics --- Biomathematics. Biometry. Biostatistics --- toegepaste wiskunde --- bio-informatica --- biometrie
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Kobayashi-hyperbolic manifolds are an object of active research in complex geometry. In this monograph the author presents a coherent exposition of recent results on complete characterization of Kobayashi-hyperbolic manifolds with high-dimensional groups of holomorphic automorphisms. These classification results can be viewed as complex-geometric analogues of those known for Riemannian manifolds with high-dimensional isotropy groups, that were extensively studied in the 1950s-70s. The common feature of the Kobayashi-hyperbolic and Riemannian cases is the properness of the actions of the holomorphic automorphism group and the isometry group on respective manifolds.
Mathematics --- wiskunde
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