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Uniqueness Theorems For Variational Problems By The Method Of Transformation Groups
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Book Synopsis Uniqueness Theorems for Variational Problems by the Method of Transformation Groups by : Wolfgang Reichel
Download or read book Uniqueness Theorems for Variational Problems by the Method of Transformation Groups written by Wolfgang Reichel and published by Springer. This book was released on 2004-04-30 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: A classical problem in the calculus of variations is the investigation of critical points of functionals {\cal L} on normed spaces V. The present work addresses the question: Under what conditions on the functional {\cal L} and the underlying space V does {\cal L} have at most one critical point? A sufficient condition for uniqueness is given: the presence of a "variational sub-symmetry", i.e., a one-parameter group G of transformations of V, which strictly reduces the values of {\cal L}. The "method of transformation groups" is applied to second-order elliptic boundary value problems on Riemannian manifolds. Further applications include problems of geometric analysis and elasticity.
Book Synopsis Uniqueness Theorems for Variational Problems by the Method of Transformation Groups by : Wolfgang Reichel
Download or read book Uniqueness Theorems for Variational Problems by the Method of Transformation Groups written by Wolfgang Reichel and published by Springer Science & Business Media. This book was released on 2004-05-13 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: A classical problem in the calculus of variations is the investigation of critical points of functionals {\cal L} on normed spaces V. The present work addresses the question: Under what conditions on the functional {\cal L} and the underlying space V does {\cal L} have at most one critical point? A sufficient condition for uniqueness is given: the presence of a "variational sub-symmetry", i.e., a one-parameter group G of transformations of V, which strictly reduces the values of {\cal L}. The "method of transformation groups" is applied to second-order elliptic boundary value problems on Riemannian manifolds. Further applications include problems of geometric analysis and elasticity.
Book Synopsis Topological Complexity of Smooth Random Functions by : Robert Adler
Download or read book Topological Complexity of Smooth Random Functions written by Robert Adler and published by Springer Science & Business Media. This book was released on 2011-05-18 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes, based on lectures delivered in Saint Flour, provide an easy introduction to the authors’ 2007 Springer monograph “Random Fields and Geometry.” While not as exhaustive as the full monograph, they are also less exhausting, while still covering the basic material, typically at a more intuitive and less technical level. They also cover some more recent material relating to random algebraic topology and statistical applications. The notes include an introduction to the general theory of Gaussian random fields, treating classical topics such as continuity and boundedness. This is followed by a quick review of geometry, both integral and Riemannian, with an emphasis on tube formulae, to provide the reader with the material needed to understand and use the Gaussian kinematic formula, the main result of the notes. This is followed by chapters on topological inference and random algebraic topology, both of which provide applications of the main results.
Book Synopsis Stability of Nonautonomous Differential Equations by : Luis Barreira
Download or read book Stability of Nonautonomous Differential Equations written by Luis Barreira and published by Springer. This book was released on 2007-09-26 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers the stability of nonautonomous differential equations in Banach spaces in the presence of nonuniform hyperbolicity. Topics under discussion include the Lyapunov stability of solutions, the existence and smoothness of invariant manifolds, and the construction and regularity of topological conjugacies. The exposition is directed to researchers as well as graduate students interested in differential equations and dynamical systems, particularly in stability theory.
Book Synopsis Quantum Potential Theory by : Philippe Biane
Download or read book Quantum Potential Theory written by Philippe Biane and published by Springer Science & Business Media. This book was released on 2008-09-23 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers the revised and completed notes of lectures given at the 2007 conference, "Quantum Potential Theory: Structures and Applications to Physics." These lectures provide an introduction to the theory and discuss various applications.
Book Synopsis Punctured Torus Groups and 2-Bridge Knot Groups (I) by : Hirotaka Akiyoshi
Download or read book Punctured Torus Groups and 2-Bridge Knot Groups (I) written by Hirotaka Akiyoshi and published by Springer. This book was released on 2007-05-26 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is the first part of a work that provides a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization. It offers an elementary and self-contained description of Jorgensen's theory with a complete proof. Through various informative illustrations, readers are naturally led to an intuitive, synthetic grasp of the theory, which clarifies how a very simple fuchsian group evolves into complicated Kleinian groups.
Book Synopsis Lower Central and Dimension Series of Groups by : Roman Mikhailov
Download or read book Lower Central and Dimension Series of Groups written by Roman Mikhailov and published by Springer. This book was released on 2008-10-20 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fundamental object of study in group theory is the lower central series of groups. Understanding its relationship with the dimension series, which consists of the subgroups determined by the augmentation powers, is a challenging task. This monograph presents an exposition of different methods for investigating this relationship. In addition to group theorists, the results are also of interest to topologists and number theorists. The approach is mainly combinatorial and homological. A novel feature is an exposition of simplicial methods for the study of problems in group theory.
Book Synopsis A Nonlinear Transfer Technique for Renorming by : Aníbal Moltó
Download or read book A Nonlinear Transfer Technique for Renorming written by Aníbal Moltó and published by Springer Science & Business Media. This book was released on 2009 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract topological tools from generalized metric spaces are applied in this volume to the construction of locally uniformly rotund norms on Banach spaces. The book offers new techniques for renorming problems, all of them based on a network analysis for the topologies involved inside the problem. Maps from a normed space X to a metric space Y, which provide locally uniformly rotund renormings on X, are studied and a new frame for the theory is obtained, with interplay between functional analysis, optimization and topology using subdifferentials of Lipschitz functions and covering methods of metrization theory. Any one-to-one operator T from a reflexive space X into c0 (T) satisfies the authors' conditions, transferring the norm to X. Nevertheless the authors' maps can be far from linear, for instance the duality map from X to X* gives a non-linear example when the norm in X is Fréchet differentiable. This volume will be interesting for the broad spectrum of specialists working in Banach space theory, and for researchers in infinite dimensional functional analysis.
Book Synopsis Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction by : Alberto Parmeggiani
Download or read book Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction written by Alberto Parmeggiani and published by Springer Science & Business Media. This book was released on 2010-04-22 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume describes the spectral theory of the Weyl quantization of systems of polynomials in phase-space variables, modelled after the harmonic oscillator. The main technique used is pseudodifferential calculus, including global and semiclassical variants. The main results concern the meromorphic continuation of the spectral zeta function associated with the spectrum, and the localization (and the multiplicity) of the eigenvalues of such systems, described in terms of “classical” invariants (such as the periods of the periodic trajectories of the bicharacteristic flow associated with the eiganvalues of the symbol). The book utilizes techniques that are very powerful and flexible and presents an approach that could also be used for a variety of other problems. It also features expositions on different results throughout the literature.
Book Synopsis The Analysis of Fractional Differential Equations by : Kai Diethelm
Download or read book The Analysis of Fractional Differential Equations written by Kai Diethelm and published by Springer Science & Business Media. This book was released on 2010-09-03 with total page 251 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fractional calculus was first developed by pure mathematicians in the middle of the 19th century. Some 100 years later, engineers and physicists have found applications for these concepts in their areas. However there has traditionally been little interaction between these two communities. In particular, typical mathematical works provide extensive findings on aspects with comparatively little significance in applications, and the engineering literature often lacks mathematical detail and precision. This book bridges the gap between the two communities. It concentrates on the class of fractional derivatives most important in applications, the Caputo operators, and provides a self-contained, thorough and mathematically rigorous study of their properties and of the corresponding differential equations. The text is a useful tool for mathematicians and researchers from the applied sciences alike. It can also be used as a basis for teaching graduate courses on fractional differential equations.
Book Synopsis Geometric Theory of Discrete Nonautonomous Dynamical Systems by : Christian Pötzsche
Download or read book Geometric Theory of Discrete Nonautonomous Dynamical Systems written by Christian Pötzsche and published by Springer Science & Business Media. This book was released on 2010-09-17 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes).
Book Synopsis Intersection Spaces, Spatial Homology Truncation, and String Theory by : Markus Banagl
Download or read book Intersection Spaces, Spatial Homology Truncation, and String Theory written by Markus Banagl and published by Springer Science & Business Media. This book was released on 2010-07-08 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present monograph introduces a method that assigns to certain classes of stratified spaces cell complexes, called intersection spaces, whose ordinary rational homology satisfies generalized Poincaré duality.
Book Synopsis Generalized Bessel Functions of the First Kind by : Árpád Baricz
Download or read book Generalized Bessel Functions of the First Kind written by Árpád Baricz and published by Springer Science & Business Media. This book was released on 2010-05-25 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume studies the generalized Bessel functions of the first kind by using a number of classical and new findings in complex and classical analysis. It presents interesting geometric properties and functional inequalities for these generalized functions.
Book Synopsis Symmetries of Compact Riemann Surfaces by : Emilio Bujalance
Download or read book Symmetries of Compact Riemann Surfaces written by Emilio Bujalance and published by Springer Science & Business Media. This book was released on 2010-10-06 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph deals with symmetries of compact Riemann surfaces. A symmetry of a compact Riemann surface S is an antianalytic involution of S. It is well known that Riemann surfaces exhibiting symmetry correspond to algebraic curves which can be defined over the field of real numbers. In this monograph we consider three topics related to the topology of symmetries, namely the number of conjugacy classes of symmetries, the numbers of ovals of symmetries and the symmetry types of Riemann surfaces.
Book Synopsis Inverse Problems and Imaging by : Luis L. Bonilla
Download or read book Inverse Problems and Imaging written by Luis L. Bonilla and published by Springer. This book was released on 2009-06-19 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nowadays we are facing numerous and important imaging problems: nondestructive testing of materials, monitoring of industrial processes, enhancement of oil production by efficient reservoir characterization, emerging developments in noninvasive imaging techniques for medical purposes - computerized tomography (CT), magnetic resonance imaging (MRI), positron emission tomography (PET), X-ray and ultrasound tomography, etc. In the CIME Summer School on Imaging (Martina Franca, Italy 2002), leading experts in mathematical techniques and applications presented broad and useful introductions for non-experts and practitioners alike to many aspects of this exciting field. The volume contains part of the above lectures completed and updated by additional contributions on other related topics.
Download or read book Lévy Matters I written by Thomas Duquesne and published by Springer Science & Business Media. This book was released on 2010-09-05 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on the breadth of the topic, this volume explores Lévy processes and applications, and presents the state-of-the-art in this evolving area of study. These expository articles help to disseminate important theoretical and applied research to those studying the field.
Book Synopsis Compactifying Moduli Spaces for Abelian Varieties by : Martin C. Olsson
Download or read book Compactifying Moduli Spaces for Abelian Varieties written by Martin C. Olsson and published by Springer Science & Business Media. This book was released on 2008-08-25 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the construction of canonical modular compactifications of moduli spaces for polarized Abelian varieties (possibly with level structure), building on the earlier work of Alexeev, Nakamura, and Namikawa. This provides a different approach to compactifying these spaces than the more classical approach using toroical embeddings, which are not canonical. There are two main new contributions in this monograph: (1) The introduction of logarithmic geometry as understood by Fontaine, Illusie, and Kato to the study of degenerating Abelian varieties; and (2) the construction of canonical compactifications for moduli spaces with higher degree polarizations based on stack-theoretic techniques and a study of the theta group.
