Stability Of Spherically Symmetric Wave Maps
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Stability Of Spherically Symmetric Wave Maps
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Author : Joachim Krieger
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Stability Of Spherically Symmetric Wave Maps written by Joachim Krieger 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 2006 with Mathematics categories.
Presents a study of Wave Maps from ${\mathbf{R}}^{2+1}$ to the hyperbolic plane ${\mathbf{H}}^{2}$ with smooth compactly supported initial data which are close to smooth spherically symmetric initial data with respect to some $H^{1+\mu}$, $\mu>0$.
Stability Of Spherically Symmetric Wave Maps
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Author : Joachim Krieger
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Stability Of Spherically Symmetric Wave Maps written by Joachim Krieger 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 2006 with Mathematics categories.
We study Wave Maps from ${\mathbf{R}}^{2+1}$ to the hyperbolic plane ${\mathbf{H}}^{2}$ with smooth compactly supported initial data which are close to smooth spherically symmetric initial data with respect to some $H^{1+\mu}$, $\mu>0$. We show that such Wave Maps don't develop singularities in finite time and stay close to the Wave Map extending the spherically symmetric data(whose existence is ensured by a theorem of Christodoulou-Tahvildar-Zadeh) with respect to all $H^{1+\delta}, \delta\less\mu_{0}$ for suitable $\mu_{0}(\mu)>0$. We obtain a similar result for Wave Maps whose initial data are close to geodesic ones. This strengthens a theorem of Sideris for this context.
Developments Of Harmonic Maps Wave Maps And Yang Mills Fields Into Biharmonic Maps Biwave Maps And Bi Yang Mills Fields
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Author : Yuan-Jen Chiang
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-18
Developments Of Harmonic Maps Wave Maps And Yang Mills Fields Into Biharmonic Maps Biwave Maps And Bi Yang Mills Fields written by Yuan-Jen Chiang 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 2013-06-18 with Mathematics categories.
Harmonic maps between Riemannian manifolds were first established by James Eells and Joseph H. Sampson in 1964. Wave maps are harmonic maps on Minkowski spaces and have been studied since the 1990s. Yang-Mills fields, the critical points of Yang-Mills functionals of connections whose curvature tensors are harmonic, were explored by a few physicists in the 1950s, and biharmonic maps (generalizing harmonic maps) were introduced by Guoying Jiang in 1986. The book presents an overview of the important developments made in these fields since they first came up. Furthermore, it introduces biwave maps (generalizing wave maps) which were first studied by the author in 2009, and bi-Yang-Mills fields (generalizing Yang-Mills fields) first investigated by Toshiyuki Ichiyama, Jun-Ichi Inoguchi and Hajime Urakawa in 2008. Other topics discussed are exponential harmonic maps, exponential wave maps and exponential Yang-Mills fields.
Kam Stability And Celestial Mechanics
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Author : Alessandra Celletti
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Kam Stability And Celestial Mechanics written by Alessandra Celletti 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 2007 with Mathematics categories.
KAM theory is a powerful tool apt to prove perpetual stability in Hamiltonian systems, which are a perturbation of integrable ones. The smallness requirements for its applicability are well known to be extremely stringent. A long standing problem, in this context, is the application of KAM theory to ``physical systems'' for ``observable'' values of the perturbation parameters. The authors consider the Restricted, Circular, Planar, Three-Body Problem (RCP3BP), i.e., the problem of studying the planar motions of a small body subject to the gravitational attraction of two primary bodies revolving on circular Keplerian orbits (which are assumed not to be influenced by the small body). When the mass ratio of the two primary bodies is small, the RCP3BP is described by a nearly-integrable Hamiltonian system with two degrees of freedom; in a region of phase space corresponding to nearly elliptical motions with non-small eccentricities, the system is well described by Delaunay variables. The Sun-Jupiter observed motion is nearly circular and an asteroid of the Asteroidal belt may be assumed not to influence the Sun-Jupiter motion. The Jupiter-Sun mass ratio is slightly less than 1/1000. The authors consider the motion of the asteroid 12 Victoria taking into account only the Sun-Jupiter gravitational attraction regarding such a system as a prototype of a RCP3BP. for values of mass ratios up to 1/1000, they prove the existence of two-dimensional KAM tori on a fixed three-dimensional energy level corresponding to the observed energy of the Sun-Jupiter-Victoria system. Such tori trap the evolution of phase points ``close'' to the observed physical data of the Sun-Jupiter-Victoria system. As a consequence, in the RCP3BP description, the motion of Victoria is proven to be forever close to an elliptical motion. The proof is based on: 1) a new iso-energetic KAM theory; 2) an algorithm for computing iso-energetic, approximate Lindstedt series; 3) a computer-aided application of 1)+2) to the Sun-Jupiter-Victoria system. The paper is self-contained but does not include the ($\sim$ 12000 lines) computer programs, which may be obtained by sending an e-mail to one of the authors.
Invariant Differential Operators For Quantum Symmetric Spaces
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Author : Gail Letzter
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Invariant Differential Operators For Quantum Symmetric Spaces written by Gail Letzter 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 2008 with Mathematics categories.
This paper studies quantum invariant differential operators for quantum symmetric spaces in the maximally split case. The main results are quantum versions of theorems of Harish-Chandra and Helgason: There is a Harish-Chandra map which induces an isomorphism between the ring of quantum invariant differential operators and the ring of invariants of a certain Laurent polynomial ring under an action of the restricted Weyl group. Moreover, the image of the center under this map is the entire invariant ring if and only if the underlying irreducible symmetric pair is not of four exceptional types. In the process, the author finds a particularly nice basis for the quantum invariant differential operators that provides a new interpretation of difference operators associated to Macdonald polynomials.
The Generalized Triangle Inequalities In Symmetric Spaces And Buildings With Applications To Algebra
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Author : Michael Kapovich
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
The Generalized Triangle Inequalities In Symmetric Spaces And Buildings With Applications To Algebra written by Michael Kapovich 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 2008 with Mathematics categories.
In this paper the authors apply their results on the geometry of polygons in infinitesimal symmetric spaces and symmetric spaces and buildings to four problems in algebraic group theory. Two of these problems are generalizations of the problems of finding the constraints on the eigenvalues (resp. singular values) of a sum (resp. product) when the eigenvalues (singular values) of each summand (factor) are fixed. The other two problems are related to the nonvanishing of the structure constants of the (spherical) Hecke and representation rings associated with a split reductive algebraic group over $\mathbb{Q}$ and its complex Langlands' dual. The authors give a new proof of the Saturation Conjecture for $GL(\ell)$ as a consequence of their solution of the corresponding saturation problem for the Hecke structure constants for all split reductive algebraic groups over $\mathbb{Q}$.
Gravitation And Astrophysics
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Author : James M. Nester
language : en
Publisher: World Scientific
Release Date : 2007
Gravitation And Astrophysics written by James M. Nester and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Science categories.
The ICGA series of conferences is specially aimed to serve the needs of the workers in this research area in the Asia-Pacific region. The previous conferences of this series have attracted a growing number of local, regional and international participants. 2005 was an auspicious year. Not only was it the International Year of Physics, commemorating Einstein''s great achievements of 1905, it also was the anniversary of Einstein''s development of General Relativity: he submitted the final form of his field equations on 25 November, 1915. Nine decades years later, around 40 Taiwan-based participants were joined by over 40 distinguished visitors from Canada, China, France, Japan, Korea, Russia, and the USA, and this volume includes many of the papers that were presented. The depth and breadth of these contributions reflect the high quality of the meeting and the development of the field in the Asia-Pacific region. Sample Chapter(s). Chapter 1: Progress in Testing Newtonian Inverse Square Law (234 KB). Contents: Experimental Tests of Gravity; Numerical Relativity; Cosmology; Astrophysics; Quantum Gravity; Classical Gravity. Readership: Graduate students and researchers in astrophysics, gravitation, cosmology and theoretical physics.
Semisolvability Of Semisimple Hopf Algebras Of Low Dimension
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Author : Sonia Natale
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Semisolvability Of Semisimple Hopf Algebras Of Low Dimension written by Sonia Natale 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 2007 with Mathematics categories.
The author proves that every semisimple Hopf algebra of dimension less than $60$ over an algebraically closed field $k$ of characteristic zero is either upper or lower semisolvable up to a cocycle twist.
Tangential Boundary Stabilization Of Navier Stokes Equations
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Author : Viorel Barbu
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Tangential Boundary Stabilization Of Navier Stokes Equations written by Viorel Barbu 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 2006 with Mathematics categories.
In order to inject dissipation as to force local exponential stabilization of the steady-state solutions, an Optimal Control Problem (OCP) with a quadratic cost functional over an infinite time-horizon is introduced for the linearized N-S equations. As a result, the same Riccati-based, optimal boundary feedback controller which is obtained in the linearized OCP is then selected and implemented also on the full N-S system. For $d=3$, the OCP falls definitely outside the boundaries of established optimal control theory for parabolic systems with boundary controls, in that the combined index of unboundedness--between the unboundedness of the boundary control operator and the unboundedness of the penalization or observation operator--is strictly larger than $\tfrac{3}{2}$, as expressed in terms of fractional powers of the free-dynamics operator. In contrast, established (and rich) optimal control theory [L-T.2] of boundary control parabolic problems and corresponding algebraic Riccati theory requires a combined index of unboundedness strictly less than 1. An additional preliminary serious difficulty to overcome lies at the outset of the program, in establishing that the present highly non-standard OCP--with the aforementioned high level of unboundedness in control and observation operators and subject, moreover, to the additional constraint that the controllers be pointwise tangential--be non-empty; that is, it satisfies the so-called Finite Cost Condition [L-T.2].
Weakly Differentiable Mappings Between Manifolds
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Author : Piotr Hajłasz
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Weakly Differentiable Mappings Between Manifolds written by Piotr Hajłasz 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 2008 with Mathematics categories.
The authors study Sobolev classes of weakly differentiable mappings $f: {\mathbb X}\rightarrow {\mathbb Y}$ between compact Riemannian manifolds without boundary. These mappings need not be continuous. They actually possess less regularity than the mappings in ${\mathcal W}{1, n}({\mathbb X}\, \, {\mathbb Y})\, $, $n=\mbox{dim}\, {\mathbb X}$. The central themes being discussed a