On Some Aspects Of Oscillation Theory And Geometry

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On Some Aspects of Oscillation Theory and Geometry

Author : Bruno Bianchini
Publisher : American Mathematical Soc.
ISBN 13 : 0821887998
Total Pages : 208 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis On Some Aspects of Oscillation Theory and Geometry by : Bruno Bianchini

Download or read book On Some Aspects of Oscillation Theory and Geometry written by Bruno Bianchini and published by American Mathematical Soc.. This book was released on 2013-08-23 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this paper is to analyze some of the relationships between oscillation theory for linear ordinary differential equations on the real line (shortly, ODE) and the geometry of complete Riemannian manifolds. With this motivation the authors prove some new results in both directions, ranging from oscillation and nonoscillation conditions for ODE's that improve on classical criteria, to estimates in the spectral theory of some geometric differential operator on Riemannian manifolds with related topological and geometric applications. To keep their investigation basically self-contained, the authors also collect some, more or less known, material which often appears in the literature in various forms and for which they give, in some instances, new proofs according to their specific point of view.

Recent Trends in Nonlinear Partial Differential Equations I

Author : James B. Serrin
Publisher : American Mathematical Soc.
ISBN 13 : 082188736X
Total Pages : 323 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Recent Trends in Nonlinear Partial Differential Equations I by : James B. Serrin

Download or read book Recent Trends in Nonlinear Partial Differential Equations I written by James B. Serrin and published by American Mathematical Soc.. This book was released on 2013-07-22 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first of two volumes which contain the proceedings of the Workshop on Nonlinear Partial Differential Equations, held from May 28-June 1, 2012, at the University of Perugia in honor of Patrizia Pucci's 60th birthday. The workshop brought t

Combinatorial Floer Homology

Author : Vin de Silva
Publisher : American Mathematical Soc.
ISBN 13 : 0821898868
Total Pages : 126 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Combinatorial Floer Homology by : Vin de Silva

Download or read book Combinatorial Floer Homology written by Vin de Silva and published by American Mathematical Soc.. This book was released on 2014-06-05 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors define combinatorial Floer homology of a transverse pair of noncontractible nonisotopic embedded loops in an oriented -manifold without boundary, prove that it is invariant under isotopy, and prove that it is isomorphic to the original Lagrangian Floer homology. Their proof uses a formula for the Viterbo-Maslov index for a smooth lune in a -manifold.

Effective Hamiltonians for Constrained Quantum Systems

Author : Jakob Wachsmuth
Publisher : American Mathematical Soc.
ISBN 13 : 0821894897
Total Pages : 96 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Effective Hamiltonians for Constrained Quantum Systems by : Jakob Wachsmuth

Download or read book Effective Hamiltonians for Constrained Quantum Systems written by Jakob Wachsmuth and published by American Mathematical Soc.. This book was released on 2014-06-05 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider the time-dependent Schrödinger equation on a Riemannian manifold with a potential that localizes a certain subspace of states close to a fixed submanifold . When the authors scale the potential in the directions normal to by a parameter , the solutions concentrate in an -neighborhood of . This situation occurs for example in quantum wave guides and for the motion of nuclei in electronic potential surfaces in quantum molecular dynamics. The authors derive an effective Schrödinger equation on the submanifold and show that its solutions, suitably lifted to , approximate the solutions of the original equation on up to errors of order at time . Furthermore, the authors prove that the eigenvalues of the corresponding effective Hamiltonian below a certain energy coincide up to errors of order with those of the full Hamiltonian under reasonable conditions.

Near Soliton Evolution for Equivariant Schrodinger Maps in Two Spatial Dimensions

Author : Ioan Bejenaru
Publisher : American Mathematical Soc.
ISBN 13 : 0821892150
Total Pages : 120 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Near Soliton Evolution for Equivariant Schrodinger Maps in Two Spatial Dimensions by : Ioan Bejenaru

Download or read book Near Soliton Evolution for Equivariant Schrodinger Maps in Two Spatial Dimensions written by Ioan Bejenaru and published by American Mathematical Soc.. This book was released on 2014-03-05 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider the Schrödinger Map equation in 2+1 dimensions, with values into \mathbb{S}^2. This admits a lowest energy steady state Q, namely the stereographic projection, which extends to a two dimensional family of steady states by scaling and rotation. The authors prove that Q is unstable in the energy space \dot H^1. However, in the process of proving this they also show that within the equivariant class Q is stable in a stronger topology X \subset \dot H^1.

On the Spectra of Quantum Groups

Author : Milen Yakimov
Publisher : American Mathematical Soc.
ISBN 13 : 082189174X
Total Pages : 104 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis On the Spectra of Quantum Groups by : Milen Yakimov

Download or read book On the Spectra of Quantum Groups written by Milen Yakimov and published by American Mathematical Soc.. This book was released on 2014-04-07 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: Joseph and Hodges-Levasseur (in the A case) described the spectra of all quantum function algebras on simple algebraic groups in terms of the centers of certain localizations of quotients of by torus invariant prime ideals, or equivalently in terms of orbits of finite groups. These centers were only known up to finite extensions. The author determines the centers explicitly under the general conditions that the deformation parameter is not a root of unity and without any restriction on the characteristic of the ground field. From it he deduces a more explicit description of all prime ideals of than the previously known ones and an explicit parametrization of .

Global and Local Regularity of Fourier Integral Operators on Weighted and Unweighted Spaces

Author : David Dos Santos Ferreira
Publisher : American Mathematical Soc.
ISBN 13 : 0821891197
Total Pages : 86 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Global and Local Regularity of Fourier Integral Operators on Weighted and Unweighted Spaces by : David Dos Santos Ferreira

Download or read book Global and Local Regularity of Fourier Integral Operators on Weighted and Unweighted Spaces written by David Dos Santos Ferreira and published by American Mathematical Soc.. This book was released on 2014-04-07 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors investigate the global continuity on spaces with of Fourier integral operators with smooth and rough amplitudes and/or phase functions subject to certain necessary non-degeneracy conditions. In this context they prove the optimal global boundedness result for Fourier integral operators with non-degenerate phase functions and the most general smooth Hörmander class amplitudes i.e. those in with . They also prove the very first results concerning the continuity of smooth and rough Fourier integral operators on weighted spaces, with and (i.e. the Muckenhoupt weights) for operators with rough and smooth amplitudes and phase functions satisfying a suitable rank condition.

Weighted Bergman Spaces Induced by Rapidly Increasing Weights

Author : Jose Angel Pelaez
Publisher : American Mathematical Soc.
ISBN 13 : 0821888021
Total Pages : 136 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Weighted Bergman Spaces Induced by Rapidly Increasing Weights by : Jose Angel Pelaez

Download or read book Weighted Bergman Spaces Induced by Rapidly Increasing Weights written by Jose Angel Pelaez and published by American Mathematical Soc.. This book was released on 2014-01-08 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is devoted to the study of the weighted Bergman space $A^p_\omega$ of the unit disc $\mathbb{D}$ that is induced by a radial continuous weight $\omega$ satisfying $\lim_{r\to 1^-}\frac{\int_r^1\omega(s)\,ds}{\omega(r)(1-r)}=\infty.$ Every such $A^p_\omega$ lies between the Hardy space $H^p$ and every classical weighted Bergman space $A^p_\alpha$. Even if it is well known that $H^p$ is the limit of $A^p_\alpha$, as $\alpha\to-1$, in many respects, it is shown that $A^p_\omega$ lies ``closer'' to $H^p$ than any $A^p_\alpha$, and that several finer function-theoretic properties of $A^p_\alpha$ do not carry over to $A^p_\omega$.

Relative Equilibria in the 3-Dimensional Curved $n$-Body Problem

Author : Florin Diacu
Publisher : American Mathematical Soc.
ISBN 13 : 0821891367
Total Pages : 92 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Relative Equilibria in the 3-Dimensional Curved $n$-Body Problem by : Florin Diacu

Download or read book Relative Equilibria in the 3-Dimensional Curved $n$-Body Problem written by Florin Diacu and published by American Mathematical Soc.. This book was released on 2014-03-05 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: Considers the 3 -dimensional gravitational n -body problem, n32 , in spaces of constant Gaussian curvature k10 , i.e. on spheres S 3 ?1 , for ?>0 , and on hyperbolic manifolds H 3 ?1, for ?

Nonlinear Stability of Ekman Boundary Layers in Rotating Stratified Fluids

Author : Hajime Koba
Publisher : American Mathematical Soc.
ISBN 13 : 0821891332
Total Pages : 142 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Nonlinear Stability of Ekman Boundary Layers in Rotating Stratified Fluids by : Hajime Koba

Download or read book Nonlinear Stability of Ekman Boundary Layers in Rotating Stratified Fluids written by Hajime Koba and published by American Mathematical Soc.. This book was released on 2014-03-05 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: A stationary solution of the rotating Navier-Stokes equations with a boundary condition is called an Ekman boundary layer. This book constructs stationary solutions of the rotating Navier-Stokes-Boussinesq equations with stratification effects in the case when the rotating axis is not necessarily perpendicular to the horizon. The author calls such stationary solutions Ekman layers. This book shows the existence of a weak solution to an Ekman perturbed system, which satisfies the strong energy inequality. Moreover, the author discusses the uniqueness of weak solutions and computes the decay rate of weak solutions with respect to time under some assumptions on the Ekman layers and the physical parameters. The author also shows that there exists a unique global-in-time strong solution of the perturbed system when the initial datum is sufficiently small. Comparing a weak solution satisfying the strong energy inequality with the strong solution implies that the weak solution is smooth with respect to time when time is sufficiently large.

Stochastic Flows in the Brownian Web and Net

Author : Emmanuel Schertzer
Publisher : American Mathematical Soc.
ISBN 13 : 0821890883
Total Pages : 172 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Stochastic Flows in the Brownian Web and Net by : Emmanuel Schertzer

Download or read book Stochastic Flows in the Brownian Web and Net written by Emmanuel Schertzer and published by American Mathematical Soc.. This book was released on 2014-01-08 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is known that certain one-dimensional nearest-neighbor random walks in i.i.d. random space-time environments have diffusive scaling limits. Here, in the continuum limit, the random environment is represented by a `stochastic flow of kernels', which is a collection of random kernels that can be loosely interpreted as the transition probabilities of a Markov process in a random environment. The theory of stochastic flows of kernels was first developed by Le Jan and Raimond, who showed that each such flow is characterized by its -point motions. The authors' work focuses on a class of stochastic flows of kernels with Brownian -point motions which, after their inventors, will be called Howitt-Warren flows. The authors' main result gives a graphical construction of general Howitt-Warren flows, where the underlying random environment takes on the form of a suitably marked Brownian web. This extends earlier work of Howitt and Warren who showed that a special case, the so-called "erosion flow", can be constructed from two coupled "sticky Brownian webs". The authors' construction for general Howitt-Warren flows is based on a Poisson marking procedure developed by Newman, Ravishankar and Schertzer for the Brownian web. Alternatively, the authors show that a special subclass of the Howitt-Warren flows can be constructed as random flows of mass in a Brownian net, introduced by Sun and Swart. Using these constructions, the authors prove some new results for the Howitt-Warren flows.

A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations with Inverse Square Potentials

Author : Florica C. Cîrstea
Publisher : American Mathematical Soc.
ISBN 13 : 0821890220
Total Pages : 97 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations with Inverse Square Potentials by : Florica C. Cîrstea

Download or read book A Complete Classification of the Isolated Singularities for Nonlinear Elliptic Equations with Inverse Square Potentials written by Florica C. Cîrstea and published by American Mathematical Soc.. This book was released on 2014-01-08 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: In particular, for b = 1 and λ = 0, we find a sharp condition on h such that the origin is a removable singularity for all non-negative solutions of [[eqref]]one, thus addressing an open question of Vázquez and Véron.

Large Deviations for Additive Functionals of Markov Chains

Author : Alejandro D. de Acosta
Publisher : American Mathematical Soc.
ISBN 13 : 0821890891
Total Pages : 120 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Large Deviations for Additive Functionals of Markov Chains by : Alejandro D. de Acosta

Download or read book Large Deviations for Additive Functionals of Markov Chains written by Alejandro D. de Acosta and published by American Mathematical Soc.. This book was released on 2014-03-05 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Spectra of Symmetrized Shuffling Operators

Author : Victor Reiner
Publisher : American Mathematical Soc.
ISBN 13 : 0821890956
Total Pages : 121 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Spectra of Symmetrized Shuffling Operators by : Victor Reiner

Download or read book Spectra of Symmetrized Shuffling Operators written by Victor Reiner and published by American Mathematical Soc.. This book was released on 2014-03-05 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a finite real reflection group W and a W -orbit O of flats in its reflection arrangement - or equivalently a conjugacy class of its parabolic subgroups - the authors introduce a statistic noninv O (w) on w in W that counts the number of O -noninversions of w . This generalises the classical (non-)inversion statistic for permutations w in the symmetric group S n. The authors then study the operator ? O of right-multiplication within the group algebra CW by the element that has noninv O (w) as its coefficient on w.

Geometric Aspects of Probability Theory and Mathematical Statistics

Author : V.V. Buldygin
Publisher : Springer Science & Business Media
ISBN 13 : 9401716870
Total Pages : 314 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Geometric Aspects of Probability Theory and Mathematical Statistics by : V.V. Buldygin

Download or read book Geometric Aspects of Probability Theory and Mathematical Statistics written by V.V. Buldygin and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is well known that contemporary mathematics includes many disci plines. Among them the most important are: set theory, algebra, topology, geometry, functional analysis, probability theory, the theory of differential equations and some others. Furthermore, every mathematical discipline consists of several large sections in which specific problems are investigated and the corresponding technique is developed. For example, in general topology we have the following extensive chap ters: the theory of compact extensions of topological spaces, the theory of continuous mappings, cardinal-valued characteristics of topological spaces, the theory of set-valued (multi-valued) mappings, etc. Modern algebra is featured by the following domains: linear algebra, group theory, the theory of rings, universal algebras, lattice theory, category theory, and so on. Concerning modern probability theory, we can easily see that the clas sification of its domains is much more extensive: measure theory on ab stract spaces, Borel and cylindrical measures in infinite-dimensional vector spaces, classical limit theorems, ergodic theory, general stochastic processes, Markov processes, stochastical equations, mathematical statistics, informa tion theory and many others.

String Theory and the Scientific Method

Author : Richard Dawid
Publisher : Cambridge University Press
ISBN 13 : 1107029716
Total Pages : 213 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis String Theory and the Scientific Method by : Richard Dawid

Download or read book String Theory and the Scientific Method written by Richard Dawid and published by Cambridge University Press. This book was released on 2013-05-02 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explains why string theorists develop a strong belief in their theory despite the lack of empirical confirmation.

On Some Aspects of Oscillation Theory and Geometry

Author : Bruno Bianchini
Publisher :
ISBN 13 : 9781470410568
Total Pages : 208 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis On Some Aspects of Oscillation Theory and Geometry by : Bruno Bianchini

Download or read book On Some Aspects of Oscillation Theory and Geometry written by Bruno Bianchini and published by . This book was released on 2014-09-11 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The aim of this paper is to analyze some of the relationships between oscillation theory for linear ordinary differential equations on the real line (shortly, ODE) and the geometry of complete Riemannian manifolds. With this motivation we prove some new results in both directions, ranging from oscillation and nonoscillation conditions for ODE's that improve on classical criteria, to estimates in the spectral theory of some geometric differential operator on Riemannian manifolds with related topological and geometric applications. To keep our investigation basically self-contained we also collect some, more or less known, material which often appears in the literature in various forms and for which we give, in some instances, new proofs according to our specific point of view."--Page v.