Strong electric field eigenvalue asymptotics for the Schrödinger operator with electromagnetic potential

We consider the Schrödinger operator with electric potential V, which decays at infinity, and magnetic potential A. We study the asymptotic behaviour for large values of the electric field coupling constant of the eigenvalues situated under the essential-spectrum lower bound. We concentrate on the cases of rapidly decaying V (e.g. V L ^m/2( ^m ) for m 3) and arbitrary A, or slowly decaying V (i.e. V(x |x|^– , (0,2), as |x| ) and magnetic potentials A corresponding to constant magnetic fields B = curl A.Partially supported by the Ministry of Culture, Science and Education under Grant No. 52.     

SO q (n+1,n−1) as a real form of SO q (2n,ℂ)

Quantum pseudo-orthogonal groups SO _q (n+1,n–1) are defined as real forms of quantum orthogonal groups SO _q (n+1,n–1) by means of a suitable antilinear involution. In particular, the casen=2 gives a quantized Lorentz group.     

Convergence rate estimate for a domain decomposition method

Summary We provide a convergence rate analysis for a variant of the domain decomposition method introduced by Gropp and Keyes for solving the algebraic equations that arise from finite element discretization of nonsymmetric and indefinite elliptic problems with Dirichlet boundary conditions in ². We show that the convergence rate of the preconditioned GMRES method is nearly optimal in the sense that the rate of convergence depends only logarithmically on the mesh size and the number of substructures, if the global coarse mesh is fine enough.This author was supported by the National Science Foundation under contract numbers DCR-8521451 and ECS-8957475, by the IBM Corporation, and by the 3M Company, while in residence at Yale UniversityThis author was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy under Contract W-31-109-Eng-38This author was supported by the National Science Foundation under contract number ECS-8957475, by the IBM Corporation, and by the 3M Company     

Convex hull of powers of a complex number,trinomial equations and the Farey sequence

The color of a complex number is defined as the number of vertices of the convex hull of powers of that number. This induces a coloring of the unit disk. The structure of the set of points where the color changes is investigated here. It is observed that there is a connection between this fractal set and some family of trinomial equations. Three algorithms for coloring the unit disk are described, the last one (related to the Farey sequence) arising out of a conjecture. This conjecture is formulated and proved in this presentation.     

A supraconvergent scheme for the Korteweg-de Vries equation

Summary A finite-difference method for the integration of the Korteweg-de Vries equation on irregular grids is analyzed. Under periodic boundary conditions, the method is shown to be supraconvergent in the sense that, though being inconsistent, it is second order convergent. However, such a convergence only takes place on grids with an odd number of points per period. When a grid with an even number of points is used, the inconsistency of the method leads to divergence. Numerical results backing the analysis are presented.     

On the ?ojasiewicz-Simon gradient inequality

We prove a general version of the ?ojasiewicz-Simon inequality, and we show how to apply the abstract result to study energy functionals E of the form

     

Eu3+、Tb3+与1-乙酰乙酰吲哚、1,10-邻菲啰啉二元、三元体系在溶液中荧光光谱研究

观察了以不同比例溶解在乙醇中的Eu3+、Tb3+、1-乙酰乙酰吲哚(HL)和1,10-邻菲啉(Phen)的荧光光谱.结果表明HL能有效地把吸收的能量传递给Tb3+,而不能有效地传递给Eu3+.讨论了HL和Phen对Eu3+、Tb3+的配位作用及其对Eu3+或Tb3+所组成的三元体系中敏化发光性能的影响.     

Extended non-abelian gauge symmetries in the classical WZNW model

Higher spin extensions of the non-Abelian gauge symmetries for the classical WZNW model are considered. Both linear and nonlinear realizations of the extended affine Kac-Moody algebra are obtained. It is a characteristic property of the WZNW model that it admits a higher spin linear realization of the extended affine Kac-Moody algebra which is equivalent to the corresponding higher spin nonlinear realization of the same algebra. However, in both cases, the higher spin Noether currents do not span an invariant space with respect to their generating transformations. Here, the current space is extended to an invariant space which allows us to gauge the symmetry.Supported by Bulgarian Foundation on Fundamental Research under contract Ph-318/93-95.     

Eu~（3＋）、Tb~（3＋）与1－乙酰乙酰吲哚、1，10－邻菲啰啉二元、三元体系在溶液中荧光光谱研究

观察了以不同比例溶解在乙醇中的ＥＵ（３＋）、Ｔｂ（３＋）、１－乙酰乙酰吲哚（ＨＬ）和１，１０－邻菲啉（Ｐｈｅｎ）的荧光光谱．结果表明ＨＬ能有效地把吸收的能量传递给Ｔｂ（３＋），而不能有效地传递给Ｅｕ（３＋）．讨论了ＨＬ和Ｐｈｅｎ对Ｅｕ（３＋）、Ｔｂ（３＋）的配位作用及其对Ｅｕ（３＋）或Ｔｂ（３＋）所组成的三元体系中敏化发光性能的影响．