二米真空紫外光栅摄谱仪

本文叙述了新近建造的一台二米真空紫外光栅摄谱仪的构造、性能和得到的结果,仪器是法线入射式,入射角7.5°,记录波段为2100?—200?。平均色散率为8.7?/mm。应用低气压电容放电光源,获得强而清晰的线状谱,包括大量的高次离化谱线。我们辨认了这个光源发射的大部分谱线共554条。 关键词：     

Global Geometry of 3-Body Motions with Vanishing Angular Momentum Ⅰ

Following Jacobi＇s geometrization of Lagrange＇s least action principle, trajectories of classical mechanics can be characterized as geodesics on the configuration space M with respect to a suitable metric which is the conformal modification of the kinematic metric by the factor （U ＋ h）, where U and h are the potential function and the total energy, respectively. In the special case of 3-body motions with zero angular momentum, the global geometry of such trajectories can be reduced to that of their moduli curves, which record the change of size and shape, in the moduli space of oriented m-triangles, whose kinematic metric is, in fact, a Riemannian cone over the shape space M^＊≌S^2 （1/2）.
In this paper, it is shown that the moduli curve of such a motion is uniquely determined by its shape curve （which only records the change of shape） in the case of h≠0, while in the special case of h = 0 it is uniquely determined up to scaling. Thus, the study of the global geometry of such motions can be further reduced to that of the shape curves, which are time-parametrized curves on the 2-sphere characterized by a third order ODE. Moreover, these curves have two remarkable properties, namely the uniqueness of parametrization and the monotonieity, that constitute a solid foundation for a systematic study of their global geometry and naturally lead to the formulation of some pertinent problems.     

SL(2,R) PRINCIPAL PROLONGATION STRUCTURES OF SOLITON EQUATIONS AND THEIR CONSERVATION LAWS

We present the concept of principal prolongation structure (PPS) and a covariant criterion of the completeness of conserva-tion currents for the PPS of class of nonlinear evolution equations (NEES).The SL(2,R) × R'(l) PPS for AKNS systems is constructed, a new set of infinite number of polynomial conservation currents (PCCs) corresponding to the nonlinearity of SL (2,R) group manifold is given. These currents together with the usual PCCS of AKNS systems satisfy a covariant equation for the SL(2,R) × R'(l) PPS. This equation gives rise to a criterion of completeness of these currents. As an example,the sine-Gordon system is analysed.     

Three-body Problem in Quantum Mechanics

No Abstract. . Lecture held in the Seminario Matematico e Fisico on May 26, 2004 Received: August 2004     

等周问题的一个初等证明

本文把欧氏平面，半球面和非欧面之中，不含给定边界，含有给定边界和含有边界而且在其上给定端点这样三种等周问题、给以初等、统一的证明。其要点在于把它们的存在性和唯一性简明扼要地归结到下述初等引理，即一个给定凹边边长的四边形的面积以四顶共圆时为其唯一的极大