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.     

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     

CONNECTION THEORY OF FIBRE BUNDLE AND PROLONGATION STRUCTURES OF NONLINEAR EVOLUTION EQUATIONS

It is shown that the proper geometrical framework for the nonlinear evolution equations (NEEs) and the soliton equations Should be the fibre bundle theory, the principal bundle and its associated bundle and their connection theory. Based upon the requirement of covariance of the geometrical quantities, a covariant generic geometry theory for the prolongation strutures of the NEEs is proposed and the fundamental equations for the prolongation structures are presented. From the fundamental equations it immediately follows that the comections corresponding to these NEEs always flat but with torsion and the covariant formulae satisfied by the conservation quantities associated with these NEEs are obtained. The prolongation structure of the MKdV equation, as an example, is concretely worked out by means of the covariant theory of the prolongation structure presented in this paper.     

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* ～- S2 (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 monotonicity, that constitute a solid foundation for a systematic study of their global geometry and naturally lead to the formulation of some pertinent problems.     

On the Volume Formulas of Cones and Orthogonal Multi-cones in S~n(1) and H~n(-1)

In the study of n-dimensional spherical or hyperbolic geometry, n ≥3, the volume of various objects such as simplexes, convex polytopes, etc. often becomes rather difficult to deal with. In this paper, we use the method of infinitesimal symmetrization to provide a systematic way of obtaining volume formulas of cones and orthogonal multiple cones in Sn(l) and Hn(-1).     

Stoner集体电子铁磁理论的圖示

在stoner集体电子铁磁理论的三个前提假设的基础上,一系列的能带图示被提供出来。这些图示鲜明地描绘了Stoner理论的物理情况。Stoner的铁磁判据,即在kθ′/ε₀=ξ>2/3时始能发生铁磁性及在ξ≥2^-1/3时磁化始完全,可利用图示简捷地得到。在铁磁状态下由d-带分裂引致的自d-带至s-带的电子边移,可利用图示加以考虑,并对0°K时的镍作了估算,结果约为1％。     

On the Volume Formulas of Cones and Orthogonal Multi-cones in S^n（1） and H^n（-1）

Abstract In the study of n-dimensional spherical or hyperbolic geometry, n≥ 3, the volume of various objects such as simplexes, convex polytopes, etc. often becomes rather difficult to deal with. In this paper, we use the method of infinitesimal symmetrization to provide a systematic way of obtaining volume formulas of cones and orthogonal multiple cones in Sⁿ(1) and Hⁿ(—1). (Dedicated to the memory of Shiing-Shen Chern)     

感应磁场压缩下氢等离子体中巴耳末系谱线的斯塔克加宽

本工作研究感应磁场压缩下,氢等离子体中的巴耳末系谱线的斯塔克加宽。电容器对围绕在放电管外部的线圈放电,产生交变轴向磁场,使放电管中氢气离化、压缩与加热。放电周期14微秒,放电电压20千伏,最大电流165千安,初始工作气压2.0×10^-1毫米汞高。用照相方法研究H_β和H_γ的轮廓。这些谱线有显著的加宽。在整个发光阶段中,H_β的平均半宽度为14—16(埃),H_γ为18—19(埃),相应的离子密度为1.7—2.5×10¹⁶厘米^-3。实验轮廓与Griem,Kolb和Shen的理论较为接近,与Holtsmark理论相差较远。光电测量进一步表明:H_β的轮廓随着时间而改变,相应的离子密度亦在改变。在放电的第三半周期初级电流极大时,离子密度最大,达到3.2×1O¹⁶厘米^-3,为初始氢原子密度的2.2倍。