超新星(续)

超新星爆炸是发生在宇宙空间中极为壮观、丰富多彩和引人入胜的重要现象,涉及许多有趣的、尚待探索的物理学研究领域和天体物理学及宇宙学若干相关分支的重要应用.本文试图描述超新星现象研究在各方面的重要意义,提供基本观测事实和理论框架信息以及介绍我们正在从事的部分相关研究工作.     

具有广义协变的包含重力场贡献的重力场方程

利用半度规λ^(α)_μ表象的数学工具定义一个对广义坐标具有协变形式的重力场矢势函数ω^(α)_μ≡-cλ^(α)_μ，给出一个具有广义协变的包含重力场贡献的重力场方程R_μν-g_μνR/2+Λg_μν=8πG(T^(Ⅰ)_μν+T^(Ⅱ)_μν) 关键词： 重力场方程 协变形式 能量-动量张量 量子化     

Bifurcation of travelling wave solutions in a nonlinear variant of the RLW equation

By using the method of planar dynamical systems to a nonlinear variant of the regularized long-wave equation (RLW equation in short), the existence of smooth and non-smooth solitary wave (so called peakon and valleyon) and infinite many periodic wave solutions is shown. Under different regions of parametric spaces, various sufficient conditions to guarantee the existence of above solutions are given. The formulas to compute the travelling waves are also educed. We notice that some results in [Wazwaz AM. Analytic study on nonlinear variants of the RLW and the PHI-four equations. Commun Nonlinear Sci Numer Simul, in press, doi:10.1016/j.cnsns.2005.03.001] are incorrect.     

Spatial distribution of SiCln （n=O-2） in SICl4 plasma measured by mass spectroscopy

For a better understanding of the deposition mechanism of thin films in SiCl4 source gas, we have measured the spatial distributions of SiCln （n=0-2） radicals in SICl4 radio frequency glow discharge plasma utilizing a mass spectrometer equipped with a movable gas sampling apparatus. The experimental results demonstrate that the relative densities of SiCln （n=0-2） radicals have peak values at the position of 10 mm above the powered electrode along the axial direction; the relative densities of the Si and SiCIn （n=1, 2） radicals have peak values at the positions of 27mm and 7 mm away from the axis along the radial direction, respectively. Generally speaking, in the whole SICl4 plasma bulk region, the relative density of Si is one order of magnitude higher than that of SICl, and the relative density of SiCl is several times higher than that of SICl2. This reveals that Si and SiCl may be the primary growth precursors in forming thin films.     

Fixed points for operators in a space of continuous functions and applications

This paper investigates the fixed points for self-maps of a closed set in a space of abstract continuous functions. Our main results essentially extend the Banach contracting mapping principle. An application to integro-differential equations is given.

     

Nonlinear convection of a viscoelastic fluid with inclined temperature gradient

The energy method is used to analyze the viscoelastic fluid convection problem in a thin horizontal layer, subjected to an applied inclined temperature gradient. The boundaries are considered to be rigid and perfectly conducting. Both linear and nonlinear stability analyses are carried out. The eigenvalue problem is solved by the Chebyshev Tau-QZ method and comparisons are reported between the results of the linear theory and energy stability theory.Received: 12 March 2004, Accepted: 19 April 2004, Published online: 17 September 2004PACS: 47.20 Ky, 47-27 Te, 83.60 Wc Correspondence to: P.N. Kaloni     

On a Nonlinear Discretized LKR System: Reductions and Underlying Virasoro Symmetry Algebras

A differential-difference version of the Loewner–Konopelchenko–Rogers (LKR) system is constructed by discretization of the spatial variables in the continuous LKR system. The differential-difference LKR system admits a diversity of significant reductions. The symmetry algebras of the discrete LKR system and its reductions are shown to possess underlying Kac–Moody–Virasoro type structure. A discrete dromion-like solution of the LKR system is constructed via finite symmetry group transformation.     

Isomerization of 2-seleno-1,3,2-diazaphospholidine derivatives

For the first time the isomerization of 1,3,2-diazaphospholidine-2-selenide derivatives in refluxing benzene in the presence of trace water was observed, and the structure of isomerized product was determined by X-ray diffraction, IR, ¹H NMR, ³¹P NMR, and elemental analysis. The mechanism of isomerization was also proposed. The isomerized phosphoroheterocycle (C₂₆H₃₈N₃O₅PSe, Mr = 582.52) is orthorhombic with space group Pbca, a = 17.1010(9) Å, b = 16.6404(9) Å, c = 20.7517(11) Å, V = 5905.3(5) ų, Z = 8, Dr = 1.310 g/cm³, λ = 0.71073 Å, μ (Mo Kα) = 1.363 mm^?1, F(000) = 2432. The structure was refined to R1 = 0.0482, wR2 = 0.1204 for 5214 unique reflections with I > 2σ(I). Intramolecular and intermolecular hydrogen bonds are observed in the crystal packing.     

哈密顿Ermakov系统的形式不变性

把形式不变性的方法用于研究哈密顿Ermakov系统，从哈密顿Ermakov系统的形式不变性出发，运用比较系数法得到与形式不变性相应的点对称变换生成元的表达式及势能所满足的偏微分方程.结果表明，在点对称变换下，只有自治的哈密顿Ermakov系统才具有形式不变性. 关键词： 哈密顿Ermakov系统 拉格朗日函数 点对称变换 形式不变性