Classical Fourier Analysis over Homogeneous Spaces of Compact Groups

This paper introduces a unified operator theory approach to the abstract Fourier analysis over homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Let G/H be the left coset space of H in G andμ be the normalized G-invariant measure on G/ H associated to the Weil's formula.Then, we present a generalized abstract framework of Fourier analysis for the Hilbert function space L~2(G/H,μ).     

基于紧致差分的Grad-Shafranov方程快速解法

在等离子体平衡重建迭代计算过程中,需要快速求解Grad-Shafranov方程(G-S方程)。构造了具有四阶精度紧致差分格式的离散方程,采用离散正弦变换技术对其进行快速求解并采用CUDATM实现GPU并行加速,将其应用到EAST等离子体平衡重建PEFIT代码中,实现基于紧致差分格式的快速G-S方程求解。结果表明,在65×65的网格下,给定方程右端项电流分布的前提下,使用GPU求解G-S方程所需时间为大约34μs。     

高速CT阻滞产生X射线辐射的数值模拟研究

以Ar等离子体为例,应用一维辐射流体力学模型,对高速度、高密度的紧凑等离子体环(CT)撞击静态靶减速产生软X射线辐射的物理过程进行了数值模拟研究。利用分裂格式方法计算得到了描述碰撞物理过程的各力学量随时间的演化关系,以及固定CT动能时使停滞CT成为最有效辐射源的初始速度和质量的最优搭配。对计算过程中相关物理量的跟踪分析表明,在1%的误差范围内计算格式满足能量守恒方程。     

CONSERVATION OF THREE—POINT COMPACT SCHEMES ON SINGLE AND MULTIBLOCK PATCHED GRIDS FOR HYPERBOLIC PROBLEMS

For nonlinear hyperbloic problems,Conservation of the numerical scheme is important for convergence to the correct weak solutions.In this paper the the conservation of the well-known compact scheme up to fourth order of accuracy on a single and uniform grid is studied,and a conservative interface treatment is derived for compact schemes on patched grids .For a pure initial value problem,the compact scheme is shown to be equivalent to a scheme in the usual conservative form .For the case of a mixed initial boundary value problem,the compact scheme is conservative only if the rounding errors are small enough.For a pactched grid interface,a conservative interface condition useful for mesh fefiement and for parallel computation is derived and its order of local accuracy is analyzed.     

Potential Energy Function for State X1∑+ of LaH

The present work has derived the potential energy function for the ground state X1∑+of LaH in Murrell-Sorbie function form. In the first place, the electronic state and it′ s rea sonable dissodation limits are correctly determined based on Atomic and Molecular Reaction Statics (AMRS), and then, using the relativistic compact effective potential (RCEP) for La, the equilibrium geometry and dissociation energy for LaH have been calculated by the QCISD method. The calculated results for Re'De' Be' αe' ωe and ωexe are 2.125A, 2.623eV,3.7333cm-1, 0.0723 cm-1, 1461.73cm-1 and 21.383cm-1 respectively, which are in good agreement with experimental or calculated values in references.     

弱紧集与Orlicz空间

本文圆满完善了[1]的结果,并由此给出了Ｏｒｌｉｃｚ空间自反性与Ｓｈｕｒ定理的新证明。