On the coupled NBEM and FEM for a class of nonlinear exterior Dirichlet problem in R 2

In this paper, based on the natural boundary reduction advanced by Feng and Yu, we couple the finite element approach with the natural boundary element method to study the weak solvability and Galerkin approximation of a class of nonlinear exterior boundary value problems. The analysis is mainly based on the variational formulation with constraints. We prove the error estimate of the finite element solution and obtain the asymptotic rate of convergence. Finally, we also give a numerical example.

     

Spectral and Pseudospectral Approximations Using Hermite Functions: Application to the Dirac Equation

We consider in this paper spectral and pseudospectral approximations using Hermite functions for PDEs on the whole line. We first develop some basic approximation results associated with the projections and interpolations in the spaces spanned by Hermite functions. These results play important roles in the analysis of the related spectral and pseudospectral methods. We then consider, as an example of applications, spectral and pseudospectral approximations of the Dirac equation using Hermite functions. In particular, these schemes preserve the essential conservation property of the Dirac equation. We also present some numerical results which illustrate the effectiveness of these methods.     

用电磁打点计时器进行受迫振动实验--介绍我校的一个自学物理实验

介绍一种用简单的方法进行的受迫振动实验。     

Nonlinear Boundary Layers of the Boltzmann Equation: I. Existence

 We study the half-space problem of the nonlinear Boltzmann equation, assigning the Dirichlet data for outgoing particles at the boundary and a Maxwellian as the far field. We will show that the solvability of the problem changes with the Mach number ℳ^∞ of the far Maxwellian. If ℳ^∞<−1, there exists a unique smooth solution connecting the Dirichlet data and the far Maxwellian for any Dirichlet data sufficiently close to the far Maxwellian. Otherwise, such a solution exists only for the Dirichlet data satisfying certain admissible conditions. The set of admissible Dirichlet data forms a smooth manifold of codimension 1 for the case −1<ℳ^∞<0, 4 for 0<ℳ^∞<1 and 5 for ℳ^∞>1, respectively. We also show that the same is true for the linearized problem at the far Maxwellian, and the manifold is, then, a hyperplane. The proof is essentially based on the macro-micro or hydrodynamics-kinetic decomposition of solutions combined with an artificial damping term and a spatially exponential decay weight. Received: 20 April 2002 / Accepted: 4 December 2002 Published online: 21 March 2003 Communicated by H.-T. Yau     

An Improved Synthesis of Retinoic Acid from β-Ionone

A convenient and large-scale preparation of retinoic acid 1 from β-ionone in five steps with 38% overall yield is described.The key steps are the epoxidization of 2 with a new methylated agent and the condensation 4 with tetraethyl methylenediphophonate in one-pot procedure to prepare 6.     

高气压反射式高能电子衍射仪监控脉冲激光外延氧化物薄膜

在超高真空分子束外延（MBE）生长技术中，反射式高能电子衍射仪（RHEED）能实时显示半导体和金属外延生长过程，给出薄膜表面结构和平整度的信息，成为MBE必备的原位表面分 析仪.为了研究氧化物薄膜如高温超导（YBa₂Cu₃O₇） 、铁电薄膜（Sr_1-xBa_x TiO₃）及它们的同质和异质外延结构的生长机理，获得高质量的符合各种应用 需要的氧化 物多层薄膜结构，在常规的制备氧化 关键词： 高温超导薄膜 RHEED     

Duffing-van der Pol振子随机分岔的全局分析

应用广义胞映射方法研究了参激和外激共同作用的Duffing-van der Pol振子的随机分岔.以 系统参数通过某一临界值时，如果系统的随机吸引子或随机鞍的形态发生突然变化，则认为 系统发生随机分岔为定义，分析了参激强度和外激强度的变化对于随机分岔的影响.揭示了 随机分岔的发生主要是由于系统的随机吸引子与系统的随机鞍碰撞产生的.分析表明，广义 胞映射方法是分析随机分岔的有力工具，这种全局分析方法可以清晰地给出随机分岔的发生 和发展. 关键词： 随机分岔 全局分析 广义胞映射方法 随机吸引子 随机鞍     

A new regioselective synthesis and bioactivity of 1H‐pyrazolo[3,4‐d]pyrimidin‐4(5H)‐one derivatives

A series of new 1H‐pyrazolo[3,4‐d]pyrimidin‐4(5H)‐one Derivatives 5 has been designed and regio‐selectively synthesized via a tandem aza‐Wittig reaction. The structures of all compounds prepared have been confirmed by ¹H NMR, IR, EI‐MS spectroscopy and elemental analyses. The results of preliminary bioassay indicate that most compounds 5 possess an inhibition effect against Botrytis cinereapers and Pyricularia oryzae at the concentration of 50 mg/L.     

系综分布和它的小涨落近似

由“从正则分布出发，在小涨落近似下得出的能量涨落分布公式”求得的能量涨落的二次矩与直接由正则分布求得的二次矩完全相同，但分别由二求得的高次矩并不完全相同。     

对激光等离子体中X射线的产生与辐射加热研究

利用一维辐射流体力学程序MULTI数值模拟研究了功率为1014Wcm2、脉冲宽度为300ps、波长为0.44μm的强激光辐照平面Au靶时产生X射线的过程,给出了X射线转换效率和能谱分布.通过将靶物质划分为对所产生的X射线光学薄的转化区和光学厚的再发射区,得到了作为黑体辐射热源的最佳靶厚度,并给出了辐射加热靶所产生的等离子体的密度和温度的空间分布. 关键词： 辐射流体力学 激光等离子体 X射线转换 辐射热波