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.     

微波吸收法研究Mn,Cu掺杂对ZnS:Mn,Cu光生载流子复合过程的影响

采用微波吸收法，测量了ZnS:Mn,Cu粉末材料受到超短脉冲激光激发后，其光生电子和浅束缚态电子的衰减过程.发现Mn,Cu的浓度对导带电子的寿命有明显的影响，提高掺杂浓度会使光生电子的寿命大大缩短，还研究了掺杂浓度对光致发光强度的影响. 关键词： 发光材料 硫化锌 光电子 微波吸收技术     

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     

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.     

On the limit cycles of a quintic planar vector field

This paper concerns the number and distributions of limit cycles in a Z_2-equivariant quintic planar vector field.25 limit cycles are found in this special planar polynomial system and four different configurations of these limit cycles are also given by using the methods of the bifurcation theory and the qualitative analysis of the differential equation.It can be concluded that H(5)≥25=5~2, where H(5)is the Hilbert number for quintic polynomial systems.The results obtained are useful to study the weakened 16th Hilbert problem.     

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     

A New Pathway to Synthesize Cyclomercurated Ferrocenylimines Containing Heterocyclic Ring

The cyclomercurated ferrocenylimines containing heterocyclic ring were prepared by the condensation of cyclomercuration of acylferrocene with the appropriate heterocyclic amine.This procedure provides an efficient method for the synthesis of cyclomerucurated ferrocenylimines containing heterocyclic ring which are difficultly synthesized by the conventional method.The reaction mechanism is proposed.     

聚能射流的断裂时间

从描述聚能射流失稳的一维近似方程出发，导出了聚能射流断裂时间的近似公式。这个近似公式定量显示了屈服应力、本构关系、粘度和径向收缩效应等对射流断裂时间的影响，在４个不同的特殊近似下，可以自然演化为近１０年来所发表的几个半经验解析公式，并且在合理的参数范围内，公式给出的断裂时间曲线覆盖了射流断裂时间的全部实验点。