On the Bose-Einstein condensation of free relativistic bosons with or without mass

The Bose-Einstein condensation of free relativistic particles [=(M ² c ⁴ +c ² p ² ) ^1/2 –Mc ² ] is studied rigorously. For massless bosons (=cp), the condensation transition of third (second) order occurs in2 (3) dimensions (D). The molar heat capacity follows the T ² (T ³ ) law below the condensation temperature T_c [k ^B T_c=(2 ² c ² n/1.645) ^1/2 [( ^{2 3} c ³ n/1.202) ^1/3 ], reaches4.38 (10.8) R at T=T_c, and approaches the high-temperature-limit value2 (3) R with no jump (a jump equal to6.75R) in2 (3)D. For finite-mass (M) bosons, the phase transition occurs only in3D with the condensation temperature T_c always smaller than that of the corresponding nonrelativistic bosons [=(2M) ^–1 p ² ]. If the mass M is reduced to zero, the condensation temperature T_c grows monotonically and reaches eventually that of massless relativistic bosons. This mass-dependence of T_c is therefore distinct from the case of nonrelativistic bosons, where T_c grows to infinity as M 0. A brief discussion is given for a possible connection with the normal-to-super transition of the independently moving Cooper pairs (bosons).     

计及风和湍流的热晕及其相位补偿的数值研究

本工作用包括热晕、湍流和风等效应的等压近似下四维激光传输程序，数值计算了激光大气传输中的整束热畸变效应及其理想相位补偿，得到了各种情况下的激光大气传输畸变图象，并分析了热晕和湍流的相互作用。另外，还讨论了时、空步长的选取原则。     

系列柱形薄壁腔靶制备工艺研究

为了从实验上深入研究超热电子产生规律，从而减少或抑制超热电子对惯性约束聚变（ＩＣＦ）的危害，我们制备了一系列薄壁腔靶，以供实验研究。本文详细地描述了柱形薄壁腔靶的制备工艺。利用ＮＧ－１０４型精密单向纵切车床，采用金刚石刀具车削，提高心轴质量，表表粗糙度可达０．１μｍ。采用电镀和磁控溅射二种方法镀膜，为了使腔靶壁厚均匀，在镀膜时，必须使心轴匀速旋转。利用磁控溅射在腔靶外表面再涂上１μｍ左右厚的二氧化硅，以提高超薄壁腔靶的强度和自立能力。在腐蚀心轴时，必须仔细控制酸的浓度，防止在腐蚀时因产生气泡太多，太快而使腔靶破裂。用Ｘ射线照相法和扫描电子显微镜测量腔靶的几何参数。制备系列柱形薄壁腔靶达到指标为：壁厚范围２～３０μｍ，壁厚均匀性小于１０％，表面粗糙度０．２～０．３μｍ。最后介绍了在“神光Ⅰ”上打靶结果。结果表明，实验值与理论值符合较好。     

厚翅片管内流体流动和传热的数值分析

本文应用Ｐａｔａｎｋａｒ等人［１］研究薄翅片管的湍流模型，对一种工业化的厚翅片管内的流体流动和传热进行了数值分析。计算范围包括了层流和湍流（Ｒｅ＝１０１～１０６），所得计算结果与较窄范围内实验所测的传热与阻力数据相当符合，本计算结果具有较大的推广价值。     

The Selmer Groups of Elliptic Curves

Let E/K be an elliptic curve with K-rational p-torsion points.The p-Selmer group of E is described by the image of a map λk and hence an upper bound of its order is given in terms of the class numbers of the S-ideal class group of K and the p-division field of E.     

多小波子空间上的单小波表示

本文在较弱的条件下,建立了2重多小波子空间与单小波子空间的关系.即由2重多小波构造出单小波.一方面,这种单小波的平移伸缩与2重多小波的平移伸缩生成的子空间是完全相同的;另一方面,它具有插值性.因此通过构造出的单小波建立了多小波子空间上的Shannon型采样定理.     

关于二部图Km1m2-Hm2的升分解

在文献[2]中作者定义了图的一种新分解-升分解(Ascending subgraph Decomposition简记为ASD)，并提出了一个猜想：任意有正数条边的图都可以升分解．本文主要证明了二部图Km1m2-Hm2(m1≥m2)可以升分解，其中Hm2是至多含m2条边的Km1m2的子图．     

Estimation of the mean lifetime in non-parametric model under modified type I censoring

The methods to estimate the means of the lifetimes under modified Type I Censoring are discussed, in which case the distribution function of the lifetimes is unknown and the information about the individuals is cut by the fixed timeC. As a slight modification, we suggest observing small percentage of the lifetimes to construct the estimations. These estimations are unbiased and consistent.     

基于扫描隧道显微镜的原子电子云结构

本文简要介绍了扫描隧道显微镜的基本工作原理，展示了一些扫描样品（石墨和铜）的电子云图，在简要介绍量子力学关于原子电子云结构基本理论的基础上，通过理论上的电子云结构与扫描结果的比较，在一定程度上验证了量子力学关于原子电子云结构理论的正确性．     

Linear Theory of Free Electron Laser with a Plasma-Loaded Cylindrical Waveguide

The dispersion characteristics of plasma–loaded free-electron laser has been analyzed using linear fluid model. The device under consideration consists of the cylindrical metallic waveguide, completely filled with background plasma and a relativistic electron beam which passes through a helical wiggler magnetic field. The result predicts that reasonable plasma density tends to improve the growth rate of the low-frequency optical wave of FEL and causes an shiftup in the operating frequency, However it has little effect on the growth rate of the high-frequency wave. In the plasma–loaded FEL, for the FEL oscillator, it may be tuned by varying the plasma density; and for the FEL amplifier, the wider frequency bandwidth is gained. A critical density n ^c _p for the background plasma density is found.