线性离散事件动态系统的可达性

可达性是动态系统的重要性质之一。本文讨论离散事件动态系统的可达性,给出了系统完全可达的充要条件,得到了利用系统的特征矩阵判断系统可达性的判据,证明了系统可按可达性进行分解、状态反馈不影响系统可达性等结论,还进一步讨论了一类流水线生产加工系统的可达性,本文的结果对于这类系统的分析和控制是有意义的。     

波动方程反演问题的一种新的逼近方法

本文给出了一种求解波动方程反演问题的“多目标函数法”.这种方法简单、有效,并具有明确的物理意义.对于三维问题的程序化它有很强的优越性.     

基于数学形态学的表面原子熔融相的 STM图像识别算法

高温扫描隧道显微镜(HT-STM)可以实时原位地捕捉到表面原子的熔化相变过程.在这一原位变温实验中,快速可靠地识别出每帧STM图像中的熔融相十分关键.传统的手工统计方法存在效率低下、随意性大等问题.我们发展出一套基于数学形态学的算法,来自动快速地识别.与人工方法相比,该算法消除了人为主观误差,使确定的边界更加准确、光滑,处理效率提高了266倍.     

完全找到整系数不可约多项式的一种新方法

本利用一种独特的映射方法将整系数多项式映射为正有理数，运用谊映射方法和数论理论，可以找到任意多个整系数不可约多项式，因此，为扩频通信与信道密码利用不可约多项式提供了一种可行且实用的技术。     

紧急输送策略的线性规划模型

以美国南弗洛里达州递避飓风袭击为例建立了紧急输送情况下的线性规划模型。其中具体建立了以SCEPD(美国南弗洛里达州紧急情况预防部门)提出的公路反向，地区分块撤离，使用小路等三个最受人们关注的策略的模型。模型的灵敏度分析能很好地解释建立更多的临时避难所、限制车辆等策略对撤离的影响。在相近的环境下，中模型解得的结果很接近官方预测的结果，并且本的模型能对更广泛的情况进行分析．可给SCEPD提供一定参考。     

The negative gradient flow for the <Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript>-integral of Ricci curvature

 In this paper, the negative gradient flow for the L ²-integral of Ricci curvature on a 3-manifold is considered. It is not known whether the solution to this fourth order geometric evolution equation exists, and whether it will develop singularities in finite time. Based on the trick of De Turck and the idea of Hamilton on the flow of Ricci curvature, the local existence on any compact Riemannian manifold is obtained. In addition, the conditions for the occurences of singularities in finite time during the evolution and the asymptotic behavior of the flow on a 3-manifold are discussed. Received: 22 April 2002 / Revised version: 5 January 2003 Published online: 24 April 2003 This work is partially supported by the Foundations of NNSF of China, the Foundation for University Key Teacher by MEC and Shanghai Priority Academic Discipline.     

Some Limit Theorems in Geometric Processes

Geometric process (GP) was introduced by Lam[4,5], it is defined as a stochastic process {Xn, n = 1, 2,…} for which there exists a real number a > 0, such that {an-1 Xn, n = 1,2, …} forms a renewal process (RP). In this paper, we study some limit theorems in GP. We first derive the Wald equation for GP and then obtain the limit theorems of the age, residual life and the total life at t for a GP. A general limit theorem for Sn with a > 1 is also studied. Furthermore, we make a comparison between GP and RP, including the comparison of their limit distributions of the age, residual life and the total life at t.     

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。