正交各向异性矩形板受迫振动的三维分析

从正交各向异性三维弹性动力学的控制方程出发，在求得四边简支矩形板自由振动频率和位移振型的基础上，构造了受迫振动的位移函数；利用自由振动位移振型的正交性，将控制方程的空间变量和时间变量分离，得到了广义质量、广义力和频率表示的关于时间的2阶常微分方程，从而得到了正交各向异性弹性矩形板在受迫振动下的位移场和应力场．给出了本文方法与薄板理论的算例．     

正电子产生靶上初级电子束半径的最小化研究

为获得尽可能高的正电子(e⁺)产额,严格控制初级电子(e^－)束在e⁺产生靶上的束半径是至关重要的.首先分析了使e^－束半径增大的各因素和对这些因素的制约;然后以北京正负电子对撞机(BEPC)的正电子源为例,给出了束半径的实测值和计算值的比较,以具体说明这些因素的影响;最后讨论了北京正负电子对撞机二期工程(BEPC-Ⅱ)的相应优化设计研究,提出了获得靶上最小束半径的若干途径.     

On the capacitated vehicle routing problem

 We consider the Vehicle Routing Problem, in which a fixed fleet of delivery vehicles of uniform capacity must service known customer demands for a single commodity from a common depot at minimum transit cost. This difficult combinatorial problem contains both the Bin Packing Problem and the Traveling Salesman Problem (TSP) as special cases and conceptually lies at the intersection of these two well-studied problems. The capacity constraints of the integer programming formulation of this routing model provide the link between the underlying routing and packing structures. We describe a decomposition-based separation methodology for the capacity constraints that takes advantage of our ability to solve small instances of the TSP efficiently. Specifically, when standard procedures fail to separate a candidate point, we attempt to decompose it into a convex combination of TSP tours; if successful, the tours present in this decomposition are examined for violated capacity constraints; if not, the Farkas Theorem provides a hyperplane separating the point from the TSP polytope. We present some extensions of this basic concept and a general framework within which it can be applied to other combinatorial models. Computational results are given for an implementation within the parallel branch, cut, and price framework SYMPHONY. Received: October 30, 2000 / Accepted: December 19, 2001 Published online: September 5, 2002 Key words. vehicle routing problem – integer programming – decomposition algorithm – separation algorithm – branch and cut Mathematics Subject Classification (2000): 20E28, 20G40, 20C20     

关于阶乘的Erds-Stewart猜想

摘要:设n是正整数;P_0=1,P_i(i=1,2,…)是第i个素数.本文证明了:方程 n!+1=P_k~aP_(k+1)~b,P_(k-1)0,b>0,仅有解(n,P_k,P_(k+1),a,b)=(1,1,2,1,0),(2,3,5,1,0),(3,5,7,0,1),(4,5,7,2,0),(5,7,11,0,2).上述结果证实了Erds和Stewart提出的一个猜想.     

晶态-非晶态复合锂离子导体的电学性质

本文研究了晶态LiCl-非晶态Li₂O·3B₂O₃复合锂离子导体的电学性质。实验发现这种晶态-非晶态新型复合离子导体的电学性质变化具有新的现象,即在宏观电导率σ_m-组成曲线上出现了电导率增加的“双峰”效应。相应地,在表观活化能E_m-组成曲线和介电常数ε_m-组成曲线上出现了“双谷”。本文还详细讨论了这些实验现象,得到了与理论相符合的结果。 关键词：