A tree search algorithm for the multi-commodity location problem

The multi-commodity location problem is an extension of the simple plant location problem. The problem is to decide on locations of facilities to meet customer demands for several commodities in such a way that total fixed plus variable costs are minimized. Only one commodity may be supplied from any location.In this paper a primal and a dual heuristic for producing good bounds are presented. A method of improving these bounds by using a new Lagrangean relaxation for the problem is also presented. Computational results with problems taken from the literature are provided.     

Finding shortest paths in the plane in the presence of barriers to travel (for any lp - norm)

This paper develops an efficient algorithm for the computation of the shortest paths between given sets of points (origins and destinations) in the plane, when these paths are constrained not to cross any of a finite set of polygonal (open or closed) barriers. It is proved that when distances are measured by an 1_p - norm with 1 < p < ∞, these paths are formed by sequences straight line segments whose intermediate (e.g. apart from origin and destination) end points are barrier vertices. Moreover, only segments that locally support the barriers to which their end points belong are elligible for inclusion in a shortest path. The special case of one origin and one destination is considered, as well as the more general case of many origins and destinations. If n is the number of nodes (origins, destinations and barrier vertices), an algorithm is presented that builds that network of all shortest paths in O(n² log n) time. If the total number of edges in this network is e (bounded by n²), the application of Dijkstra's algorithm enables this computation of the shortest paths from any origin to all destinations in O(e log n) time. If the origins, shortest paths from all origins to all destinations can thus be found in O(ne log n) ≤ O(n^{3 log n}) time.It is also shown that optimal solutions when distances are measured according to the rectilinear or max-norm (i.e. l_p-norm with p = 1 or p = ∞) can be deduced from the results of the algorithm.     

混流式水轮机准三元流动分析及性能予估基础上的水电站过渡过程仿真

本文根据电站参数用计算机予设计转轮后进行其性能予估，并在此基础上进行过渡过程仿真，其结果与用实验得到的综合特性曲线进行仿真的计算结果比较，在较高效率区结果符合很好，低效率区有一定缺陷，但不失为一种在没有合适转轮及其综合特性曲线情况下进行电站过渡过程预测计算的方法。     

Laser and absorption saturation measurements of Cr crystals, pumped by broadband pulsed 940 nm radiation

The characteristics of a 940 nm pumped Cr⁴⁺:forsterite laser have been investigated using a pulsed colour centre laser as the excitation source. Laser threshold, slope efficiency and temporal behaviour have been determined for high and low Cr⁴⁺ doped material. 940 nm pumping is found to be more efficient than 532 and 730–770 nm excitation. Discrepancies with 1064 nm pumping are attributed to excited state absorption. Absorption saturation measurements have been used to assess the potential applications of Cr⁴⁺:forsterite, Cr⁴⁺:YAG and Cr⁴⁺: Lu₃A1₅O₁₂ (LuAG) as passive Q-switches for Nd lasers in the 940 nm region.     

Network flows and non-guillotine cutting patterns

Up till now there has been no exact and effective algorithm for the problem of finding optimal cutting patterns of rectangles which are not restricted to those with the ‘guillotine’ property. This problem can be interpreted in a resource constrained scheduling context. The contribution of this paper to this topic is a good characterization of the flow functions and graphs corresponding to cutting patterns.     

高性能高分子材料和高分子设计

高性能高分子材料发展迅速,其发展符合历史的“点～链～片～体”模式。根据已有的高分子科学知识和理论,有目的地设计合成和加工工艺,以满足特定的高性能目标已成为必然趋势。为此,作者提出了若干建议。     

Location Problems with Different Norms for Different Points

Given a finite set in a linear space X, we consider two problems. The first problem consists of finding the points minimizing the maximum distance to the points in A; the second problem looks for the points that minimize the average distance to the points in A. In both cases, we assume that the distances at different points are defined as

Steiner's problem and fagnano's result on the sphere

This note describes the nature of optimal solutions for the spherical Steiner-Weber location problem for the case of unit weights and either 3 or 4 demand points (requireing 4 demand points to lie in an open hemisphere). Geometrically appealing results which are necessary conditions for optimum solutions and spherical analogs of known planar results are obtained.     

An algorithm for the minimax weber problem

The paper presents an algorithm for finding the weighted absolute center of a given set of points in the Euclidean plane.The algorithm is a specialized implementation of the method of feasible directions.The presentation includes a proof of convergence as well as computational experience.