Ready, Set, Go! The Voronoi diagram of moving points that start from a line

It is an outstanding open problem of computational geometry to prove a near-quadratic upper bound on the number of combinatorial changes in the Voronoi diagram of points moving at a common constant speed along linear trajectories in the plane. In this note we observe that this quantity is Θ(n²) if the points start their movement from a common line.     

关于解决黄牛鞋面革松面问题的探讨

本文讨论了在黄牛鞋面革生产过程中产生松面的原因，并经过多年的生产实践，摸索出解决松面问题行之有效的技术措施。     

L~∞（0，1）上一个WeakL~P（0，1）有关的格半范数

本文引进一个定义在Ｌ~∞（０，１）上格半范数ρｐ与一个熟知的格半范数ρ０关系，证明了在Ｌ~∞（０，１）中的序区间上，ρ０－拓扑与ρｐ－拓扑等价，从而证明了（Ｌ~∞（０，１），ρｐ）′的闭单位球是（Ｌ~∞（０，１），ρｐ）′的某个子集的弱－闭包，本文还证明了（Ｌ~∞（０，１），ρｐ）′可看作ＷｅａｋＬｐ（０，１）对偶空间的奇异部一个理想，而且这奇异部可由（Ｌ~∞（０，１），ρｐ）′与一算子族生成．（ｆ）ａｌｌ（ｌ．＼ｎ，ｏｏ（ｊ．）＝ｈｉｌｌｓｉｌｌ）ｔ￣．，ｉｆｆ￣＊（ｔ）ｒｅｓｐｅｃｔｉｖｅｌｙａｌｌ＇ｌ，Ｌ（ｑ，１）ｉｓｔｈｅｐｒｅｄｌｓｌａｌｏｆｔｙｒｅａｋＬＩ＇，ａｌｌｌｌｈ，ｒｌｌｏｌｌ－－ａｔ（，ｌｌｌｉ（＇ｌｌｌｅａｓｌｌｒｅａｌｇａ（ｌ￣ｓ，ａｒｅｐｒｅｓｅｌｌｔａ＇ｔｉｏｌｌｔｌｌｅｏｒｅｎｌｆｆ，ｒｅｌｅｌｌｌｅｌｌｔｓｉｌｌＳａｃ，ａｌｌ（ｌＳ，，．ｉｓｏｆ）ｔａｉｌｌｅ（ｌ．Ｈｏｗｅｖｅｒ，ｉｌｌ［２］，ｉｔｉｓｓｌｌｄｗｎｔｈａｔｔｉｌｅｒｅｐｒｅｓｅｌｌｔａｔｉｏｌｌｔｉｌｅｓｆ）ｒｅｌｌｌｏｆ）ｔａｉｌｌｅ（ｌｉｌｌ［．５］ｉｓｉｌｌ（ｔｏｒｒｅ（？ｔ．Ｉｎｔｈｉｓｎｏｔｅ，ｗｅｄｅ     

Axisymmetric extrusion through adaptable dies—Part 1: Flexible velocity fields and power terms

An adaptable die is one that not only produces the correct geometrical shape, but also is designed through an adaptable method to impart other desirable properties to the product or process. In this first part of a series of papers, six kinematically admissible velocity fields are developed for use in upper bound models for axisymmetric extrusion through various dies, including extrusion through adaptable dies. Three base velocity fields are presented:

(1) assuming proportional angles in the deformation zone,

(2) assuming proportional areas in the deformation zone, or

(3) assuming proportional distances from the centerline in the deformation zone.

The base velocity is modified by an additional term comprised of two functions. One function allows extra flexibility in the radial direction, and the second function allows extra flexibility in the angular direction. There are two forms of the second function, which meet the required boundary conditions. The flexibility function in the radial direction is represented by a series of Legendre polynomials, which are orthogonal over the deformation region. The power terms derived for these velocity fields for use in upper bound models are also presented.Part 2 of this series compares the results obtained in upper bound models for the six velocity fields for a spherical extrusion die. In Part 3, the use of the best velocity field for extrusion through streamlined dies is developed to determine the adaptable die shape, which minimizes the required extrusion pressure. Additionally, the adaptable die shape is compared with results from Yang and Han for arbitrarily curved and streamlined dies.     

Minimum variance control and performance assessment of time-variant processes

This paper is concerned with (1) an explicit solution of a minimum variance control law for linear time-variant (LTV) processes in the transfer function form, and (2) performance assessment of LTV processes using minimum variance control as the benchmark. It is shown that there exists a time-variant, absolute lower bound of process variance that is achievable under LTV minimum variance control and can be estimated from routine operating data. This lower bound can subsequently be used to assess the benefit of implementing LTV control such as adaptive control. The proposed methods are illustrated through simulated examples and an industrial case study.     

Lower bound limit analysis using non‐linear programming

This paper describes a new formulation, based on linear finite elements and non‐linear programming, for computing rigorous lower bounds in 1, 2 and 3 dimensions. The resulting optimization problem is typically very large and highly sparse and is solved using a fast quasi‐Newton method whose iteration count is largely independent of the mesh refinement. For two‐dimensional applications, the new formulation is shown to be vastly superior to an equivalent formulation that is based on a linearized yield surface and linear programming. Although it has been developed primarily for geotechnical applications, the method can be used for a wide range of plasticity problems including those with inhomogeneous materials, complex loading, and complicated geometry. Copyright © 2002 John Wiley & Sons, Ltd.     

Tight upper bound on the number of edges in a bipartite K3,3-free or K5-free graph with an application

We show that an n-vertex bipartite K_3,3-free graph with n?3 has at most 2n−4 edges and that an n-vertex bipartite K₅-free graph with n?5 has at most 3n−9 edges. These bounds are also tight. We then use the bound on the number of edges in a K_3,3-free graph to extend two known NC algorithms for planar graphs to K_3,3-free graphs.     

Efficient primal-dual heuristic for a dynamic location problem

In this paper the dynamic location problem with opening, closure and reopening of facilities is formulated and an efficient primal-dual heuristic that computes both upper and lower limits to its optimal solution is described. The problem here studied considers the possibility of reconfiguring any location more than once over the planning horizon. This problem is NP-hard (the simple plant location problem is a special case of the problem studied). A primal-dual heuristic based on the work of Erlenkotter [A dual-based procedure for uncapacitated facility location. Operations Research 1978;26:992–1009] and Van Roy and Erlenkotter [A dual-based procedure for dynamic facility location. Management Science 1982;28:1091–105] was developed and tested over a set of randomly generated test problems. The results obtained are quite good, both in terms of the quality of lower and upper bounds calculated as in terms of the computational time spent by the heuristic. A branch-and-bound procedure that enables to optimize the problem is also described and tested over the same set of randomly generated problems.