监测Lévy稳定过程均值变点的平均运行时间估计

平均运行长度(时间)(ARL)是判断一控制图监测变点效果好坏的一个重要工具.本文主要研究Lévy稳定过程的均值变点监测问题.我们给出了三个控制图,即EWMA,GEWMA和GLR的ARL估计,并通过数值模拟比较了4个控制图监测均值变点的效果和差异.     

Fast computation of a rational point of a variety over a finite field

We exhibit a probabilistic algorithm which computes a rational point of an absolutely irreducible variety over a finite field defined by a reduced regular sequence. Its time-space complexity is roughly quadratic in the logarithm of the cardinality of the field and a geometric invariant of the input system. This invariant, called the degree, is bounded by the Bézout number of the system. Our algorithm works for fields of any characteristic, but requires the cardinality of the field to be greater than a quantity which is roughly the fourth power of the degree of the input variety.

     

The practice for eight-year operation of the cobalt-60 irradiation facility at Beijing Radiation Application Research Center

The radiation facility was made by Sulzer Company in Switzerland. The designed capacity is 3.7 × 10¹⁶Bq( 1MCi) and 12.21 × 10¹⁵Bq(330kCi)of Cobalt -60 source was loaded at the first phase. Current cobalt -60 source-loading is 2.4 × 10¹⁶Bq(650kCi). The equipment assembling and installation regulating and testing were completed at the end of 1988. The facility was put into commissioning in 1989. It operates 7000–8000 hours per year. The facility has been utilized to carry out many research work and irradiate many kinds of items. Lots of economical benefits have been gained since then. Now it is becoming a radiation processing model base in China. This paper summarized the strong and weak points of the design of the facility through in eight years' practice and analysed the economical benefits.     

An extended continuous Newton method

This paper describes a numerical realization of an extended continuous Newton method defined by Diener. It traces a connected set of locally one-dimensional trajectories which contains all critical points of a smooth functionf: ⁿ . The results show that the method is effectively applicable.The authors would like to thank L. C. W. Dixon for pointing out some errors in the original version of this paper and for several suggestions of improvements.     

Optimality for set functions with values in ordered vector spaces

Let (X, , ) be a finite atomless measure space,L a convex subfamily of , andY andZ locally convex Hausdorff topological vector spaces which are ordered by the conesC andD, respectively. LetF:LY beC-convex andG:LZ beD-convex set functions. Consider the following optimization problem (P): minimizeF(), subject to L andG() _D . The paper generalizes the Moreau-Rockafellar theorem with set functions. By applying this theorem, a Kuhn-Tucker type optimality condition and a Fritz John type optimality condition for problem (P) are established. The duality theorem for problem (P) is also studied.This work was partially supported by National Science Council, Taipei, Taiwan. This paper was written while the first author was visiting at the University of Iowa, 1987-88.The authors would like to express their gratitude to the two anonymous referees for their valuable comments. Also, they would like to thank Professor P. L. Yu for his encouragement and suggestions which improved the material presented here considerably.     

Do intramolecular halogen bonds exist? Ab initio calculations and crystal structures’ evidences

Cl···O intramolecular contacts are analysed here. Hence the Cambridge Structural Database (CSD) search was performed to find five-membered Cl–C=C–C=O pseudo-rings closed through Cl···O intramolecular contacts. Such rings were analysed and it was found that some of Cl···O distances are smaller than the corresponding sum of van der Waals radii. Additionally ab initio MP2/6-311++G(d,p) calculations and AIM analyses were carried out here on 3-chloropropenal and its fluoro derivatives to deepen the nature of intramolecular Cl···O interactions, some of findings may indicate that they are attractive and stabilizing ones. This paper is dedicated to Prof. T. M. Krygowski on the occasion of his 70th birthday     

Gradient extremals and valley floor bifurcations on potential energy surfaces

Gradient extremals are curves in configuration space denned by the condition that the gradient of the potential energy is an eigenvector of the Hessian matrix. Solutions of a corresponding equation go along a valley floor or along a crest of a ridge, if the norm of the gradient is a minimum, and along a cirque or a cliff or a flank of one of the two if the gradient norm is a maximum. Properties of gradient extremals are discussed for simple 2D model surfaces including the problem of valley bifurcations.     

Data loci in algebraic optimization

We consider parametric optimization problems from an algebraic viewpoint. The idea is to find all of the critical points of an objective function thereby determining a global optimum. For generic parameters (data) in the objective function the number of critical points remains constant. This number is known as the algebraic degree of an optimization problem. In this article, we go further by considering the inverse problem of finding parameters of the objective function so it gives rise to critical points exhibiting a special structure. For example if the critical point is in the singular locus, has some symmetry, or satisfies some other algebraic property. Our main result is a theorem describing such parameters.     

曲率流的参数化有限元逼近

许多物理现象可以在数学上描述为受曲率驱动的自由界面运动,例如薄膜和泡沫的演变、晶体生长,等等.这些薄膜和界面的运动常依赖于其表面曲率,从而可以用相应的曲率流来描述,其相关自由界面问题的数值计算和误差分析一直是计算数学领域中的难点.参数化有限元法是曲率流的一类有效计算方法,已经能够成功模拟一些曲面在几类基本的曲率流下的演化过程.本文重点讨论曲率流的参数化有限元逼近,它的产生、发展和当前的一些挑战.     

The density and minimal gap of visible points in some planar quasicrystals

It has previously been observed that the limiting gap distribution of the directions to visible points of planar quasicrystals may vanish near zero, that is, there exist planar quasicrystals with a positive limiting minimal normalised gap between the angles of visible points. The exact values of these limiting minimal normalised gaps have not been determined. In this paper we give explicit formulas for the densities of visible points for planar quasicrystals from several families, which include the Ammann–Beenker point set and the vertex sets of some rhombic Penrose tilings. Combining these results with a known characterisation of the limiting minimal gap in terms of a probability measure on an associated homogeneous space of quasicrystals, we give explicit values of the limiting minimal normalised gap between the angles of visible points for several families of planar quasicrystals, in particular, for the Ammann–Beenker point set and for the vertex sets of some rhombic Penrose tilings. We also compare our results with numerical observations.