The product of two dependent random variables with regularly varying or rapidly varying tails

Let X and Y be two nonnegative and dependent random variables following a generalized Farlie-Gumbel-Morgenstern distribution. In this short note, we study the impact of a dependence structure of X and Y on the tail behavior of XY. We quantify the impact as the limit, as x→∞, of the quotient of Pr(XY>x) and Pr(X^∗Y^∗>x), where X^∗ and Y^∗ are independent random variables identically distributed as X and Y, respectively. We obtain an explicit expression for this limit when X is regularly varying or rapidly varying tailed.     

Shape and topology optimization for elliptic boundary value problems using a piecewise constant level set method

The aim of this paper is to propose a variational piecewise constant level set method for solving elliptic shape and topology optimization problems. The original model is approximated by a two-phase optimal shape design problem by the ersatz material approach. Under the piecewise constant level set framework, we first reformulate the two-phase design problem to be a new constrained optimization problem with respect to the piecewise constant level set function. Then we solve it by the projection Lagrangian method. A gradient-type iterative algorithm is presented. Comparisons between our numerical results and those obtained by level set approaches show the effectiveness, accuracy and efficiency of our algorithm.     

First-passage failure of a business cycle model under time-delayed feedback control and wide-band random excitation

First-passage failure of a classical business cycle model subject to time-delayed feedback control and wide-band random excitation is investigated in this paper. First, we get the averaged equation by using a stochastic averaging method, and then a backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. The conditional reliability function, the conditional probability density and moments of first-passage time are obtained by solving the backward Kolmogorov equation and generalized Pontryagin equations analytically and numerically with suitable initial and boundary conditions. The results show that time delay in the feedback control forces may remarkably reduce the conditional reliability and the mean first-passage time of the controlled economics system.     

便携式多源光谱融合水质分析仪的研制

采用光谱信息融合理论,研制了一种新型便携式多参数水质分析仪,自行设计了仪器的分析方法、硬件结构、内部工作原理及软件功能.可作为一种无须化学试剂、体积小、快速、易于野外现场作业的绿色水质检测工具.通过对少量水质样品的光谱测量分析,快速检测了总有机碳(TOC)、化学需氧最(COD)等6类水质有机污染物指标.实际测量结果表明,本仪器采用的基于多源光谱信息融合的水质分析方法测量精度显著优于目前市场上普遍采用的常规紫外吸收光谱法.     

小波聚类方法和近红外光谱技术用于药片种类判别

对310个药片样品的近红外光谱数据进行了聚类分析.首先使用小波变换对光谱数据矩阵进行多尺度分解,在进行有效压缩之后,采用经典分类方法对合适选取的小波系数组合进行聚类分析,提出了小波聚类方法.该方法分别用于实验室药片、中试药片和规模生产药片样品的分析,按药片样品的组成得到4个类别.结果表明,对实验室药片和中试药片样品分类的精确度均达到100%;对于规模生产药片的分类,共120个样品中只有1个样品被错误划分,精确度也高达99.2%.近红外光谱技术结合小波聚类方法的聚类性能是令人满意的,相比经典聚类分析,更加快速,易于使用,对制药行业约片质量以及成本控制均有积极作用.     

基于低分辨率色散型拉曼光谱仪的汽油苯含量快速分析

针对汽油苯含量的快速分析问题,提出了基于低分辨率色散型拉曼光谱仪的新的检测方法.由于色散型拉曼光谱中存在着严重的测量噪声和荧光背景干扰,应用多项式平滑滤波除噪声和迭代多项式拟合基线校正方法减少荧光背景的干扰.随后,分别采用岭回归,主成分同归、偏最小二乘回归方法,对炼油厂的汽油样本建立了三个苯含量的快速分析模型并对其进行验证.实验表明,基于低分辨率色散型拉曼光谱仪进行汽油苯含量分析,结合常规建模方法,重复性和再现性均满足SH/T0713-2002标准的要求,此外由于其具有低成本、小型易携带等优点,适用于日常快速分析.     

On some new Hilbert-type inequalities

In the present paper we establish some new inequalities similar to extensions of Hilbert’s double-series inequality and give also their integral analogues. Our results provide some new estimates to these types of inequalities.     

The Gaussian approximation for generalized Friedman’s urn model with heterogeneous and unbalanced updating

The Friedman’s urn model is a popular urn model which is widely used in many disciplines.In particular,it is extensively used in treatment allocation schemes in clinical trials.Its asymptotic properties have been studied by many researchers.In literature,it is usually assumed that the expected number of balls added at each stage is a constant in despite of what type of balls are selected,that is,the updating of the urn is assumed to be balanced.When it is not,the asymptotic property of the Friedman’s urn model is stated in the book of Hu and Rosenberger(2006) as one of open problems in the area of adaptive designs.In this paper,we show that both the urn composition process and the allocation proportion process can be approximated by a multi-dimensional Gaussian process almost surely for a general multi-color Friedman type urn model with heterogeneous and unbalanced updating.The Gaussian process is a solution of a stochastic differential equation.As an application,we obtain the asymptotic properties including the asymptotic normality and the exact law of the iterated logarithm.     

The maximal size of 6- and 7-arcs in projective Hjelmslev planes over chain rings of order 9

We complete the determination of the maximum sizes of (k,n)-arcs,n≤12,in the projective Hjelmslev planes over the two (proper) chain rings Z 9=Z/9Z and S 3=F 3 [X]/(X 2) of order 9 by resolving the hitherto open cases n=6 and n=7.Parts of our proofs rely on decidedly geometric properties of the planes such as Desargues’ theorem and the existence of certain subplanes.