Asymptotics for solutions of a defective renewal equation with applications

In this paper, we derive non-exponential asymptotic forms for solutions of defective renewal equations. These include as special cases asymptotics for compound geometric distribution and the convolution of a compound geometric distribution with a distribution function. As applications of these results, we study the Gerber-Shiu discounted penalty function in the classical risk model and the reliability of a two-unit cold standby system in reliability theory.      

单调递增分形函数上、下界的估计

Mass distribution principle is one of important tools in studying Hausdorff dimension and Hausdorff measure.In this paper we will give a numerical approximate method of upper bound and lower bound of mass distribution function f(x)(it is a monotone increasing fractal function)and its some applications.     

Large deviations: An introduction to 2007 Abel prize

2007 Abel prize has been awarded to S R S Varadhan for creating a unified theory of large deviations. We attempt to give a flavour of this branch of probability theory, highlighting the role of Varadhan.     

Differential transport and dispersion of colloids relative to solutes in single fractures

This work employed numerical experiments simulating colloid and solute transport in single parallel-plate fractures, using the random walk particle tracking method, to demonstrate that (1) there exists an aspect ratio of the colloid radius to half the fracture aperture, δ_o, where the average velocities of colloids and solutes are similar. When δ > δ_o, the velocity distribution assumption is satisfied, and the fact that the ratio of the colloid transport velocity to the solute transport velocity, τ_p, decreases as δ increases is well documented in the literature. However, when δ < δ_o, the velocity distribution assumption is violated, and τ_p increases as δ increases and (2) the Taylor dispersion coefficient and its extension by James and Chrysikopoulos [S.C. James, C. V. Chrysikopoulos, J. Colloid Interface Sci. 263 (2003) 288] will overestimate the colloid dispersion coefficient significantly. Additionally, numerical experiments simulating colloid and solute transport in variable-aperture fractures demonstrated that τ_p and D_L,coll/D_L,solute decrease with increasing CoV, and the anisotropy ratio only plays a minor role compared to the CoV. These observations have important implications towards the interpretation of colloid transport in both porous and fractured media.     

风沙两相流跃移层中沙粒相的速度分布

从单个跃移沙粒在气流中的运动方程出发导出了风沙两相流中沙粒相速度分布函数的Boltzmann方程，对风沙流研究中几种不同的分布函数及其相应的统计平均值等基本概念给出了严密的数学定义，指出了不同分布函数之间的区别和联系，在略去铅垂方向空气阻力的情况下，给出了沙粒相速度分布函数沿铅垂方向的边缘分布，作为风沙流中跃移理论的主要基础之一。利用结果对前人在风沙流研究中发现的某些重要规律和现象进行了解释。     

基于数码相机的双向反射率分布函数测量方法

除传统领域外,双向反射率分布函数(BRDF)在计算机图形学、虚拟现实等方面具有广泛的应用,但缺乏价格适中的测量工具。试验了一种基于单个数码相机的BRDF测量方法。该法综合了摄影测量学、光学、计算机图形学等学科的知识,测量装置成本低廉、易于实现,并集成于专门编制的测量程序中。测量操作过程方便、易行,测量数据可直接以视化形式输出。给出了某种油漆的测量实例,初步验证了该方法的可行性。     

Kinetics of dispersion polymerization: Effect of medium composition

The effect of the medium composition (monomer and solvent) on the kinetics of dispersion polymerization of methyl methacrylate (MMA) was studied via reaction calorimetry. It was found that increasing the monomer concentration increased the reaction rate; the exponent of the dependency of the initial reaction rate on the MMA concentration was found to be 0.93. Narrow particle size distributions were achieved at the lower monomer concentrations (0.24–0.81 mol/L) and a minimum size (2.45 μm) was found at an intermediate concentration (0.44 mol/L). The average molecular weight of the PMMA increased and the molecular weight distribution broadened with increasing monomer concentration. During a dispersion polymerization, the MMA concentration was found to decrease linearly with conversion in both phases, whereas the ratio of concentrations in the particles and continuous phase ([M]_p/[M]_c) remained constant (0.47) with partitioning favoring the continuous phase. The average number of free radicals per particle in MMA dispersion polymerization was estimated to be high from the nucleation stage onward (>5000). The increasing rate during the first ～ 40% conversion was primarily caused by the increasing volume of the polymer particle phase. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3638–3647, 2008     

Error bounds for asymptotic expansions of the distribution of the MLE in a GMANOVA model

Summary In this paper we obtain asymptotic expansions for the distribution function and the density function of a linear combination of the MLE in a GMANOVA model, and for the density function of the MLE itself. We also obtain certain error bounds for the asymptotic expansions.     

The distribution of a generalized least squares estimator with covariance adjustment

The distribution theory is developed for a generalized least squares estimator of the growth curve model. A special case of the estimator is the maximum likelihood estimator which is weighted by the sample covariance matrix. The distribution of two conditional forms of the estimator are derived and from these its density is obtained. Two general pivots and their distributions are derived from the conditional forms and special cases of these are investigated. The results obtained are linked to carlier work.     

General Regular Variation of n-th Order and the 2nd Order Edgeworth Expansion of the Extreme Value Distribution （Ⅰ）

In Part Ⅰ the concept of the general regular variation of n-th order is proposed and its construction is discussed. The uniqueness of the standard expression and the higher order regularity of the auxiliary functions are proved.