一类二阶变系数微分方程的解

通过变量变换 ,将变系数线性常微分方程化为常系数线性常微分方程 ,再利用常数变易法给出了一类二阶变系数非齐线性微分方程的通解。     

Significance of the Dermal Route of Exposure to Risk Assessment

The skin is a route of exposure that needs to be considered when conducting a risk assessment. It is necessary to identify the potential for dermal penetration by a chemical as well as to determine the overall importance of the dermal route of exposure as compared with inhalation or oral routes of exposure. The physical state of the chemical, vapor or liquid, the concentration, neat or dilute, and the vehicle, lipid or aqueous, is also important. Dermal risk is related to the product of the amounts of penetration and toxicity. Toxicity involves local effects on the skin itself and the potential for systemic effects. Dermal penetration is described in large part by the permeability constant. When permeability constants are not known, partition coefficients can be used to estimate a chemical's potential to permeate the skin. With these concepts in mind, a tiered approach is proposed for dermal risk assessment. A key first step is the determination of a skin-to-air or skin-to-medium partition coefficient to estimate a potential for dermal absorption. Building a physiologically-based pharmacokinetic (PBPK) model is another step in the tiered approach and is useful prior to classical in vivo toxicity tests. A PBPK model can be used to determine a permeability constant for a chemical as well as to show the distribution of the chemical systemically. A detailed understanding of species differences in the structure and function of the skin and how they relate to differences in penetration rates is necessary in order to extrapolate animal data from PBPK models to the human. A study is in progress to examine anatomical differences for four species.     

Approximate Bayesian Computation for Exponential Random Graph Models for Large Social Networks

We consider the issue of sampling from the posterior distribution of exponential random graph (ERG) models and other statistical models with intractable normalizing constants. Existing methods based on exact sampling are either infeasible or require very long computing time. We study a class of approximate Markov chain Monte Carlo (MCMC) sampling schemes that deal with this issue. We also develop a new Metropolis–Hastings kernel to sample sparse large networks from ERG models. We illustrate the proposed methods on several examples.     

A Bayesian method of sample size determination with practical applications

Summary.  The problem motivating the paper is the determination of sample size in clinical trials under normal likelihoods and at the substantive testing stage of a financial audit where normality is not an appropriate assumption. A combination of analytical and simulation-based techniques within the Bayesian framework is proposed. The framework accommodates two different prior distributions: one is the general purpose fitting prior distribution that is used in Bayesian analysis and the other is the expert subjective prior distribution, the sampling prior which is believed to generate the parameter values which in turn generate the data. We obtain many theoretical results and one key result is that typical non-informative prior distributions lead to very small sample sizes. In contrast, a very informative prior distribution may either lead to a very small or a very large sample size depending on the location of the centre of the prior distribution and the hypothesized value of the parameter. The methods that are developed are quite general and can be applied to other sample size determination problems. Some numerical illustrations which bring out many other aspects of the optimum sample size are given.     

关于平面对称紧凸集不等式

本文简论平面对称紧凸集不等式问题,引伸Favard不等式,对不等式中的相关常数给出两种证法。     

A GALTON-WATSON BRANCHING PROCESS IN VARYING ENVIRONMENTS WITH ESSENTIALLY CONSTANT OFFSPRING MEANS AND TWO RATES OF GROWTH1

A Galton-Watson process in varying environments (Z_n), with essentially constant offspring means, i.e. E(Z_n)/mⁿ→α∈(0, ∞), and exactly two rates of growth is constructed. The underlying sample space Ω can be decomposed into parts A and B such that (Z_n)_n grows like 2ⁿon A and like mⁿon B (m > 4).     

Generalized Quasi-Regression

Quasi-regression, an approach for approximating an unknown function on the unit cube in very high dimensions, has very high computational efficiency. In this article, generalized quasi-regression is introduced. Some theoretical results on the generalized quasi-regression are provided, and numerical examples are illustrated.     

Asymptotic Minimax Risk for the White Noise Model on the Sphere

Estimation of an unknown function on the unit sphere of the Euclidean space is considered. The function is observed in Gaussian continuous time white noise. Uniform norm is chosen as a loss function and exact asymptotic minimax risk is derived extending the result of Korostelev (1993). The exact asymptotic minimax risk is also given for the L ₂-loss, applying the result of Pinsker (1980).     

我国农产品物流要素贡献率实证研究

本文根据1991-2005年我国农产品物流行业投入产出数据,利用生产函数拟合法对影响农产品物流行业发展的劳动力、资本、技术三大要素贡献率进行计算与分析:资本投入和技术进步是推动我国农产品物流行业增长的主要力量,劳动要素对农产品物流行业的贡献相对有限。我国农产品物流行业面临劳动要素贡献低,而资本、技术要素虽贡献率高但起点较低的困境。因此必须完善硬件设施、提高技术水平和劳动者素质。