关于Directly-Riemann积分的中值定理

本文在研究Directly－Riemann积分~[1，2]的基础上，得到了Directly—Riemann积分的中值定理。     

一个一般的Gale定理及其应用

考虑局部凸拓扑向量空间中包含多值映射的不等式系统，在所谓广义近次类凸条件下建立了一个Gale型择一定理，并给出了该定理在向量最优化问题中的应用．本文结果涵盖并推广了许多已知的择一定理．     

引力场两个定理的探讨

从引力场是矢量场出发，讨论了引力场的性质，引入了描述引力场的高斯定理和环路定理，得出了相应的微分和积分形式。根据引力场的两个定理，导出了引力势的微分和积分形式。     

On Bayesian D-optimum Design Criteria and the Equivalence Theorem in Non-linear Models

The concavity of some Bayesian D -optimality criteria is investigated and is found in some cases to depend on the prior distribution. In the case of a non-concave criterion, the standard equivalence theorem may fail, but a local version continues to apply.     

Moments of the sampled autocovariances and autocorrelations for a Gaussian white-noise process

Cumulants, moments about zero, and central moments are obtained for the mean-corrected serial covariances and serial correlations for series realizations of length n from a white-noise Gaussian process. All first and second moments (and some third, fourth, and higher moments) are given explicitly for the serial covariances; and the corresponding moments for the serial correlations are derived either explicitly or implicitly.     

Approximating moments of continuous functions of random variables using Bernstein polynomials

Bernstein polynomials have many interesting properties. In statistics, they were mainly used to estimate density functions and regression relationships. The main objective of this paper is to promote further use of Bernstein polynomials in statistics. This includes (1) providing a high-level approximation of the moments of a continuous function $g\left(X\right)$ of a random variable $X$, and (2) proving Jensen’s inequality concerning a convex function without requiring second differentiability of the function. The approximation in (1) is demonstrated to be quite superior to the delta method, which is used to approximate the variance of $g\left(X\right)$ with the added assumption of differentiability of the function. Two numerical examples are given to illustrate the application of the proposed methodology in (1).     

On a Pandemic Threshold Theorem of the Early Kermack–McKendrick Model with Individual Heterogeneity

A pandemic threshold theorem of the Kermack–McKendrick epidemic system with individual heterogeneity is proved from the definition of R ₀ by Diekmann, Heesterbeek, and Metz. The early Kermack–McKendrick epidemic model is extended to recognize individual heterogeneity, where the state variable indicates an epidemiological state or genetic, physiological, or behavioral characteristics such as risk of infection. With the basic reproduction number R ₀ for the heterogeneous population, the final size equation of the limit epidemic starting from a completely susceptible steady state at t = ?∞ has a unique positive solution if and only if R ₀  > 1. The main result is that the positive solution of the final size equation gives the lower bound of the intensity of any epidemic starting from a host population composed of susceptible and a few infected individuals who spread on a noncompact domain of the trait variable.     

一类半线性椭圆型方程的整体解

本文研究一类二阶半线性椭圆型方程正的整体解，所得的结果优于文[1]、[2]。     

不安抗辩权试析

<中华人民共和国合同法>虽然确立了不安抗辩权制度,但在实践中如何正确贯彻实施,尚有许多需要研究的问题.弄清发生不安抗辩权法定事由的判定标准,弄清难为对待给付的发生原因、发生时间以及不安抗辩权的法律效果,对于正确实施不安抗辩权制度,保护债权人的正当合法权益,稳定社会主义市场经济秩序,都具有十分重要的意义.     

On a confidence interval about a parameter estimated by a ratio of normal random variables

A confidence interval is geometrically constructed about a parameter estimated by the ratio of bivariate normal random variables. The resulting confidence interval is equivalent to that of Fieller's theorem. The geometric construction shown that such intervals are conservative. Bioassay examples are used to demonstrate the technique.