高等代数中常用的数学方法(Ⅰ)──叠加法

本文从数学方法论的角度出发，提出了高等代数中常用的一种数学方法──叠加法，并在不同的领域里讨论了它的应用．     

Estimation of an exponential quantile under pitman's measure of closeness

We consider the problem of estimating a quantile of an exponential distribution with unknown location and scale parameters under Pitman's measure of closeness (PMC). The loss function is required to satisfy some mild conditions but is otherwise arbitrary. An optimal estimator is obtained in the class of location-scale-equivariant estimators, and its admissibility in the sense of PMC is investigated.     

Robust scale estimation in the error-components model using the empirical characteristic function

Robust estimators of the scale parameters in the error-components model are described. The new estimators are based on the empirical characteristic functions of appropriate sets of residuals and are affine equivariant, consistent and asymptotically normal. The robustness of the new estimators is investigated via influence-function calculations. The results of Monte Carlo experiments and an example based on real data illustrate the usefulness of the estimators.     

A lower bound for the transition density function of a stochastic differential equation

Let W_t be a one-dimensional Brownian motion on the probability space (Ω,F,P), and let dx_t = a(x_t)dt + b(x_t)dw_t, b²(x) > 0, be a one-dimensional Ito stochastic differential equation. For a(x) = a₀ + a₁x + … + a_nxⁿ on a bounded interval we obtain a lower bound for p(t,x,y), the transition density function of the homogeneous Markov process x_t, depending directly on the coefficients a₀,a₁, …, a_n, and b(x).     

Postnatal Effects of Prenatal Insult

Exogenous agents may perturb development during the embryonic period and adversely affect the formation of organs. However, adverse effects on development are not limited to the embryonic period nor are the manifestations restricted solely to outright gross structural malformation, but may instead be expressed as a decrement or abberration of postnatal function. Susceptibility to altered development may extend well into the postnatal period. Studies of functional parameters in several organ systems have demonstrated the broad-based susceptibility, subtlety of expression and potential of long-lasting effects of altered development assessed by physiologic assays. Adverse effects on functional development, whether in the CNS, reproductive, gastrointestinal, genitourinary, respiratory, or immune systems, etc., merit continuing investigation. From the viewpoint of risk estimation and hazard detection, evaluations of postnatal functional parameters may be relevant for several reasons. First, such parameters may serve as low-dose triggers. Second, they may be useful as a focal point for epidemiological studies. Finally, a more thorough understanding of the degree and magnitude of such postnatal functional deficits is needed since an adverse maternal effect may be transient, considered acceptable, or unperceived, but the effect on the conceptus may be permanent and severe. The immune and respiratory systems are discussed as two examples of how subtle and protean adverse effects on functional development may be.     

FP中并行粒度的研究

并行粒度是并行处理系统的关键问题之一。本文引入启发函数(Heuristic Function,简称HF)和加速因子的概念,并用一阶启发函数HF对FP中并行成分进行检测,以便得到一个较合适的并行粒度。     

级数sum from n = 1 to ∞ ()[1/n~(2k)](K∈N)求和的一个递推公式

级数[1/n~(2k)]（Ｋ∈Ｎ）求和的一个递推公式王慧兴（河南驻马店高中４６３０００）取定Ｋ∈Ｎ，则无穷级数收敛。为得到其和，通常要用某个函数的Ｆｏｕｒｉｅｒ级数来完成，并且对不同的自然数Ｋ，要寻求不同函数的Ｆｏｕｒｉｅｒ级数，文献［１］用初等方法证明了等...     

浅谈有限域上的一元多项式

本文对有限域的一元多项式易混淆的几个问题作了初步讨论和说明．     

Estimation of the MSE matrix of the stein estimator

Uniformly minimum-variance unbiased (UMVU) estimators of the total risk and the mean-squared-error (MSE) matrix of the Stein estimator for the multivariate normal mean with unknown covariance matrix are proposed. The estimated MSE matrix is helpful in identifying the components which contribute most to the total risk. It also contains information about the performance of the shrinkage estimator with respect to other quadratic loss functions.     

形成函数在溶液平衡研究中的应用

本文从广义上对形成函数进行了定义,并深入研究了它在溶液平衡中的应用。