REMARKS ON OPTIMAL INFERENCE FOR MARKOV BRANCHING PROCESSES: A SEQUENTIAL APPROACH

Use of a suitable stopping rule yields exact uniformly most powerful tests and minimum variance unbiased estimators of various parameters of a Markov branching model with or without immigration. The population model discussed includes the pure birth, simple epidemic, immigration-death, M/M/ 1 queue, linear birth-death and a branching diffusion process, among others, as special cases.     

STEIN'S METHOD AND THE BERRY-ESSÉEN THEOREM

Stein's method is used to prove the Lindeberg-Feller theorem and a generalization of the Berry-Esséen theorem. The arguments involve only manipulation of probability inequalities, and form an attractive alternative to the less direct Fourier-analytic methods which are traditionally employed.     

用余弦调制PR－FIR方法构造M带正交小波基

离散小波变换将离散时间信号分解为一系列不同分辨率下的离散近似信号和离散细节，紧支的正交规范小波与完全重构正交镜像滤波器（ＰＲ－ＱＭＦ）相对应。在紧支正交小波基的构造条件下，利用余弦调制完全重构滤波器组的方法，实现了Ｍ带紧支正交小波基的构造，计算机模拟表明该方法非常简单、有效。     

On uniform approximation of Poisson variates by normal ones

In this paper the accuracy of the normal approximation to the Poisson is treated from the viewpoint of direct approximation of Poisson variables by normal ones. The conclusions that are derived on the accuracy of this approximation lead (among others) to very useful results on confidence limits for the mean of a linear combination of independent Poisson variables; these latter are employed in precise determination of the composition of a mixture of radioactive isotopes by means of a scintillation counter.     

Coherency conditions for finite exchangeable inference

Summary We idenify the invertible coherent functional relation between an array of asserted conditional probabilities and the probability distribution for the sum of events that are regarded exchangeably, in the regular case thatP(N _N+1 |S _N =a) ∈ (0, 1) for everya=0, 1, ...,N. The result is used to construct a useful algebraic and geometrical representation of all coherent inferences in the regular case, including those that are nonlinear in the sum of the conditioning events. The special case in which conditional probabilities mimic observed frequencies within (0, 1) receives an exact solution, which allows an easy interpretation of its surprising consequences. Finally, we introduce a new direction in research on prior opinion assessment that this approach, inverse to the usual one, suggests.     

一般动力学系统在相空间的Noether定理及其逆定理

根据一般动力学系统在相空间的作用积分在无穷小群变换下的变换性质,分别建立起完整和非完整非保守系统的Noether定理和逆定理.由给出的例子表明,在相空间中可以呈现出动力学系统新的对称性.     

高阶非完整非保守系统的广义Noether定理

应用万有D＇Alembert微分变分原理研究了高阶非完整非保守力学系统的守恒定律 得到了高阶非完整非保守力学系统的广义Noether定理。     

Optimal Prediction in Stochastic Regression Models with Application to the Analysis of Repeated Surveys

Several results relating to the optimal prediction of regression coefficients and random variables under a general linear model with stochastic coefficients are presented. These results are then applied to the analysis of repeated sample surveys over time. In particular, if the finite population can be modelled by a superpopulation model, a fully efficient method for the analysis of repeated surveys is proposed.     

On the distribution of quadratic forms in normal random variables

This paper provides necessary and sufficient conditions for a quadratic form in singular normal random variables to be distributed as a given linear combination of independent noncentral chi-square variables. Using this result, an extension of Cochran's theorem to quadratic forms of noncentral chi-square variables is derived.     

用算子展开法求解 Fredholm 积分方程

提供了另一种求解积分方程的方法。利用 Hilbert 空间来研究 Fredholm 积分算子,并证明了可利用一组标准正交基将 Fredholn 积分算子展开,从而使积分方程得到简化。应用这一方法给出了一般第二类 Fredholm 积分方程的严格解析解。文中还对具体积分方程进行了求解并与严格解和其它方法所得的解进行了比较,结果吻合得很好。