Integrated Burgers方程的三阶对称循环算子

利用线性化方法确定了 Integrated Burgers方程的三阶对称循环算子的一般形式 .为产生线性偏微分方程 (组 )更多的对称给出了具有参考价值的理论与实算结果 .且所采用的方法具有普遍性 .     

Optimal distribution-free confidence bands for a distribution function

Distribution-free confidence bands for a distribution function are typically obtained by inverting a distribution-free hypothesis test. We propose an alternate strategy in which the upper and lower bounds of the confidence band are chosen to minimize a narrowness criterion. We derive necessary and sufficient conditions for optimality with respect to such a criterion, and we use these conditions to construct an algorithm for finding optimal bands. We also derive uniqueness results, with the Brunn–Minkowski Inequality from the theory of convex bodies playing a key role in this work. We illustrate the optimal confidence bands using some galaxy velocity data, and we also show that the optimal bands compare favorably to other bands both in terms of power and in terms of area enclosed.     

Quotas on runs of successes and failures in a multi-state markov chain

For the time-homogeneous multi-state Markov chain {X_n,n≧0} with states labeled as "0" (success) and "f"(failure), f=1,2,… the waiting time problems to be discussed arise by setting quotas on runs of success and failures. Some particular cases are considered.     

An Approximate Bayesian Marginal Likelihood Approach for Estimating Finite Mixtures

Estimation of finite mixture models when the mixing distribution support is unknown is an important problem. This article gives a new approach based on a marginal likelihood for the unknown support. Motivated by a Bayesian Dirichlet prior model, a computationally efficient stochastic approximation version of the marginal likelihood is proposed and large-sample theory is presented. By restricting the support to a finite grid, a simulated annealing method is employed to maximize the marginal likelihood and estimate the support. Real and simulated data examples show that this novel stochastic approximation and simulated annealing procedure compares favorably with existing methods.     

一个(3 1)维可积Sinh-gordon-MKdV方程

利用MKdV方程的递推算子的遗传性，构造了一个（3＋1）维的Sinh-Gordon－MKdV型的可积模型。该模型是（1＋1）维Sinh－Gordon方程和（1＋1）维MKdV方程的推广。同时给出了该模型的丰富的对称性。     

Researches on Arithmetic Power Series

By studying arithmetic power series this paper gives two recurison formulas and one polynomial theorem.     

排队模型中计算队长分布的递推式

从队长过程本身出发，利用拉普拉斯变换工具，直接研究了Ｍ／Ｇ／１／∞型排队模型的队长分布，获得在任意时间ｔ的瞬时队长分布的拉普拉斯变换递推表达式，以及便于计算的平稳分布的递推式，最后在一些特殊排队模型中给出了更实用的递推式     

语篇结构分析中的递归现象透视

功能句法研究者把递归分为两类:线性递归和嵌入递归。语篇结构中同样存在这样的递归现象,它有两个特点:递归的可选性和理论上的无限性。这样,实际语篇的结构就既呈现一定的基本规律又富于变化。研究递归性可以把握语篇结构的基本模式和变化规律,有利于理解语篇和生成合乎规范的语篇。     

用递归关系计算n阶行列式的规律

给出了用递归关系方法求任意ｎ阶行列式的值的一般方法：首先，把已知的ｎ阶行列式看作为阶数ｎ的一个函数，记为Ｄ（ｎ）；其次，按行或按列展开这个行列式，并仔细观察存在于余子式及Ｄ（ｎ）里的关系，建立关于Ｄ（ｎ）的某一递归关系，此关系总为一个齐次的或非齐次的递归关系；最后。借助于Ｄ（０）、Ｄ（１）和Ｄ（２）等求出递归关系的通解的系数．虽然此法不一定简单，但毕竟是一个有用的方法．     

A NEW CONFIDENCE BAND FOR CONTINUOUS CUMULATIVE DISTRIBUTION FUNCTIONS

We consider confidence bands for continuous distribution functions. Following a review of the literature we find that previously considered confidence bands, which have exact coverage, are all step-functions jumping only at the sample points. We find that the step-function bands can be constructed through rectangular tolerance regions for an ordered sample from the uniform distribution R(0, 1). We then construct a set of new bands. Two criteria for assessing confidence bands are presented. One is the power criterion, and the other is the average-width criterion that we propose. Numerical comparisons between our new bands and the old bands are carried out, and show that our new bands perform much better than the old ones.