阶乘幂多项式及其基本恒等式

考虑两类阶乘幂多项式，由向前或向后差分公式，得到两个同类阶乘幂多项式等价的充分必要条件．给出并证明了阶乘幂代数系统的两类基本恒等式，一类是阶乘幂的二项式定理；另一类是同阶阶乘幂之差的因式分解定理(乘方差定理)．     

Eisenstein判别法的推广

论述了Eisenstein判别法的若干具有实用价值的推广形式,并把Eisenstein判别法推广到了整环上.     

在油藏岩中驱替化学溶液模拟方程的差分方法

讨论了将一些不可压缩的可混化学溶液去驱替油藏岩中的石油这一模拟过程的边值问题，提出了解决这一类问题的两种差分格式及其算法，并给出了其收敛条件。     

Abel分部求和公式与排序定理

Ａｂｅｌ分部求和公式与排序定理王慧兴众所周知，排序定理在不等式的证明和最优化设计方面发挥着出奇制胜的作用。本文运用Ａｂｅｌ分部求和公式给出排序定理一个新证明，因而排序定理可作为Ａｂｅｌ分部求和公式的一个推论，进而开拓Ａｂｅｌ分部求和公式在中等数学中的...     

浅议数学分析教学的几个问题

浅议数学分析教学的几个问题王保全１关于极限运算问题极限概念、极限方法是数学分析最基本最重要的概念和方法。它既是教学的重点又是教学的难点。明析极限运算的特性，对教好极限十分有益。１．１极限运算的非初等性初等数学主要以数作为研究对象，讨论数与数之间的联系...     

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).     

一种新的内插算法的研究

有效的插值算法是现代医学三维成像中的一个焦点。针对ＣＴ断层图像的特点，文中提出了一种新的分区域位置映射插值算法，阐明了算法的基本思路及实施步骤，最后给出实验结果。     

A note on the joint distribution of correlated quadratic forms

In the present paper, the authors obtained exact and asymptotic expressions for the joint distribution of correlated quadratic forms when the underlying distribution is a multivariate normal.     

Two Variations of the Minimum Steiner Problem

Given a set S of starting vertices and a set T of terminating vertices in a graph G = (V,E) with non-negative weights on edges, the minimum Steiner network problem is to find a subgraph of G with the minimum total edge weight. In such a subgraph, we require that for each vertex s S and t T, there is a path from s to a terminating vertex as well as a path from a starting vertex to t. This problem can easily be proven NP-hard. For solving the minimum Steiner network problem, we first present an algorithm that runs in time and space that both are polynomial in n with constant degrees, but exponential in |S|+|T|, where n is the number of vertices in G. Then we present an algorithm that uses space that is quadratic in n and runs in time that is polynomial in n with a degree O(max {max {|S|,|T|}–2,min {|S|,|T|}–1}). In spite of this degree, we prove that the number of Steiner vertices in our solution can be as large as |S|+|T|–2. Our algorithm can enumerate all possible optimal solutions. The input graph G can either be undirected or directed acyclic. We also give a linear time algorithm for the special case when min {|S|,|T|} = 1 and max {|S|,|T|} = 2.The minimum union paths problem is similar to the minimum Steiner network problem except that we are given a set H of hitting vertices in G in addition to the sets of starting and terminating vertices. We want to find a subgraph of G with the minimum total edge weight such that the conditions required by the minimum Steiner network problem are satisfied as well as the condition that every hitting vertex is on a path from a starting vertex to a terminating vertex. Furthermore, G must be directed acyclic. For solving the minimum union paths problem, we also present algorithms that have a time and space tradeoff similar to algorithms for the minimum Steiner network problem. We also give a linear time algorithm for the special case when |S| = 1, |T| = 1 and |H| = 2.An extended abstract of part of this paper appears in Hsu et al. (1996).Supported in part by the National Science Foundation under Grants CCR-9309743 and INT-9207212, and by the Office of Naval Research under Grant No. N00014-93-1-0272.Supported in part by the National Science Council, Taiwan, ROC, under Grant No. NSC-83-0408-E-001-021.     

Smooth Goodness-of-Fit Specification Tests Under the Lagrange Multiplier Principle

This article generalizes Neyman's smooth test for the goodness-of-fit hypothesis using orthogonal polynomials of the density function under the null hypothesis, and derives a Lagrange Multiplier (LM) statistic based on the generalized form of the smooth test. Under the null hypothesis, using the joint limiting normality of the orthogonal functions imbedded into the smooth alternative density function and the restricted parameter estimators, the covariance matrix of the LM statistic can be estimated. The procedure of constructing monic orthogonal polynomials from a given moment function is developed. This procedure is applied to examples of testing for normal, Poisson, and gamma distributions.