一类非线性方程分歧点的存在性

讨论多参数非线性方程F（λ，x）=0的分歧问题，给出了（λ0，0）是F（λ，x）=0的分歧点的一个充分条件．     

一类积分型边界条件下的积—微分方程的可解性

本文研究了一类具有积分型边界条件,带参数λ的与时间无关的积-微分方程的可解性,得出了参数λ使得方程存在解,特别是存在正解的取值条件,并给出了使正解存在时λ的取值的估计。     

三角域上带两个形状参数的Bézier曲面的扩展

给出了三角域上带双参数λ1,λ2的类三次Bernstein基函数,它是三角域上三次Bernstein基函数的扩展.分析了该组基的性质并定义了三角域上带有两个形状参数λ1,λ2的类三次Bernstein-Bézier(B-B)参数曲面.该基函数及参数曲面分别具有与三次Bernstein基函数及三次B-B参数曲面类似的性质.当λ1,λ2取特殊的值时,可分别得到三次Bernstein基函数及三次B-B参数曲面以及参考文献中所定义的类三次Bernstein基函数及类三次B-B参数曲面.由实例可知,通过改变形状参数的取值,可以调整曲面的形状.     

截尾试验下指数分布的贝叶斯估计

在指数分布场合，定数或定时截尾试验，文[1]给出了参数λ在先验分布为Г(α，β)分布的假设下的Bayes估计．文[3]给出了在平方损失下的Bayes估计,本文讨论先验分布为B(a，b)分布时，参数λ的Bayes估计。     

参数最短路的原始-对偶算法

本文利用原始－对偶方法,对于含参数λ的网络（Ｖ,Ｅ,ｆ_１-λｆ_２）,给出了某一点至其它各点的参数最短路的求解算法,其时间复杂度为 Ｏ（ｎｍ＋ｎ~２ｌｏｇｎ）．     

关于Hodge-Dirac微分算子的Caccioppoli不等式

利用广义Hlder不等式、满足Dirac-调和方程的微分形式的弱逆Hlder不等式等重要引理,在已有的关于Hodge-Dirac微分算子的Caccioppoli-型不等式的基础上,首先给出局部的双权Caccioppoli-型积分不等式的参数形式.进一步,作为上述局部结论的应用,在有界域Ω上给出了相应的全局加权积分不等式.结论中的四个参数λ_1,λ_2,λ_3,α使得到的结论更具灵活性,若赋予参数以适当的值可以得到了其它经典权函数的加权积分不等式.     

二阶中立型泛函微分方程的周期解

考虑如下一类二阶中立型泛函微分方程的周期解:u″(t)-cu″(t-δ)+a(t)u(t)=λf(t,u(t-τ(t))),其中,λ>0为参数,c和δ为常数.通过应用Krasnoselskii锥不动点定理及一些分析技巧给出了这类方程周期正解的存在性非存在性和多解性.     

截尾试验下指数分布的贝叶斯估计

在指数分布场合，定数或定时截尾试验，文［１］给出了参数λ在先验分布为Γ（α，β）分布的假设下的Ｂａｙｅｓ估计．文［３］给出了在平方损失下的Ｂａｙｅｓ估计．本文讨论先验分布为Ｂ（ａ，ｂ）分布时，参数λ的Ｂａｙｅｓ估计．     

半参数回归模型的渐近有效L-估计

对半参数回归模型yi=χiTβ+g(χi)+ei,i=1,2,…,n,对非参数函数g(·)采用核估计的方法,构造了参数向量β的L-估计量λn,在一些正则条件下,获得了λn的渐近正态性和非参数函数g(·)的估计量gn(t)的最优收敛速度可达到O(n-(1/3)),并且给出了标准化L估计量λn的渐近分布的Berry-Esseen界.     

一类非线性方程的分歧问题

考虑方程Tx-λAx+G(λ,x)=0,其中T、A是一个Banach空间到另一个Banach空间的有界线性算子,G是具有某些性质的非线性算子,λ为实参数。当对于某个λ∈R,算子T-λA为Fredholm型时,此方程可能会发生分歧现象,本文给出了一些充分条件。     

一类三次几何Hermite插值曲线及其优化

通过引入新的节点,提出了一类三次几何Hermite插值曲线的构造方法,给出了能量最小化时对应的参数取值公式。所给表达式中保留了切向的合理调节参数,便于几何设计的控制。实例表明该方法是有效的。     

利用有限域上对合阵构作认证码

本文利用有限域上ｎ阶对合阵给同了构作Ｃａｒｔｅｓｉｏｎ认证码的一种新方案,计算了这类认证码的参数,在编码规则等概率分布选取的假设下,给出了这类认证码被被成功地模仿攻击的最大概率Ｐ１和被成功地替换攻击的最大概率Ｐｓ     

Computation of the second term of the series of the ray method in the dimension two and a half

An algorithm for computing the second term of the series of the ray method suggested in this paper is specified for the case of the dimension two and a half. By this is meant that the elastic paramenters of a medium depend on x, z only and the source and observation points are placed in a plane orthogonal to the y axis. Thus, to compute the wave field we need to take into account the rays which are placed in the plane indicated. This enables us to simplify the algorithm. We discuss the algorithm in detail for the case of a point source. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 210, 1994, pp 94–108 Translated by N. Ya. Kirpichnikova.     

基于粗糙集理论的超稠油油藏水平井吞吐效果评价及其影响因素分析

影响超稠油油藏水平井蒸汽吞吐开发效果的因素包括地质参数、流体参数、开发参数、水平井设计参数等众多因素,寻找主要因素对于超稠油油藏水平井吞吐效果评价及开发调整设计具有重要意义.基于粗糙集理论对影响超稠油油藏水平井吞吐效果的10个因素进行数据属性约简,同时利用灰色关联分析,对这些因素进行敏感性分析;应用Elman神经网络比较上述两种结果,证明了粗糙集理论进行数据属性约简的方法更准确.最终得到注汽干度、注汽强度、注汽速度、水平段长度和注汽压力对水平井的开发效果影响最大.实例计算表明,方法实用有效,精度较高,可用于超稠油油藏水平井吞吐效果评价及开发、调整设计.     

On the Green Function of the Annulus

Using the Gegenbauer polynomials and the zonal harmonics functions we give some representation formula of the Green function in the annulus. We apply this result to prove some uniqueness results for some nonlinear elliptic problems.     

函数超越性研究中的若干命题

本文对高师院校教材《初等代数研究》中关于函数超越性研究的问题 ,提出改进的意见及相应的若干命题 .     

John's Decomposition of the Identity in the Non-Convex Case

We prove an extension of the classical John's Theorem, that characterises the ellipsoid of maximal volume position inside a convex body by the existence of some kind of decomposition of the identity, obtaining some results for maximal volume position of a compact and connected set inside a convex set with nonempty interior. By using those results we give some estimates for the outer volume ratio of bodies not necessarily convex.     

Column generation decomposition with the degenerate constraints in the subproblem

In this paper, we propose a new Dantzig–Wolfe decomposition for degenerate linear programs with the non degenerate constraints in the master problem and the degenerate ones in the subproblem. We propose three algorithms. The first one, where some set of variables of the original problem are added to the master problem, corresponds to the Improved Primal Simplex algorithm (IPS) presented recently by Elhallaoui et al. [7]. In the second one, some extreme points of the subproblem are added as columns in the master problem. The third algorithm is a mixed implementation that adds some original variables and some extreme points of a subproblem to the master problem. Experimental results on some degenerate instances show that the proposed algorithms yield computational times that are reduced by an average factor ranging from 3.32 to 13.16 compared to the primal simplex of CPLEX.     

Weak Forms of the Axiom of Choice and the Generalized Continuum Hypothesis

In this paper we study some statements similar to the Partition Principle and the Trichotomy. We prove some relationships between these statements, the Axiom of Choice, and the Generalized Continuum Hypothesis. We also prove some independence results. MSC: 03E25, 03E50, 04A25, 04A50.     

Application of the frontal algorithm in the collocation method

The author reports on a numerical experimentation with the collocation finite element procedure using Hermite basis functions and the frontal elimination technique to solve some large-scale problems where up to 1000 linear equations are involved. Several test cases, including some applications to engineering problems, are presented. The implementation of the frontal technique applied to collocation is discussed to some extent.