需求价格弹性与边际收益研究

研究特定需求价格弹性条件下需求函数的确定问题和特定边际收益条件下需求函数的确定问题,并给出了有关的计算公式.研究结果表明,为了实现既定的需求价格弹性或边际收益,对应的需求函数有无穷多个.     

微分方程零解的弱渐近稳定与不稳定的判定定理

给出了平凡解弱渐近稳定定义及在已知导函数 d Vdt负定的情况下 ,通过 V( t,x)函数的符号性质来判定微分方程平凡解的弱渐近稳定性与不稳定性 ,并举例说明定理的应用 .     

Knight's paths towards Catalan numbers

We provide enumerating results for partial knight's paths of a given size. We prove algebraically that zigzag knight's paths of a given size ending on the x-axis are enumerated by the generalized Catalan numbers, and we give a constructive bijection with peakless Motzkin paths of a given length. After enumerating partial knight's paths of a given length, we prove that zigzag knight's paths of a given length ending on the x-axis are counted by the Catalan numbers. Finally, we give a constructive bijection with Dyck paths of a given length.     

The weak and strong Gaussian probabilistic realization problem

A classification is given of all σ-algebras that make two given σ-algebras conditionally independent in the case that the σ-algebras are generated by finite dimensional Gaussian random variables. In addition a classification is given of all Gaussian measures that have the conditional independence property and such that restricted to a subspace, they coincide with a given measure.     

循环图圈空间的最小基

For most of circular graph the length of the minimum cycle basis is given.For the others a bound of the length of the minimum cycle basis is given and the given bound is reached.     

Counting matrices over finite fields having a given number of rows of unit weight

We present a formula enumerating matrices over a finite field of a given rank and a given number of rows of unit weight, i.e., each having a single nonzero entry. We also determine the number of subspaces of a given dimension containing a given number of vectors of unit weight.     

三维医学模型表面积和体积计算方法研究

应用MATLAB语言描述了测量任意给定的颌、颧骨区域的表面积和体积的方法,并且在临床上用实例给出了计算结果.     

扩充偏微分方程(组)守恒律和对称的辅助方程方法及微分形式吴方法的应用

首先,我们给出了引入伴随方程(组)扩充原方程(组)的策略使给定偏微分方程(组)的扩充方程组具有对应泛瓯即,成为Lagrange系统的方法,以此为基础提出了作为偏微分方程(组)传统守恒律和对称概念的一种推广-偏微分方程(组)扩充守恒律和扩充对称的概念;其次,以得到的Lagrange系统为基础给定了确定原方程(组)扩充守恒律和扩充对称的方法,从而达到扩充给定偏微分方程(组)的首恒律和对称的目的;第三,提出了适用于一般形式微分方程(组)的计算固有守恒律的方法;第四,实现以上算法过程中,我们先把计算(扩充)守恒律和对称问题均归结为求解超定线性齐次偏微分方程组(确定方程组)的问题.然后,对此关键问题我们提出了用微分形式吴方法处理的有效算法;最后,作为方法的应用我们计算确定了非线性电报方程组在内的五个发展方程(组)的新守恒律和对称,同时也说明了方法的有效性.     

区间有限元方法及其在抗滑稳定性分析中的应用

通过区间值函数和实值函数的关系探讨了区间相关性导致的区间扩张的问题,给出了保证区间计算获得足够精度的计算方法;提出了基于单元的子区间摄动有限元计算方法,并给出了提高计算效率的一些方法和获得较好计算精度时的子区间数目的近似计算公式.结合工程实例,基于单元的子区间有限元方法和抗滑稳定性分析方法给出了稳定性的区间范围,为更合理地估计和评价结构的抗滑稳定性提供一定的依据.     

Compact differences of composition operators

A characterization of compact difference is given for composition operators acting on the standard weighted Bergman spaces and necessary conditions are given on a larger scale of weighted Dirichlet spaces. Conditions are given under which a composition operator can be written as a finite sum of composition operators modulo the compacts. The additive structure of the space of composition operators modulo the compact operators is investigated further and a sufficient condition is given to insure that two composition operators lie in the same component.     

两个逆网络选址问题的计算复杂性

本文考虑两个我们称之为逆网络选址的改进问题,它们是修改网络上各个边的长度,分别使得网络上某个给定的顶点到网络上所有点的最大距离以及该点到其它顶点的距离之和不大于预先给定的上界,并且所做的修改总量最小.我们将证明这两个逆网络选址问题都是强NP困难的.     

Two sufficient conditions for supersolvability of finite groups

In this paper two sufficient conditions for supersolvability of finite groups are given considering the maximal subgroups of Sylow subgroups of the group. An example is given to show that the conditions given are not necessary for supersolvability.     

基于光滑化方法求解非线性l1问题

讨论了求解非线性l1问题的一种新的光滑函数法.通过对非线性l1问题模型的转化,将该问题化为一个不可微优化问题,据此提出了基于BFGS迭代的非线性l1问题的光滑函数法,介绍了非线性l1问题的光滑函数的有关性质、算法步骤及其收敛性.数值仿真显示了提出的光滑函数方法可以避免数值计算的溢出,具有一定的有效性.     

A new proof of Frobenius theorem and applications

A proof of Frobenius theorem on local integrability of a given distribution on a finite or infinite dimensional manifold under weak differentiability conditions is given using holonomy methods and the curvature two form of the associated connection. The local curvature two form, which measures the non-integrability of a given distribution, is studied and a variety of applications are given. The Inverse Problem in the Calculus of Variations appears as a particular case.     

A Comparison of Two Variational Methods

A discussion is given of the relation between the maximum functionaltheorem and Schwinger's variational principle, and it is shownthat the bound given by Schwinger's principle is better thanor the same as that given by the maximum functional theorem.     

关于Schottky定理与Hayman常数

本文对于在单位圆盘中不取值0与1的正则函数,利用了这种函数的对数导数模的准确上界与及Hayman常数有关的上界,得到了这种函数模的显式上界与Hayman常数的关系及这种函数的正规级.     

具有模糊支付的模糊合作对策中局中人间的相互影响

基于郭嗣琮[19～21]提出的关于模糊数的限制运算,本文探讨了具有模糊支付的模糊合作对策中局中人间的相互影响问题。给出了局中人间相互影响的表达式。当所给模糊合作对策具有相互独立性和k-单调性时,论述了一些基本性质。通过对Shapley函数概念的推广,得到相应的模糊Shapley度量指标。并对所给指标满足的性质进行了研究。最后通过算例分析来说明所给指标有效性和实用性。     

Boundary control in critical time by elastic forces applied at two ends of an inhomogeneous rod for the case in which the wave propagation time over each of the inhomogeneity parts is the same

We study boundary control in critical time by elastic forces at two ends of an inhomogeneous rod consisting of two parts of distinct densities and elasticities for the case in which the wave propagation time over each of these parts is the same. We present a closed-form expression for the boundary control by elastic forces bringing the originally quiescent stick into a given terminal state specified by a given terminal displacement and a given terminal velocity in a given critical time.     

Regularity for solutions of nonlinear second order evolution equations

This paper deals with the existence of solutions for the class of nonlinear second order evolution equations. The regularity and a variation of solutions of the given equations are also given. As particular cases of our general formulation, some results for Volterra integrodifferential equations of the hyperbolic type are given.     

Controlled selection a technique in random sampling

Summary The paper gives a method of constructing a random sampling design corresponding to a given population and a given sample sizen by means of which the probability of drawing a non-preferred combination of units can be reduced up to a certain level. Appropriate methods of analysing the data obtained from samples selected by this procedure are also given. A numerical example is given to illustrate the method developed in the paper.