凸函数的次微分与微分中值定理的逆定理

利用凸函数的性质,证明了次微分情形下微分中值定理的逆定理.     

(φ,γ)-凸函数与(φ,γ)-次微分

定义了基于Ben-T al广义代数运算的(,φγ)-凸函数,(φ,γ)-次微分,进而获得了关于(,φγ)-凸函数及(φ,γ)-次微分的一些分析性质.讨论了(φ,γ)-凸函数的等价条件.     

半严格不变凸函数

文章在Banach空间中定义了一种新的广义凸函数—半严格不变凸函数.对于满足局部Lipschitz条件的半严格不变凸函数,得到了它的广义Clarke次微分性质.文中还讨论了半严格不变凸函数与不变凸函数及半严格预不变凸函数之间的关系,得到了半严格不变凸函数的一些性质.     

半严格不变凸函数

文章在Banach空间中定义了一种新的广义凸函数—半严格不变凸函数.对于满足局部Lipschitz条件的半严格不变凸函数,得到了它的广义Clarke次微分性质.文中还讨论了半严格不变凸函数与不变凸函数及半严格预不变凸函数之间的关系,得到了半严格不变凸函数的一些性质.     

（φ，γ）-凸函数与（φ，γ）一次微分

定义了基于Ben—Tal广义代数运算的（φ，γ）-凸函数，（φ，γ）-次微分，进而获得了关于（φ，γ）-凸函数及（φ，γ）-次微分的一些分析性质．讨论了（φ，γ）-凸函数的等价条件。     

回收函数与函数的无界性

主要利用回收锥和回收函数来研究函数的下无界性。首先, 针对凸函数在非可微条件下,利用中值定理和回收锥刻画了凸函数次微分的性质, 并在此基础上给出了基于次可微条件下回收向量的充要条件。其次,将凸性推广到E-凸, 在一定条件下,利用回收函数研究了E-凸函数的下无界性。最后,通过举例说明这些结果不能推广到拟凸条件.     

关于凸函数的定义和性质

主要研究了凸函数的几种定义及他们在不同的条件下的关系,并讨论了连续凸函数的一些性质.     

P-凸函数及其性质

给出P-凸函数的定义及其性质,将一个有关凸函数的命题推广到P-凸函数情形,并指出赵海清等人关于该命题的证明过程是错误的.     

强预不变凸函数的充要条件

本文讨论了强预不变凸函数与预不变凸函数、严格预不变凸函数及半严格预不变凸函数之间的关系,得到它的三个充要条件：(i)在一定条件下,f是强预不变凸函数的充分必要条件是f是预不变凸函数且f满足中间点强预不变凸性；(ii)在一定条件下,f是强预不变凸函数的充分必要条件是f是严格预不变凸函数且f满足中间点强预不变凸性；(iii)在一定条件下,f是强预不变凸函数的充分必要条件是f是半严格预不变凸函数且f满足中间点强预不变凸性．     

凸函数的一个等价性质

函数的凸性在研究不等式、函数逼近论等领域有着十分重要的应用,但是在不同条件下的凸函数具有不同的一些等价性质.利用凸函数已有的性质及确界定理,给出并证明了凸(严格凸)函数的又一等价性质,所得结果与在可导条件下凸函数的不等式性质类似.     

First and second order sufficient conditions for strict minimality in nonsmooth vector optimization

In this paper we present first and second order sufficient conditions for strict local minima of orders 1 and 2 to vector optimization problems with an arbitrary feasible set and a twice directionally differentiable objective function. With this aim, the notion of support function to a vector problem is introduced, in such a way that the scalar case and the multiobjective case, in particular, are contained. The obtained results extend the multiobjective ones to this case. Moreover, specializing to a feasible set defined by equality, inequality, and set constraints, first and second order sufficient conditions by means of Lagrange multiplier rules are established.     

Research on the properties of some planar polynomial differential equations

In this article, we use the new method of reflecting function to study the behavior of solutions of nonlinear time-vary differential equations, and give the sufficient conditions for these equations which have the reflecting function in the form of linear and fractional. We applied the obtained results to discuss the qualitative behavior of solutions of the higher degree polynomial differential systems and derive the sufficient conditions for a critical point to be a center.     

线性模型中不可估参数的线性估计的可容许性

对一般线性模型在平方损失函数下，得到了一维不可估参数函数的线性估计为可容许估计的充要条件，以及模型中参数向量（非线性可估）的线性估计为可容许估计的两个充要条件，并得到了多维参数函数（可估或不可估）的线性估计为可容许估计的一个充分条件以及特殊情况下的一个充要条件．     

平衡损失下有限总体回归系数的线性可容许预测

本文研究了平衡损失函数下正态总体和非正态总体中有限回归系数的可容许预测.利用统计决策理论,获得了非正态总体中齐次线性预测为可容许预测的充分必要条件和在正态总体中齐次线性预测在一切预测类中可容许性的充要条件,推广了二次损失下的若干相关结果.     

GLOBAL ATTRACTIVITY IN AN ALMOST PERIODIC PREDATOR-PREY-MUTUALIST SYSTEM

In this paper, the almost periodic predator-prey-mutualist model with Holling type II functional response is discussed. A set of sufficient conditions which guarantee the uniform persistence and the global attractivity of the system are obtained. For the almost periodic case, by constructing a suitable Lyapunov function, sufficient conditions which guarantee the existence of a unique globally attractive positive almost periodic solution of the system are obtained. An example together with its numerical simulations shows the feasibility of the main results.     

Implicit Function Theorem for Systems of Polynomial Equations with Vanishing Jacobian and Its Application to Flexible Polyhedra and Frameworks

 We study the existence problem for a local implicit function determined by a system of nonlinear algebraic equations in the particular case when the determinant of its Jacobian matrix vanishes at the point under consideration. We present a system of sufficient conditions that implies existence of a local implicit function as well as another system of sufficient conditions that guarantees absence of a local implicit function. The results obtained are applied to proving new and classical results on flexibility and rigidity of polyhedra and frameworks.     

Implicit Function Theorem for Systems of Polynomial Equations with Vanishing Jacobian and Its Application to Flexible Polyhedra and Frameworks

 We study the existence problem for a local implicit function determined by a system of nonlinear algebraic equations in the particular case when the determinant of its Jacobian matrix vanishes at the point under consideration. We present a system of sufficient conditions that implies existence of a local implicit function as well as another system of sufficient conditions that guarantees absence of a local implicit function. The results obtained are applied to proving new and classical results on flexibility and rigidity of polyhedra and frameworks. (Received 13 July 2000; in revised form 11 December 2000)     

On Polynomial Functions over Finite Commutative Rings

Let R be an arbitrary finite commutative local ring. In this paper, we obtain a necessary and sufficient condition for a function over R to be a polynomial function. Before this paper, necessary and sufficient conditions for a function to be a polynomial function over some special finite commutative local rings were obtained.     

关于分形插值函数的连续性和可微性

获得了由迭代函数系统(IFS)定义的两类分形插值函数具有Hlder连续性的充分条件,给出了这两类分形插值函数连续可微的充要条件,并证明了可微分形插值函数的导函数是由关联IFS生成的分形插值函数.     

一种新广义凸多目标分式规划的最优性充分条件

提出了（F,α,ρ,θ）-b-凸函数的概念,它是一类新的广义凸函数,并给出了这类广义凸函数的性质.在此基础上,讨论了目标函数和约束函数均为（F,α,ρ,θ）-b-凸函数的多目标分式规划,利用广义K-T条件,得到了这类多目标规划有效解和弱有效解的几个充分条件,推广了已有文献的相关结果.