一种新型区间数多属性决策算法研究

随着多属性决策问题的复杂性、不确定性日益增强，基于区间数的多属性决策理论与应用研究越来越广泛。基于算子有序性的构建思想，本文提出并构建了基于有序欧几里德算子的区间数多属性决策算法模型，证明了有序欧几里德算子的单调性、齐次性和幂等性。采用基于有序欧几里德算子的区间数多属性决策方法对某火炮采购问题进行了决策计算，证明了该方法的有效性与可行性。     

非线性多比例延迟微分方程向后Euler方法的散逸性

本文讨论了多比例延迟微分方程的散逸性，证明了应用向后Euler方法求解多比例延迟微分方程数值解仍保持散逸性，它可视为文献[9]中相应结果的推广。     

一种基于决策者风险态度的区间数多指标方法的注记

本对基于决策风险态度的区间数多指标方法的映射函数的可区分性、理想点的存在性进行了论证，确保了区间数多指标决策方法的正确性，并对决策风险态度因子进行随机化，使此方法更合理，更有深度。     

多比例延迟微分方程的散逸性

本文讨论多比例延迟微分方程的散逸性，给出了多比例延迟微分方程是散逸的充分条件，它可视为文献[8]中相应结果的推广。     

多目标半定规划的互补弱鞍点和G-鞍点最优性条件

对于含矩阵函数半定约束和多个目标函数的多目标半定规划问题，给出Lagrange函数在弱有效意义下的互补弱鞍点和Geofrrion恰当有效意义下的G-鞍点的定义及其等价定义．然后，在较弱的凸性条件下，利用含矩阵和向量约束的择一性定理，建立多目标半定规划的互补弱鞍点和G-鞍点充分必要条件．     

多总体球性检验的似然比准则的非零渐近分布

多总体球性检验的似然比准则的非零渐近分布龚力强（华南建设学院西院广州５１０４０５）关键词：多总体球性；似然比检验；渐近分布ＡＭＳ（１９９１）主日分类：６２Ｅ２０．设ｘ。１，ｘ。。，…，ｘ；《１＝１，２，…，ｚ；Ｎ；＞户）为从卢维正态总体Ｎｐ（８，工）...     

一类微分方程组的多重正解

本文讨论了 Ｂａｎａｃｈ空间中 Ｓｔｕｒｍ－Ｌｉｏｕｖｉｌｌｅ问题正解的存在性与多解性，通过线性算子的谱半径，给出其正解存在与多解的条件．     

椭圆边值系统的正径向解的存在性与多解性

通过利用锥拉伸及锥压缩型的Krasnosel‘skii不动点定理，我们研究了一类椭圆边值系统的正径向解的存在性，非存在性与多解性。     

数论中的存在性问题

数论中的存在性问题冯志刚（上海市上海中学２００２３１）数论中存在性问题常常是高层次竟赛的热门试题，下面介绍解这类问题的几种常用方法．一、直接构造例１如果自然数Ｎ的质因数分解式中，所有指数都大于１，则称Ｎ为幂数．能否举出无穷多个自然数，它们自身及任意多...     

一维p-Laplacian方程边值问题多解的存在性

利用Clark定理，研究了一维p-Laplacian方程边值问题多解的存在性，得到了这类边值问题至少有n对非平凡解的充分条件．     

直觉模糊关系的截集性质

定义了直觉模糊关系的截集以及并给出了它们的基本性质,同时分别讨论了自反、对称、传递直觉模糊关系与经典二元关系之间的等价刻画;其次,提出直觉模糊关系的定义域与值域的概念;最后,分析了直觉模糊关系合成的截集性质.     

L－fuzzy集网的R－收敛性质

本文在ＬＦ拓扑空间中建立了Ｌ－ｆｕｚｚｙ集网的弱收敛（Ｒ－收敛）概念，应用文［４］中的Ｒ－闭包，系统讨论了它们的性质，证明了等式ＲｌｉｍＡ＿ｎ＝∧（∨Ａ＿ｍ）＿Ｒ和ＲｌｉｍＡ＿ｎ＝Ａ＿ｎ＝∧（∨Ａ＿ｍ）＿Ｒ并且给出了Ｌ－ｆｕｚｚｙ集网与其子网之间的关系。     

一类三阶牛顿变形方法

A class of third-order convergence methods of solving roots for non-linear equation,which are variant Newton's method,are given.Their convergence properties are proved.They are at least third order convergence near simple root and one order convergence near multiple roots.In the end,numerical tests are given and compared with other known Newton's methods.The results show that the proposed methods have some more advantages than others.They enrich the methods to find the roots of non-linear equations and they are important in both theory and application.     

Stability of oscillatory solutions of differential equations with general piecewise constant arguments of mixed type

We examine scalar differential equations with general piecewise constant arguments of mixed type, in short DEPCAG of mixed type, that is, the arguments are general step functions. Criteria of existence of the oscillatory and nonoscillatory solutions of such equations are proposed. Necessary and sufficient conditions for stability of the zero solution are obtained. Our results are new, extend and improve earlier publications. Several numerical examples and simulations are also given to show the feasibility of our results.     

On the Least Number of Fixed Points of an Equivariant Map

The problem on the least number of fixed points of an equivariant map of a compact polyhedron on which a finite group acts is considered. For such a map, the least number of fixed points and the least number of fixed orbits are estimated in terms of invariants of the type of Nielsen numbers. The estimates obtained are sharp. The results are similar to those of P. Wong, but their assumptions are essentially weaker. Some notations are refined. The proofs are constructive.     

Estimation of Parameters of Partially Linear Errors-in-variables Models with Replicated Net Points of Observation

A kind of partially linear errors-in-variables models with replicated net points of observation are studied in this paper. Estimators of unknown parameters are given. Under certain regular conditions, it is shown that the estimators of the unknown parameters are strongly consistent and their a.s. convergence rates are achieved.     

一种Sieve极大似然估计的渐近性质

该文针对部分线性模型,在响应变量的观测值为Ⅰ型区间删失数据的情形下,讨论Ｓｉｅｖｅ极大似然估计的渐近性质．用三角级数来构造Ｓｉｅｖｅ空间,在一定条件下证明了该估计具有强相合性;得到了该估计的弱收敛速度,并且非参数部分的估计达到了最优收敛速度;还算出了参数部分的信息界．     

Analysis of Dynamic Properties of Forest Beetle Outbreak Model

This paper mainly studies the dynamic properties of the forest beetle outbreak model. The existence of the positive equilibrium point and the local stability of the positive equilibrium point of the system are analyzed, and the relevant conclusions are drawn. After that, the existence of Turing instability, Hopf bifurcation and Turing-Hopf bifurcation are discussed respectively, and the necessary conditions for existence are given. Finally, the normal form of the Turing-Hopf point is calculated, and some dynamic properties at the point are analyzed by numerical simulation.     

随机向量的函数的独立性的一个问题

给出了随机变量 X1,X2 ,X3 ,X4 每三个相互独立 ,但 X1±X2 与 X3 ± X4 不相互独立的例子 ,以及 X1,X2 ,X3 每两个相互独立 ,但 X1± X2 与 X3 不相互独立的例子 .     

Enumeration of point-determining graphs

Point-determining graphs are graphs in which no two vertices have the same neighborhoods, co-point-determining graphs are those whose complements are point-determining, and bi-point-determining graphs are those both point-determining and co-point-determining. Bicolored point-determining graphs are point-determining graphs whose vertices are properly colored with white and black. We use the combinatorial theory of species to enumerate these graphs as well as the connected cases.