Fixed-Point Theorems for Generalized Nonexpansive Mappings

Using the concept of asymptotic center we obtain the existence of fixed points having preassigned location for a wider class of asymptotic nonexpansive mappings in a uniformly convex Banach space. This generalization leads us to get a recent result of Alfuraidan and Khamsi for continuous monotone asymptotic nonexpansive mappings as well as the classical fixed-point result of Geobel and Kirk for asymptotic nonexpansive mappings in a uniformly convex Banach space. Also we prove a fixed-point theorem for order preserving continuous maps on a quasiordered closed convex subset of a uniformly convex Banach sapce having monotone norm.     

Sliding and transversal motions on an inclined boundary in a periodically forced discontinuous system

In this paper, sliding and transversal motions on the boundary in the periodically driven, discontinuous dynamical system is investigated. The simple inclined straight line boundary in phase space is considered as a control law for such a dynamical system to switch. The normal vector field for a flow switching on the separation boundary is adopted to develop the analytical conditions, and the corresponding transversality conditions of a flow to the boundary are obtained. The conditions of sliding and grazing flows to the separation boundary are presented as well. Using mapping structures, periodic motions of such a discontinuous system are predicted, and the corresponding local stability and bifurcation analysis of the periodic motion are carried out. Numerical illustrations of periodic motions with and without sliding on the boundary are given. The local stability analysis cannot provide the proper prediction of the sliding and grazing motions in discontinuous dynamical systems. Therefore, the normal vector fields of periodic flows are presented, and the normal vector fields on the switching boundary points give the analytical criteria for sliding and transversality of motions.     

可用性观点下的烟叶质量粗糙集评价方法

通过对现代卷烟产业中烟叶质量新需求的理解和归纳,构建了可用性观点下的烟叶质量综合评价新指标体系。考虑到实际烟叶质量评价中的数据的复杂性和问题求解的特殊性,将基于等价关系的Pawlak粗糙集模型扩展为基于上、下近似相似关系的扩展粗糙集模型,并设计了相应的可用性观点下烟叶质量粗糙集智能评价模型,在实现了不依赖主观先验信息求取各指标客观权重的同时,进一步引入了专家的主观权重信息,以达到对烟叶“可用性”需求的动态调整。文章首次尝试了基于定量化解决途径来应用和阐释烟叶的“可用性”概念,文末的实证分析验证了本文方法的可行性和一定程度的优越性。     

不连续随机算子随机不动点定理及其应用

该文利用半序理论和随机压缩映象原理,得到了一类不连续随机增算子随机不动点的唯一存在定理.作为应用,考虑了R~n中含间断项的一阶随机微分积分方程初值问题.     

不连续泛函微分方程周期边值问题解的单调迭代技巧(英文)

文章通过运用上下解的方法证明了一类带有周期边值条件的不连续泛函微分方程解的存在性.并且采用不连续的上下解显著扩大了上下解的选择范围.进而,通过构造具有一致收敛性的上下解的单调迭代序列,得到了该周期边值问题的极值解,即最大、小解.     

广义近似空间的拓扑结构

在本文中,我们引入了论域X上的自反关系θ的传递化表示θs的概念,研究了拓扑空间(X,тθ)的基本性质,得到了一些有较大价值的结果,这不仅有助于理解粗糙集理论中的一些基本概念及其性质,而且对拓扑学本身都有理论和实际意义.     

模糊关系方程在预测深部开采地面下沉中的应用

根据深部矿体开采岩体移动变形的特点,建立了地面下沉值与影响因素间的模糊关系方程.确定出各指标间的模糊关系并对模糊关系方程进行了求解;然后通过模糊变换得出采区下沉的预测值.通过工程实例对比分析结果表明,理论分析结果与实测资料是一致的.