How to recognize nonexpansive mappings and isometric mappings

In two real Banach spaces, we shall present two conditions, under one of which each nonexpansive mapping must be an isometry.     

Rounded data analysis based on multi-layer ranked set sampling

Observations of sampling are often subject to rounding, but are modeled as though they were unrounded. This paper examines the impact of rounding errors on parameter estimation with multi-layer ranked set sampling. It shows that the rounding errors seriously distort the behavior of covariance matrix estimate, and lead to inconsistent estimation. Taking this into account, we present a new approach to implement the estimation for this model, and further establish the strong consistency and asymptotic normality of the proposed estimators. Simulation experiments show that our estimates based on rounded multi-layer ranked set sampling are always more efficient than those based on rounded simple random sampling.     

No Gap Second-Order Optimality Conditions for Circular Conic Programs

In this article, we study the second-order optimality conditions for a class of circular conic optimization problem. First, the explicit expressions of the tangent cone and the second-order tangent set for a given circular cone are derived. Then, we establish the closed-form formulation of critical cone and calculate the “sigma” term of the aforementioned optimization problem. At last, in light of tools of variational analysis, we present the associated no gap second-order optimality conditions. Compared to analogous results in the literature, our approach is intuitive and straightforward, which can be manipulated and verified. An example is illustrated to this end.     

微分特征列法在拟微分算子和Lax表示中的应用

微分特征列法用于拟微分算子和非线性发展方程Lax表示的计算.首先,利用微分特征列法和微分带余除法计算拟微分算子的逆和方根,由于不必求解常微分方程组,并将解代入,因此,使得计算得以简化.其次,利用微分特征列法,约化从广义Lax方程和Zakharov-Shabat推出的非线性偏微分方程,并得到相应的非线性发展方程.在Mathematica计算机代数系统上,编写了相关程序,从而可以利用计算机辅助完成一些非线性发展方程Lax表示的计算.     

基于代表的交叉验证分类

基于代表的邻域覆盖粗糙集分类算法,在某些数据集上表现良好,数据的类别不平衡问题严重影响算法的分类精度.为尽量消除类别不平衡问题的影响,在k折交叉验证方法的基础上,针对基于代表的邻域覆盖粗糙集分类算法,提出了3种集成策略.策略1依靠k折交叉验证,获得对应的k个基分类器,所有的基分类器组成委员会对未分类样本分类;在策略1的基础上,策略2选择分类精度相对较高的基分类器组成委员会,对未分类的样本进行分类;策略3在前2种策略的基础上,利用主动学习的思想,对训练集进行扩充,得到新的分类器再对未分类样本分类.实验所用数据集为UCI标准数据集,且对k的取值做了对比实验.结果显示,3种策略均有不同程度的提升,且k取5时总能取得较好的提升效果.对于不同数据集,应选择相适应的改进策略.     

Quantum set theory: Transfer Principle and De Morgan's Laws

In quantum logic, introduced by Birkhoff and von Neumann, De Morgan's Laws play an important role in the projection-valued truth value assignment of observational propositions in quantum mechanics. Takeuti's quantum set theory extends this assignment to all the set-theoretical statements on the universe of quantum sets. However, Takeuti's quantum set theory has a problem in that De Morgan's Laws do not hold between universal and existential bounded quantifiers. Here, we solve this problem by introducing a new truth value assignment for bounded quantifiers that satisfies De Morgan's Laws. To justify the new assignment, we prove the Transfer Principle, showing that this assignment of a truth value to every bounded ZFC theorem has a lower bound determined by the commutator, a projection-valued degree of commutativity, of constants in the formula. We study the most general class of truth value assignments and obtain necessary and sufficient conditions for them to satisfy the Transfer Principle, to satisfy De Morgan's Laws, and to satisfy both. For the class of assignments with polynomially definable logical operations, we determine exactly 36 assignments that satisfy the Transfer Principle and exactly 6 assignments that satisfy both the Transfer Principle and De Morgan's Laws.     

基于中智犹豫模糊语言优先QUALIFLEX方法的绿色供应商选择

针对绿色供应商选择过程中,评价指标数量明显超过可供选择的供应商数量且指标之间存在优序关系等特点,提出了基于中智犹豫模糊语言优先QUALIFLEX方法的绿色供应商选择方法.首先,利用中智犹豫模糊语言表征评价信息和评价权重;其次,构造优先矩阵对指标权重做精确化处理,考虑到决策者对指标的要求和指标之间的优序关系,对指标权重进行修订;然后,提出改进的中智犹豫模糊语言余弦距离测度,在此基础上借助QUALIFLEX方法确定备选供应商的最终排序;最后,利用化学制药企业选择原料供应商的案例验证了所提方法的有效性.     

基于Ph,e下Riemann-Liouville分数阶微分方程解的存在唯一性

利用基于集合P_h,e上的一类混合单调算子不动点定理,研究了一类Riemann Liouville分数阶微分方程两点边值问题,获得了这类方程在集合P_h,e中解的存在性与唯一性,并用一组单调迭代序列逼近了该方程的唯一非平凡解.最后,利用一个实例验证了主要结论.     

基于Vague集距离与灰色关联的区域产业技术供需协同发展评价研究

技术供需有效协同是实现产业中高端发展的重要驱动,本文综合考虑产业技术供需子系统发展水平、供需子系统间耦合作用及协同效应等因素,将Vague集相似性度量与距离协同模型结合,运用灰色关联分析计算技术供需子系统间的灰色关联度,建立了基于Vague集距离与灰色关联的区域高技术产业技术供需复合系统的综合协同发展模型,并利用该模型对2009年至2016年京津冀地区高技术产业技术供需协同水平数据进行了实证分析。实证分析结果表明,京津冀地区技术供需协同发展处于高协同低发展阶段,综合协同发展水平增速缓慢;供需子系统间相互作用关系显著;北京和天津的技术供给发展较快,需求相对不足,而河北需求旺盛,但供给不足。因此,兼顾技术供需高质量发展与区域技术供需协同匹配是创新引领产业发展的有效路径。     

基于相似度和改进雷达图的概率犹豫模糊多属性决策方法

为了解决属性权重未知的概率犹豫模糊多属性决策问题,构建基于相似度和改进雷达图的多属性决策方法。首先基于概率犹豫模糊元的信息完全度构建概率犹豫模糊集的距离测度和灰色关联系数,然后基于灰色关联理想解法定义了概率犹豫模糊集的相似度,最后根据概率犹豫模糊集的相似度和改进雷达图构建多属性决策模型,并通过案例进行了验证分析。