Applications of the representative points in statistical simulations

The paper gives a new approach to statistical simulation and resampling by the use of number-theoretic methods and representative points. Resempling techniques take samples from an approximate population. The bootstrap suggests to use a random sample to form an approximate population. We propose to construct some approximate population distribution by the use of two kinds of representative points, and samples are taken from these approximate distributions. The statistical inference is based on those samples. The statistical inference in this paper involves estimation of mean, variance, skewness, kurtosis, quantile and density of the population distribution. Our results show that the new method can significantly improve the results by the use of Monte Carlo methods.     

A note on the lower semicontinuity of efficient solutions for parametric vector equilibrium problems

By using a new assumption, the lower semicontinuity of the efficient solution mappings for parametric vector equilibrium problems without a monotonicity assumption is established. Our result is different from recent ones in the literature. Some examples are given to illustrate the case.     

基于MIV-BP型网络实验的房地产项目风险识别研究

为了更准确更客观地识别房地产项目中的风险,为房地产项目投资决策提供科学依据和参考,有效地规避风险,本研究在BP神经网络 (Back-Propagation Neural Network)建模的基础上,采取MIV(Mean Impact Value)算法对BP神经网络模型进行变量筛选的网络优化和改良,从而形成新的优化后的MIV-BP(Mean Impact Value Back-Propagation Neural Network)神经网络,并以此用于评价房地产项目中的风险度以及各因素在风险度中的影响作用大小;同时选取目前相关的房地产项目数据进行仿真实证分析和验证。验证实验结果表明,MIV-BP型神经网络对于房地产项目风险度识别具有良好的适应性和准确性,实验结果客观,达到专家评价的要求,并在风险因素作用度分析上具有良好的应用价值。     

A kinematic formula for integral invariant of degree 4 in real space form

In this paper,kinematic formulae in a real space form are investigated.A kinematic formula for homogeneous polynomial of degree 4 on the second fundamental forms in a real space form is obtained.The formula obtained is a concrete form of the result of Howard and the analogue of the known formula of Chen and Zhou.     

On the Shadowing Property and Shadowable Point of Set-valued Dynamical Systems

In this article, the authors introduce the concept of shadowable points for set-valued dynamical systems, the pointwise version of the shadowing property, and prove that a set-valued dynamical system has the shadowing property iff every point in the phase space is shadowable; every chain transitive set-valued dynamical system has either the shadowing property or no shadowable points; and for a set-valued dynamical system there exists a shadowable point iff there exists a minimal shadowable point. In the end, it is proved that a set-valued dynamical system with the shadowing property is totally transitive iff it is mixing and iff it has the specification property.     

教师课堂教学质量的多元统计分析

应用多元统计分析中的聚类分析法和主成分分析法对教师高等数学的课堂教学质量进行了统计分析,通过对数据的聚类分析结果提出教师应注重启发性教学并善于引导学生解决实际问题.同时利用主成分分析将原先众多的评价指标用三个指标代替,为进一步提高教学质量提供科学的依据.     

退化时滞微分系统的Hopf分支

本文讨论了一般二雏退化时滞微分系统当r≠0时平衡点稳定性的范围，并以滞量r为分支参数研究系统出现Hopf分支的条件．     

算子Dα及其刻划的亚纯p叶函数类

用算子Dα刻划了亚纯星象函数,亚纯凸象函数,亚纯近于凸函数和亚纯拟凸函数的新子类,建立了包含关系,讨论了这些类中函数积分算子的性质.     

区间数可能度的二维定义

利用二维空间的面积,提出了一个新的区间数可能度的定义,并给出了简单实用的计算公式和证明了相关的性质,最后,通过实例说明了该定义的实用性.     

Interior estimates for solutions of a fourth order nonlinear partial differential equation

Let be a locally strongly convex hypersurface, given by the graph of a convex function xn+1=f(x₁,…,xn) defined in a convex domain Ω⊂Rn. M is called a α-extremal hypersurface, if f is a solution of