A characterization of spaces of constant curvature by minimum covering radius of triangles

In this paper, we prove that if in a Riemannian manifold, the minimum covering radius of a point triple of small diameter depends only on the geodesic distances between the points, then the manifold must be of constant curvature. This implies that if in a complete connected Riemannian manifold, the volume of the intersection of three small geodesic balls of equal radii depends only on the distances between the centers and the radius, then it is one of the simply connected spaces of constant curvature. This generalizes an earlier result of the first author and D. Kunszenti-Kovács (2010).     

Convergence of densities of some functionals of Gaussian processes

The aim of this paper is to establish the uniform convergence of the densities of a sequence of random variables, which are functionals of an underlying Gaussian process, to a normal density. Precise estimates for the uniform distance are derived by using the techniques of Malliavin calculus, combined with Stein?s method for normal approximation. We need to assume some non-degeneracy conditions. First, the study is focused on random variables in a fixed Wiener chaos, and later, the results are extended to the uniform convergence of the derivatives of the densities and to the case of random vectors in some fixed chaos, which are uniformly non-degenerate in the sense of Malliavin calculus. Explicit upper bounds for the uniform norm are obtained for random variables in the second Wiener chaos, and an application to the convergence of densities of the least square estimator for the drift parameter in Ornstein–Uhlenbeck processes is discussed.     

Exact analytical inversion of TSK fuzzy systems with singleton and linear consequents

In literature, exact inversion methods for TSK fuzzy systems exist only for the systems with singleton consequents. These methods have binding limitations such as strong triangular partitioning, monotonic rule bases and/or invertibility check. These extra limitations lessen the modeling capabilities of the TSK fuzzy systems. In this study, an exact analytical inversion method for TSK fuzzy systems with singleton and linear consequents is presented. The only limitation of the proposed method is that the inversion variable should be represented by piecewise linear membership functions (PWL-MFs). In this case, the universe of discourse of the inversion variable is divided into specific regions in which only one linear piece exists for each PWL-MF at most. In the proposed method, the analytical formulation of TSK fuzzy system is expressed in terms of the inversion variable by using linear equations of PWL-MFs. Thus, the fuzzy system output in any region can be obtained by using the appropriate parameters of the linear equations of PWL-MFs defined within the related region. This expression provides a way to obtain linear and quadratic equations in terms of the inversion variable for TSK fuzzy systems with singleton and linear consequents, respectively. So, it becomes very easy to find exact inverse solutions for each region by using explicit analytical solutions for linear or quadratic equations. The proposed inversion method has been illustrated through simulation examples.     

Probabilistic solution of random homogeneous linear second-order difference equations

This paper deals with the computation of the first probability density function of the solution of random homogeneous linear second-order difference equations by the Random Variable Transformation method. This approach allows us to generalize the classical solution obtained in the deterministic scenario. Several illustrative examples are provided.     

基于提前期压缩的两阶段供应链的契约协调

研究了基于提前期压缩的信息对称和信息不对称两种情况下的供应链协调问题,重点解决了在信息不对称时采用线性转移支付策略解决供应链的不协调问题.当压缩提前期时,制造商的成本增加,成本的增加值信息对销售商有对称和不对称两种情况.在信息对称时采用收益共享契约可以实现供应链的协调;在信息不对称,采用收益共享契约时,为了激励制造商,销售商不得不对制造商生产成本的不确定性付出成本,导致利润下降,而制造商由于拥有私有信息而使得利润增加,所以整个供应链并没有达到集中决策时的水平,只得到了帕累托改善的次优结果.创新点在于采用线性转移支付策略实现了供应链的协调,达到了帕累托最优,解决了收益共享契约不能实现供应链协调的问题.最后通过算例进行了说明.     

基于多元线性回归模型的东北地区需水量分析

多元线性回归模型在社会、经济、技术以及众多自然科学研究领域中已被广泛使用,某个地区需水量应与该地区多种因素有关,故选取东北地区的GDP、水库蓄水总量、人均可支配收入、城市绿地面积和工业用水量等5个因素,借助MATLAB软件阐明了多元线性回归模型在东北地区需水量分析中的应用.并通过皮尔森相关性检验、拟合优度检验、F检验、t检验和残差分析的方法对模型进行优化,得到了准确可靠的多元线性回归模型,此模型具有拟合程度高、简易、直观等优势,为多元线性回归模型在需水量分析中的应用提供了有力参考.     

基于GWR模型的河南省人口分布的影响因素研究

近年来,人口作为一种基本信息已成为目前研究的热点问题之一.人口分布可能受自然,经济,社会,政治等诸多因素的影响.因此,人口分布的研究对于了解不同类型区域的人口资源与经济发展之间的关系,因地制宜地发展本地经济具有重大意义.课题以河南省统计年鉴数据为基础,研究河南省人口分布的影响因素.具体来说,首先利用Surfer软件的可视化技术研究了河南省人口数量的空间变化特征.其次,利用近年来发展起来的地理加权回归模型对河南省人口分布的影响因素进行了定量分析.通过上述分析提取有效信息,从而为制定合理的人口政策和实现人口的有序流动提供必要的理论支持.     

线性正则变换域的复能量密度函数

线性正则变换是经典Fourier变换的广义形式,目前在非平稳信号的参数检测与估计方面取得了优异的应用效果,但线性正则变换理论体系还不完善.探讨了线性正则变换相关的复能量密度函数的基本概念,并详细推导研究了其基本的数学性质与特点,在上述理论的基础上,通过仿真实验来验证所得到结论的准确性.为其在实际应用中发挥更大的作用奠定了基础.     

部分线性模型的随机约束岭估计

研究了部分线性回归模型附加有随机约束条件时的估计问题.基于Profile最小二乘方法和混合估计方法提出了参数分量随机约束下的Profile混合估计,并研究了其性质.为了克服共线性问题,构造了参数分量的Profile混合岭估计,并给出了估计量的偏和方差.