Hilbert Space of Probability Density Functions Based on Aitchison Geometry

The set of probability functions is a convex subset of L1 and it does not have a linear space structure when using ordinary sum and multiplication by real constants. Moreover, difficulties arise when dealing with distances between densities. The crucial point is that usual distances are not invariant under relevant transformations of densities. To overcome these limitations, Aitchison＇s ideas on compositional data analysis are used, generalizing perturbation and power transformation, as well as the Aitchison inner product, to operations on probability density functions with support on a finite interval. With these operations at hand, it is shown that the set of bounded probability density functions on finite intervals is a pre-Hilbert space. A Hilbert space of densities, whose logarithm is square-integrable, is obtained as the natural completion of the pre-Hilbert space.     

全球化知识经济潮流与两岸未来教育发展趋势（Ⅱ）——以指标评价为基础的检证观点

3．3评价结果 3．3．1多元尺度法 (1)评价对象 1)检定值 依据多元尺度法分析结果，采三维构面进行17个评价对象的空间配置，压力系数可达0．03769．R^2为0．98917，介于“非常好”与“好”之间；若采二维构面进行空间配置，则压力系数值为0．14148，介于“还可以”与“不好”之间(参表2)，R^2为0．89671．     

中部地区教育投资效应实证分析

利用面板数据模型着重分析中部地区之间教育投资效应差异及其原因.得出结论:由于对教育的投资力度不同,导致了中部地区发展的不平衡.     

探究n阶常系数线性非齐次方程L[y]=e^ax的公式解

本文探究了n阶常系数线性非齐次方程L[y]=e^ax的公式解，得到了几个重要的公式，进而应用在求解L[y]=e^ax类型的方程上，使此类问题的求解更简单明了。     

用力敏传感器测量乙醇水溶液的表面张力系数与浓度的关系

用硅压阻式力敏传感器测量了纯水、乙醇的表面张力系数，并测量了不同浓度的乙醇水溶液的表面张力系数，得到了乙醇水溶液的表面张力系数随浓度的变化曲线．     

Blind equalization of underwater acoustic channelusing a combined constant modulus algorithm

A kind of Combined Constant Modulus Algorithm (CCMA) is presented to compensate the defects of the Constant Modulus Algorithm (CMA) and the Sign Error CMA (SECMA). And CCMA is applied to the equalization of the underwater acoustic channel (UWAC). Based on the decision of the equalizer‘s output, its iteration process switches between CMA and SECMA automatically. It is more robust than SECMA, and more computationally efficient than CMA. Therefore, it is very suitable for the recovery of the underwater data transmission. The performance of CCMA is proven by computer simulation for the equalization of the UWAC.     

用待定系数法求均匀刚体的转动惯量

研究了转动惯量的计算 ,利用“待定系数法” ,不用积分求出一些均匀刚体的转动惯量。     

南淝河水质S-P模型参数K1、K2的估值

对南淝河河流水质S-P模型中碳化BOD衰减系数K1和大气复氧系数K2分段进行了估值.根据实验测定数据,用最小二乘法、图解法和两点法等3种方法对K1进行了估值,应用公式估算法对K2进行了估值,并对估值的结果与南淝河的有机污染状况进行了对比和分析,从而为模型提供准确的参数值,也为南淝河的水污染控制和水质规划提供有益的借鉴.     

非设计工况下叶轮进口附近的流动及其控制

对叶轮进口附近流动在偏离设计工况下的回流和汽蚀(空化)两大特性进行了系统的描述,阐述了它们的诱发机理及其对泵性能的影响.根据回流的诱发机理对诱导轮的作用进行了全面的分析,提出了控制回流发生的有效方法,从叶片进口流动这一角度完善了离心泵叶片设计理论.