基于相对误差意义下的最小二乘法

最小二乘法一直广泛应用于科学技术各领域 ,但仅适用于等精度数据———因其评价依据是大致相同的绝对误差。而大多数科研及观测数据往往按被观测量的相对误差进行评价 ,即被观测量愈大 ,允许及实际测量误差也愈大。从这个意义上讲 ,若以相对拟合误差的平方和最小为条件 ,建立一套新的最小二乘法 ,那么当然可以期望新方法将具更广泛的用途和实际的意义。本文给出了新最小二乘法的实用结果     

First and Second Order Optimality Conditions Using Approximations for Nonsmooth Vector Optimization in Banach Spaces

We use the first and second order approximations of mappings to establish both necessary and sufficient optimality conditions for unconstrained and constrained nonsmooth vector optimization problems. Ideal solutions, efficient solutions, and weakly efficient solutions are considered. The data of the problems need not even be continuous. Some often imposed compactness assumptions are also relaxed. Examples are provided to compare our results and some known recent results.This work was partially supported by the National Basic Research Program in Natural Sciences of Vietnam.     

Relative Compactness for Capacities, Measures, Upper Semicontinuous Functions and Closed Sets

We prove an Ascoli theorem for capacities. This theorem which characterizes relatively compact sets of capacities is widely applicable and many Ascoli theorems for particular classes of capacities can immediately be deduced as corollaries. Indeed it is usually necessary only to demonstrate that these classes are closed and then to simplify the characterization when possible. In particular, we show that the proof of the classical Prohorov theorem can be naturally factored into the shorter proof of the Ascoli theorem for capacities and into the somewhat longer proof that the class of probability measures is closed in the class of capacities. We also deduce new and known Ascoli theorems for sup measures, upper semi-continuous functions, the Vietoris hyperspace topology, and various classes of measures.     

Hermite and Smith normal form algorithms over Dedekind domains

We show how the usual algorithms valid over Euclidean domains, such as the Hermite Normal Form, the modular Hermite Normal Form and the Smith Normal Form can be extended to Dedekind rings. In a sequel to this paper, we will explain the use of these algorithms for computing in relative extensions of number fields.

     

相对孔径与曝光量

本文对照相物镜相对孔径的定义、光圈数、像面照度、像面曝光量以及它们之间的关系进行了讨论。     

相关扭曲Hopf模的基本同构定理与相关Yetter-Drinfel'd模

扭曲的方法在构造新的代数结构与余代数结构中起了重要的作用.本文首先把扭曲的方法运用到模与余模的构造中,得到扭曲模和扭曲余模;其次在更加一般的情形下给出相关扭曲Hopf模的基本同构定理;最后考虑在HopfYD模中如何使扭曲模构成相关Yetter-Drinfel'd模和相关Hopf模.     

基于改进DEA模型的科技投入产出有效性分析

合理地评价各地区的科技投入产出,对于资源的合理利用,提高资金的使用效率具有十分重要的现实意义.采用一种改进的DEA模型(简称M DEA),对2000—2002年间我国各地区的科技投入产出相对效率进行了充分评价和排序.并将三年的数据放在一起组成一个新的参考集,用同样的M DEA模型进行评估,得出各地区三年科技投入产出相对效率的变化情况.     

结合分析的原理和应用

沈浩，柯惠新．结合分析的原理和应用．数理统计与管理，１９９８，１７（４），３９～４５．结合分析用来分析消费者对产品／服务的偏好。本文通过对采用部分因子设计估计主效应的全轮廓法以及用一般最小二乘法（ＯＬＳ）回归计算属性水平的效用分析，介绍了这种结合分析法的概念、步骤和应用     

干湿球湿度计相对湿度的计算

本文介绍了干湿球温度计的测温原理及计算相对湿度的公式．     

荧光粉相对亮度测量的色修正

由于很难将光接收器的相对光谱灵敏度S(λ)调到与CIE标准观察者V(λ)完全一致,不同荧光份又具有不同的相对光谱功率分布,因此测量荧光粉的相对亮度与测量其它光度量一样,必须进行色修正。本工作针对实际使用的光接收器和相对光谱功率分布不同的几种荧光粉的相对亮度计算了色修正系数。