变量

In this paper we have found the main component s in a n -dimension random vector X , the so called main compon ents don′t contain linear relation and the others of X can be expressed as the linear combination of the main component s.

本文提供了在多维随机变量中寻找主成分的一种方法，证明了其余分量均可表示为主成分的线性组合，解决了多维随机变量的各个分量之间所存在的线性关系问题。

Infer:with the dynamical system in any state, any result of a measurement of a real dynamical variable is one of its eigenvalues.

如果力学系统处于属于力学变量e属于本征值e'的本征态，则对力学变量e的测量肯定得到结果e'。

In the regression add variables and delete the variables of each step, the regression equation of the series solution of regression coefficients, and calculation of regression coefficients significant test statistic.

在逐步回归添加变量和删除变量的每一个步骤，都要解一系列的回归方程，求回归系数，计算回归系数显著性检验的统计量。

Exception: if the new regressor is perfectly multicollinear with the original regressors, then OLS cannot be implemented.

例外：如果这个新解释变量与原有的解释变量完全共线，那么OLS不能使用。

Has only one nonconstant regressor x, it is called a simple linear regression model, or two-variables regression model, or bivariate linear regression model.

等式y = b0 + b1x + u只有一个非常数回归元。我们称之为简单线性回归模型，两变量回归模型或双变量线性回归模型。

The advantages and limitations of every kind of methods for calculating the failure probability is reviewed. The frist order reliability method, the second order reliability method and many kinds of boundary method have achieved remarkable success and formed nature fields of reliability. However, the precision of these methods decrease as the increase of complexity of problem. The numrical methods are versatile, except numerical intergration is only adaptable to special problems which have small number variables and regular intergral domain. Particularly, the advanced variance reduction techniques own the following character: high precision and a small amount computation. But some questions remain to study in the future because only an initial work about these techniqes is developed.

全面评述了计算失效概率各种方法的优点和局限性，其中经典的解析法包括一次可靠性方法、二次可靠性方法、一阶边界法、Vanmarcke上边界、PENT上边界和Ditlevsen二阶窄边界法，这些方法对于多设计点、变量较多且相关、密度函数不是正态以及极限状态方程较复杂的情况，其计算精度较差；而已有的数值方法却是具有较好的通用性，其中除数值积分法只对变量较少、积分域较规则的特殊问题适用外，各种数值模拟方法均具有较广的适应性，特别是各种改进的方差减小技术，精度高、计算量小，但由于其处在研究的初级阶段，还有许多问题有待于解决。

Since in some instance, the variance of response variable might be changeable along withthe alteration of explanatory variable, in the procedure of model constructing, a fixedeffects model should be considered firstly, then the random effects model or randomcoefficient model when necessary. The best fit model should be chosen by comparing thealterations of between-study variance and residual variance, as well as their relationshipswith covariates.

基于各研究中因变量与自变量间的曲线形状可能存在较大差异，建模时可依次考虑固定效应模型、随机效应模型和带协变量的随机系数模型，并观察研究水平的方差与残差方差的变化，以及与协变量的关系，从而选择最优模型。

The lateral deformation of a retaining wall is a very important variable in excavation engineering.

基坑围护结构墙体的侧向位移是基坑开挖与施工中首要控制的变量，也是基坑施工中的关键变量。

Firstly, based on the force acting on a single-particle, establish a discriminant formula of the sand threshold, and prove that the sand threshold belongs to the cusp catastrophe. Then establish the basic equation of the cusp catastrophe using coordinate transformation and catastrophe theory. Finally, while particle Reynold number and equivalend diameter are the state variables and Shields parameter is the control variables, we can obtain the model of cusp catastrophe of sand threshold, putting those variables into the basic equations of the cusp catastrophe. The model is derived from the mathematics, which has a certain mathematical theory foundation.

首先从单颗沙粒受力分析出发，建立沙床沙粒起动条件判别公式，进而证明了风沙起动属于尖点型突变；然后通过坐标变换和突变理论建立了尖点突变的基本方程；最后本文选择颗粒雷诺数和等效粒径作为控制变量，希尔兹参数作为状态变量，并把它们代入尖点突变的基本方程，经过拓扑变换得到风沙起动的尖点突变模型，并与前人的公式及实验数据进行比较。

Coefficient function I1 ,I2 ,I3 of quadratic carve is the invariant under the right - angled coordinate transform.

二次曲线的系数的函数I1，I2，I3是直角坐标变换下的不变量，而系数函数k只是转轴变换下的不变量。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。