等价的

We use Hodges-Lehmann statistic to do significance test for those factors. The multiplication model is applied in the quantitative analysis and weighted least squares method is introduced to solve the multiplication model. Although the matrix of coefficients is not of full rank and the solutions of the multiplication model are not unique, we prove that all those solutions are equivalent in some sense.

本文用Hodges-Lehmann统计量对风险因子作显著性检验，将乘法模型用于数据修匀和风险因子的定量分析中，并提出了用加权最小二乘法求解风险因子的风险度量，在系数矩阵不满秩、解不唯一的情况下证明了所有解在某种意义下的等价性。

Moreover, the equivalance between regularity of a ring and a full matrix ring is proved with a new method.

当 R是一个有单位元的环时，本文引进并刻划了Mm× n的正则性并由此重新证明了环 R与全矩阵环 Mn正则的等价性，这种方法比原有的证明方法简

As for the multiple objective decision making and analysis problem under risk is concerned, a practical decision analysis principle called Aspiration level principle is proposed, the concept system for solutions and the model system for determinitive equivalence are developed based on the classifications of decision objectives and constraints, which lay a necessary theoretical fundation of study on the multiple objective decision making and analysis problem under risk.

本文就风险型多目标决策分析问题，提出了一种适用的决策分析原则──希望水平原则，并基于决策目标和约束的分类，给出了解的概念体系及确定性等价模型体系，为进一步研究风险型多目标决策问题提供了必要的理论基础。

Equivalent linear method based on multiple reflection theory is used in the analysis, the shear wave velocity is calculated from empirical equation got from ground investigation, the dynamic characteristic of soi is taken from the laboratory test and is revised to simulate the liquefaction at the surface.

计算方法采用建立于重复反射理论上的等价线形化法，根据地层探查资料建立了推求地层剪切波速的经验公式，上体的动力作有下变形模量随应力水平的变化规律采用试验曲线。

Thirdly,we define a equivalence relation Rin the topology space X by the fibrewise function f ,and then we get the fibrewise quotient space X / R,we call it the fibrewise decomposition space of X .And last we discuss the relation between f and the natural mapping.

其三是，通过一个纤维映射f ： X→Y，在B上的纤维拓扑空间X中定义了一个等价关系R，得到X的纤维商空间X / R，称其为X的分解空间，最后也讨论了f与自然投射的关系。

On the other hand, it is exemplified in the present paper that the principle of material frame – indifference with the admissible equivalent dynamic processes of a body by Truesdell and Noll (1965) [14] is more convenient than the form-invariance of constitutive functionals by Svendsen and Bertram (1999) [13] and Liu (2004)[4], especially for the rate-form constitutive equations.

通过例子说明了Truesdell和Noll 用等价动力过程，关于物质标架无关性原理的陈述，比Svendsen 和Bertram及Liu的本构关系在参考标架变换下的形式不变性更合理且方便，尤其是对微分方程形式的本构关系更是如此。

The necessary and sufficient condition for that the problem P〓 is nonsingular is derived.

利用原问题与P〓的等价性，给出了原系统二次指标最优控制器的设计，保证了闭环对给定的初值有唯一的光滑轨线且零解渐近稳定。

In this paper, we will study the definination of lines of curvature and the correlative conception, for example, normal curvature, principal direction and principal curvature and so on, the connection of lines of curvature and correlative conception, especially probe into the solution with the equation of lines of curvature and the equivalence with its determinant theorem.

本课题主要研究曲率线的定义及其相关概念如法曲率、主方向、主曲率等，曲率线与相关概念的关系，重点探讨了曲率线方程的求解及曲率线判定的等价定理。

The benefit of this analysis is, a class hierarchy obtained is guaranteed to be behaviourally equivalent to the original hierarchy of the application program, and in new hierarchy the object only contains the members really required but no redundancies.

这样做的好处是：所得到的类体系不仅等价于应用程序最初的类体系，而且在新体系中对象只包含它真正需要的成员，没有冗余成员。

Some other conditions which the implicative operator of a Implication Algebra should satisfied in a logic system are given. The relations between MV-Algebra and Distributive Implication Algebra, Implication Algebra with condition are gained.

对于偏序集上蕴涵代数中的蕴涵算子引入了一些逻辑条件，得到了偏序集上具有不同条件的蕴涵代数与MV-代数之间的关系，给出了偏序集上蕴涵代数与MV代数之间的几个等价定理。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。