等价关系

And they found an intrinsic inyariant of any algebraic curve by means of spline approach. So, We can apply some methods and conclusions of one hand to the other hand.

由此，我们可以看出，通过此等价关系，我们可以把一个方面的某些方法与结论应用到另一个方面。

In presented method, the correlated variables are transformed into uncorrelated variables equivalently, and the performance functions in the correlated variables space are transformed into those in the equivalent uncorrelated variables space, in which the reliability sensitivity of the system failure probability with respect to the distribution parameters of the uncorrelated variables can be solved by the moment method for the uncorrelated variables. Finally the equivalent relationship between the correlated variables and the uncorrelated variables, the chain rule for derivative are employed to obtain the reliability sensitivity of the system failure probability with respect to the means of the correlated variables.

在所提的方法中，首先将相关变量空间等效转化为不相关变量空间，并将系统多个失效模式的功能函数转化为不相关变量空间的功能函数，进而利用矩方法得到多模式系统失效概率对不相关变量空间基本分布参数的灵敏度，最后利用相关变量空间与不相关变量空间的等价关系及复合函数求导法则，求得多模式系统失效概率对相关变量空间中变量均值的灵敏度。

The characteristic exponent based on a probabilistic dynamical system is calculated, which provides some useful information on unstable periodic orbits of the chaotic economic dynamical system. An effective controlling parameter is chosen by discussing the sign of the characteristic exponent. Furthermore, the control regions of the parameter variable are proposed. Therefore the controllable domain of chaos in the chaotic economic model can be obtained.

提出一种等价关系，计算基于概率的动力系统的特征指数，给出混沌经济动力系统的不稳定周期轨道的有用信息，通过讨论特征指数的符号，选择有效的控制参数，得到相应的控制参数取值范围，从而得到混沌经济模型中的参数变量的混沌控制域。

It also provided the conditions for the existence of large cores of symmetric games. It proved the equivalence relation of convex games and monotonic symmetric games.

本章还给出了对称对策的广义核心存在的条件，证明了凸对策与单调对称对策的等价关系。

As the special characteristic of nonlinearity, several notions are introduced and used in this paper, such as differential manifold, vector field, diffeomorphism, tangent space, topological equivalence. Stable manifold and unstable manifold are also introduced.

针对非线性的特殊性，本文专门介绍了非线性中几个比较特殊的概念，如微分流形、向量场、微分同胚、切空间以及等价关系等，对稳定和不稳定流形也作了介绍。

By the aid of defineding an equivalence relation on the disjoint union of a family of quantales, the direct limit structure in the category of quantale was obtained.

利用在一族Quantale的不交并上定义的等价关系，给出了范畴Quant的定向极限的结构。

Based on the partition of equivalent classes,the resolving of a linear system of equations and the calculation of the dual basis of the standard basis,three methodologies are presented.

以此解释了Rijndael算法S盒代数表达式复杂度低的本质原因，给出其分量函数间等价关系的一种直接证明方法。1 引言插入攻击[1]对代数次数和复杂程度低的分组密码尤其凑效。

It is proved in theory that with the introduction of item constraints, Eclat+ could greatly improve the efficiency and speed of association rule mining, and the Eclat+ is compared with some other related algorithms.

通常这些规则中仅有很小的一部分是用户所关心的，因此泛泛的挖掘既降低了算法的运行速度也使挖掘结果失去了核心。Zaki提出的 Eclat[4]算法利用垂直的数据库结构，并利用基于前缀的等价关系将搜索空间划

We study the Dirac structures on protobialgebroid, give the integrable conditions for maximally isotropic subbundle being Dirac structure for protobialgebroid by the notion of characteristic pair. From the integrable conditions, we found out that Dirac structure has closed relations with twisting of protobialgebroid. Further, the closed relations are explained, the fact that twisting of protobialgebroids is a equivalence relation is verified.

详细研究了proto双代数胚匕的Dirac结构，给出了极大迷向子丛可积的充要条件，发现在这些充要条件中蕴含了proto双代数胚的扭关系，进一步阐明了扭与Dirac结构之间的内在联系，证明了扭在proto双代数胚范围内是等价关系。

A fuzzy indiscernibility relation is changed into the indiscernibility relation by using a λ-cut in the rough approximation of decision classes, and an extension of VPRS method is proposed in which probabilistic rules are obtained from fuzzy decision tables.

为了从模糊近似空间中获取用于概率决策的规则，在决策类的粗糙近似中，通过应用λ-截集，将模糊不可分辨关系转化为等价关系，提出一种可从模糊决策表中获取概率规则的扩展变精度粗糙集方法。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。