等价

A complete series of the piecewise algebraic curve consists of all effective ordinary cycles in an equivalence class {A} and all effective singular cycles which are equivalent specifically to cycle A.

分片代数曲线的完全列是由所有属于同一等价类的有效正常循环以及所有与它特等价的有效奇异循环构成。

Finaly, we introduce the Bernstein-Kantorovich quasi interpolant and study the approximation equivalent theorem with pointwise modulus (o≤λ≤1 ) in space L[0,1] and approximation equivalent theorem with Ditzian-Totik modulusin space L_[0,1](1 ≤p ≤ω).

最后，引入Bernstein-Kantorovich拟中插式，利用点态光滑模ω_~(2r)(0≤λ≤1)讨论了其在L_∞[0，1]空间的逼近等价定理和其在L_p[0，1](1≤p≤∞)空间关于模ω_ψ~(2r)的逼近等价定理。

Secondly, using the relation between the weighted modified K-functional, the weighted modulus of smoothness ,the weighted main-part modulus of smoothness . we get the pointwise direct and inverse approximation theorem with Jacobi weight for Szdsz-Kantorovich operator. Thus some results on w = 0w(x denotes the weight function, Ditzian-Totik modulus and classic modulus are extend.

其次，引入一种改变的带权K-泛函，利用带权光滑模和带权主部光滑的关系及带权光滑模与改变带权K-泛函的等价性，关于Szász-Kantorovich算子，讨论了一阶矩不为零的算子的点态带Jacobi权逼近正定理及等价定理，推广了已有的权为零及Ditzian-Totik光滑模和古典光滑模的结果。

An independent axiomatic system that describes the upper approximation of Pawlak rough sets is formulated by three simple formulas.

获得的结果深刻地揭示了经典等价关系与模糊等价关系的本质区别，进一步深化了Pawlak粗集理论。

Among those; studies, Liu and Bek have obtained many important results for the theory and applications of Banach spaces and their geometry on complex number,(see [3],[41])Here, we have investigated the TP modulus of convexity and TP modulus of smoothness, on the one hand, we have defined a class of new spaces called uniformly TP convex ,on the other hand, we have extended martingale inequalities and the martingale spaces.This article is divided into four parts, in the first part, we define the TP modulus of convexity and TP modulus of smoothness of Banach space, and prove that the space which is characterized by uniform convexity is same as the space which is characterized by TP uniform convexity. Then we give TP q-uniformly convex and TP p-uniformly smoothable characterization of the Banach space. At the same time, we prove the famous renormed theorem.

本文分为四部分，第一部分在Banach空间上定义了一个新的TP凸性模和TP光滑模并证明了在Banach空间上它分别和一致凸性和一致光滑性刻划的空间是同构的，即如果Banach空间X是一致TP凸的充分必要条件是存在一个等价范数，使得在此范数下，它是一致凸的；Banach空间X是一致TP光滑的充分必要条件是存在一个等价范数，使得在此范数下，它是一致光滑的，我们还分别得出了判定一致TP凸和一致TP光滑的一些充分必要条件，同时还证明了箸名的重赋范定理。

Afterward Waldhausen ([7]) showed that this topological hypothesis was true. Besides, Stallings ([11]) gave another conjecture that was equivalent to Poincare"s Conjecture. Thus we know both conjectures made respec- tively by Traub and Stallings are equivalent to Poincare"s Conjecture.

另外Stallings([11])又提出了另一个代数的猜想并同时证明也证明了这个猜想与庞加莱猜想是等价的，由此可知Traub所给的猜想与Stallings的猜想都与庞加莱猜想是等价的，从而这两个代数的猜想也是等价的。

In order to make problems simple relative map germs which map proper subspace R~s of R~m to proper subspace R~t of R~n are considered in the paper.

本文将相对映射芽的基本理论与经典奇点理论相结合，把A等价的判断条件应用到相对映射芽环中，推广了原有结论，得出了在两个C~r相对映射芽κ等价条件下判断其A等价的方法。

This paper present the meaning of semantic equivalence and Herbrand equivalence based upon denotational sematics with concrete programming language.Herbrand equivalence is weaker than Semantic equivalence, it has much wider utility.

从指称语义出发，结合具体语言，用形式化的方法讨论了语义等价和H-等价。H-等价的判定条件相对来说更容易得到满足，具有更广泛的可用性。

As a result, when in , subset of MA, obtained by imposing constraints on MA, AL is intensional because =L is equivalent with ≡.

在考虑了复制操作和限制操作的情况下，提出了逻辑等价的协归纳操作描述，并利用协归纳关系与进程结构同余关系进行比较，证明了若对MA加上约束条件得到子集MAsynIF，此时逻辑等价与结构同余关系是等价的，即AL在MAsynIF中是内涵的。

In the first part of the second chapter,we obtain a equivalent condition of the convolution closure of the extended long-tailed distributions,generalize and improve the corresponding results of Pakes(2004),and then receive a kind of equivalent conditions of convolution-equivalence distributions.In the last part of the second chapter,we prove these results.

本文第二章的前一部分得到了有关广义长尾分布的卷积封闭性的等价条件，推广和改进了Pakes(2004)的一个相应结果，进而得到一类卷积等价分布的等价条件；第二章的后一部分证明了这些结果。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。