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In the section, the definitions and main properties of the operator have been discussed systematically, the operational rules of one dimensional PGOPO have been strictly established based on the theory of convergence in the mean square, error and convergence analysis of approximation by PGOPO has been discussed.

系统地论述了分段广义正交多项式算子的定义、性质，并为一维PGOPO算子严格地建立一套在均方收敛意义下的代数运算规则，给出了分段广义正交多项式算子作用下的误差及收敛性分析结果。

By the use of the relations between fuzzy points and fuzzy sets, some new definitions of a convex fuzzy subset are introduced.

其次，运用模糊点与模糊集之间的邻属关系，引入了关于凸模糊子集的几种新的定义。

Firstly, we give out the definitions of L-graph and partial L-subgraph, and we ob-tain some properties of partial L-subgraphs. Secondly, continuous mapping is intro-duced respectively between L-graphs and between L-cotowers, and the relationshipbetween the category L-FG of L-graphs and the category FG_L~C of L-cotowers isstudied. At last, we study the finite topological property of the category L-FG, andgive out the concrete constructions of finite product and finite coproduct.

本章首先给出了L-图和部分L-子图的概念，得到了部分L-子图的若干性质；其次，给出了L-余塔的概念，在L-图之间和L-余塔之间分别引入连续映射，研究了L-图范畴L-FG和L-余塔范畴FG_L~G之间的联系；最后，研究了L-图范畴L-FG的有限拓扑性质，给出了L-图范畴L-FG的有限积和有限余积的具体构造。

The definitions of generalized directional derivative and generalized gradient of Lipschitz functions defined on Riemannian manifold are presented. Some properties of the directional derivative and gradient are proved by using tangent and cotangent mapping. The minimization necessary condition of nonsmooth Lipschitz functions is given. Moreover, Fritz John necessary optimality condition in mathematical programming is provided on Riemannian manifold.

在黎曼流形上给出了Lipschitz函数的广义方向导数和广义梯度的概念，利用黎曼流形局部上与欧氏空间开集微分同胚的性质以及切映射和余切映射导出了广义梯度的性质和运算法则，证明了定义在黎曼流形上的函数取得极小值的必要条件是广义梯度包含零元素，并利用这些性质给出了黎曼流形上数学规划问题的Fritz John型最优性条件。

Some definitions of pop are very broad and inclusive, covering all contemporary popular forms, including rock, country, reggae, rap, and so on.

一些定义是非常广泛的流行和包容，覆盖所有的现代流行的形式，包括摇滚、国家、雷、说唱，等等。

Based on the analysis of landscape definitions, the principles of landscape classification were expounded in this article. The authors pointed out that different landscape have different characteristics and research contents, and the values of landscape's uniqueness, diversity, function, coziness and aesthetics were discussed.

在分析景观定义的基础上，概述了景观分类的生态学原则，提出了自然、经营和人工等不同景观类型的特性和研究重点，并对景观的独特性、多样性、功效性、宜人性及美学价值的评价进行了探讨。

In the first section, we introduce some backgrounds and recall the definitions of weak action. crossed product and twisted H-module. At the same time, we give Lemmas 1.3. 1.5 and 1.6 being used in the following sections.

文中在给出了弱作用、crossed积、twisted H-模等基本概念的同时，又给出了在后续中需要使用的一些引理，即引理1.3、引理1.5、引理1.6。

I'll explain some definitions related to Spyware Crusade.

我会解释有关间谍圣战的定义。

I'll explain some definitions related to Crusader Antivirus.

我要解释一些有关的十字军定义防毒。

The main works of this paper are as follows:(1) The various methods for determining the cryolite ratio of electrolyte were summarized and compared. The phase constituents of aluminium electrolyte system were studied, the various cryolite ratio definitions for this reason were discussed.

本文研究和测定了工业铝生产中与电解质相关的几项重要的物理化学参数，包括铝电解质分子比的测定研究，氧化铝溶解性能的研究及测定，氧化铝浓度的测定及工业铝电解槽氧化铝浓度—槽电阻曲线的绘制，铝在电解质中溶解度的研究及测定。

We stopped by the old fashion ice cream parlor Manhattan Beach Creamery for some refreshment. The "No Shoes, No Shirt, No Problem" sign on the wall epitomizes the beach lifestyle.

我们去商店区的一家老式冰淇淋店坐坐，墙上挂著「没鞋，没上衣，没问题」的牌子完全捕捉了海滩生活的随性及风格。

"If therefore", argues Bellarmine we can offer our prayers and our satisfactions in behalf of those detained in purgatory, because we are members of the great body of Christ, why may not the Vicar of Christ apply to the same souls the superabundant satisfaction of Christ and his saints--of which he is the dispenser?

" "因此，如果"，认为贝拉明（德indulgentiis ，十四）"我们可以提供我们的祈祷和我们满意的代表那些被拘留在炼狱，因为我们是成员的伟大基督的奥体，为什麼可能不是牧师基督适用於同样的灵魂满意的过剩是耶稣和他的圣人-他是在配药？