查询词典 countable infinite set

For an abitrary set X, appropriate order relations on WCL (the set of all weak closure operators), WIN (the set of all weak interior operators), WOU (the set of all weak exterior operators), WB (the set of all weak boundary operators), WD (the set of all weak derived operators), WD*(the set of all weak difference derived operators), WR (the set of all weak remote neighborhood system operators) and WN (the set of all weak neighborhood system operators) can be defined respectively, which make WCL, WIN, WOU, WB, WD, WD*, WR and WN to be complete lattices that are ismorphic to CS(X,CS is the set of all closure systems on X.

证明了可以在WCL(X上的弱闭包算子的全体)、 WIN(X上的弱内部算子的全体)、 WOU (X上的弱外部算子的全体)、 WB (X上的弱边界算子的全体)、WD、 WD*(X上的弱差导算子的全体)、 WR(X上的弱远域系算子的全体)和WN(X上的弱邻域系算子的全体)上定义适当的序关系，使它们成为与CS(X，〖JX-*5[JX*5]同构的完备格其中CS(X是给定集合X上的闭包系统的全体。

In chapter three, we prove that there exist solutions to the Ky Fan variation inequality, as the set-valued mappings are defined on spheres in infinite dimensional Banach spaces or odd dimensional Euclidean spaces, following from these theorems, we obtain some fixed point theorems for set-valued mappings defined on a sphere. When G is an approximate compact convex subset of E, or G is a almost quasi-convex set-valued mapping, we prove that there exist solutions to and type generalized Ky Fan variation inequality, following these theorems, we prove several best approximation theorems and coincidence theorems involving two set-valued mappings and two different spaces. In chapter four, we first present a new Simplicial algorithm for computing the Leray - Schauder fixed points, the algorithm can solve the set-valued nonlinear complementarily problem. We give a condition to guarantee the computation proceeding in a bounded region. We present integer-labeling algorithms for computing fixed points of some set-valued mappings, the best approximation points and solutions to a kind of set-valued variation inequalities.

第四章给出了计算定义在非凸集上的非自映射的Leray-Schauder不动点的算法，而现有的不动点算法都是计算凸集的上半连续集值自映射的不动点；给出了保证计算有界的一个充分条件，我们的条件大大弱于Mdrrill条件，我们的算法也可用来计算Eaves不动点；给出了集值非线性互补问题存在解的一个充分条件，此时可利用Leray-Schauder不动点算法来求解；向量标号算法以往是计算集值映射不动点的唯一有效算法，我们给出用整数标号算法计算一类集值映射的Kakutani 不动点的算法；定义在紧凸集上的连续映射不一定有不动点，但一定有最近点，最近点是不动点概念的推广，我们给出了计算最近点的算法；集值映射变分不等式尚无有效的求解算法，我们给出求解一类集值映射变分不等式的算法。

And, like natural numbers , integers is a countable infinite set.

和自然数一样，整数也是一个可数的无限集合。

And, like natural numbers , integers are a countable infinite set.

和自然数一样，整数也是一个可数的无限集合。

Are countable sets:Λ-Γ,〓-Γ are either empty or countably infinite, where Γ denotes the set of γ-limit points of f; tree map's depth of attracting center is finite and the attracting center is Γ provded all the branching points are periodic points. In chapter Ⅲ. we discuss certain relationship between isolated chain recurrent point and eventually periodic point of some continua.

主要利用树的特殊偏序关系证明了：不在周期点集闭包中的ω极限点都有无限轨迹；Ω-〓，Ω-Γ为可数集，Λ-Γ，〓-Γ或为空集或可数无限，其中Γ为f的γ极限点集；当分支点都是周期点时，连续树映射的吸引中心深度有限，且吸引中心就是Γ。

By introducing the two dimensional homogeneous coordinates of an infinite point on Euclidian plane,the point coordinates and linear coordinates of an infinite point in straight lines,some theorems and conclusions referred to infinite points are applied in the classifications of structures in this paper.

引入了欧氏平面上无限远点的二维齐次坐标和直线上无限远点的点坐标及线坐标，引用了与无限远点有关的一些定理及结论于结构的分类中。从而给出了可变体系中的常变与瞬变在结构形式上的区别，完善了杆系平面结构几何组成规则的内容

A method for integrating infinite integrals that occur in solving the fields of source coil and equivalent coils is presented. Subtraction of asymptotic terms is proposed to speed up the truncation process of an infinite integration interval, which greatly improves the infinite integrals.

给出了一种简单有效的数值积分方法计算激励线圈和等效线圈解析解中遇到的无穷积分，提出了一种加速无穷积分收敛的有效方法，显著提高了磁场及涡流场的计算效率。

A method of integrating infinite integrals which occur in axisymmetrical field in eddy current testing is presented. Subtraction of asymptotic terms is proposed to speed up the truncation process of an infinite integration interval, which greatly improves the integration of infinite integrals.

本文对涡流检测中解析求解轴对称场时遇到的无穷积分给出一种简单有效的数值积分方法，提出一种改进积分收敛性的方法，加速了无穷积分的截断，显著提高了轴对称场的计算效率。

First, in the physics level, emptiness of Buddhism means dependently rising's infinite possibilities, and science also finally point to "infinite great" and "infinite small" with the quest of macro scale and microcosmic, both of common targets is contact with whole, organic, and subjective-objective unity the purpose is to find out the truth of universe.

一、 从物理学层面看，佛教之"空"本指"因缘和合"、"真空妙有"的"无限可能性"，而科学对宏观本体与微观本体的探索也最终指向"无限大"与"无限小"，两者共同的目标是在整体的、有机的、主客观交融的普遍联系中探索与揭示宇宙存在的实相与本来面目。

To suit it for this usage, the ideal operational amplifier would have infinite input impedance, zero output impedance, infinite gain and an open-loop 3 dB point at infinite frequency rolling off at 6dB per octave.

为了得到这样的特性，理想 OP 应该有无限大的输入阻抗，0 输出内阻抗，无限大的增益，无限大的开环增益带宽(3dB 带宽)，以及其 6dB/每 2 倍频程的频率滚降。

I was just taking her hand, to help her out of a car, and I knew it.

我只是握着她的手，扶她下车，但我知道这一切。

China and South Korea have excoriated Japan over its approval of new school books which they say whitewash the atrocities committed during Japanese occupation, and anti-Japanese protests have been held in Chinese cities. The lingering bitterness over Japan's past imperialism still threatens to mar relations between the big East Asian powers

中国和韩国强烈谴责日本通过新的中学历史教科书，他们认为这一教科书掩盖了日本在其占领期间所犯下的残酷暴行，反日抗议活动在中国数座城市发生，历史上日本帝国主义制造的痛楚无法被忘却，这有可能破坏东亚强国间的关系。