集合的

That is, formally speaking, a representation or encoding over an alphabet ∑ of a set D is a function f from D to 2^∑* that satisfies the following condition: f(e1) and f(e2) are disjoint nonempty sets 不相交的非空子集 for each pair of distinct elements e1 and e2 in D.

形式地说，对信息对象集合 D 进行基于字母表∑的物化或编码是从 D 到 2^∑*的函数 f，并且函数 f 满足以下条件：对于 D 内任一对不相同的元素 e1 和 e2，f(e1)和 f(e2)是不相交的非空子集。

As pointed out in my doctoral thesis, we are allowed to abstract a limited form of this from our experience with finite collections, since we know that, should we doubt the conclusion derived by means of this, the conclusions can always be checked out by finite sequence of trials! But we have no such experienced assurance of the safety of this procedure with infinite collections!

正如我在博士论文里指出的，我们可以从对有限集合的体验中抽取有限形式的逻辑规则，因为假定我们对运用这些规则推导出来的结论持怀疑态度，那么我们可以用有限数量的实验步骤对这些结论加以检验！

I visited Bonn first in 2005. I could still bring back vivid reminiscence of strolling down the banks of Rhine with my friends from NUS, relishing the vanilla ice-cream, visiting the Beethovenhaus (well, we did not have time to go in so we kinda window-visited it), and rally at the Markt in front of the Rathaus at the end of the trip. And now I will trot along the footmarks of the past and venture into unfathomed territories in this little town of utter pulchritude.

这次在波恩是故地重游，4年前来欧洲背包游，期间流窜到德国，与国大交换生旅行团队纠集并一起游历了包括波恩的几座城市，当年与几位同学一起在这里漫步莱茵河畔、吃冰激凌、看贝多芬房子、最后在Rathaus前的Markt集合的情景依旧历历在目，而今我将踏着昔日的足迹伴着莱茵河清澈的浅韵再次游历这座美丽城市。

And (2) we should assign to the dispersed units clearly defined tasks, fields of operation, time limits for actions, places for reassembly and ways and means of liaison.

给各分散部队以明确的任务、行动的地区、行动的时期、集合的地点、联络的方法等。

On global optimal algorithms, a heuristic 0-1 Integer Liner Programming algorithm is achieved, which combines heuristic enumeration method and revised simplex method. Simulation experiments show that the degree and optimization efficiency in our algorithm is obviously improved compared with the MATLAB 7 bintprog function that is a 0-1 integer programming algorithm. Moreover our algorithm isn\'t relevant to the scale changes of Web services composition and candidate service sets, thus it is applicable for the scenes that the scales of Web services composition changed dynamically. But for Web services composition with service alliance, the algorithm is unable because the non-linear global optimal model of the fitness function and QoS constraints can\'t be expressed in linear mode.

在全局优化算法研究上，基于启发式0-1整线性规划算法结合了修正单纯形法和启发式枚举法，仿真实验表明该算法与MATLAB 7的0-1整数规划方法比较，在优化程度及优化效率上得到了显著改进，并且对服务组合和候选服务集合的规模变化没有明显的相关性，因而该算法可用于服务组合规模动态变化的场景，但该算法不能应用于存在服务联盟的非线性全局优化模型。

This kind of problems is first changed into the model of perceptrons in neural theory, Under the assumption of a finite set of social states. a sufficient and necessary condition for single-valued choice functions to be sum-fuzzy implementable is obtained: a geometric characterization is also given: an efficient algorithm for the sumfuzzy implementation of single-valued choice func...

本文在有限社会状态集合的情形，给出了单值选择函数是和型Fuzzy可实现的一个充要条件；并给出了相关几何描述结论；借助于感知器的学习算法规则给出了单值选择函数的和型Fuzzy实现的有效算法；最后还给出了一个具体例子。

It first partitions the complex solid body into fine regular cells, which provides an intermediate structure for the grain filling and makes the locating of grains much easy. Then, an iterative adjustment process is performed to remove the overlaps between adjacently located grains based on their enclosing boxes.

首先以规则化基网格来剖分待填的实体，提供了一个中间层次，简化随机颗粒定位的复杂性；然后在生成满足统计特征的颗粒集合的基础上，提出先快速预填充，再基于包围盒进行颗粒交叠区域小步长迭代调整的改进技术。

Sometimes, as in this recipe, you may choose some simple task, such as concatenating to the empty string, as a stand-in for a much richer set of properties (such as all the various operations and methods available on string objects).

有时候，象在这个配方里一样，你可以选择一些简单的任务，例如连接到空的string，作为一个更丰富的属性集合的替代（诸如所有的变量操作和方法在string对象上都可利用

Enhanced insulation would make this thing quieter than a small fan humming, not the beast that sloshes water around in our kitchen, forcing us to crank the volume on our televison sets.

改进的绝缘材料比哼唱着一台小的迷，在我们的厨房里搅动水不是的野兽将使这件事安静，迫使我们加速在我们的televison集合的容量。

E. Construction of optional transhipment station's set provides a practical interface for man_mechine interaction in model computation, and an effective method to prevent some absurd cases, such as: uptrains trasship in down yard, or down trains tranship in up yard.

e。可选中转站集合的设立，为模型计算过程中的人机交互提供了一个接口，也为避免上行车流选择下行编组线、或下行车流选择上行编组线进行改编中转的不合理的情形，提供了一行之有效的解决办法。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷