集合

With the idea and the technique of the newly constructed basitheoryology ~ [1] , this article discusses two different concepts of infinite set existing in present set theory: potential infinity and actual infinity.

从新构建的基础理论学的角度，以全新的基础理论学的方法[1]，讨论同时存在于现有集合论中两种性质上截然不同的"无穷集合"概念：潜无穷式的与实无穷式的无穷集合。

Assume a Lie algebra g has a form B which has all the useful properties of Killingform:bilinearity nondegeneracy,symmetry and invariance.Note that for such a Liealgebra the adjoint representation is equivalent to the coadjoint representation.We callit a symmetric self-dual Lie algebra and the form B an invariant scalar product.

在第一部分的最后一节，我们引进了拟Heisenberg代数的概念，证明了这些李代数均为具有非极大秩的CN李代数，进一步我们还证明了这些CN李代数构成的集合与极大秩幂零李代数构成的集合之间存在着1-1对应关系。

Firstly, we analyze the deficiencies ofexisting ones, extend domains of fuzzy logical operators from the cap product withtwo sets to them with arbitrary (finite, enumerable, or non-enumerable) number ofsets to form two general mappings so as to conform them to the fuzzy conjunctionand infimum, and to fuzzy disjunction and supremum, respectively, and fuzzify theset inclusion of fuzzy sets. Similar to the classical adjunction, the concept of fuzzyadjunction is introduced.

首先分析了原有"模糊形态学"框架的缺陷，进而将模糊合取和模糊析取算子的定义域从两个集合的笛卡儿乘积推广到任意多个集合的笛卡儿乘积，形成两个一般的映射，使得模糊合取与下确界、模糊析取与上确界保持一致，以此将模糊集的包含关系一般化。

To ensure the continuity of the states of the SLS systems,for a given switching sequence an admissible control set is introduced.

对给定的切换序列定义了容许控制集合，以保证在该容许控制集合中的任意控制律的作用下，相应切换系统的状态都是连续的。

Preliminaries: An introduction to the basic ingredients of the algebraic system, such as sets and mappings of these sets.

预备知识：介绍代数系的基本要素，即集合，集合的映照。

We have proposed the switching adaptive control law for the systems and designed the Lyapunov function in this thesis. It is proved that the proposed switching adaptive control law guarantees the solutions of the nonlinear systems boundedness and convergence of the tracking error to a residual set based on the Lyapunovs stability theory. The residual set can be made arbitrarily small by choosing a certain design parameters.

文中设计出了这类系统的切换自适应控制律，并构造出相应的Lyapunov函数，基于Lyapunov稳定性理论证明了系统在所设计的控制律作用下，闭环信号都有界并且跟踪误差收敛到一个集合，通过选择适当的参数可使这个集合任意小。

In this paper, I have constructed models for local population and metapopulation dynamics. Then by mathematical analysis and numerical simulation, I focus my studies on the relation between the Allee-like effects at the metapopulation level and the Allee effects at the local population level and their impacts on the stability of ecological systems.

在本文中，通过建立局域种群和集合种群的理论模型，把局域种群动态和集合种群动态结合起来，用数学分析和数值模拟分析的方法研究了集合种群水平上的似Allee效应与局域种群的Allee效应之间的关系以及它们对生态学系统稳定性的影响，并对含Allee效应的物种的自然保护提供了理论依据。

In this set system, the set element named quorum is a set of points, and every two quorums intersect.

在这种集合系统中；所有集合元素都是节点的集合，任何两个quorum都有交集。

Experimental results show that the 3D SPEZBC algorithm has the same rate-distortion performances of three-dimensional embedded zero block coding (3D EZBC) algorithm, obviously outperforms three-dimensional set partitioned embedded block (3D SPECK) algorithm, three-dimensional set partitioning in hierarchical trees(3D SPIHT) algorithm and (AT-3D SPIHT) algorithm, and is slightly better than JPEG2000 multi-component (JPEG2000-MC) algorithm at different bit rate in the compression performances.

实验结果表明，3D SPEZBC算法具有与三维嵌入式零块编码(3D EZBC)算法相同的压缩编码性能，在各比特率下编码性能均明显优于三维集合分裂嵌入式块编码(3D SPECK)、三维等级树集合分裂(3D SPIHT)和非对称三维等级树集合分裂(AT-3D SPIHT)算法，并且略好于多分量JPEG2000编码(JPEG2000-MC)算法。

In order to detect the integrity of migrating instance in migrating workflows system,an immune entity composed of self-set,detector-set,r-continuous bits match detection function and vaccine gene-set is defined based on artificial immunology principle.

针对迁移工作流系统中迁移实例的完整性检测，基于人工免疫原理，构造一个由自我集合、检测器集合、r-连续位匹配函数和疫苗基因集合组成的免疫体。

On closer examination, though, this is not a vote for multilateralism but just the opposite.

仔细审视后我们发现，这并非是对多边主义投出的赞成票，而是恰好相反。

Uncovering their weak spots, so I can defeat them.

揭露出他们的弱点，这样我就可以打败他们了。