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The course contains four sections as follows: mathematical logic (including basic concepts of propositional logic and predicate logic, propositional calculuses and inference theories), set theory (including set algebras, relations, functions and cardinal numbers), algebraic structure (including algebraic systems, semigroups and groups, rings and fields, lattices and Boolean algebras), graph theory (including basic concepts of graph, Euler graphs and Hamiltonian graphs, trees, planar graphs and coloring graphs, some special vertex subsets and edge subsets).

本课程包含四部分内容：数理逻辑（包含命题逻辑与一阶逻辑的基本概念、等值演算以及推理理论），集合论（包含集合代数、二元关系、函数和基数），代数结构（包含代数系统、半群与群、环与域、格与布尔代数），图论（包含图的基本概念、欧拉图与哈密顿图、树、平面图及图的着色、图的某些特殊的顶点子集与边子集）。

As the application, we obtain an upper bound of the Hausdorff measure for the Cartesian product set of the middle-third Cantor set with itself.

采用这种方法，本文得到三分Cantor集自乘积集的Hausdorff测度的一个上界。

One convex set which is Cartesian product of nonregular convex polygons is used instead of the other convex set which is Cartesian product of regular polygons.

采用不规则凸多边形的笛卡儿积构成的凸集代替正多边形的笛卡儿积构成的凸集，前者比后者更紧凑。

Through using category theory, this paper investigates the properties of subcoalgebras, especially, the properties of subcoalgebras on Set, the category of sets and functions. This paper shows that all the subcoalgebras on Set are regular.

以范畴理论为工具讨论子共代数的性质，特别是集合范畴上的子共代数的性质，证明了集合范畴上的子共代数都是正则子共代数。

The situation after the first M step is shown in plot, in which the mean of the blue Gaussian has moved to the mean of the data set, weighted by the probabilities of each data point belonging to the blue cluster, in other words it has moved to the centre of mass of the blue ink. Similarly, the covariance of the blue Gaussian is set equal to the covariance of the blue ink.

图显示了初始的 E 步骤，用红色表示用红色 component 产生的后验概率，蓝色也是同样的情况，还有一些不太确定的点是用紫色显示的，在图中蓝色的高斯的均值已经移到了蓝色数据集的中心上，类似的，蓝色高斯的协方差设为蓝色点的协方差。

In the fourth chapter we discuss the set of chain equivalent points of chain recurrentpoints,the set of unilateral γ-limit points and topological entropies of tree maps.

在第四章，我们讨论树映射的链等价集、单侧〓-极限集和拓扑熵。

Among the many remarkable final projects that have been proposed and presented at the end of the course have been a Renaissance hourglass blown in the MIT glass shop and set into a frame turned on our set shop lathe; a four harness loom built by a student who then wove cloth on it; a number of chain mail tunics and coifs; a wide variety of costume and furniture pieces and electrified period lighting fixtures.

在以往的课程中，学生们构想并于期末展示出了很多优秀的作品，比如一个文艺复兴时期的沙漏，它是学生在麻省理工学院的玻璃工作坊吹制、并在我们布景工作坊的车床上成形的；一台由学生制作的四综纺织机，制作者真正用它来织布；许多锁子甲束腰外衣和头巾；各式各样的服饰、家俱和电气化时代的照明设备。

Chapiter 2 discusses the theory of assets portfolios, which starts to analyze investor, arid deduces framed investor"s feasible set arid efficient set, discUss different forms and characteristic of efficient portfolio, and systematic analyzes the effect of portfolio, risk diversification, followed briefly summarizes the formation, development, application and limit of the "theory of portfolio, created by Markowitz.

本章从投资者开始分析，给出了框定投资者的可行集和有效集，并讨论了各种不同的有效组合类型及其性质，同时系统研究了资产组合的效应——风险分散，最后简要综述了马柯维茨投资组合理论的产生、发展、应用与局限。

Besides, it is possible to set a string or character set for viewing.

此外，是有可能订出一个字符串或字符集观赏。

The second and third tags set the language and character set for the page.

第二个和第三个标签设置了网页的语言和字符集。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。