集合函数

First we give the characterization of subsets on which every real-valued convex function bounded above is continuous on the space, and give the βperturbed optimization in Banach space by introducing new locally convex topology.

给出了广义实值凸函数在集合A上有上界则连续的一类子集的特征性刻画；并且通过引入新的局部凸拓扑的方法，给出任意Banach空间的β扰动优化。

First we give the characterization of subsets on which every real-valued convex function bounded above is continuous on the space, and give the fi-perturbed optimization in Banach space by introducing new locally convex topology.

给出了广义实值凸函数在集合A上有上界则连续的一类子集的特征性刻画；并且通过引入新的局部凸拓扑的方法，给出任意Banach空间的β扰动优化。

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）。

Then our choice function can choose the least element of every set under our unusual ordering.

那么我们的选择函数可以在我们的不寻常的排序下选择没有集合的最小元素。

So sets must not exist in space. But as before, there is reason to doubt the cogency of such an inference.

我们可以承认纯粹集合类似余弦函数那样，不在任何时空中。

Returns the first item in the collection which elicits a true return value from the passed selection function.

集合中返回能通过选择函数筛选并返回true值的第一项。

It is also pointed out that the fuzzy controller implemented through this way can approximate any continuous real function.

摘要基于对模糊集基本特性的分析，提出了一种模糊集合的距离度量方法，与传统方法不同的是它不但与模糊集的质心有关，而且与模糊集的基数有关；其次讨论了如何基于这种距离的定义来实现模糊控制，并指出基于这种方法实现的模糊控制器可以逼近任意连续函数。

The convexity monotonicity and correlation theory of functions are studied.

用集合的近似凸性研究函数的拟凸性。

The maximum principle of the optimal control for the stochastic systems described by Zakaj stochastic partial sifferential equationis proved by approximately minimum point theorem of E. Ekeland. The convexity and compactness of the set of control values is not assumed, and it is not necessary for the maximum principle about differentiability in control variables included in drift term of the stoch astic system and the integrand in index functional, and costate process satisfies the stochastic partial ...

在不假便定控制变量取值的集合是凸的和紧的，不要求随机系统的漂移项和指标泛函的被积函数关于控制变量具有可微性的情况下，用E，Ekeland的近似极小点定理证明了Zakai随机偏微分方程描述的随机系统的最优控制的最大值原理，和用很简洁的方法证明了协态过程满足一个随机偏微分方程。

On this newconcept, we succeed to prove the uniqueness of Cauchy Problem of the aboveequation by the methods of using the Hausdorff measure of the set of the discontinuous points of BV solution and Kruzkov technique etc.

基于此概念，通过对BV函数的间断点集合Hausdorff测度的仔细分析，以及利用Kruzkov技巧等我们证明了上述方程BV解的存在唯一性。

Chrysanthemum of 10 thousand birthday is lax to edaphic requirement, with the arenaceous qualitative loam with fecund, good drainage had better.

万寿菊对土壤要求不严，以肥沃。排水良好的砂质壤土为好。

He unstepped the mast and furled the sail and tied it.

他拔下桅杆，把帆卷起，系住。