有界闭集

At last, it is proved for the two systems that when the control domain U is a bounded, closed set, the reachable set is the same as that when the control domain is the convex of U.It is an advancement for original results.

最后证明了当控制区域U是有界闭集时上述两个系统的等时区域与控制区域是U的凸包时的等时区域相同，推广了有限维的结论。

On this basis, we give the characterization of the compact set in E〓,τ

引入了模糊数网的最终等度左连续概念，利用它得到了模糊数序列在水平收敛意义下存在极限的一个充要条件，在此基础上给出了空间E〓，τ(l中紧集的特征刻画，即空间E〓，τ(l中的闭集U是紧的当且仅当U一致支集有界，且U的每个网有在（0，1上最终等度左连续、在λ=0处最终等度右连续的子网。

Since bounded closed sets in infinite dimensional space are notcompact generally,in order to employ Horn's fixed point theorem the compactness of operator Pis initially proved in section 3 in this chapter.

由于无限维空间的有界闭集一般不具备紧性，为了应用Horn不动点定理，我们先证明了Poincare算子P的紧性。

Does research in a common fixed point theorem of fuzzy mapping s in inequality conditions and the cut set is the nonempty closed bounded subsets of,while is complete metric space.

2，研究了在完备度量空间中一对模糊映象满足一些特定不等式条件，以及当其截集是中非空有界闭集时，该对模糊映象的公共不动点的存在性问题。

In this paper,with the aid of the w~*- sequential compactness of bounded closed balls in the conjugate space of a separable space,we proved that the convex hull of a finite union of bounded closed balls in l~∞ is closed.

借助可分空间的共轭空间中有界闭球的弱星序列紧性，证明在无穷维数列空间l∞中有限个闭球之并的凸包仍为闭集

H-2: The measurable set-valued mapping F : X - CC is -bounded (n+1)-lower semicontinuos where X is a closed, bounded and convex subset of a n-dimension Bana...

的。 H-3：X是1-维赋范线性空间中的有界闭凸子集，可测集值映射F：X→C_c是2-下半连续的(2-l.s.c。)。

Thirdly, the problems of institution investor'optimal liquidation strategy and optimal liquidation time were investigated with the conditions that the price of risky asset followed arithmetic Brown motion and liquidation velocity was limited. The problems involved the following scenes: price impact function was linear expression of liquidation velocity which was boundary closed set with an isolated point; price impact function was stochastic; price impact function was nonlinear.

接着，当风险资产的价格服从算术布朗运动，且对投资者的变现速度做出限制时，研究机构投资者的最优变现策略和最优变现时间问题，其中包括：价格冲击函数为变现速度的线性函数，变现速度是一带有孤立点的有界闭集；价格冲击是随机形式；价格冲击是变现速度的非线性函数。

uniform continuity ; Lebesgue number ; property L ; compactness

在〔11中，常庚哲等证明了R中的有界闭集具有这样的

Our study bases on following environment and conditions: H-1: The measurable set-valued mapping F : X - CC is e-bounded almost lower semicontinuos

这些研究是在如下环境和条件下进行的： H-1：X是n-维Banach空间(n＞1)中的有界闭凸集，且可测集值映射F：X→C_c是ε-有界几乎下半连续

The research is carried on from four aspects. One is, based on answering the above open problem on a finite dimensional Euclidean space by means of partially ordered theory, to research the existence of solutions, global error bounds of proximal solutions and sensitivity of parametric unique solutions and present a class of variable-parameter three-step iterative algorithms for generalized set-valued variational inclusion problems by using - resolvent operator of set-valued mapping.Two is to consider the convexity, closedness and boundedness of the solution set of general set-valued variational inclusion problems and the sensitivity of the parametric solution set by means of graphical convergence theory. Three is to discuss directly the existence of solutions by using analytical methods for set-valued mixed quasi-variational-like inequalities and suggest a class of direct variable-parameter three-stepiterative algorithms for solving generalized set-valued variational inclusions.

研究分有三个方面：一是借助于偏序理论在有限维欧氏空间中解决了上述公开问题，在此基础上利用集值映射的η-预解算子，研究了广义集值变分包含问题解的存在性、逼近解的全局误差界、参数唯一解的灵敏性，并提出了一类变参数三步迭代算法；二是借助于图收敛理论研究了一般集值变分包含问题解集的凸性、闭性和有界性以及参数解集的灵敏性；三是用分析的方法直接讨论了集值混合拟类变分不等式问题解的存在性并提出了一类求解广义集值变分包含问题的直接变参数三步迭代算法。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。