凸的

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。

It was found that with the increase in the oscillating frequency for a fixed oscillating angle, the film thickness increases, which may contribute to the formation of the oil film; however, the maximum pressure and the pressure scope during an oscillation cycle also increase; which may shorten the fatigue life of the bounding surface in the latter situation.

结果表明：在摆程不变的条件下，膜厚随摆动频率增加而增大，有利于润滑膜的建立，但同时会增加1个周期中的最大压力及压力波动幅度，使工件易于疲劳；对于相同凸度量，在低频摆动工况下边缘效应较高频工况下的严重，因此在低频摆动工况下使用滚子设计时需要增大其凸度量。

In chapter two, under the assumption that the set of decision variables is convex and the objective functions are concave, it is shown that the set of noninferior solutions in valued space of the objective functions turns out to be a strictly decreasing, concave and no chinky block of surface, and it can be constructed recursively.

在第2章凸性假设下非劣解集的构造及其几何性质中，在假设决策变量集为凸集，目标函数向量是凹的情况下，证明了目标函数向量值空间中的非劣解集是一严格单调递减，无缝隙且凹的曲面块，并给出了m维目标函数向量值空间中非劣解集的一种递归构造方式。

In the end of this text gives a description about the compactness of somecertain locally convex topological space with convergence and the completenessproblem.

某种确定的收敛下的局部凸拓扑空间以及凸拓扑下的紧性，完备性问题，在文章的最后给与了阐述。

Inthe paper, we study the relation of pairs of lines and pairs of needles, and two results ofintegral formulas are gained. Thus, the geometric probability problem is solved. Also.we give a solution to the problem: pick two points randomly in a convex body K anddraw two lines passing through two points.

文章考虑了线偶与针偶的依附关系，得到了两个积分公式的结果，从而解决了这一问题，并得到了随机地在凸体K内任取两点，通过这两点任意投掷两直线，两直线的交点落入凸体K内的概率及其它的一些结果和推论。

So we mention another geometricprobability problem which is the geometric probability of the intersection of pairs ofintersecting lines belonzs to convex body K in R~2 by using the concept of doublechord-power integrals and a kinematic invariant density formula for pairs of lines.

利用R~2上双弦幂积分的概念和线偶的运动不变密度公式，提出了另一个几何概率问题：R~2上两根与凸体K相交的小针依附在两直线上，求两直线的交点落入凸体K内的几何概率。

In reference to existing price models, a new price model--price formation model is formulated, which concludes that the price of current period product can be shown as the convex combination of unit product material consumption of the previous period and current period plus the convex combination of gross profit gained when the unit product of previous period and current period is sold at current period.

该模型表明，本期的产品价格可以表示成上期和本期单位产品物耗成本的凸组合与上期和本期单位产品在本期出售所获得的广义毛利的凸组合之和，这一结论是非常耐人寻味的。

Each pixel on multispectral and hyperspectral imagery can also be regarded as one vector and the whole image is a convex cone formed by a number of nonnegative discrete vectors,so endmember selection is equivalent to search for the vertices of a convex cone.

遥感图像中的每个像元都可以看作一个多维向量，整幅影像看作由离散的非负向量构成的凸锥，通过寻找凸锥的角点来自动获取图像的端元。

To use linear program, we have to take care of two problems. The first problem is that the actual relationship between intensity and duration is nonlinear convex function. In this study, we propose to use piece-wise linear curve to approximate the nonlinear convex curve. The second problem is that there are many feasible event sequences.

使用线性规划遭遇的困难有二：第一，作业强度与作业时间呈非线性之凸函数关系，因此本研究将使用片段线性曲线(piece-wise linear curve)近似作业强度与作业时间呈非线性之凸函数关系；第二，专案有很多组可能事件顺序，事件顺序的不同会产生不同的资源限制式，本研究提出一个系统化的方法求解问题。

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％。