界

And then, we introduce the concepts of ρ-bounded sets,ρ-semi-bounded sets and ρ-unbounded sets in a F~* space, and study some of thier properties.

然后，在此空间中引入p-有界集、p-半有界集和p-无界集的概念，并研究它们的某些性质。

Otherwise, beings forever wander through the impermanent and suffering-generating realms of desire, form, and formlessness, collectively termed samsara .

否则，人类永远流浪在无常和产生痛苦的欲界，色界，无色界，全部被统称为轮回。

Property 1 (Boundedness and max-min theorem) Let be a continuous function of several variables on a closed region D, then has an absolute maximum and an absolute minimum on the region.

性质1（有界性与最大值最小值定理）在有界闭区域D上的多元留恋许函数，必定在D上有界且一定能取得它的最大值和最小值。

On the other hand, when we are proving the upper bounds of the Hausdorff measure functions for the level sets, although we get the answer to the cases for the symmetric processes, we had to consider multi-integral of highly dimensional functions, the proof is quite complex. Therefore, we suggest that the proof for the corresponding problem needs some new ways.

另一方面，我们在证明严格稳定过程的水平集的Hausdorff测度函数的上界时，虽然我们得到了对称的多参数稳定过程的水平集的Hausdorff测度函数上界，但是我们的方法必须考虑多重的高维积分，其证明过程也已经相当复杂，因此，我们认为，为了得到一般的严格稳定过程的水平集的Hausdorff测度函数上界，还需要引入其它新的研究方法。

Secondly, the author gives some exact values of mb(2 q) for some values of b, which impliesthat the above lower bound is not only the lower bound but also the infimum.

其次，对于部分b值，给出了m_b（2，q）的确切值，从而说明了上面给出的下界值不仅是下界而且是下确界。

From this,it is proved that when all the ratios of a subaddtive function defined on the interval(0,+∞) to the value of its variable form a bounded function ,the subaddtive function must have supremum and infimum functions,which are homogeneously linear functions.

从这一结果出发证明了，当定义在(0，+∞)上的次可加函数与其自变量之比为有界函数时，次可加函数必存在上下确界函数，并证明了其上下确界函数均为齐次线性函数。

By extending the concepts of supremum and infimum in real space to the casein any finite-dimensional Euclidean space a weak supremum set and infimumset theory with respect to cones for the set in finite-dimensional Euclideanspace is developed,and several similar properties to the set in real space are ob-tained,with the concepts of this weak supremumset,w-D-conjugate maps and w-D-subdifferentials theory for the point-to-setmap are developed,and its several properties and its relationships with weakefficient solutions of the multiobjective programming are studied.

推广实空间中上、下确界的概念至任意有限维欧氏空间，建立了有限维欧氏空间中集合的锥弱上、下确界集理论，得到了与实空间中十分相似的性质。借助于这一理论，应用上、下确界的概念，给出了点集映象的w-D-共轭映象及w-D-次微分理论，并研究了它们的若干特性及其与弱有效解之间的关系，此外还讨论了弱鞍点问题。

If the infimum of sectional curvature R_c in M~n satisfies: then M~n must be totally geodesic in M~,T_c is the supremum of Ricci curvature and t_c is the infimum of Ricci curvature in M~

如果M~n的截面曲率下确界R_c满足：则M~n一定是全测地的其中T_c，t_c分别是M~(n+p上Ricci曲率上确界和下确界。

Ablish two decision theorems of relative compactness for unbounded function groups in an infinite interval.

sect；2.3我们建立了判定无穷区间上抽象无界连续函数组和抽象无界可微函数组相对紧性的充分必要条件，并对无穷区间上抽象二阶微分方程两点边值问题无界解的存在性做了研究。

In the study area, the thinning-out line of albic horizon is coincident with the 55.74m contour line, and the maximum horizon error was less than 1m and the maximum vertical error less than 0.04m.

基于湿地边界标准的湿地的定义应为：湿地是陆地和水体之间的过渡带，是由于地表淹水／土壤水饱和而形成的一种隐域性自然综合体，其上界位于陆地土壤诊断层的尖灭点处，其下界是有根植物下界。

Plunder melds and run with this jewel!

掠夺melds和运行与此宝石！

My dream is to be a crazy growing tree and extend at the edge between the city and the forest.

此刻，也许正是在通往天国的路上，我体验着这白色的晕旋。