上有界的

This paper gives a smooth variational principle of lower semicontinuous functions which are bounded below on each bounded set.

本文给出了在每个有界子集上有下界的下半连续广义实值函数的一个光滑变分原理。

This result can best be viewed as a quantum black hole version of the third law of thermodynamics. As a result of this area spectrum, the spectrum of M is discrete, bounded below, and can be made positive. Prom the physical point of view, the semiboundedness and positivity of the spectrum are very satisfying results: The semi-boundedness of the spectrum implies that one cannot extract an infinite amount of energy from the system, whereas the positivity of the spectrum is in agreement with the well-known positive-energy theorems of general relativity.

同时根据EMDA黑洞动力学，存在与面积谱对应的大于零且有下界的质量离散谱，从物理上来看，质量谱的半有界性意味着不可能从系统吸取无限的能量，而正定性则与广义相对论中的正能定理一致，也就说稳态轴对称EMDA时空的ADM能量总是大于零。

Firstly, we get the necessary and sufficient conditions for Toeplitz operators that commutes with another such operator whose symbol is a monomial, meanwhile, we completely characterize when the mellin transform of the bounded function on the interval 0,1 is a rational function.

首先得到了以有界函数为符号的Toeplitz算子和以单项式函数为符号的Toeplitz算子可交换的充要条件，同时给出了0，1区间上的有界函数的Mellin变换为有理函数的充要条件。

In Chapter Three, we use the method of interpolation spline of differential operater to come up with the reproducing kernel in H01 with respect to bounded linear operator in H10. Then we use the reproducing kernel to develop the expression of the best approximating of bounded linear operator in H10 and prove its convergence.

第三章中，对于H_0~1中的有界线性算子，用微分算子插值样条函数的方法给出了H_0~1空间中的再生核，利用此再生核给出了H_0~1上的有界线性算子的最佳逼近的表达形式，并证明了其收敛性。

The waiting times of the first message class have a determinable upper bound which are given in this paper and verified with simulation results.

实时信息从产生到被服务的时间有确定的上界值，推导了实时信息的这种等待时间上界。

In chapter 3,we prove that a complete noncompact n-dimensional Riemannian manifold M whose Ricci curvature Ric_M ≥(n- 1) has finite topological type or diffeomorphic to R~n if its Excess function has some upper bound at a point.

第三章，我们证明了对于Ricci曲率Ric_M≥-(n-1)的完备非紧n维Riemann流形M，若它的共轭半径有正的下界且共轭半径的某个函数为M在某一点的Excess的上界时，它就有有限拓扑型或者微分同胚于n维欧几里德空间。

Property 2 Let be a continuous function of several variables on a closed region D, then can obtain any number between its absolute maximum M and its absolute minimum m.

性质2在有界闭区域D上的多元连续函数，必定在D上取得界于最大值M与最小值m之间的任何值。

Moreover, the semiopen mapping theorem, the semiclosed graph theorem and the semibounded inverse theorem are established under some conditions of weaker t-norms.

对MengerPN空间上的线性算子引入β-半有界，β-半开及β-半闭等概念，讨论了它们间的关系，并在较弱的t-模条件下建立了半开射定理，半闭图定理和半有界逆定理。

The numerical solution would be a good approximation of the original solution restricted in the computational domain.

这样我们可以将原无界区域上的定解问题约化为定义在有界计算区域上的边值问题。

Results of inversion show that pre-Tertiary deposition in Dongying depression is controlled with westnorth structures. Archaean group is the crystal basement of Dongying depression, which is a north steep and south gentle rift subsidence basin striking from eastnorth to near westeast, and the deepest position is up to 12000 m at the area of Xianhe and Xinzhen. The configuration of Ordovician of lower Palaeozoic system highly inherits that of Archaean group and both have a strong consistency. The configuration of Mesozoic inherits that of lower Palaeozoic system as a whole, but filling and local reconstruction are distinct, and the scope of Dongying depression has obviously decreased.

结果表明，东营凹陷前古近系沉积主要受北西向构造的控制，太古界构成东营凹陷的结晶基底，是一个北东转近东西向的北陡南缓的断陷，最深处位于现河、辛镇一带，可达12000 m；下古生界奥陶系构造具有很强的继承性，其构造格局与太古界有很强的一致性；中生界宏观上继承了下古生界的构造形态，但填平补齐和局部改造比较明显，凹陷范围明显缩小。

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。