有界性

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。

Theorem 1 (Boundedness and max-min theorem) If is a continuous function on a closed interval, then has an absolute maximum and an absolute minimum on the interval.

定理 1 (有界性与最大值最小值定理)在闭区间上连续的函数在该区间上有界且一定能取得它的最大值和最小值。

We establish some connections between geometric properties, properties in analysis and analytic properties of the inducing map ψ and operatortheoretic properties of composition operator C〓: f〓fοψ on various analytic function spaces mentioned above, include the boundedness, compactness, weak compactness, collective compactness and the Schatten class operator ideal, etc. Our results extend some previous results, for instance, the Shapiro's Nevanlinna counting function condition and the MacCluer's Carleson measure condition for the compactness of C〓 on Hardy space.

本文建立了D上解析自映射φ：D→D的几何性质、分析性质和解析性质与复合算子C〓：f→foφ在上述各种解析函数空间上的限制的算子性质之间的联系，涉及到复合算子C〓的有界性、紧性、弱紧性、总体紧性及Schatten类算子理想等算子特征，推广了前人的一系列结果，如Shapiro关于C〓的紧性的Nevanlinna计数函数条件，MacCluer关于C〓的紧性的Carleson测度条件等。

We proved that this kind of operators were bounded from Hardy space to Lebesgue space, and they were bounded operators on the Hardy space if they satisfied some special conditions.

利用Hardy空间和Herz型Hardy空间的原子和分子分解特征，文中首先给出了此类算子从Hardy空间到Lebesgue空间上的有界性，而且，在满足一定的消失矩时，它又是Hardy空间上的有界算子。

Applying the boundness and some propertities of the mean of integration, we get the sufficient condition of weak persistence in the mean, and the curve of demarcation between weak persistence in the mean and going-to death.

本文利用比较原理证明系统解的有界性，由解的有界性及积分均值的一些性质得到了种群弱平均持续生存的充分条件，并在一定条件下得到了种群弱平均持续生存与绝灭之间的分界曲线。

Applying the boundness and some propertities of the mean of integration, we get the sufficient condition of weak persistence in the mean, and the curve of demarcation between weak persistence in the mean and going-to death. An optima!

本文利用比较原理证明系统解的有界性，由解的有界性及积分均值的一些性质得到了种群弱平均持续生存的充分条件，并在一定条件下得到了种群弱平均持续生存与绝灭之间的分界曲线。

Tolksdorf [62] to prove the weak solutions of equation (2) are of C1,a if fand u are bounded with the help of some results in [40]. And by Morse iteration,we prove that the solutions are of C1,a even if f is of critical growth.

Tolksdor[62]的方法以及[40]中的一些定理证明了方程(1)弱解的C1，a的正则性；当f满足临界指数增长时，应用Morse迭代，我们首先证明了解的有界性，然后证明方程(1)的解也有C1，a的正则性。

In Chapter 5,we obtain a boundedness results of commutators of convolution opera-tors on MK_~according to the corresponding boundedness of the sublinear operators on the homogeneous Morrey-Herz spaces.

第五章通过次线性算子在齐次Morrey-Herz空间上的有界性导出了一个卷积型交换子在MK_~上有界的结果。

The results in this chapter improve and generalize some of the earlier foundings of IFDE with finite delay and infinite delay, therefore the applications are more extensive.In chapter two, we study the boundedness of system (1) mainly by the method of several Lyapunov functions containing partial components coupled with Razumikhin technique.

在第二章中，我们主要用含部分变元的Lyapunov函数和Razumikhin技巧得到了系统(1)的一致有界性和一致最终有界性定理。

Then we find out the exact bounded wave solutions for WBK equation in chapter four. According to the theory of dynamical system, we investigate the explicit exact traveling wave solutions of nonlinear wave equations by using the characters of the closed trajectory connecting equilibrium points and the relations between obits and traveling waves.

在对系统进行定性分析、了解了系统所有可能解的大致形态的基础上，论文第四章给出了WBK方程的精确有界解，应用动力系统理论，利用连接平衡点的闭轨线的特点结合轨线与行波之间的对应关系来研究非线性波方程行波解的有界性及精确的显式表达式。

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。