定理

According to that Caristi fixed point theorem is equivalent to Ekeland variational principle, we weaken the condition that the functional is bounded from below in Ekeland variational principle, then we enlarge the area of the applicable functionals.

鉴于Caristi不动点定理和Ekeland变分原理的等价性，我们对Ekeland变分原理中泛函的下方有界的要求作了相应的削弱，从而扩大了适用泛函的范围。

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 2 The product of a bounded function and an infinitesimal is an infinitesimal.

定理 2 有界函数与无穷小的乘积是无穷小。

There exist Engel groups for each of which the Engel length of the product of two elements is not bounded by any polynomial function of the Engel lengths of the factors.

定理1。每个团体存在的恩格尔恩格尔产物长度两个因素并不是什么北临多项式函数恩格尔长度因素。

In this dissertation, we mainly discuss the resonance theorems for families of linear and nonlinear operators, and the theory of bounded linear operator space in F~* spaces.

本文主要研究F~*空间上的线性、非线性算子族的共鸣定理和有界线性算子空间理论。

As a result, we have demonstrated that the best approximating operator and the best approximating of bounded linear operator in H10 and H1a,+∞ are consistent and, at the same time, we have generalized the theorem of the best approximating of bounded linear operator to the more universal H1

然后，我们说明了在这样的索伯列夫空间上定义的样条插值算子和最佳逼近算子是一致的，同时把有界线性算子的最佳逼近定理也推广到了一般的索伯列夫空间H~1a，+∞上去。

In this dissertation, the best simultaneous approximation with weight to infinite sequence from simultaneous-suns in complex normed linear space is considered, and in the case when the weight satisfies a certain condition, the characterizations of approximation from a simultaneous-sun and uniqueness of approximation from a RS-set are obtained; moreover, in the case when the weight is free, the characterizations of approximation to a totally bounded sequence from a convex set are established.

本文在复赋范空间中研究了同时太阳集对无限序列的加权同时逼近问题，在权满足一定条件时，通过把所研究问题转化为连续向量值函数空间中相应集对一个上半连续函数的最佳逼近问题，得到了逼近的特征和RS集逼近的唯一性定理，有例表明它们是已有结果的本质推广；在权不受限制时，得到了凸集对全有界序列逼近的特征。

The problem of paths with bounded length, being a variation and a generalization of Menger's theorem, is of very important significance in the design and analysis of real-time or fault-tolerant interconnection networks.

设给出了h，ψ-η限长路径问题是图论中的Menger定理的变形和推广，在实时容错网络设计和分析中有重要意义。

At the same time, the variational stability of bounded variation solutions at the effect of perturbation and non-perturbation for the impulsive differential system are discussed, the Ljapunov type theorems for variational stability and asymptotically variational stability for impulsive differential systems are established.

同时，讨论了在无扰动和有扰动的情况下，这类固定时刻脉冲微分方程有界变差解的变筹稳定性，建立了此类微分系统有界变差解变差稳定性和渐近变界稳定性的两个Ljapunov型定理。

The results show that Cauchy's criterion for convergence, sign theorem, and boundedness theorems are kept.

结果表明，柯西收敛准则、符号定理和有界定理仍然成立。我们的结果推广了经典复分析中的已知结论。

By the time of its fall, most of the prisoners were writers who had written against the corruptions of the government.

到它被攻陷的时候，里面多数的犯人是写了反对政府贪污文章的作家。

The most obvious variation to ovum morphological character was that the color was changed from light green to sepiaceous in embryonic development, and all the ovums were almost hatched after 96h.

在胚胎发育过程中卵的形态特征最明显的变化是颜色从淡绿到深褐色，卵在发育96h后卵基本全部孵化。