查询词典 bounded below

In Chapter 2, we use Zorn lemma and generalized order set general principle [47] to generalize classical Caristi fixed point theorem, respectively, which weaken the condition that the functional is bounded from below.

在第二章中，我们首先分别利用Zorn引理和推广的序集一般原理[47]推广了古典的Caristi不动点定理，削弱了泛函下方有界这个条件。

The composite nonsmooth optimization problem is defined as follows:〓where h is a convex function defined on〓and is bounded from below,and〓〓is a mapping from〓to〓and〓are twicecontinuously differentiable function on〓.

复合NDO问题被定义如下：〓这里h是一个定义在〓上的凸函数，并且有下界，〓，〓是一个从〓到〓上的映照。

If the flow does not go to infinity, or the functional is bounded from below on the flow and satisfy the condition, then the limit of the flow maybe a critical point.

如果流线不走向无穷远处，或泛函在此流线上下方有界且满足条件，那么极限点就可能是临界点。

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。

Lots of empirical studies show that the actual processesand results of investors'decision-making are very different from that described byMFT's optimal investment decision-making model because of judgement anddecision biases arising from investors'psychological biases and informationasymmetry , investors'bounded rationality below the MFT's requirement.

大量的实证研究表明，实际中由于投资者固有的一些心理偏差和信息不对称的存在，使得投资者的认知能力和判断能力以及判断的准确度往往存在偏差，远远低于经典现代金融理论对投资者的理性要求，投资者的实际决策过程和决策结果与经典现代金融理论的最优投资决策模型所描述的大相径庭。

FR conjugate gradient methods with perturbations are proposed. The global convergence property of the first method is proved under the condition of main directions' sufficient descent. Whereas, in the proof of the convergence for the other two methods, we only need main directions' descent. Importantly and quite interesting, boundedness conditions such as objective function being bounded below, boundedness of level set are not needed. Chapter 5 presents a version of Dai-Yuan conjugate gradient method with perturbations.

在主方向充分下降的条件下证明了第一个方法的全局收敛性，而后两个方法的收敛性是在主方向下降的条件下证明的，这些收敛性证明的一个共同特征就是不需要目标函数有下界或水平集有界等有界性条件，第5章采用Wolfe或Armijo步长规则提出了带扰动项的Dai-Yuanabbr。

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。

In their exercise of power, the primary task of modern nation-states is to transform "people" into politically, culturally and volitionally bounded "citizens," so that the state, instead of the "ruler," will be regarded by the ruled as the object of loyalty, and supportive forces that uphold from below the identity of political communities will occur.

现代民族国家的政治权力之遂行，首要工作乃是将「人」打造成有政治边界、文化边界与意志边界的「公民」，以使被统治者政治效忠的对象由「统治者」转变为「国家」，并且产生具有再生产性质由下而上支撑政治共同体同一性的支持力量。

North Beach is a San Francisco, California neighborhood bounded by the former Barbary Coast, now Jackson Square, and the Financial District south of Broadway (except North Beach institutions extend down Columbus to Washington and Montgomery, where the Black Cat originally was), Chinatown to the southwest of Columbus below Green, and then Russian Hill to the west, Telegraph Hill to the east and Fisherman's Wharf at Bay Street to the north.

北滩是加利福尼亚州旧金山地区范围内的前北非海岸，现在杰克逊广场，以及金融区南部的百老汇（除北滩机构延长了哥伦布华盛顿和蒙哥马利，在那里黑猫原），唐人街西南哥伦布低于绿色，然后俄罗斯山以西，电报山以东和渔人码头湾街以北。

This dissertation gives a special research in microcomputer relay protection for power transformer of 110kV or below voltage ratings, which based on widely summarizing the theory of power system relay protection and its advanced trend. After analyzing the working character of the transformer in details and absorbing the advantages in other power transformer protection, a scheme which is fit to power transformer of 110kV or below voltage ratings is put forward.

本文在全面介绍和评述电力系统微机保护原理及其发展趋势的基础上，对电力系统中大量应用的110kV及以下各电压等级的变压器保护进行了专门研究，根据这一类电力变压器的运行特点，吸取以往各种保护方法的长处，提出了这类电力变压器保护方案。

The dissecting of samples in group2 were difficult. The root of pulmonary artery and ascending aorta failed to be unfolded because fibrous tissue was tough, right and left fibrous trigone were too firm to be solved by hand. Cardiac muscle fibers couldn't be stripped along myofibrillar trajectory since they were prone to break because of their friability.

组2的心脏解剖困难，表现为纤维组织坚韧，游离肺动脉非常困难；徒手无法松解左、右纤维三角，肺动脉和主动脉根部的游离非常困难；心肌纤维坚硬、质脆，解剖时容易断离成碎块，无法沿纤维走行方向剥离。

We have battled against the odds in a province that has become increasingly violent.

我们对在一个争夺日益激烈省的可能性。