查询词典 bounded below

Hence, in order to enlarge the range of the applicable functionals, weakening the restriction of bounded from below is very necessary.

因此为了扩大适用泛函的范围，削弱下方有界性这个条件是非常有必要的。

But we can prove that the corresponding Eulur\'s function is bounded from below in a proper set S of W_0~(1,p)× W_0~(1,q), and then a minimizer of Eulur\'s function in S gives rise to a solution of the problem.

但是，我们可以证明欧拉泛函在合适的集合S中有下界，因此在该集合中利用变分方法寻找泛函的极小就可以得到原问题的解。

In this thesis,we mainly study complete noncompact Riemannian manifolds with Ricci curvature bounded from below. We study the topology of these manifolds via comparisonal geometry methods.In chapter 1 ,we will make a general description on the recent researches in our field.

在本文中，我们主要研究了Ricci曲率有下界完备非紧的Riemann流形的拓扑问题，在比较几何的基础上研究了有特定曲率条件的Riemann流形的拓扑，得到了有关其拓扑结构的一些结果。

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。

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。

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。