查询词典 order bounded set

At first we establish two lemmas for C〓-functionals defined on finite dimensional spaces. These lemmas describe the behavior near infinity of a functional that is bounded from either above or below.

我们首先对有限维空间上的C〓-泛函建立两个引理，它们实际上完全描述了有上界或有下界的泛函在无穷远处的行为。

Prove that if this quantity is bounded above by that value of the Veronese surface then x is either a totally umbilical sphere or a conformal Veronese surface.

最后我们模仿3维的情况，引进一个保角不变量，并证明此保角不变量的上界若为Veronese曲面之值，则x不是全脐球面就是Veronese曲面的保角类。

EUR/USD continued to be bounded in established range above 1.2706 last week as consolidation continued. While some more sideway trading might be seen, upside is expected to be limited by 1.3093. On the other hand, below 1.2706 will suggest that whole decline from 1.4719 is resuming for a retest of 1.2329 low next. However, note that a break above 1.3329 resistance will indicate that fall from 1.4719 has completed and bring strong rebound.

EUR/USD 继续着上周建立的1.2706底部之上的反弹，会有更多的震荡交易，上涨的限度预期在1.3093，与此相反，低于1.2706将预示着从1.4719点开始的整个下降趋势将重新再试1.2329的新低，然而，请注意，一但突破1.3329，预计从1.4719开始的下降已经完成，并将带来强劲的反弹

We then introduce a conformal invariant quantity which is formulated in terms of the square of the length of the trace free part of the second fundamental form and the mean curvature, and prove that if this quantity is bounded above by that value of the Clifford torus then x is either a totally umbilical sphereor a conformal Clifford torus.

接著我们介绍一个由第二基本型式迹为零部份的张量长度平方与平均曲率形成的保角不变量，并证明此保角不变量的上界若为Clifford环面之值，则x不是全脐球面就是Clifford环面的保角类。

A "time-dependent relaxation" method is proposed to accurately implement given photospheric footpoint displacements and force-free conditions. The method is applied to analyzing the energy buildup of coronal magnetic fields, and the numerical results confirm the Aly conjecture (the magnetic energy of the force-free field is bounded above by the fully-open field energy), and extends it from fully-open to partially-open force-free fields.

提出计算无力磁场的"时变松弛"方法，能精确实现光球足点位移和无力条件；采用该方法分析日冕磁场的剪切储能，验证了Aly猜想（无力场磁能以全开放场磁能为上限），并将该猜想由全开放无力场推广至部分开放无力场。

We know that more functionals are not bounded from below.

我们知道更多的泛函都不具有下方有界性。

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。

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。

We are forbidden from giving money to these shoeless, skinny children, as this will perpetuate begging.

向光着脚，骨瘦如柴的孩子施舍是不可以的，因为要招来无休无止的乞讨。

It would be hard not to fall victim to some sharpeyed policeman.

要想不被某个目光锐利的警察抓到，谈何容易。