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They often form along the boundary between the dune and thesurface below.

它们通常沿着沙丘与坡面间的分界线分布。

This research method is independent of Green"s function and variational structure. So it can tackle with the BVP for non self-adjoint and self-adjoint difference equations and overcome the difficulties brought about by the establishment of Green"s function, a study of the sign and the estimate of below and above bounded for Greens function.

本章的研究方法既不依赖于Green函数又不依赖于变分结构，因而能解决非自共轭的差分方程边值问题，且克服了Green函数的建立、其符号的判断及其上下界的估计给研究带来的困难，该方法同样适用于研究自共轭的差分方程边值问题。

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。

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 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。

This paper gives a smooth variational principle of lower semicontinuous functions which are bounded below on each bounded set.

本文给出了在每个有界子集上有下界的下半连续广义实值函数的一个光滑变分原理。

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。

In the days of sailing vessels the crew were afraid they would be becalmed on the ocean.

在使用帆船的时代，船员们担心他们会因为无风而无法在海洋上航行。

As long as foreign donors pay the PA's salary bill, few expect a new intifada.

只要外国继续为巴权力机构的薪水买单，希望发动新暴动的人便寥寥无几。