Global convergence for the algorithm is established under the assumption that the objective function is bounded from below, The authors also generalize the algorithm to constrained convex optimization and obtain the convergence that is the same as unconstrained algorithm.

The sequences generated by the new algorithm are proved to converge to a new solution if the three conditions that the peak selection p is continuous, the separable condition and the energy functional is bounded below are all satisfied.

证明了新算法产生的点列在满足峰选择p连续、可分离条件以及能量泛函下方有界三个条件之下一定能收敛到新解。

Here, the nonlinear term is bounded below and need not be nonnegative.

这里，非线性项是下有界的并且不需要是非负的。

Bounded below Property of Composition Operator on Bloch Space in Cn Unit Ball

单位C~n球上Bloch空间上复合算子的下有界性

Let J' be a bounded below complex.

设J~+是下有界复形。

Most work in application often uses second order moment method and point estimation and bounded below method.

工程中常用的β分布近似方法有二阶矩法和点估计下限法。

Secondly, we prove the certain populations of the system are bounded below and get sufficient conditions of permanent living of populations by applying comparison theorem.

其次利用比较定理证明了该系统确定的种群是有下界的，得到了种群永久生存的充分条件。

The theorems show that the existence of solution and positive solution depends upon the "height" of principal part of nonlinear term on a bounded set.

这些定理表明解和正解的存在性取决于非线性项的主要部分在某个集合上的“高度”。

The bounded set of annotations that do depend on an EJB3 container are geared specifically for that environment.

的确依赖于EJB3容器的一组有限的注释则是专用于那个环境的。

A Radon measure on a locally compact complete metric space is called a strong Radon measure if each bounded set has finite measure.

称局部紧完备度量空间上的Radon测度为强Radon测度，若每个有界集的测度都是有限的。

By considering the growth of nonlinear term at infinite and the height of nonlinear term on a bounded set, several new existence results are obtained.

通过考察非线性项在无穷远处的增长或者非线性项在某个有界集上的高度获得了若干新的存在性结论。

Totally Bounded Set in Locally β-convex Space

局部β-凸空间中的完全有界集

X-Bounded Set and Its Good Refined Cover

X&有界集及其良加细覆盖

Construction and Property of a Bounded Set Family in Locally Convex Space

局部凸空间中一类有界集的构造及其性质

Compared with the long-standing friendship between the two countries, their boundary dispute is only an issue of a temporary and limited nature.

两国之间的边界争论，比起两国的悠久友谊来说，是一个暂时性和局部性的问题。

Some facts about and the background of the Sino-Indian boundary dispute

有关中印边界争端的一些情况和背景

Role of the cavity field, the electrostatic repulsive force at the doma-in boundary and self-enhanced diffraction light induced by physical imperfection on laser-induced surface damage are discussed.

本文讨论了由晶体缺陷所致的自增强衍射光，富集于缺陷的空间电荷所致的空洞场，以及由此场导致的发生在畴界上的静电斥力对此损伤所起的作用。

To others, it's the world they live in: a boundary zone flooded with light, which is why they are countless green algae floating around here.

而对于生活在这里的生物，这是一个充满了阳光的分界地带，无数的藻类生活在此。

Moreover, the auto-body surface quality specification requests the boundary line shape light between various curved surface, and adjacent region has no obvious distortion.

而且，车身曲面质量标准要求各曲面片间的边界线形态光顺，连接处没有明显畸变。

Many feminist authors adopted various genre reformations and new artistic techniques, their works combined SF canon with utopianism, furthermore, those works broke the strict boundary between light literature and high literature.

作家们采用多种多样的文类革命，将科幻传统与乌托邦因素扭合在一起，尤其要打破通俗文学与经典文学的界限。

The characterization of the curved liquid surface is described by the boundary light reflected from the sunk curved liquid surface.

基于激光在润湿效应形成的凹形弯曲液面上边界反射，研究了凹形弯曲液面的特性。