Theorem 1 and are equivalent infinitesimals if and only if. Theorem 2 The product of a bounded function and an infinitesimal is an infinitesimal.

His paper studies the degree of approximation of bounded function with discontinuity of the first kind and functions of bounded variation of order p by Meyer Konig Zeller operators Mn ( f, x). The result of [ 1] is extended and improved.

本文研究Meyer Konig Zeller算子Mn（f，x），对有界函数和p阶有界交差函数在第一类间断点的逼近度，推广和改进了文〔1〕的结果。

Pointwise convergence has no completeness in bounded function space B ( I).

有界函数空间B（I）中的点态收敛不具备完备性。

Isolate Point of Operator Essential Spectrum in the Approximation for Bounded Linear Operator

有界线性算子逼近问题中算子本质谱孤立点的处理

The best approximating of bounded linear operator in the space W and Application

W空间中有界线性算子的最佳逼近及其应用

For a linear bounded operator in finite dimensional Hilbert space, we first introduce the definition of exactly positive and give a sufficient and necessary condition by the way of space decomposition of the operator;

对有限维Hilbert空间的线性算子，引入了恰好正的概念，并利用算子的空间分解，得到了其存在惟一正逼近的充分必要条件；

We discuss the best generalized inverse of linear bounded operator in finite dimension Hilbert space. We proved Moore-Penrose generalized inverse is the best generalized inverse.

本文讨论了有限维Hilbert空间中有界线性算子的最佳广义逆问题，证明了Moore-Penrose广义逆为最佳的。

Convolution and bounded operator

卷积与算子的有界性

Let k ∈ C ( R++) and B be a linear bounded operator.

设k∈C（R+）和B是一个有界线性算子。

In this paper a new linear, continuous and bounded operator& piecewise general orthogonal polynomials operator ( PGOPO) is proposed, and its main properties and operational rules are described.

提出了一类新型的线性、有界算子&分段广义正交多项式算子（PGOPO），建立了其主要性质及运算规则；

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.

此外还把算法推广到约束凸规划问题，得到了与无约束问题同样的收敛结果，如果约束是线性的，则算法是数值可行的。

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。