It is shown that the swarm members will converge to a bounded region around weighted center of swarm in a finite time.

In the bounded region, affine stretching is an extremal mapping.

在有界区域上，仿射拉伸是极值映射；

For a general case of three dimensional bounded region, we put forward a kind of fractional step characteristic difference schemes.

在考虑三维有界区域的一般情况下，提出了一类分数步长特征差分格式。

A Boundary Value Problem on a Bounded Region for the Hyperbolic System of PDEs

双曲方程组在具特征斜率边界的区域内的边值问题

By the introduction of a compensation term in the design of the sliding mode observer that counteracts the effect of system deviations to the velocity reconstruction, the exponential observation error is converged to a bounded region.

在滑模观测器设计中引入补偿项，动态抵消系统偏差对速度重构的影响，确保观测误差指数收敛到有界域。

The ( p, q) forms of the Bounded Region with C ￣ 2-boundary in C ￣ n

C~n中具C~2边界的有界域上的（p，q）形式

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

定理1与是等阶无穷小的充分必要条件为。

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。