有界性

This paper makes use of a Lyapunov function and a nonlinear integral inequality of Gronwall-Bellman-Bihari type to study the asymptotic hehaviors of solutions of a second-order nonlinear functional differential equation. In part I, a group of sufficient conditions is given on continuation of solutions and three groups of sufficient conditions are given on boundedness of solutuicns of equation.

本文利用李雅普诺夫函数及一个Gronwall—Bellman—Bihari型的非线性积分不等式，研究一类二阶非线性泛函微分方程解的渐近性态，在第一部份，给出一组方程的全体解可延展到t=+∞的充分条件及三组方程的全体解有界的充分条件。

To make the constant in the interpolation error independent of element size,the ratio of the diameter of the element and the diameter of the biggest ball contained in the element,is uniformly bounded.

传统的有限元方法误差估计需要满足正则性条件或非退化条件，即：单元的直径和单元的最大内切圆直径的比值是一致有界的。

In this paper, we study the existence of sign-changing and multiple nontrivial solutions for a kind of quasilinear elliptic equations with Dirichlet boundary value by applying minimax methods and Morse theory.

本文我们将应用极大极小方法和Morse理论研究一类拟线性椭圆方程Dirichlet边值问题多解的存在性和解的变号性质。设Ω是R~N(N≥1)中的有界区域，具有光滑边界？

The sufficient conditions to guarantee robust exponential stability for the closed-loop systems are obtained based on Linear Matrix Inequality, moreover, the approach of design of robust H# output feedback controller is introduced.3 The problem of reliable H# control for a class of Lur"e systems with polytopic uncertainties is studied when all control components are operational as well as when some control components experience failures, the design approach of reliable H# controller is also obtained.4 Considering a class of uncertain Lur"e singular system with time-delays, the problem of robust stability is investigated based on Barbalats Lemma and nonsingular linear transformation of model reduction.

针对一类不确定Lur'e奇异时滞系统，基于Barbalat引理以及非奇异降阶变换，讨论了Lur'e奇异时滞系统的鲁棒稳定问题，提出了鲁棒H_∞状态浙江大学博士学位论文反馈控制器的设计方法。5、针对一类具有饱和执行器的不确定Lur'e奇异系统，提出了时滞依赖的鲁棒稳定与鲁棒二次镇定的充分条件，所的结果不需要参数的整定。6、针对任意协方差有界的有色噪声，讨论了一类不确定Lur'e奇异系统的鲁棒凡滤波问题，得出了鲁棒几滤波器设计的充分条件。7、针对一类不确定Lur'e时滞系统，通过线性变换，把它转换成奇异系统，根据奇异系统鲁棒控制理论所得出的鲁棒稳定与鲁棒镇定控制器设计的充分条件具有很小的保守性。

For compact hypersurfaces and highcodimension compact submanifolds initial data respectively, we prove that the flow hasa smooth solution for all time under almost optimal conditions. Those conditions arethat the second fundamental form on the initial submanifolds is not too large, the exter-nal force field, with its any order derivatives, is bounded, and the field is convex with itseigenvalues satisfying a pinch inequality.

我们分别对紧超曲面初值和高余维紧子流形初值证明了当初始曲率比较小，并且外力场除了要各阶导数一致有界外，还要满足凸性条件以及特征值的一个pinch条件时，这种热流的光滑解长时间存在。

Unboundedness has a greater empirical credibility.

无界性有更大的经验可信性。

The method attempts to transform the original problem into a series of unconstraint optimization problems.

在这些研究中，均假定在对数障碍函数是严格凸的及解集是非空有界的情况下，证明了方法的全局收敛性。

Moreover, classical multigrid methods, such as W-cycle and Variable V-cycle, are shown to be convergent uniformly for this mortar type TRUNC element.

我们还用经典多重网格方法（可变的V-循环、W-循环）求解带mortar条件的TRUNC元解，证明所构造的网格转移算子满足收敛性条件，从而传统多重网格方法作预处理的条件数为一致有界。

We also study the weighted composition operators between Hardy spaces on the unit ball, as well as between Bergman spaces. Some equivalent conditions that the operators are bounded or compact are given in term of the Carleson type measure.

另外，我们也考虑了单位球上Hardy空间之间及Bergman空间之间的加权复合算子，利用Carleson型测度，给出了有界和紧性的等价条件。

The existence of the bounded solution of unstable internal dynamics is the key to tracking reference trajectory stably.

研究表明，不稳定内部动态有界解的存在性是非最小相位系统能够稳定跟踪期望输出轨迹的关键。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。