查询词典 boundedness

It is proved in the paper that the uniformly ultimate boundedness of solutionsimplies the existence of periodic solutions to functional differential equations with infinite delayin admissible phase space with fading memory .

本文证明了在具有衰减记忆的允许相空间中，无限时滞泛函微分方程的解的一致最终有界性蕴含了周期解的存在性。

FR conjugate gradient methods with perturbations are proposed. The global convergence property of the first method is proved under the condition of main directions' sufficient descent. Whereas, in the proof of the convergence for the other two methods, we only need main directions' descent. Importantly and quite interesting, boundedness conditions such as objective function being bounded below, boundedness of level set are not needed. Chapter 5 presents a version of Dai-Yuan conjugate gradient method with perturbations.

在主方向充分下降的条件下证明了第一个方法的全局收敛性，而后两个方法的收敛性是在主方向下降的条件下证明的，这些收敛性证明的一个共同特征就是不需要目标函数有下界或水平集有界等有界性条件，第5章采用Wolfe或Armijo步长规则提出了带扰动项的Dai-Yuanabbr。

In this paper, we discuss uniform boundedness and uniform ultimate boundedness of differential systems with infinite delay.

研究了非线性无穷时滞微分系统解的一致有界性和一致最终有界性。

And the sufficient conditions for uniform boundedness and uniform ultimate boundedness are obtained respectively.

分别得到了一致有界和一致最终有界的充分条件。

This paper investigates topological properties of the general gradient system, and demonstrates by results of differential topology that the boundedness of the general gradient system is equivalent to the boundedness of the potential energy boundary surface. Moreover, a general gradient system is bounded if, and only if the system has both sink point and source point.

该文研究了广义梯度系统的拓扑性质，应用微分拓扑学原理证明，广义梯度系统的完全稳定性与势能界面的有界性是等价的；广义梯度系统完全稳定当且仅当该系统既有渊点又有源点。

At last the results have been applied to the tracking problem of a class of mechanical systems with discontinuous friction term. Chapter 3 mainly deals with uniformly ultimate boundedness of a class of nonautonomous systems with discontinuous right-hand sides and corresponding perturbed systems (in the sense of Filippov solutions). The definitions of globally uniformly strongly ultimate boundedness and globally uniformly weakly ultimate boundedness of discontinuous systems and the definition of globally equiuniformly strongly ultimate boundedness of corresponding perturbed systems are presented firstly.

首次给出不连续系统全局强一致最终有界、全局弱一致最终有界的定义，以及针对于扰动系统的全局强等度一致最终有界性的定义，并基于非光滑的Lyapunov函数得到了不连续系统全局一致强、弱最终有界的Lyapunov定理和扰动系统全局强等度一致最终有界性的Lyapunov定理。

Consisting of 3 Chapters, the Paper mainly includes the following contents: Chapter 1 of Introduct on presents the significance of extending uniform boundedness principle and elso reviews one hundred years development of uniform boundedness principle iind the work done by people in this aspect; Chapter 2 mainly introduce some preparatory knowledge including definitions of dissecting operators, absorbing operators, equicontinuity and some relative examples; In Chapter 3, We discuss the new researching results of equicontinuity principle,uniform boundedness principle and Banach-Steinhaus type theorem .

本文共分三章，主要内容如下：在第一章绪论中说明了推广一致有界原理的意义；回顾了已知一致有界原理一百多年来的发展及人们在此方面所做的工作。在第二章中主要介绍了一些预备知识，其中包括：解剖算子、吸收算子、等度连续的定义并举了一些相关的例子。

The main results are:(1) the L1 boundedness of the Cesaro means operator of the harmonic expansions on the unit sphere with reflection-invariant measures is proved, and the characterization of the convergence index is given; for the points not in the planes with singularities, the pointwise convergence is also proved; these results are the generalizations of those both for the classical spherical harmonic expansions and for the Jacobi expansions;(2) Using the differential-reflection operators of Dunkl type, the uncertainty principle of a class of Sturm-Liouville operators is established, and as consequences, the uncertainty principles of some well-known classical orthogonal expansions such as Jacobi, Hermite and Laguerre expansions are obtained;(3) by introducing the Cauchy-Riemann equations in terms of the differential-reflection operators of two variables, the harmonic analysis of the extended Jacobi expansions is studied; the results include the Lp boundedness and the weak-L1 boundedness of the conjugate extended Jacobi expansions; specially, for some indexes p smaller than 1, the basic theory of the related Hardy spaces is established.

主要成果有：（1）证明了带有反射不变测度的球面调和展开蔡沙罗平均算子的L1有界性，给出了收敛指标的特征刻划，对不在奇性平面上的点，还证明了点态收敛性，这些成果同时推广了经典球面调和展开和雅可比展开的结果；（2）利用Dunkl型的微分-反射算子建立了一类斯特姆-刘威尔算子的测不准原理，并由此得到一些著名的经典正交展开如雅克比展开、赫米特展开和拉盖尔展开的测不准原理；（3）利用由两个变量的微分-反射算子定义的柯西-黎曼方程组来研究扩展雅克比展开的调和分析，证明了共轭扩展雅克比展开的Lp有界性和弱L1有界性，特别是对小于1的一些指标p，建立了相应的哈代空间的基本理论。

Since the commutators of both sing-ular integral operators and fractional integral operator with BMO functions areone of the special cases of〓,so the discussion of the boundedness of〓notonly gives a new proof of the boundedness of the two commutators,but al-soweakens some of restrictions into discuss the problem,thus it impro-vessome of results inwith the method of complex analysis,show-ed boundedness of〓,then directly obtained boundedness of the commutato-rs of fractional integral operator with BMO functions.

既然奇异积分算子和分数次积分算子与BMO函数的交换子是其特殊情形，所以〓的有界性的讨论不仅给出了中关于这两类交换子有界性的一个新的证明，而且减弱了中讨论这一问题时对齐型空间所作的限制，从而改进了中的结果（利用复分析的方法，先证明〓的有界性，从而直接得到分数次积分算子与BMO函数的交换子〓的有界性。

In Chapter 5,we obtain a boundedness results of commutators of convolution opera-tors on MK_~according to the corresponding boundedness of the sublinear operators on the homogeneous Morrey-Herz spaces.

第五章通过次线性算子在齐次Morrey-Herz空间上的有界性导出了一个卷积型交换子在MK_~上有界的结果。

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。