连续性定理

The definition of the absolute value for a fuzzy number is obtained.Furthermore,a lot ofproblems,such as absolute integrability,bounded variation and absolute continuity,arepresented and discussed.The representation theorem of the absolute values of fuzzy num-bers is established.It plays an important role in discussing the problems conceming theabsolute value.The relation between the absolute integrability and integrabili-ty is discussed,and the following result is obtained:aintegrable fuzzy-number-valued function is absolutely integrable iff it is integrable.The relation between theabsolute integrability and the absolute continuity of the primitive for fuzzy-number-valuedfunctions is dealt with.It is also pointed out that a fuzzy number valued function is ab-solutelyintegrable if and only if its integral primitive is fuzzy absolutely continuous.

提出了模糊数绝对值的概念并讨论了与绝对值相关的一系列问题，如绝对可积性、有界变差性、绝对连续性等，给出了模糊数绝对值的定义以及表示定理，该表示定理在涉及绝对值问题的讨论中起非常重要的作用；讨论了绝对可积与可积之间的关系，得到了结论：可积的模糊数值函数绝对可积的充要条件是该模糊数值函数可积；给出了模糊数值函数绝对可积与其积分原函数绝对连续性之间的关系，指出模糊数值函数绝对可积的充要条件是其原函数模糊绝对连续。

In the proof,sufficient conditions are proved mainly by properties of K function and continuity of Lyapunov function:in necessary proof,we separately structure Lyapunov functions which satisfy the conditions of the theorems, such that the results establish.

在定理的证明中充分性主要利用K类函数严格单调递增和Lyapunov函数的连续性；必要性的证明中，分别构造Lyapunov函数，满足定理的条件，使得定理的结论成立。

In this paper,making use of hyperplane method,we improve the proof of the separation theorem;On the other hand,we use a new method of moving neighborhood to simplify the proof for the continuity of a subconvex function defined on a convex in a normed linear space.

在巴拿赫空间理论中，Hahn-Banach泛函延拓定理作为泛函分析三大基本定理之一，分隔性定理是Hahn-Banach定理的重要应用，本文利用"超平面"的方法，改进了一个分隔性定理的证明；另外，本文利用邻域的"平移"方法，给出了定义在赋范线性空间内的凸集上的次凸泛函连续性的简捷证明。

In Chapter 3, by using the continuity theorem of coincidence degree theory, we obtain a sufficient condition for the existence of positive periodic solutions to population models with impusives.

在第三章，利用重合度理论中的连续性定理研究了在脉冲作用下种群模型的全局周期解存在性。

It introduces normal families, including equicontinuity, Arzela's theorem, Montel's and Marty's theorems, Zalcman's lemma; univalent functions, including Koebe's and de Branges' theorems; quasiconformal mappings, including conformal length, extremal length, geometric, analytic and metric definitions, quasiconformal extension, distortion theorem, quasicircle; iteration of rational functions, including fixed points, the Fatou and Julia sets, periodic points, Siegel disks, the Hausdorff measure and dimension, etc.

具体为：正规族，包括等度连续性、Arzela定理、Montel和Marty正规定则、Zalcman引理；单叶函数，包括Koebe定理和de Branges定理；拟共形映照，包括共形模、极值长度、几何、分析和距离定义、拟共形延拓、偏差定理，拟圆周等；有理函数的迭代，包括不动点、Fatou集和Julia集、周期点、Siegel盘、Hausdorff测度和维数，等等。在教学内容上充分体现综合性、前沿性。

For the analysis properties of infinite matrix,first,it establishes the automatic conti-nuity theorems on the sequence spaces with 0-GHP or WGHP,and the automaticboundedness theorem on the sequence spaces with 0-GHP.

在无穷矩阵的分析性质方面，建立了具有0-GHP或具有WGHP的矢值序列空间上无穷矩阵算子的自连续性定理，以及具有0-GHP矢值序列空间上无穷矩阵算子的自有界性定理。

By using Mawhin\'s continuous theorem and liapunov function, sufficient conditions for the existence and globally asymptotic stability of positive periodic solutions of three systems are derived, respectively.

我们还利用Mawhin连续性定理分别建立了两个系统正周期解存在的充分条件。

First,we consider the lower semicontinuity property fora functional with linear growth in LDΩthe second, in the SBD space,we discussthe lower semicontinuity of an integral functional that the integrand is a Carathéodoryfunction and that satisfies a symmetric quasi-convex assumption, by the compactnesstheorem of the SBD space,blow-up method and Morrey theorem,prove that integral functional is lower semicontinuous with respect to L~1- convergence;then by using theone-dimentional sections method and the structure theorem of the BD functions, dis-cuss the lower semicontinuity of the integral functional in the whole BD space.

首先我们考虑LD空间满足线性增长的积分泛函的下半连续性；其次在SBD函数空间讨论了被积函数为Carathéodory函数时的积分泛函在满足对称拟凸条件时的下半连续性，主要利用SBD函数空间的紧性定理和blow-up方法以及Morrey定理等给出了积分泛函关于L~1-强收敛的下半连续性；然后利用BD函数的一维截断方法和结构定理，讨论了在BD全空间上的积分泛函的下半连续性。

We investigate the continuity and fuzzy continuity of fuzzycomplex functions on 〓,prove depictive theorems of the continuityand fuzzy continuity.

在模糊复数度量空间〓上研究了模糊复函数的连续性和模糊连续性，证明了模糊复函数的连续性刻划定理和模糊连续性刻划定理。

In this paper,making use of hyperplane method,we improve the proof of the separation theorem;On the other hand,we use a new method of moving neighborhood to simplify the proof for the continuity of a subconvex function defined on a convex in a normed linear space.

在巴拿赫空间理论中，Hahn-Banach泛函延拓定理作为泛函分析三大基本定理之一，分隔性定理是Hahn-Banach定理的重要应用，本文利用&超平面&的方法，改进了一个分隔性定理的证明；另外，本文利用邻域的&平移&方法，给出了定义在赋范线性空间内的凸集上的次凸泛函连续性的简捷证明。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。