查询词典 continuity theorem

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。

The potential functions of incident and scattered waves were expanded into Fourier-Bessel series, and the coefficients of scattering waves field were determined by imposing continuity conditions of stress and displacement at the soil-pile interfaces with the help of a set of cylindrical coordinate systems and in accordance with the Graff's addition theorem.

将倾斜入射波和散射坡的势函数展开成Fourier-Bessel函数的无穷级数的形式，利用一组圆柱坐标系统和Graff加法转换定理，通过施加桩土界面处的应力和位移连续的边界条件，求解出散射波势函数的待定系数，进而得到饱和土体中任意点的位移和应力。

And we also prove the existence theorem of minimizer for the new model by means of Poincares inequality and the lower semi-continuity of bounded variation functions.

根据有界变差泛函中的Poincare不等式和下半连续性，证明了该模型极小值的存在性。

In Chapter 1,some elementary knowledge was introduced,such as theBernstein-Bezier representation for polynomials,conform triangulation,theconditions of convexity for Bézier spline surfaces,the funtional andgeometric continuity condition for neibour Bézier surface patches etc.,specially,based on the Liu-Ding-Yuan Theorem for geometric continuity,some simple and practical conditions were obtained.

第一章介绍一些基本知识，如多项式的Bernstein-Bézier表示，相容三角剖分的定义，Bézier三角样条曲面保凸的条件，相邻Bézier曲面片函数连续和几何连续的条件等，特别地，在刘鼎元关于几何连续条件的一般定理的基础上，导出了几个较简单的实用的一阶几何连续条件。

In this paper,at first we transformed the nonlinear elliptic system of 2m first order equations into the complex form, then by use the results on the Riemann-Hilbert problem for nonlinear elliptic complex equation of first order, the method of continuity, the Schauder fixed-point theorem and the Leray-Schauder theorem, we proved that the modified Riemann-Hilbert boundary value problem for the complex system with some conditions is solvable.

本文先将较一般的多个未知函数的一阶椭圆型实方程组化为复方程组，然后讨论这些复方程组在某些条件下的一些边值问题的可解性。这里所考虑的方程组既包含线性的，也包含非线性的，比广义超解析函数所满足的方程组还要广，又本文主要研究较一般的Riemann-Hilbert边值问题，先给出这种边值问题解的先验估计式，然后用参数开拓法及Leray-Schauder定理证明这种边值问题的可解性结果。

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。

Under some conditions, by using Mawhin continuity theorem and degree theory, the existence of the periodic solution of the periodic neural network is proved.

利用Mawhin连续定理以及拓扑度理论，证明了在一定条件下该周期神经网络系统周期解的存在性。

Secondly, based on the Mawhin's continuity theorem in coincidence degree theory and the Brousk's theorem, some novel criteron of the existence on periodic solutions are obtained under the more generalized assumptions than before.

主要工作是：第一，应用构造Liapunov函数以及Lasalle不变性原理，给出了解的有界性与收敛性的一些新的充分条件和充分必要条件，这些结果包含或扩展了已有文献关于同样问题的一些重要结果。

Because of the condition of 〓 for two neighbour parametricspline surfaces is too strong,here,instead of it,some simple and practicableconditions of 〓 resulted from the general theorem obtained by Prof.LiuDing Yuan in Chapter 1 were proved,and three 〓 triangular splinesurfaces schemes wre presented:one is piecewise cubic spline surface patcheshaving local 〓 and whole 〓 continuity based on the refined HCTtriangulation,another is the same degree spline surface patches but based onthe refined Powell-Sabin triangulation,the third is piecewise quartic splinesurface patches having local 〓 and whole 〓 continuity based on therefined P-S triangulation.

由于对参数曲面，一阶导数连续的要求较强，我们采用第一章从刘鼎元定理导出的简单实用的几何连续条件，讨论了基于HCT加细三角剖分和P-S加细三角剖分上的两种局部达一阶导数连续而整体有一阶几何连续的分片三次样条曲面构造算法，一种局部达二阶导数连续整体有一阶几何连续的分片四次样条曲面构造方法。

At first, the existence of extended form of approach to continuous selection for any set valued mapping without any continuity restriction in para-compact metric space is proved ;by the topologically separated mappings , the approximate selection theorem of sub-lower-semi-continuous mapping is established, furthermore , continuous selection problem in H-space is studied. Next, with W-correspondence, an improved variational inequality is obtained ; by the H-KKM mapping ,Ky Fan\'s minimax inequality is generalized to H-space . At last, with H-convexity instead of the linear topological structure, a new version of Browder fixed point theorem is established.Chapter 3 deals with set-valued mapping vector variational inequality and minimax problems.

第二章首先在仿紧的度量空间上对任意的集值映射建立了新的逼近连续选择定理，利用映射的拓扑可分性，在H-空间上建立了次下半连续映射的逼近连续选择定理和一个新的连续选择定理；然后利用W-对应，在H-空间上建立了广义的变分不等式；利用H-KKM映射，在H-空间上建立了广义的KyFan极小极大不等式；最后，利用H-凸性代替拓扑线性结构，在H-空间上建立了一个新型的Browder不动点定理。

In the United States, chronic alcoholism and hepatitis C are the most common ones.

在美国，慢性酒精中毒，肝炎是最常见的。

If you have any questions, you can contact me anytime.

如果有任何问题，你可以随时联系我。