查询词典 theorem of residues

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。

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。

Properties of measurable functions; approximation by simple functions and by continuous functions; convergence in measure; Egoroff's theorem; Lusin's theorem; Jensen's inequality.

可测函数。可测函数的性质；简单和连续函数逼近；测度收敛；叶果洛夫定理；鲁津定理；詹森不等式

In chapter 2, we point out that some condition of a convergence theorem of generalized fuzzy integral in [8] (Theorem 1) is not valid by a counterexample.

通过一个反例，指出了文[8]给出的一个广义模糊积分序列的收敛定理(即定理1)中，有的条件不合理。

The convergence theorem of the neural networks algorithm and the theorem of numerical integration solution and its inferences are presented and proved.

摘要该文提出了一种基于三角基函数神经网络算法求解数值积分的新方法，提出并证明了神经网络算法的收敛定理和数值积分的求解定理及推论。

Theorem Let be a function of period . If satisfies the convergent theorem, the Fourier series of is

定理 设周期为的周期函数满足收敛定理的条件，则它的傅立叶级数展开式为

The Lyapunov theorem and its converse theorem of globally exponential stability for the discrete-time systems family in which the sampling period is a parameter are proved.

对以采样周期为参数的离散时间系统族，证明了全局指数稳定的Lyapunov定理和逆定理。

In Chapter 3,we discuss theconvergence of Newton's method for nonlinear inclusion problems with values in aclosed convex cone,using the new theory developed by Wang Xinghua,we generalizeRobinson's Kantorovich theorem for this problem to a more widely function classes,inthe same time our results take Smale theorem as a special case.

在第三章，我们利用王兴华最近提出的理论框架研究在闭凸锥中取值的非线性包含问题的Newton方法，将Robinson在特殊Lipshitz条件下建立的Kantorovich型收敛性定理推广至满足中心Lipshitz条件的函数类，我们建立的一般的收敛性定理同时将Smale型收敛性定理包容其中。

Tan and Xu [1] had proved the theorem on convergence of Ishikawa iteration processes of asymptotically nonexpansive mapping on a compact convex subset of a uniform convex Banach space , Then Liu Qihou [3] presents the necessary and sufficient conditions for the Ishikawa iteration of asymptotically quasi-nonexpansive mapping with an error member on a Banach space convergent to a fixed point . Xu and Noor [5] had proved the theorem on convergence of three-step iterations of asymptotically nonexpansive mapping on nonempty closed, bounded and convex subset of uniformly convex Banach space.

Tan和Xu已经证明了建立在一致凸Banach空间紧凸子集上的渐进非扩张映射的Ishikawa迭代序列的收敛原理，随之，刘齐侯又阐述了Banach空间上渐进准非扩张映射T的具误差的Ishikawa迭代序列收敛于T的不动点的充分必要条件；之后，Xu和Noor也证明了定义在一致凸Banach空间某非空有界闭凸子集上的渐进非扩张映射的三步迭代序列的收敛原理。

Then is the property of fourier transform detally,it contains linar, symmetry,uncover,switch,time-move,frequency-move,time-differentialcoefficient,frequency-differential coefficient,time-intergrate, frequency-intergrate,odd even, theorem of Parseval ,and theorem of convolution,and make testify to some property,some have the example.

接着详细概括了傅立叶变换的性质，即线性、对称性、折叠性、尺度变换性、时移性、频移性、时域微分性、频域微分性、时域积分性、频域积分性、帕塞瓦尔定理、奇偶性及卷积定理等，对某些性质相应的做了推导，并附有适当事例。

The shaping method of noncircular part and the tool holder's radial motion characters in noncircular turning process are discussed in detail in the thesis.

论文详细研究了非圆零件的成型方法和加工过程中刀架的径向运动规律。

I have not really liked him,I do not like his this kind of disposition.

我没有真的喜欢他，我不喜欢他的这种性格。