查询词典 atiyah singer index theorem

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。

Stationary process: spectral decomposition of covariance function, spectral decomposition of stationary process, linear time invariant system, ergodic theorem, sampling theorem.

平稳过程：协方差函数的谱分解，平稳过程的谱分解，线性时不变系统，遍历定理，采样定理。

Because the kinematically-admissble cyclic strain rate field required in kninematical-type theorem of shakedown analysis is rather difficult to be constructed, shakedown analysis based on kinematcal theorem cannot be directly applied.

在竖向载荷与水平载荷共同作用下，研究了地基土体的强度特性与土层分布特征对地基承载力的彤响，对地基的极限载荷与安定戳荷进行了比较分析，为全面、综合地评价非均质地基的稳定性提供了有益的参考。

Listen,point and check your answers.

听，指出并且检查你的答案。

Warming needle is one of effective treatment methods for knee arthralgia aggravated by cold,and it is simple,safety,so it should be developed in clinical acupuncture and moxibustion extensively.

但以本院科针灸门诊在2005年1月—2006年6月期间共收治膝痛患者100余例，经过临床的诊断后，其中施以温针治疗的48例，疗效显著，报道如下。1临床资料本组病例48