定理

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。

In the fourth chapter,we quoted a normal matrix,and proved a convergence theorem about nonhomogeneous Markov chains.

第四章通过引进一正规矩阵，证明了一个关于非齐次马氏链的收敛定理，是杨卫国等人的一个关于非齐次马氏链Cesaro平均收敛定理的推广。

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。

The theorem of convergence of opinions is regarded as the dynamic principle of rationality concerning the subjective probability, and therefore is used to resolve Hume's problem, i.

意见收敛定理是主观主义概率论的一条重要定理，它表明随着证据的增加，验前概率的主观性将被验后概率的客观性所代替。

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

Invariant theorem of the operator series multiplier convergent. Using operator series multiplier convergent,AK-space of concept ,we obtained the theorem of operator series multiplier convergent invariant and the old theorem of general series multiplier convergent invariant is looked as special case.

第三章 算子级数乘数收敛的不变性：利用算子级数乘数收敛、AK—空间的定义，得到了算子级数乘数收敛的不变性定理，从而将以往的普通级数乘数收敛的不变性定理作为特殊情况。

Aimed to the differential equation in form of convolution and the functional presented by M. E. Gurtin, the matrix operator which includes the differential equation and the boundary condition is proved self-adjoint, furthermore a general variational principles in form of convolution and the preparation theorem are given and proved.

针对M.E.Gurtin提出的含卷积运算的抛物型偏微分方程及其对应的泛函，运用泛函势算子理论，从理论上证明了含卷积运算的抛物型偏微分方程及其边界条件所对应的矩阵算子有势，进而给出并证明了具有普适意义的含卷积运算的变分定理及预备定理。

A human model using polynomial convolution surface is presented which is modeled by articulated skeletons convolved with some kernel function. The convolution surface and curve correspondence theorem under orthogonal projection is presented. The human contour is approximated with a convolution curve and 3D human pose can be estimated using a nonlinear optimization algorithm.

首先建立了一种新颖的多项式密度卷积曲面人体模型，该模型由连接体线骨架与某种卷积核卷积而成，整个曲面是一张连续曲面，调节多项式和半径参数可以让人体任意变形；给出了正交投影下卷积曲面和曲线对应的概念和相关定理，为二维的图像轮廓和三维人体模型之间建立对应关系；根据正交投影下卷积曲面与曲线对应定理，用卷积曲线去逼近人体的图像轮廓曲线，从而估计和恢复出三维人体运动姿态。

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。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。