级数的和

The content of this course is: analytic function (the definition of analytic function, elementary functions, etc.), conformal mapping (the definition if conformal mapping, fractional linear functions, elementary mappings, etc.), complex integration (Cauchy's integral formula, Cauchy's theorem, etc.), Series (Laurent Series, singularities, local property, etc.), residues and its applications (the Residues Theorem, integration by residues, the Argument Principle, the Maximum Principle, Schwarz's Lemma, etc.), analytic continuation and harmonic functions, etc.

本课程内容主要包括：解析函数(解析函数的定义、初等函数等)、共形映射(共形映射的定义、分式线性变换及初等映射等)、复积分(Cauchy 积分公式、 Cauchy 定理等)、级数(Laurent 级数、孤立奇点、局部映射等)、留数及其应用(留数定理、利用留数计算积分、幅角原理、最大模原理、 Schwarz 引理等)、解析开拓和调和函数等内容。

Based on the laminate theory, a laminate weakened by damage is treated as an anisotropic thin plate. Using the complex potential method in the plane theory of elasticity of an anisotropic body, the series solution of finite anisotropic thin plate containing an elliptical inclusion is proposed with the help of Faber series. A hybrid element with an elliptical inclusion for anisotropic materials is obtained by using the hybrid variable principle, and the element efficiency is verified by numerical examples. The state of the damage is modeled by an elliptical soft inclusion, and using the point stress criterion based on characteristic curve and Yamada-Sun etc. criteria, the prediction of the strength of a composite laminate with damage is set up. The effects of various parameters on the stress distribution and the residual strength of a composite laminate weakened by damage are detailedly studied.

首先基于经典层板理论，将复合材料层板的弹性问题化归为均匀各向异性板来求解；采用各向异性体平面弹性理论中的复势方法，以Faber级数为工具，给出了有限大含椭圆核各向异性板弹性问题的级数解形式；利用杂交变分原理，成功导出含椭圆核各向异性板杂交应力有限元，并用算例验证了该单元的可行性和有效性；采用含刚度折减椭圆形弹性核的冲击损伤模型，引入基于特征曲线和Yamada-Sun破坏准则的点应力判据，建立了含损伤复合材料层板剩余强度的分析方法；通过数值计算详细讨论了各种几何参数对损伤层板应力分布、剩余强度的影响，得到了一系列对工程应用具有实用价值的结论。

Furthermore,we obtain a sufficient and necessary condition about continuity of functional series and integral with parameter,and show the sufficient condition about differential .

将数学分析中一致收敛性的概念加以推广，分别对函数项级数和含参量积分引入次一致收敛的概念，证明了函数项级数、含参量非正常积分连续性的充要条件和可微性的充分条件，推广了数学分析中的相应结

And the radius of convergence of the differentiated series is the same as for the orginal series.

逐项求导后所得到的幂级数和原级数有相同的收敛半径。

We also use the Schr〓der transformation, Abel transformation, power series and Dirichlet series theory to discuss the existence and uniquness of analytic solutions for an extensive class of nonlinear iterative equations.

进而还利用Schr〓der变换、Abel变换以及幂级数与Dirichlet级数理论研究一类具有相当广泛性的非线性迭代函数方程解析解的存在性和唯一性问题。

It was found that VAC can be smoothly photografted onto LDPE film with"film combination"system, e. g. conversion percent and grafting efficiency are 70％ and 76％, irrespcetively, with UV intensity of 5400μw/cm〓 and irradiation time of 3min. The reaction orders of polymerization rate to monomer concentration and photoinitiator concentration are about 1 and 0.76, irrespectively, showing that chain transfer reaction takes place with much ease in VAC/LDPE system.

发现利用本文所设计的方法可将VAC快速地接枝在LDPE膜表面，如在光强为5400μw/cm〓，光照3min时，转化率和接枝效率可分别达到70％和76％；聚合反应速率对单体的反应级数约为1，而对光引发剂的反应级数为0.76，说明VAC光接枝聚合中链转移反应占相当大的比例。

Firstly, a two-dimension tensor product space is constructed, in which reproducing kernel exists. Secondly a multiresolution analysis is constructed in the reproducing kernel space. Then an orthonormal basis in is obtained. Thus,the reproducing kernel space can be expressed by wavelets spaces. Wavelets approximation formula and sampling formula can also be obtained in the space. Besides, the wavelets approximation formula is simple and easy for calculation. That completes the theory of multiresolution analysis in finite interval fully and provides theoretical base and algorithm for application.

首先，构造二维张量积空间，并证明该空间具有再生核；其次在再生核空间中，建立多尺度分析，获得该空间的一个标准正交基，使得再生核空间可以由小波空间来刻画，进而得到小波级数和相应的采样公式，而且给出的小波级数形式简单易于数值分析，进一步完善了有限区间上的多尺度分析方法，也为实际应用提供了良好的理论基础和算法。

In SMFSIA/CAG, to increase computational efficiency in solving the matrix equation, both the speed of the iterative convergence and the matrix-vector multiplication are picked up based on iterative theory. The extended formula of the high order Taylor's series about the horizontal distance is derived. The relationship between the Taylor's series or the neighborhood distance and the efficiency of the arithmetic are analyzed.

在SMFSIA/CAG中，基于迭代法的原理，通过加快迭代收敛速度和加速矩阵向量积两个方面对该算法进行了改进，推导了关于平面展开的高阶泰勒级数展开公式，并对近场相关距离和泰勒级数展开阶数对算法效率的影响进行了分析。

The hydrolysis rate constant of TEOS in mixed systems was larger compared with TEOS in single precursor systems.

与单前驱体水解一致的是，在双前驱体系中TEOS和DDS自身的反应级数仍保持一级，但是氨和水的反应级数都有不同程度的增大。

In order to obtain the order of reaction between propanone and iodine, colorimeter sensor can be used. The variation of transmittance and absorbance can be fed into the computer. The statistics wizard of the software can perform linear fitting of the data. The order of reaction can then be calculated through the manipulation of the line slope and y-intercept. Download Teachers' Notes

至於研究丙酮与碘的反应级数方面，则可利用比色计感应器，反应时混合物的吸光度和透射比数据均可传送到电脑，利用软件所提供的统计精灵更可以把数据进行图线分析，从所得的直线斜率和Y轴截距等有关资料便可计算出反应级数。

I can not make it blossom and suits me

我不能让树为我开花

When temperatures are above approximately 80 °C discolouration of the raceways or rolling elements is a frequent feature.

当温度高于 80 °C 左右时，滚道或滚动元件褪色是很常见的特征。