级数

Hilbert space and generalized Fourier series in Hilbert space,etc.

Hilbert空间与广义Fourier级数，主要讲授内积空间内积空间中的正交系，投景定理，与广义Fourier级数。

Of the series and several columns do not understand please see this article: Series and the concept of a1, a1q, a1q2, a1q3 ...., called the common ratio for the q of the geometric sequence.

对级数和数列不了解的请先看这篇文章：数列与级数的概念a1， a1q， a1q2， a1q3。。。。，称为公比为q的等比数列。

We know that although the geometric series is the most basic series, it has very useful properties, which can be used to solve the problems encountered in complex analysis.

首先我们都知道几何级数是级数中最简单、也是最基础的级数，但是其具有非常好的性质，可以用来解决我们在复分析中的遇到的一些问题。

In this paper, the analysis model of crustal vertical movement is established based on the hypothesis of the global flux isostatic datum, and its harmonic function series solution is proposed.

根据全球通量均衡假说建立了地壳垂直形变场的分析模型，在球面近似下求得了该模型的球谐函数级数解并拟合了两个不同区域的地壳垂直形变场，编绘了等值线图，继而在密切平面坐标系下导出了该模型的Fourier级数解。

Then steady forced vibration of the nonlinear Disk spring-mass system under base excitation and force excitation is obtained individually by using the Fourier series analysis and harmonic balance method.

详细探讨了考虑静力载荷影响的、具有弹性非线性和Coulomb摩擦阻尼非线性的碟簧元件的建模和动力学特性，首先利用Fourier级数分析技巧和平均法研究了非线性碟簧-质量系统的自由振动，讨论了影响自由振动的振幅和频率的各种因素，然后利用Fourier级数分析技巧和谐波平衡法研究了地基激励和力激励下非线性碟簧-质量系统的强迫振动，通过详细的参数研究考察了非线性碟簧元件的减振性能特征，最后采用修正的稳定性分析方法研究了两种激励下稳态响应的稳定性。

The Taylor formula holds the very important status in the differential calculus, especially in solves in some concrete problems to have the extremely important application, for instance the proof inequality, the judgment improper integral collects the divergence, asks the function the limit, asks the function the higher order derivative, determines certain complex progressions to collect the divergence, solves certain differential equation, as well as approximate calculation in and so on application, therefore this article will do the thorough research to these seven aspects.

摘 要：泰勒公式在微分学中占有非常重要地地位，尤其在处理1些具体的茄题中有10分重要的应用，比如证明不等式，判断广义积分的敛散性，求函数的极限，求函数的高阶导数，判定某些复杂级数的敛散性，求解某些微分方程，以及近似计算等中的应用，因此本文将对这七个方面做深入的研究。关键词：泰勒公式；不等式；广义积分；极限；高阶导数；复杂级数；微分方程

By means of traditional criterions of generalized integral's convergence and divergence, this paper, from the analysis of integrated function's nature, discovers a series of new criterions, which are briefer and more suitable: on the aspect of generalized integral for functions of a single variable, through the investigation of integrated function, together with the inner relationship between positive series and generalized integral in infinite interval under the condition of positive function, it gives several criterions of generalized integral's convergence and divergence, which are similar to positive series' criterions of convergence and divergence.

本文从分析被积函数本身所具的性质出发，借助传统的广义积分敛散性判别方法，发现1系列更简捷适用的新判别方法：单变量函数广义积分方面，通过考察被积函数，结合正项级数与正函数情形下无穷区间上广义积分的内在联系，给出了几个与正项级数敛散性判别法相类似的广义积分敛散性判别方法；多变量函数广义积分方面，着重讨论了广义2重积分和广义3重积分，结合被积函数的特点，运用比较判别法和柯西判别法，本文给出了判别广义2重积分收敛的1种新方法。

Be called the infinite series of functions on the interval ,where

称为定义在区间上的无穷级数，简称级数。

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。

The complex function between isochromatic fringe orders and RGB gray values of the image pixels is described by BP artificial neural network.

其特点是通过BP神经网络建立图像中像素点的R、G、B颜色值与条纹级数N之间的非线性关系；可以准确地得到3级以内等色线条纹级数。

Objective To investigate the effects of interleukin-1 β converting enzyme gene on the biologic characteristics of ovarian cancer cells.

目的 探讨白细胞介素-1 β转换酶的表达，对卵巢癌细胞生物学特性的影响。

Campylobacter: This illness is the most commonly identified cause of diarrheal illness in the world.

弯曲：这种病是最常见的原因查明腹泻病，在世界上。