级数的和

Energy density and particle density in high energy heavy-ion collisions are calculated with infinite series expansion method and Gauss-Laguerre formulas in numerical integration separately, and the results of these two methods are compared, the higher terms and linear terms in series expansion are also compared.

分别用无穷级数展开方法和数值积分计算中的高斯拉盖尔求积法对高能重离子碰撞中能量密度和粒子密度数值进行计算，并对结果及级数展开中的高次项和一次项的大小进行了比较。

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。

This course mainly contents real number muster and function, limit of number sequence, limit of function, continuity, derived number and differential, differential mean value theorem and its application, completeness of real number, integral, series(including positive series and Fourier series), multiple- differential, double integral, integral with parameter, curve integral, camber integral and so on.

理解和掌握《数学分析》的概念、理论和方法，对于学生加深理解数学的基本思想和方法，培养抽象思维能力和逻辑思维能力，提高数学素养具有重要的意义。主要内容包括：实数集和函数，数列极限，函数极限，连续性，导数和微分，微分中值定理及其应用，实数完备性，积分、级数(包括幂级数、Fourier级数)、多元微分学、重积分、含参变量积分、曲线积分、曲面积分等。

A new general kinetic equation was derived in which the effect of the removal of condensation water was taken into account completely, and was applied to the polyesterification kinetic study of AA/HPHP and AA/NPG. It was found that the reaction order of self-catalyzed polyesterification was not constant. For these polyesterifications, the reaction order was 2.5 at a low temperature, while 3.0 at a high temperature.

考虑缩合水的排除对反应体系的影响，用体积浓度单位推导出一个新的聚酯反应总包动力学方程，并应用到AA/HPHP和AA/NPG两个聚酯化反应的动力学研究中，研究发现，自催化聚酯反应的反应级数并不是固定值，对于AA/HPHP和AA/NPG两个聚酯化反应而言，低温时反应级数为2.5，高温时反应级数为3.0。

Based on the linear elastic theory, the piezoelectric theory and magnetostrictive theory, using the power series expansion series method, a three-dimensional resolution of the natural frequencies of a simply supported rectangular laminate is investigated.

基于线弹性理论、压电理论和磁致伸缩理论，使用幂级数和傅立叶级数解法，得到了四边可移简支、磁电复合材料层合板的固有频率的三维精确解。

Furthermore,the stability behavior and accuracy characteristics of the algorithmare proven by a spectral decomposition method.

在前人工作的基础上，提出了一种新的用于解决结构动力分析问题的时间积分方法——Taylor级数方法；建立了求解线性问题和非线性项可以表示为多元多项式形式的非线性问题的Taylor级数方法的理论，并给出递归求解通式；阐述了该方法的程序实施过程，给出了计算流程图，并在非线性有限元分析平台NFAP中嵌入了Taylor级数方法的计算模块；利用谱分解的方法分析了该方法的稳定性和精度特性，以封闭的解析形式给出了描述积分法特性的周期延长率和振幅衰减率的表达式；通过对该方法的理论分析和特性研究，阐述了该方法的可行性和高效性。

According to the theory of elasticity, the displacement and stress solutions of the model is expressed in the form of the sum of two infinite series of Fourier and Fourier-Bessel functions.

通过弹性理论分析，将其位移和应力表达成富氏级数和富氏—贝塞尔级数两个无穷级数之和的形式，从而求得了对应这个模型的纤维与基体之间更为精确的理论分析解。

Both the offset and tilted fedcoupling-slot array between the curved guide and sectoral guides and longitudinal radiating-slot array on sectoral guide are analyzed by moment method, taking into account of the effects of finite wall thickness and mutual coupling between the slots, employing the acceleration algorithms to accelerate the summation of slowly convergent series of the self-admittance of the waveguide-slot aperture, and introducing the surface Fock functions to simplify the computation of the self-and mutual coupling of the slots on the surface of cylinder.

采用矩量法分别分析弯波导与扇面波导间偏置倾斜馈电耦合缝阵和扇面波导轴向辐射缝面阵，其中计及有限波导壁厚及缝间互耦的影响，运用级数加速算法对波导中自导纳矩阵元级数进行加速处理，并引入表面Fock函数简化圆柱面上缝口面的自耦和互耦的计算。

Where the nth term is said to be the general term of the series, moreover, the nth partical sum of the series is given by .

叫做无穷级数，简称级数，记为，即其中第项叫做劫数的一般项。称为级数(1)的部分和。

The spin-1/2 dimerized antiferromagnetic system is related to spin-Peierls tran-sition.There are still some discrepancy on the behavior of the ground energy densityand energy gap,such as pure power-law,logarithmic correction to the pure power-law in the uniform,integer powers in the dimerized limit,etc.

自旋S-1/2的二聚化反铁磁链与spin-Peierls相变有关，在对其基态能和激发能隙的临界行为描述上仍存在一些不完全一致的观点：如均匀极限的纯幂级数律，纯幂级数律的对数修正；二聚化极限的整数幂级数行为等。

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。