级数的和

Analytical expressions for electromagnetic fields of a vertical or horizontal electric dipole over the finitely conducting plane are derived subject to the boundary conditions; Sommerfeld type integral contained in Hertz potential is expressed as the sum of two parts: zeroth order Hankel function and an absolutely convergent series of spherical Hankel function.

在此边界条件下，推导出有限导电平面上垂直和水平电偶极子电磁场的解析表达式；赫芝位函数中的索末菲型积分被表达成零阶汉克尔函数与绝对收敛的球汉克尔函数级数之和的形式。

In accordance with the principle of chemical dynamics, a new evaluation method for rate of ammonification of urea was established, and the type of reaction of ammonification of urea was confirmed.

根据化学反应动力学原理，建立了尿素氨化速度的评价方法，确定了尿素氨化反应的级数，测定了普通尿素、缓释尿素在特定条件下的氨化反应常数和半衰期，并依此评价了涂层缓释尿素的缓释性能。

Shadow effect can not be neglected for thermal analysis of spacecraft,Accroding to the angle between solar light and antenna orbit plane and its orbit location,analytical geometry method was used for accurately calculating solar radiation heat flux distribution of reflector surfaces.To analyze the temperature field under heat flux,the formulations of net radiation flux density between two gray elements and the net flux density of gray surface under external thermal flux were deduced.Based on the characteristic of space environment,the nonlinear temperature distribution in transverse direction of reflector shell self radiation were considered,the finite element formulations were given for orthogonal material layered shell by Galerkin method.A layered element including a inner heat source layer was proposed,and the finite element formulation expressed by DOF of the inner heat source layer were put forward with temperature and heat flux boundarys between adjacent layer.

单馈反射面赋形天线是未来星载天线发展的一个重要形式，分析了基于物理光学、几何光学和几何绕射理论的理想反射面辐射场；介绍了基于几何光学的反射面天线赋形方法；针对赋形过程中辐射场的快速分析要求，比较分析了基于物理光学的Fourier-Bessel和Jacobi-Bessel级数展开方法以及GB展开分析方法；利用GB展开快速分析方法在20GHz频率下对0.6m口径的天线进行赋形分析，实现中国大陆的30dB增益覆盖，通过数值计算研究了固定增益期望下的口径尺寸随频率的变化，以及频率为20GHz的不同尺寸天线赋形后的覆盖目标区域最大增益的变化情况。

For any positive integer n, about the Smarandache LCM dual function SL*, the main purpose of the fifth Chapter is using the elementary method to study the calculating problem of a Dirichlet series involving the Smarandache LCM dual function SL* and the mean value distribution property of SL*, obtain an exact calculating formula and a sharper asymptotic formula for it.

对于给定的自然数n，关于Smarandache LCM对偶函数SL~*，本文第五章利用初等方法研究了一个包含SL~*的Dirichlet级数计算问题及SL~*的均值性质，分别给出了精确计算公式和一个较强的渐近公式。

Based on the boundary integral formula and natural boundary integral equation for the boundary value problems of biharmonic equation , the non-symmetrical banding solutions to the circular plate under thermal boundary conditions are gained by the Fourier series and convolution formulae.

根据双调和方程边值问题的边界积分公式和自然边界积分方程，利用傅立叶级数及卷积的几个公式，求得了相应变温边界条件下非对称载荷圆板的弯曲解，从实践上证明了此方法的可行性。

One is CFP continuation method which is proposed by Berkhout and Verschuur (1998). The other is ISS method which is proposed by Weglein etc.

一是由Berkhout和Verschuur(1998)提出的基于CFP延拓的算法，另一是由Weglein(1997)等人提出的基于逆散射级数法的算法。

In the study of the water oxygen resume, start off the mechanism of the atmosphere oxygen resume, the paper first poses the atmosphere oxygen resume equation and oxygen resume coefficent calculation formulation of the static state water. The number of the progressing of the Blak-phelps equation is made certain, and the atmosphere oxygen resume equation and coefficent are ensured in both conditions of considering the floor reflection and unconsidering the floor reflection.

在对湖库水体复氧研究中，从大气复氧的机理出发，首先提出静态水体的大气复氧方程和大气复氧系数计算公式，其中对Blak-phelps方程级数项项数的确定，不考虑底部反射的大气复氧方程和考虑底部反射的大气复氧这三个问题进行了深入分析，得出相应的结果。

This volume summary of the main examples of these algorithms on the basic theory and extensive analysis of the computer program design and numerical analysis of the linkages between, which is particularly noteworthy is the author of Random Number Generation procedures for processing and re-form calculation of power series.

本卷总结了主要算法范例及这些算法的基本理论，广泛剖析了计算机程序设计与数值分析间的相互联系，其中特别值得注意的是作者对随机数生成程序的重新处理和对形式幂级数计算的讨论。本书附有大量习题和答案，标明了难易程度及数学概念的使用。

Considering the skin effect and skin depth, a thin wall model and a thick wall model are derived creatively with different frequencies of discharge currents, which are used to study the relation between the spark location and the potential difference for a cuboid electrode.

本文从放电电流为任意函数入手，阐述了电极电位差法的检测原理，首次利用傅立叶级数推导了电位差与放电时间的关系，证明了放电电流为阶跃函数时，电位差与放电时间成指数关系；当放电电流中含有高频振荡时，电位差与放电时间的关系为指数曲线上叠加相移后的高频振荡；根据放电电流频率的不同，考虑到趋肤效应和趋肤深度，首创了薄壁模型和厚壁模型，研究了长方体电极下表面二维放电点位置与电位差的关系。

The results show that perfect anatase nanocrystalline TiO2 can be obtained by SGRTSE method and the photocatalytic activity of TiO2 can be improved by doping and surface treatment. In the experimental system, the addings of proper salts are beneficial to the photocatalytic degradation of DBSNa. The pH value of solution, adding amount of TiO2, flow rate of air, and initial concentration are the main influence factors for the photocatalytic degradation of methyl orange, and the apparent reaction order is pseudo-first-order, which could be described by Langmuir- Hinshelwood equation.

结果表明：sol-gel法结合室温溶剂蒸发诱导可制备出晶型良好的锐钛型纳米TiO_2；过渡元素和稀土元素杂原子掺杂，贵金属掺杂和表面酸化处理是有效提高TiO_2光催化活性的途径；试验体系中，在DBSNa的降解过程中加入适量的盐，可以大大加速降解效果；光催化降解水中有机物，溶液pH值，TiO_2投加量，曝气速率，被降解物起始浓度等是影响降解效果的重要因素；对起始浓度较低的有机物光催化降解过程可利用简化的Langmuir-Hinshelwood动力学方程进行描述，反应级数为拟一级。

The concept of equivalent rotationally rigidity is offered and the formula of rotationally rigidity is obtained.

主要做了如下几个方面的工作：对伸臂位于顶部的单层框架—筒体模型进行分析，提出了等效转动约束的概念和转动约束刚度的表达式。

Male cats normally do not need aftercare with the exception of the night after the anesthetic.

男猫通常不需要善后除了晚上的麻醉。