求和

Based on the author's own teaching accumulation , this paper puts forward kinds of summations of power series and series of numbers through exmaples .

结合自己的教学积累，通过实例，给出数项级数求和的多种途径。

All the angular integrations and spin summations involved in the problem have been carried out explicitly.

完成了所有角向积分和自旋求和计算，使精细结构能量表示为若干个径向积分之和。

5 Involving four arbitrary sequences and other general bilateral summations.

并由此得到了几个基本超几何级数求和公式及其极限情况。

In the course of these derivation, the orbital integrations and the summations over spin are completed and are presented3j, 6j, 9j symbols and the radial matrix elements.

在这些推导中，完成了所有角向积分和自旋求和计算，相应的结果用3j、6j、9j符号和待定的径向矩阵元来表示。

After all the angular integrations and spin summations completed, the needed parameters in the non-relativistic wave functions have been acquired using the variational method and so the functions themselves have been established in this way.

在第三章中，利用对角和法则，导出了类硼离子基态及第一激发态非相对论能量的解析表达式，完成涉及到的角向积分和自旋求和后，利用变分原理求出了非相对论性波函数中的待定参数，从而确定了非相对论性波函数，并获得类硼离子基态及第一激发态非相对论能量。

All the angular integrations and spin summations involved in the problem have been carried out explicitly. The energy is expressed finally as a sum of radial integrations.

完成了所有角向积分和自旋求和计算，使精细结构能量表示为若干个径向积分之和。

In a word, a new method that theoretically calculates the relativistic corrections and the fine structure of the energy levels in two-electron atom, including the atomic Hamiltonian expressed by spherical tensors, the calculation of the angular matrix elements and the summations over spin of the various interactions in the atomic Hamiltonian, and the approximate calculation of the radial matrix elements, has been provided in this thesis.

总之，本文为双电子原子能级的相对论修正和精细结构的理论计算提供了一种新的方法，包括原子哈密顿算符的球张量表示方法、原子哈密顿中各种相互作用项的角向矩阵元和自旋求和的计算方法，以及径向矩阵元的近似计算方法。

On the basis of the investigation of different moments, the concept of generalized moments is firstly defined and then, an abstract algorithm framework for computing the accurate generalized moments is presented. The framework replaces integrals on 2-dimensions space by summations on 1-dimension ORBIR list without introducing the error incurred by discrete sampling, and therefore, reduces the computation complexity for moments generation.

矩在工程实践中的应用非常广泛，在考察矩的实质的基础上，定义了泛化矩的概念，并研究泛化矩的生成框架，该框架在不引入离散化过程中存在的采样误差的前提下，将矩生成过程中需要的二重积分运算转化为在一维的ORBIR矩形序列上的求和，因此降低了矩生成的计算复杂度。

All the angular integrations and spin summations involved in the problem have been carried out explicitly, the energy is expressed finally as a sum of some radial integrations.

完成了所有的角向积分和自旋求和计算，自旋-其它轨道相互作用能最终用径向积分来表示。

This invention relates to three-dimensional seismic data processing quality monitoring technology. Selecting time-window and analysis frequency for FFT to obtain frequency-domain conversion result for every channel; taking mean-filter to obtain the statistic excited energy or noise disturbance; plotting all results on plane graph to monitor the 3D excited energy or noise disturbance; taking normalization and autocorrelation to all earthquake channel; summating all autocorrelation statistic result to obtain opposite statistic autocorrelation result; finding out and plotting the zero-crossing of autocorrelation on plane position for monitoring excited wavelet.

本发明涉及一种三维地震资料处理质量监控技术，步骤是：选定时窗和分析频率；对某炮各地震道在时窗内做快速富立叶变换，得到道数据在频率域变换结果；对同炮的所有地震道做频率域中值滤波，得到该炮的统计激发能量或噪声干扰量结果；将所有炮的计算结果绘到各炮点平面图上，监控三维激发能量或噪声干扰；对地震数据某炮的各地震道做归一化自相关；对同炮的所有地震道的自相关统计求和，得到该炮的统计自相关结果；寻找该炮统计自相关的零交叉时，将所有炮的零交叉时绘到各炮点平面位置上，完成激发子波监控。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了