查询词典 expansion in series

Then the boundary element integral equation of interior and exterior form is deduced in detail, also the form with corner coefficient. The significance for numerical calculation and principle of the singular integral is analyzed, and a non-isoparametric transformation method is presented to calculate weak singular integral and Cauchy integral, the method presented provides us a very simple way to computer the two kinds of singular integral of Helmholtz boundary integral equation, and it is easy to program in computer. After the difficulty of the calculation for multi-frequency of Helmholtz boundary element is explained, a method named SECHIEF (Series Expansion Combined Helmholtz Integral Equation Formulation), which is focused on the computational efficiency, is presented.

对结构声辐射的边界积分方程的内部形式与外部形式进行了详细的推导，给出了角点系数的计算方法与边界积分方程的形式，在此基础上，分析了奇异积分产生的原理及其对数值计算的重要性，提出了一种计算奇异积分的非等参(来源：Ae8a8BC论文网www.abclunwen.com)单元的变换方法，该方法给Helmholtz 声学边界积分方程中的弱奇异积分与Cauchy 奇异积分的计算以及编程提供了极大便利。

In 3D scalar Helmholtz equation computation, for the first time, this dissertation proves that there is an analytical solution of infinite series convegence for the problems satisfying the MT expansion condition, derives the MT general solution formula and the using laws, proves or explains the using rules that are used in the GMT and but they can't be proven or explained by The GMT.

首次从理论上证明，在三维静电场分析中，存在一种无穷级数收敛，且有一定普遍性的解析解；推导出三维静电场分析的多极理论通解及其使用规则，证明或解释广义多极技术不能证明或解释的若干使用规则，用多极理论求解工程实际中的三维静电场边值问题。

In 2D eddy current field computation, for the first time, this dissertation proves that there is an analytical solution of infinite series convegence for the problems satisfying the MT expansion condition, derives the MT general solution formula and the using laws, proves or explains the using rules that are used in the GMT and but they can't be proven or explained by the GMT, and solves several real engineering examples of 2D eddy current field boundary-value problems by the MT.

本文从电磁理论和有关数学定理出发，通过引入内极、外极、内交角的概念，建立一种新的电磁场计算体系——电磁场分析中的多极理论；从理论上证明，在电磁场分析中存在一种无穷级数收敛，且有一定普遍性的解析解。

According to the theory created for the generalized multi-pole technique (in domain of half-analytical method), the center of each circle is determined as a starting point of each variable in a series expansion of the 2D-field solution function, and the arranging blank of the starting points in the generalized multi-pole technique can be filled up owing to the precise variable positioning.

根据为广义多极技术创建的理论体系，这些极点确定了解函数在级数展开式中各变量的起点。正因为这些变量的准确定位，不仅克服了广义多极技术中极，点位置设置的盲目性，而且提高了解的计算效率和计算精度。

Also, if a complex analytic function is defined in an open ball around a point x 0, its power series expansion at x 0 is convergent in the whole ball. This is not true in general for real analytic functions.

复解析函数则不同：凡复解析函数必为全纯函数（即复可导，以实变量表示则是满足柯西-黎曼方程），反之亦然，因此全纯函数与解析函数在复分析中是同一类对象。

Watts Series ET non-potable water expansion tanks may be installed in a tee or any other suitable tapping in the heating system and can be installed in a vertical or horizontal position.

美国瓦茨系列ET非饮用水膨胀罐可以安装在一个T形管或供暖系统上任何其他适合的连接端口上，可以垂直安装或水平安装。

The fiber are successfully used in the practical noise control. The model of aerodynamics in the course of the intermittence exhaust is simplified into exhaust problem of two stage series cylinder. Digital calculation program which can really imitate aerodynamics characteristics in the exhaust process is established. A simple formula which can be used for calculating the volume of the silencer expansion chamber is established.

作者指出间歇性排气过程的空气动力模型可简化为两级气缸串联的排气问题，编制的数值计算程序真实地模拟了排气过程中的空气动力学特性，建立了消声器膨胀消声室体积大小计算的表达式。

Since its establishment and years accumulation and expansion of the market, the company produced "SNOW SHOW" brand down, cotton, coat, jacket, etc. series of casual clothing in Manchuria, Sui Fen, Urumqi, three port cities, and has offices in Moscow ; in Russia, Italy, Kyrgyzstan, Tajikistan, Syria, Ukraine and other countries; in Moscow, Novosibirsk, leaf cards, Kiev, Bishkek and other regional markets to build a perfect sales network terminal system, and set a good reputation in local market.

公司成立至今，经过多年的市场积累和拓展，公司生产的&SNOW SHOW&品牌羽绒、棉服、风衣、茄克等系列休闲服饰在满洲里、绥汾河、乌鲁木齐三个口岸城市和莫斯科设有办事处；在俄罗斯、意大利、吉尔吉斯斯坦、塔吉克斯坦、叙利亚、乌克兰等国家；莫斯科、新西伯利亚、叶卡、基辅、比什凯克等地区市场构建了完善的终端销售网络体系，并在当地市场树立了良好的口碑。

After years of accumulation and expansion since it was establishment of the market, the company product of "SNOW SHOW" brand down, cotton, coat, jacket, etc. series of casual clothing have offices in Manchuria, Sui Fen, Urumqi, three port cities and in Moscow. In Russia, Italy, Kyrgyzstan, Tajikistan, Syria, Ukraine and other countries; in Moscow, Novosibirsk, leaf cards, Kiev, Bishkek and other regional markets to build a perfect sales network terminal system, and set good reputation in the local market.

公司成立至今，经过多年的市场积累和拓展，公司生产的&SNOW SHOW&品牌羽绒、棉服、风衣、茄克等系列休闲服饰在满洲里、绥汾河、乌鲁木齐三个口岸城市和莫斯科设有办事处；在俄罗斯、意大利、吉尔吉斯斯坦、塔吉克斯坦、叙利亚、乌克兰等国家；莫斯科、新西伯利亚、叶卡、基辅、比什凯克等地区市场构建了完善的终端销售网络体系，并在当地市场树立了良好的口碑。

Since its establishment, after years of accumulation and expansion of the market, the company produced "SNOW SHOW" brand down, cotton, coat, jacket, etc. series of casual clothing in Manchuria, Sui Fen, Urumqi, three port cities, and has offices in Moscow ; in Russia, Italy, Kyrgyzstan, Tajikistan, Syria, Ukraine and other countries; in Moscow, Novosibirsk, leaf cards, Kiev, Bishkek and other regional markets to build a perfect sales network terminal system, It has enjoyed a good reputation in the local market.

公司成立至今，经过多年的市场积累和拓展，公司生产的& SNOW SHOW &品牌羽绒、棉服、风衣、茄克等系列休闲服饰在满洲里、绥汾河、乌鲁木齐三个口岸城市和莫斯科设有办事处；在俄罗斯、意大利、吉尔吉斯斯坦、塔吉克斯坦、叙利亚、乌克兰等国家；莫斯科、新西伯利亚、叶卡、基辅、比什凯克等地区市场构建了完善的终端销售网络体系，并在当地市场树立了良好的口碑。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。