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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。

By the methods of reducing order and Euler s eigenvalues,we obtain the general solution formula to one kind of systems of three dimensional second order ordinary differential equation with constant coefficients.

采用降阶和特征根方法,给出了一类三维二阶常系数微分方程组的通解公式,并通过算例与拉氏变换法进行了比较。

Finally, the solution formula of the semiboundless mixed problem of the fractional diffusion equation is obtained.

最后得到分数阶扩散方程半无界混合问题的求解公式。

One kind is using the particular solution of the indefinite equation, which can be obtained by the property of the prime number , and the foundation system of solution of its corresponding homogeneous equation ,obtains its solution formula. Another kind is under the foundation of the matrix primary line transformation, and with the aid of some knowledge of numeral theory, obtains its solution formula.

一种是利用该不定方程的一个特解和其相对应的齐次方程的一个基础解系,得出该不定方程的求解公式,而这个特解可以由素数性质得到;另一种是在矩阵的初等行变换基础上,借助一些数论知识,得出该不定方程的求解公式。

Now by using Dai's exact solution formula and studying the asymptotical behavior controlcondition and using the series expression of the famous Riemann Zeta-function in number theory,after introducing and proving a new representation theory of inverse Laplace transformation wedirectly obtained Chen's solution formulae and their unique existence condition without usingLaplace transformation and〓 inverse formula.

本文从带消发散参数的严格解出发,通过研究渐近行为控制条件,利用数论中著名的Riemann-Zeta函数的级数表示,引入并证明一个逆Laplace变换的新的表示定理,直接导出了陈等发展的级数解,并得到了级数解的存在、唯一性条件。

This paper gives two kinds of solution formula of the Lai coefficient indefinite equation.

摘要本文给出了赖系数不定方程的两种求解公式。

A TRIZ general solution formula is "The problem should solve itself."

一个TRIZ的普通解决方案通式是"问题应自行解决。"

Mechanism of the components in antirusting solution for large steel structurepretreatment of coating was investigated and the solution formula was optimized.

研究了防锈液中各成分的作用机理和最佳配方,适用于大型钢结构的涂装前处理。

Please outline the composition principles for ascertaining a nutrient solution formula.

请简要说明在确定营养液配方时的组成原则。

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每逢看到沃林顿那刚毅的脸,那乌黑、忧郁的眼睛,她便会相信,他一定作过不幸的爱情的受害者。

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