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In the thesis, the fundamental formula of FFD method derives from the square root that is approximated by a continued fraction expansion in the one-way wave equation. Optimizations of the parameters of the finite-difference operator improve the validity of the method.

本论文用连分式近似单程波波动方程中的平方根导出FFD算法的基本公式，并对FFD算法中的有限差分算子进行了系数优化，进一步提高了计算的有效性。

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。

The simulation result derives the suitable convergence factor and verifies the improvement of ...

最后通过仿真对比得到算法收敛因子的合理取值，验证了可变步长功率控制算法可有效提高功率控制精度和收敛速度。

Kiln derives from the Latin word culina, meaning kitchen or cookstove.

窑源于拉丁词库利纳，这意味着厨房或炉灶。

The authority for this new Copernican revolution derives, as of the old, from hard scientific evidence.

这次新的哥白尼式的解放，其真实性依旧来自于确凿的科学证据。

This project derives a general express of experiential covariance function, which is the basis of achivement of interpolation, extrapolation and continuation of local gravity field variables and estimation theirs at different heights.

提出局部重力场元经验协方差函数的通用表达方法，为实现局部重力场元的内插、外推、延拓或其他不同高度的重力场元估计一体化奠定理论基础。

The simthsonite name derives from English mineralogist James Smithson(1765-1829), who identified two different minerals smithsonite from hemimorphite in 1807, both have long been confused as same mineral, called calamine, used to produce brass, mixed with cupper.

18世纪末在欧洲，人们称用于冶炼黄铜的，和铜矿混在一起的锌矿石为菱锌矿，实际上那是的"菱锌矿"里面混杂了含水硅酸锌、异极矿和碳酸锌。由于产状大多时葡萄状，所以很难区分两种矿物。

According to the connective equation of normal distribution function of these parameters, the paper proposes a simple and practical method for the reliability design of involute cylindric gear transmission, and derives a design formula and a proofread formula.

根据这些参数的正态分布函数的联接方程，提出了渐开线圆柱齿轮传动可靠性设计的一种简单适用的方法，并推导出了设计公式和校核公式。

According to principle of spatial mesh, this paper derives synthetical equations of cylindrical indexing cam surface.

根据空间啮合原理，推导了圆柱分度凸轮廓面的综合方程式。

According to the clear water experiment, aeration performance of the new equipment is good with high total oxygen transfer coefficient and oxygen utilization ratio.

曝气设备的动力效率在叶轮转速为120rpm～150rpm时取得最大值，此时氧利用率和充氧能力也具有较高值。

The environmental stability of that world - including its crushing pressures and icy darkness - means that some of its most famous inhabitants have survived for eons as evolutionary throwbacks, their bodies undergoing little change.

稳定的海底环境─包括能把人压扁的压力和冰冷的黑暗─意谓海底某些最知名的栖居生物已以演化返祖的样态活了万世，形体几无变化。