开普勒第三定律，就是你们在考试中和,作业中推导出的：,周期的平方等于，4π的平方乘以1,加上r2的三次方。
Kepler's Third Law, which you derived on your exam as well as on an assignment: r1 the period squared equals four pi squared times r1 plus r2 to the power three.
相信一般的船舶动力学中这些方程会有重要的应用。本文建立了一个定理以便于推导这一方程。
Such equations are deemed to have important application in general ship dynamics and a theorem is established to facilitate the derivation of the equations.
推导了冲激荷载作用下薄层单元法的基本计算公式，运用这一方法对土中的波动传播进行了模拟，并给出了计算实例。
The formulation of thin-layer element method was derived, the wave propagation process was simulated by the method, and a calculation example was given.
利用这一方法推导了在马氏相关序列下的二项分布的概率函数。
By using this method, we deduced the probability generating function of the binomial distribution in the Markov dependent sequence.
并从设计需要出发，推导了隔行扫描公式，这是一个选择扫描体制的重要公式，应用于总体设计考虑十分方便。
To meet the designing requirements, an interlaced formula has been derived. It is an important formula for selecting the scanning system and offers great convenience to overall design considerations.
通过对现金流估价法模型的推导，着重阐释了运用现金流估价法的几个关键步骤，以及运用这一方法的引进中需注意的几个问题。
By introduction of cash flow evaluation method model, this paper explains the key procedures in using it and problems that should be paid more attention to in introduction.
另一方面又利用矩阵理论等推导出含有二次项的非线性函数的协方差传播公式的矩阵形式。
On the other hand, it also derives the covariance propagation formula of non-linear function containing quadratic term in matrix form using the matrix theory etc.
本文基于半球形流的特点，利用质量守恒原理，通过推导得到了由拟压力、压力平方和压力一次方表示的产量公式。
Based on the mass conservation principle, the production formula of semi-spherical flow for pseudo-pressure, pressure-squared and pressure are derived in this paper.
其次，分析了逼近模型，推导了单圆弧逼近方法，用这一方法来逼近叶片曲面，提高了逼近速度。
Secondly, analysed the approach model, described circular arc approximation method, approaching blade curved surface with this method and realized raise of the approach speed.
对文献中已给的目标方位角的最小均方误差表达式进行了推导，并且给出了方位角的最小均方误差和噪声偏差之间的关系。
Extend the expressions of the minimum mean squared error bounds of the references, and give the relations of the minimum mean squared error bounds of pose Angle and noise standard deviation.
这种滤波器的关键是在均方意义下推导无偏转换测量误差协方差阵的最佳估计。
The key of the presented filter is to derive the best estimate of the covariance matrix of the unbiased converted measurements in the mean-square sense.
首先对具有任意自相似指数的正交异性弹性动力学问题推导了解的一般表示，给出了一般解法，然后用这一方法对若干具体问题进行求解。
In the present paper, the general representations for the solution are firstly derived for orthotropic elastic dynamic problems of arbitrary index of Self similarity.
从预测模型、反馈校正和优化控制三方面对预测函数控制基本原理进行了系统的阐述并针对一阶加纯滞后对象推导了单变量预测函数控制的基本算法。
The principle of PFC is introduced from three aspects: predictive model, error compensation and optimal algorithm. The basic PFC algorithm for first-order plus time delay system is developed.
通过公式推导，从理论上证明了增加加权数目并不能保证减小稳态均方误差。
It has been proved that the increasement of weights number can not ensure the reduction of steady state square error.
我们定义优化目标函数为前时刻轨迹和当前时刻特征提取结果的均方误差和，推导了相应的轨迹学习算法。
The optimization function is defined to be the sum of the squared error between the previous trace and the current pattern representation.
推导出供方短期单位总成本，并求出边际成本曲线，即供应函数。
According to this production function, the unit total cost and marginal cost of supplier can be calculated, so the supplier can adjust the supply according to the change of market.
推导出供方短期单位总成本，并求出边际成本曲线，即供应函数。
According to this production function, the unit total cost and marginal cost of supplier can be calculated, so the supplier can adjust the supply according to the change of market.
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