导出

By integral transformation of basic equations, the stress and displacement expressions with unknown coefficients of elastic and viscoelastic materials were obtained in Laplace domain respectively, and introducing dislocation density functions, the singular integral equations were got according to the boundary conditions and interface connection conditions, further adopting Gauss integration and Gauss-Jacobi integration formula, the problem was reduced to algebraic equations, then it can be solved with the method of collocation dots in Laplace domain. Finally, the time response of dynamic stress intensity factor was calculated with the inverse Laplace integral transformation.

采用积分变换方法，得到Laplace域内弹性和粘弹性材料的应力和位移的含未知系数的表达式；引入位错密度函数，并通过边界条件和界面连接条件，导出反映裂纹尖端奇异性的奇异积分方程组，采用Gauss积分，并运用Gauss-Jacobi求积公式化奇异积分方程组为代数方程组，利用配点法进行求解；最后经过Laplace逆变换，求得动态应力强度因子的时间响应。

It is pointed out the calculated method of the gear ratio and limit pressure angle .

通过对克林根贝格齿制的准双曲面齿轮啮合特性的分析，导出了该种齿制齿轮传动比和极限压力角公式。

With the knowledge of linear algebra, general formula for arbitrary order Taylor finite difference has been derived. In this paper, the analysis of spectral property and computational error of arbitrary order TFD is presented in detail. Then it is applied into the numerical solution of Maxwell's equations. Stability condition and numerical dispersion relation are derived.

本文借助于采样定理，详细分析了不同阶Taylor中心差分格式的谱特性以及计算误差，并将任意阶Taylor中心差分格式用于数值求解麦克斯韦方程中，严格导出了稳定性条件和数值色散关系的表达式，引入了新的误差定义来衡量算法的好坏。

Under some suppositions a general lubrication equation of natural human joints is obtained in the paper.

在作了一系列假定后，导出了具有一般意义的关节润滑方程。

When the vehicle vibrates, the ratio coefficients of the characteristics of components in fixed position and the corresponding characteristics of suspension are a function of generalized coordinates.

车辆振动过程中，实际安装位置的元件特性与悬挂特性的比例系数是广义坐标的函数。为了使数学模型尽量接近实际情况，本文导出了此比例系数与广义坐标的关系。

Based on the analytic model of an eccentric slider crank mechanism with elastic effects at both joints of the coupler and four coupler Mathieu-typed equations of motion in terms of the generalized coordinates of the system,the extract solution is developed from the improved Hill method with accelerated convergence.

在所建立的连杆接头处具有弹性效应的曲柄滑块机构的动态解析模型以及在广义坐标下推导出的4个马修型运动方程的基础上，由具有加速收敛性的改进希尔法进行了精确求解。

Firstly, the descriptions of Instantaneous Polarization Projection Sequences of signal and noise are presented and statistics of generalized distance between random EM wave and the anticipant signa are derived.

首先给出了目标散射信号和随机极化波的瞬态极化投影序列表征方法，导出了随机极化波的IPPS到期望点广义距离的统计特性。

Some formulas of the weighted Moore-Penrose generalized inverse of the sum of two matrices are given under two different kinds of conditions, related existing results are extend and modified with a sample and direct proof method.

在两种情形下，利用矩阵的加权Moore-Penrose逆导出了两矩阵和的加权Moore-Penrose逆的公式，其推导证明简洁而直接，文中还给出两矩阵可以同时加权奇异值分解的充要条件，指出了J.K。

Geodesic curvature of the pitch curve on spherical surface was introduced as a medium,through which the pitch curve on spherical surface can be changed into equivalent planar pitch curve by numerical computation method.

以曲面上曲线的短程曲率为媒介，导出了球面节曲线伸展成平面当量节曲线的算法。

In applying the preceding formulae, it should be remembered that they have be derived with the help of the laws of geometrical optics.

在使用 上述那些公式时，必须记住它们是利用几何光学的一些定律导出的。

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。