导出

Based on the magnetic-elasticity nonlinear kinetic equations, physical equations, electrical kinetic equations and the expression of Lorentz forces, the magnetic-elasticity kinetic buckling equation of a current-carrying plate applied mechanical load in a magnet field were derived. The equation was transformed into the standard Mathieu equation by using Galerkin method. Thus, the magnetic-elasticity kinetic problem was changed into a problem of solving the Mathieu equation.

在载流薄板的磁弹性非线性运动方程、物理方程、洛仑兹力表达式及电动力学方程的基础上，导出了载流薄板磁弹性动力屈曲方程，并应用Galerkin原理把屈曲方程整理为Mathieu方程的标准形式，将载流矩形薄板在电磁场与机械荷载共同作用下的磁弹性屈曲问题归结为对Mathieu方程的求解问题。

Based on the magneticelasticity nonlinear kinetic equations, physical equations, electrical kinetic equations and the expression of Lorentz forces, the magneticelasticity kinetic buckling equation of a currentcarrying plate applied mechanical load in a magnet field were derived. The equation was transformed into the standard Mathieu equation by using Galerkin method. Thus, the magneticelasticity kinetic problem was changed into a problem of solving the Mathieu equation.

在载流薄板的磁弹性非线性运动方程、物理方程、洛仑兹力表达式及电动力学方程的基础上，导出了载流薄板磁弹性动力屈曲方程，并应用Galerkin原理把屈曲方程整理为Mathieu方程的标准形式，将载流矩形薄板在电磁场与机械荷载共同作用下的磁弹性屈曲问题归结为对Mathieu方程的求解问题。

To extract the parameters in partial coefficients matrix of potential efficiently in silicon substrate integrated circuits, an approximated closed-form three-dimensional multilayered Green's function is derived with a modified complex fitting the exponential function method in spectral domain.

为了有效地提取硅衬底集成电路中导体单元之间的电位系数矩阵，在谱域中采用了改进的复数拟合指数函数方法，导出了三维有耗多层介质中的近似闭式格林函数。

The carriage positioning was finished, the coordinate transformation matrix of the bucket relative to the ground and the digging depth were obtained and it is easy to make the three-dimensional trace control of the hydraulic excavator bucket easy.

然后，推导该定位车体位姿下铲斗坐标系相对于大地的坐标变换矩阵，导出挖掘深度定位公式，实现了挖掘机挖掘轨迹的三维空间定位，为实现挖掘机的三维空间轨迹精确控制与挖掘深度控制打下了基础。

Based on the method of matrix transformation used in the compound material mechanics, the anisotropic flexibility matrix of the anisotropic sand with a certain stress state is transformed to be an isotopic one of a certain isotropic reference material with the corresponding stress state, and a corresponding stress matrix is obtained simultaneously.

借鉴复合材料力学中矩阵转换的数学方法，将各向异性砂样的柔度矩阵转化为各向同性等效参考砂的柔度矩阵，同时导出与其相当的应力状态的表达式，以使对各向异性岩土材料的分析可转换为对各向同性状态进行分析，由此可将以前基于各向同性假设的强度条件能够用于各向异性土体。

Matrix element of coordinate operator ~l of harmonic oscillator is discussed by using coherent state and normal product.

利用相干态和正规乘积对谐振子任意次幂坐标算符^Xl矩阵元进行了讨论，导出了计算^Xl矩阵元的一般公式，为处理谐振子的微扰问题提供了一种新的方法。

In addition, in the solution set of corresponding equation, the expression of the optimalapproximation solution to given matrix is derived.

另外，导出了在线性流形上矩阵方程的解集合中与给定矩阵的最佳逼近解的表达式。

In addition, in the solution set of corresponding equation, the expression of the optimal approximation solution to given matrix is derived.

另外，导出了在矩阵方程的解集合中与给定矩阵的最佳逼近解的表达式。

Aimed at actual thermal system, a new distribution method for feedwater added enthalpy was deduced, which based on mass unit matrix analytical method.

以质量单元矩阵分析法为基础，再热机组的实际热力系统为研究对象，全面运用数学推导，导出了给水焓升分配的新方法。

From the perspective of matter wave in quantum mechanics, this paper, by describing the wave function of microcosmic particle and using probability wave, derives the distributive regularity of light intensity of the single slit diffraction and circular aperture diffraction.

光具有波粒二象性，从量子力学的物质波出发，利用描述微观粒子的波函数，采用几率波的方法，导出光的单缝衍射和圆孔衍射的光强分布规律，所得结果与波动光学中用惠更新－菲涅耳原理得到的结果一致。

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。