导出

On the theroy and method of analysing the longitudinal inertia force of railway goods some fresh views are presented.

本文从分析作用于货物的纵向惯性力入手，对铁路货物运输的稳定性问题进行了理论探讨，导出了车载货物的纵向动力学方程及其有关推论，对铁路货运领域在货物纵向惯性力问题上的理论和方法提出了一些新的见解，建议统一查定我国铁路货车在各种运行和调车工况下的加速度值，做为日常确定货物稳定性的科学依据。

Based on the Hoek-Brown nonlinear strength criterion and simple Bishop's method, a new computation formula of stability safety factor for the broken jointed rock slope is presented.

基于Hoek-Brown非线性经验强度准则和简化Bishop法，导出了节理破碎岩体边坡新的稳定性系数计算公式。

Through carrying out force bearing analysis on the spring ring and utilizing the correlated theory of mechanics of materials,the relationship between bending moment and bending angle was derived while the spring was subjected to the action of bending moment.The computation formula of bending angle of spring was obtained,and an optimization was carried out on the parameters.

同时，对密圈圆柱螺旋弹簧的弯曲刚度和横向刚度的计算也有一定的研究，以往的普遍研究方法是将整个弹簧等效为一等截面的弹性圆柱体，基于普通弹性理论的方法导出了弹簧的弯曲刚度和横向刚度的计算公式，具有较大的误差[1，2]。

Based on the tensor expression for the Breit-Pauli Hamiltonian,and with the aid of irreducible tensor theory,the theory of relativistic corrections to the non-relativistic energies of many-electron atoms has been generalized to the case in which Racah wave functions are the linear combinations of multi-Slater wave functions,analytic formulism for calculating the relativistic corrections,which include mass correction,one-and two-body Darwin correction and spin-spin contact interaction,has been derived,all th...

以Breit-Pauli哈密顿的球张量形式为基础，借助不可约张量理论，将多电子原子能量的相对论修正理论拓展到了原子的拉卡波函数为多个Slater基函数的线性组合的情形，导出了此情形下多电子原子能量相对论修正(包括相对论质量修正项、单体和双体达尔文修正项、自旋-自旋接触相互作用项)的解析表达式，完成了所有角向积分和自旋求和计算。

Based on the tensor expression for the Breit-Pauli Hamiltonian,and with the aid of irreducible tensor theory,the theory of relativistic corrections to the non-relativistic energies of many-electron atoms has been generalized to the case in which Racah wave functions are the linear combinations of multi-Slater wave functions,analytic formulism for calculating the relativistic corrections,which include mass correction,one-and two-body Darwin correction and spin-spin contact interaction,has been derived,all the angular interactions and spin sums involved in the problem have been worked out explicitly by using irreducible theory.

以Breit-Pauli哈密顿的球张量形式为基础，借助不可约张量理论，将多电子原子能量的相对论修正理论拓展到了原子的拉卡波函数为多个Slater基函数的线性组合的情形，导出了此情形下多电子原子能量相对论修正(包括相对论质量修正项、单体和双体达尔文修正项、自旋-自旋接触相互作用项)的解析表达式，完成了所有角向积分和自旋求和计算。

A new method relying on the Stroh formulism and the theory of the surface impedance tensor was developed to investigate the dynamic instability of interfacial slip waves.The concept of the surface impedance tensor was extended to the case where the wave speed is of a complex value,and the boundary conditions at the frictionally contacting interface were expressed by the surface impedance tensor.Then the boundary value problem was transformed to searching for zeroes of a complex polynomial in the unit circle...

基于Stroh公式和表面阻抗张量理论，提出了研究界面滑移波动态失稳问题的一种新的方法·该方法将表面阻抗张量概念推广到复波速域，并将摩擦接触界面上的边界条件以表面阻抗张量表示·最终将边值问题化归为求解一个复多项式在单位圆内的根·以弹性半空间与刚体平面相对稳态摩擦滑移为例进行了详细的分析，导出了一个4次复特征方程并讨论了方程在单位圆内解的特性，给出了滑移界面波失稳条件的显式解析表达式

Firstly, the equation for stress intensity factors under static uniform pressure is used as the reference case, and then the weight function for a thick-walled cylinder containing a radial edge crack can be worked out. Secondly, the dynamic stresses in uncracked thick-walled cylinders are solved under internal impulsive pressure by using mode shape function method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary conditions, and the history and distribution of dynamic stresses in thick-walled cylinders are derived in terms of Fourier–Bessel series. Finally, the dynamic stress intensity factor equations for thick-walled cylinder containing a radial edge crack subjected to internal impulsive pressure are given by dynamic weight function method.

首先采用静态内压下的应力强度因子作为参考解，得到了带径向边裂纹厚壁圆筒的权函数；然后用振型函数方法推导无裂纹厚壁圆筒在冲击内压下的动应力响应，分析中将相应的弹性动力学方程解分为满足非齐次边界条件的准静态解和满足齐次边界条件的动态解的叠加，利用傅立叶-贝塞尔级数展开，推导出了厚壁圆筒内动应力的响应历程和分布规律；最后由动应力权函数方法导出带径向边裂纹厚壁筒在冲击内压下的动态应力强度因子计算公式。

By using the Fourier series expansion, approximate analytical propagation equations of laser beams through a paraxial optical ABCD system with different apertures are derived.

用傅立叶级数展开法研究光束通过有光阑限制的近轴ABCD光学系统的传输特性，导出了光阑透射率函数不同时的传输公式。

The physical significance and the logical relation of the Fresnel diffraction and the Fraunhofer diffraction,along with the influence of inclination factor on diffraction pattern are discussed in detail.

导出了描述夫琅和费衍射的正确公式，讨论了菲涅耳衍射和夫琅和费衍射的物理意义、两者间的逻辑关系，以及倾斜因子k对衍射花样的影响。

The difference of Fraunhofer diffraction between Information Optics and Physical Optics is analysed, the consistence of which is pointed out about one single object.

分析信息光学和物理光学中夫朗和费衍射的差别，指出在研究单个物体的夫朗和费衍射二者的一致性，根据普适的夫朗和费衍射的定义，导出夫朗和费衍射的近似条件。

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。