导出方程

The fine structure Hamiltonian for Hydrogen-like atoms is derived using the nonrelativistic approximation of the Dirac equation for one electron moving in the Coulomb field.

从Coulomb场中运动的电子的Dirac方程出发，取其非相对论极限导出了类氢离子的精细结构哈密顿的表达式。

Earthworks zero line is determined by constructing the spatial gridding curved surface model of the original terrain and the field leveling design terrain by digital elevation mode. The DEM data of original terrain are obtained by actual measurement. The mathematical correlation is deducted to demonstrate the relationship between the coordinates of any point on spatial line and the direction cosine by the spatial linear equation. DEM data obtaining program is compiled by Fortran9.0 and it is applied automatically to obtain the DEM data of field leveling design terrain.

目的 利用数字高程模型(digital elevation model， DEM)构造原始地形和场平设计地形的空间网格曲面模型，确定土方工程中的零线方法通过实测提取原始地形DEM数据；依据空间直线方程，推导空间线段土任意点的坐标与方向余弦的数学关系式，采用Fortran90程序设计语言编写DEM数据提取程序，自动提取场平设计地形DEM数据；应用Surfers8.0和MapInfo软件构造规则的网格空间曲面模型并导出网格节，点数据；擦除场平设计范围外数据。

A parallel algorithm for certain real symmetric block-tridiagonal linear systems on distributed-memory multicomputers is proposed. This algorithm is based on the block factorization of the coefficient matrix. This algorithm is used to solving the block-tridiagonal linear systems resulted from the finite difference approximation to Poisson's equation with Dirichlet boundary conditions. Then we get a parallel algorithm which speedup tends to linear speedup.

7研究了一类实对称块三对角线性方程组的分布式并行求解，提出了一种基于块矩阵分解的高效分布式并行算法，将其应用于求解带Dirichlet边界条件的Poisson方程导出的块三对角线性方程组，得到加速比趋于线性加速比的分布式并行算法，理论上说，这也是并行算法的理想情况。

Base on the lumped parameter model of the torsional vibration system of crankshafts with variable inertia and considering the nonlinear elasticity force and nonlinear dissipative force, a six-degree-of-freedom nonlinear dynamical equations with parametric excitation and compulsive force are deduced.

从旋转惯量变化的曲轴扭振系统的集总参数模型出发，同时考虑了系统的非线性弹性力和非线性耗散力，导出了参强联合作用下的六自由度非线性扭转振动微分方程。

The kinetics of complexing inactivation at identical enzyme and inhibitor concentrations was analyzed and the equations of product generation were derived when the free enzyme concentration is great larger or smaller than the dissociation constant of inhibitor,〓.

在游离酶浓度远大于或远小于抑制剂的解离常数的条件下，导出了产物生成的方程。

The kinematics parameters were firstly presented by establishing the mechanical model of relation between the vibration screen and particle to deduce periodicity condition of particle motion,then disturbing function of particle motion for periodic motion was educed by using Poincaré mapping method,and studied motion characteristics of particle in vibration screening in terms of numerical analysis.

利用振动筛与颗粒之间关系的运动学模型，导出颗粒运动的周期性条件；然后利用Poincaré映射方法，推导出颗粒的运动对周期运动的扰动方程；最后对振动筛分过程中颗粒运动特性进行了数值计算研究，得出了筛面上颗粒运动是经周期分叉和概周期分叉通向混沌的演化过程。

According to the point of view of mechatronics, the modeling of the dot-matrix needle printer head has been completed by the method of electromechanics.

本文从机电一体化的观点出发，运用机电动力学方法，完成了计算机的点阵针式打印头的建模，并进行了数值模拟分析，且推导出"L"形打印头的磁路、电路和动力学方程，给出了相应的初始条件和边界条件。

As an application, the completeness of the eigenfunction system of the infinite dimensional Hamiltonian operator corresponding to a wave equation is given.

作为应用，还给出了波动方程导出的无穷维Hamilton算子特征函数系的完备性。

After in- troducing of the strain energy function, we first validated the derivation of the classical elastic constitutive equation using the strain energy function.

第三章从经典弹性力学和经典牛顿流体力学入手，在引入了应变能函数W〓以后，首先验证了经典弹性力学通过应变能函数导出弹性体本构方程的过程。

Chapter 2 is started from the basic theory of elastodynamics, the zero and the first order reflection and transmission coefficients of rough interface are derived in theory, and some numerical examples are given. Also dispersion characters of diffraction waves are discussed in the case of micro-rough interface in deep layers.

第二章从弹性动力学的基本理论出发，通过求解波动方程的定解问题，从理论上导出了地震波在粗糙界面上的零阶和一阶反射透射系数，并给出了数值算例；该章还讨论了深层微粗糙界面的绕射波的频散特征。

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。