查询词典 simultaneous equations

Since the multiple scattering should be considered, the scattering problem of many-cylinders is more complicated than single cylinder. By using scattering matrix method to solve the scattering problem of many-cylinders, first we have to express the incident fieldand scattered field by special function（for example, Bessel function and Hankel function）under cylindrical coordinate, then use the addition theorem of special function to get a linear system of equations to relate the incident field coefficients and scattered field coefficients. The incident and scattered field coefficients for every cylinder can be solved from the linear equations by matching electromagnetic boundary condition pointwisely.

单颗圆柱散射体的散射场解析解很早就被解出，而多个圆柱阵列的散射场问题因为涉及到入射光在圆柱与圆柱间的多重散射，故散射行为较单颗圆柱的散射复杂，因此圆柱阵列的多重散射问题需要利用加法定理来处理；散射矩阵法的主要精神即是先用圆柱座标下的特殊函数对平面波和圆柱散射体的内外域电磁场做无穷级数展开，再藉由特殊函数的加法定理将所有圆柱散射体的展开中心移到同一个展开中心，最后可以得到一组连结整个散射系统的入射电磁场系数及散射电磁场系数的线性方程组，将该组线性方程配合电磁场在散射体边界的连续条件，便可分别求出圆柱阵列中各个圆柱体的内部电磁场与外部散射场，再利用线性叠加原理即可求得整个圆柱系统的全域电磁场分布。

The complete model of locomotive and vehicle and the exact motion equations of wheel-set are established, in which, three-dimension wheel/rail contact geometry is taken into account and the Kalker's creep theory is employed to analyze the effects of the contact region of wheel/rail. An iterative procedure of solving wheel/rail creep force is proposed to improve the existed calculating method. Finally, the motion equations of vehicle with 23 DOFs are derived using the D'Alembert principle.

建立了较完善的机车车辆分析模型和较精确的轮对运动方程：考虑三维非线性轮轨接触几何关系，用Kalker蠕滑理论研究了轮轨接触区的蠕滑效应，建立了较为详细的轮对运动方程，提出用迭代法来求解轮轨蠕滑力从而对现有蠕滑力求解方法进行了改进，并采用D′Alembert原理推导了23个自由度车辆的运动方程。

The governing equation of in-plane vibration of cable-restraint system is derived by means of D'Alembert principle, and then those partial differential equations are transformed into a set of ordinary differential equations by Garlerkin method. The method of Runge-Kutta integration is applied to solve the equation. The simulation analysis is made to prove that this vibration control has obvious damping effects and then the influence of cable tension, support mass, natural frequency and spring stiffness on the damping are discussed. Eventually, the approximate analytic solution of the optimum damping parameter is obtained to provide a simple and effective reference and design method for the engineers.

通过D'Alembert原理建立拉索－弹性约束系统振动方程，通过Galerkin方法将偏微分方程转化为常微分方程，应用龙格－库塔积分法求解方程；经过仿真分析，验证了该振动控制具有明显的减振效果，并且讨论了初始拉力、支座质量、振动频率及弹簧刚度对减振效果的影响；最后给出了计算最优阻尼参数的近似解析式，为工程师提供了简便有效的参考依据及设计方法。

An optical system with refraction and total internal reflection was proposed according to the luminous characteristic of LED and the law of energy conservation. The ordinary differential equations satisfying the spots on the contour curve of TIR refractive and reflective planes were established. The coordinates of points on profile curves were obtained by solving these ordinary differential equations using Runge-Kutta method. The profile curves were acquired by curve fitting of the coordinate spots with software UG, and then TIR model of the projector and data of the surface shape suitable for NC manufacture were obtained.

根据LED的发光特性以及能量守恒定律选择采用折射全反射光学系统，通过建立TIR折射面及全反射面轮廓曲线上的点所满足的常微分方程，利用RungeKutta求解常微分方程得到轮廓曲线上点的坐标，再在UG中对坐标点进行曲线拟合得到轮廓曲线，进而得到TIR模型及适合数控加工的面形数据。

This article mainly discusses four kinds of solution system of linear equations,such as Elementary operations, the tecnique of Orthogonalization,Gaussian elimination method and Block matrix,and some ways that how to solve the multiple polynomial equations and decomposite the multiple polynomial matrix.

本文主要讨论了利用初等变换、正交化的技巧、高斯消去法和分块矩阵的四种求解线性方程组的解法，以及一些关于多元多项式方程组求解和多元多项式矩阵分解的方法。

In this paper another deductive proof of the algorithms for the recursive solution of the system of linear equations with a Toeplitz coefficient matrix is considered, and formulas for the specific recursive solution of the various forms of the system of linear equations in accordance with a Toeplitz coefficient matrix are given.

本文给出了具有托布里兹系数矩阵线性方程组递推解法算式的另一推导证明方法，并给出了基于托布里兹系数矩阵的各种线性方程组的具体递推解法公式。

Many natural phenomena and physical laws can be described by time dependent nonlinear differential equations, such as heat conduction equation, sound wave and elastic wave equation, reaction diffusion and convection diffusion equation, fluid and aerodynamics equations, etc.

大多数的自然现象与物理规律都可归结为与时间相关的非线性偏微分方程，诸如热传导方程、声波与弹性波方程、反应扩散与对流扩散方程、流体与气体力学方程组等发展方程。

And then the influence of two of the damage models, the Kachanov and the gradient dependent constitutive equations, on the well posed properties of the fundamental equations in continuum damage mechanics is studied according to th.

首先从非局部理论出发，推导了应变梯度损伤本构方程；然后利用一阶拟线性偏微分方程组的特征理论，在一维弹性损伤情况下分析了两种不同的本构模型，即 Kachanov损伤本构方程与应变梯度损伤本构方程，对连续介质损伤力学基本方程适定性的影响。

The Galerkin's method was used to truncate the infinite-dimensional partial differential equations into a set of finite-dimensional ordinary differential equations with time dependent coefficients,which can be solved with numerical methods.

对于电梯工业来说，目前世界上绝大部分电梯仍然是依靠钢丝绳提升的曳引式电梯。

By using the theory of linear evolution systems and Sadovskii's fixed point theorem, chapter3 deals with the existence of mid-solutions,strong solutions for the Cauchy problems of neutralabstract functional differential equations dependent on time with unbounded delay, here theright function in the equations satisfies the Caratheodory conditions.

第三章利用线性发展系统理论和Sadovskii不动点定理研究了具有无穷时滞中立型时变泛函微分方程Cauchy问题mild-解、强解的存在性。其中方程的右端函数满足Caratheodory条件。

But Severus escaped the hands of those that Julianus had sent to murder him and sent a letter to the praetorian guard, giving them the signal either to desert Julianus or to kill him.

赛维鲁总算逃过了尤利阿努斯派来的杀手，并写了一封信给罗马的禁卫军，向他们发出信号，要么抛弃尤利阿努斯，要么干掉他。他们立即服从了。

This text is in terms of this of " human nature ", it is under the influence of western literature human nature thought to probe into, awakening in human nature of novel works and all sorts of limitations that affectionate The school of Mandarin Duck and butterfly.

本文便是从"人性"这一角度，探讨在西方文学人性思想的影响下，清末民初鸳鸯蝴蝶派的言情、哀情小说作品在人性方面的觉醒与种种局限。