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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。

In this paper, we study the existence of solutions for high-order ordinary differential equation systems and delay differential equations, subject to different conditions.

本文研究高阶非线性常微分方程组和高阶非线性时滞微分方程在不同的假设条件下正解的存在性和多重性。

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。

The derivative 〓 t, x (t of the V function along a solution to a determinate ordinary differential system is changed to be 〓V t, x (t for a stochastic ordinary differential system.

众所周知,用Lyapunov直接法来研究随机常微系统的稳定性与研究确定性常微系统的稳定性有许多类似之处,表现在只需要用〓Vt,x(t代替常微系统中V函数沿解的导数〓t,x

The calculated results show that the total differential cross section is the general rule and characteristics of collision between an atom and a diatomic molecule, the phenomenon of the scattering oscillation at large angles is more evident along with increase of the incident energy for low-lying rotational excitation state-to-state differential cross sections in He-BH collision system.

计算结果表明:He-BH碰撞体系的总微分截面具有原子与双原子分子散射的一般规律和特征;随着入射能量的增加,低转动激发态-态微分截面在大角区的散射振荡现象会更加明显。

This model is a group of partial differential equations. Th solution is obtained with finite difference method to give a differential equation of gas pressure, temperature and rate and its calculation step.

该模型是一组偏微分方程,采用有限差分法对其进行求解,给出了计算气体压力、温度、速度的差分方程和详细的计算步骤。

Differential equations and difference equations are powerful tools that describe the law of nature, but it is difficult to find their general solutions. Therefore , there has been an increasing interest in the study of the nature of solutions of differential equation and difference equation in theory.

微分方程及差分方程是用来描述自然现象变化规律的一种有力工具,由于寻求其通解十分困难,故从理论上探讨解的性态一直是近年来研究的热点问题。

The relation between difference equation and differential equation is studied by analyzing the mechanism in building grey models, and a "bridge" is set up between difference equation and differential equation by sampling theorem and state transition matrix.

通过对灰色系统模型建模机理进行深入剖析,利用采样定理和状态转移矩阵在差分方程和微分方程之间架起一座桥梁,通过算例仿真实验证明了该算法的有效性。

The analysis in theory proves that cellular automaton is equal with a stochastic process that described by stochastic difference equations. The primary differential equation is expectation of this stochastic process. And its variance function is controllable. These results show that cellular automata are in agreement with primary differential equation in the statistical sense.

理论分析证明:该方法设计的细胞自动机等价于一个可用随机差分方程描述的随机过程,该随机过程以原微分方程为期望函数,并且,其方差函数是可控的,表明细胞自动机和原微分方程在统计意义上是一致的。

Differential Difference Equation; Neutral Functional Differential Equation; Stability Switch; Characteristic Equation; Stability; Liapunov Method; Monotone Semiflow; Periodic Solution

基础科学,数学,数学分析微分差分系统;中立型泛函微分方程;特征方程;稳定性开关;解的稳定性;李雅普诺夫方法;单调半流;周期解

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