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Finally, combining PDE with Differential Geometry, parametrically representing the surface, tensor based image processing techniques have been proposed, such as edge detection , morphological operation? implicitly representing the surface as the level-set of the higher dimensional function, the variational problems and partial differential equations that define maps onto the given generic surface have been discussed.

本文结合微分几何学,基于曲线坐标系下的微分算子将平面上的图像处理框架推广到曲面上,得到了参数化曲面上的图像处理框架,并给出了边缘检测和形态学运算的算例;在已知给定曲面的隐式表达时,探讨了定义在任意曲面上的偏微分方程,解决了任意曲面上数据场的扩散问题。

Jacobian Davis iterative method of solving equations AX = B, least squares polynomial fitting, portfolio Simpson formula for integration, with a triangular decomposition method of solving equations AX = B.

拉格朗日插值多项式拟合,牛顿插值多项式,欧拉方程解偏微分方程,使用极限微分求解导数,微分方程组的N=4龙格库塔解法,雅可比爹迭代法解方程AX=B,最小二乘多项式拟合,组合辛普生公式求解积分,用三角分解法解方程

Char-set has triangular form structure,which is used to overcome some difficulties in differential fields problems.

本文中,我们研究微分情形吴方法,重点研究的是微分多项式系统的微分特征列集的算法及其应用。

It is found that both the total and differential cross sections increase with the increasing of screening interaction, and especially for energies below 10 keV/u, the cross sections are one to two magnitudes larger than those in the unscreened case.

研究发现,碰撞电离总截面随等离子屏蔽的增加而增大,特别是在10 keV/u以下的低能区电离截面有量级的增加。对随能量变化的一阶微分截面,在低能碰撞过程中,屏蔽作用增加,微分截面呈量级增加,高能碰撞微分截面呈倍数增加。

Using the new comparative method, the variation of constants formula, M-matrix theory, integral differential inequality, new theoretical results on global exponential stability of neural networks with bounded time-varying delays and Lipschitz continuous activation functions have been obtained.

利用新的比较方法的思想,改进了一维线性和非线性纯时滞微分系统的3/2稳定性定理,推广了Yorke条件到具两个时滞项的情形,将Yorke等人的3/2稳定性定理推广到具两个时滞项的线性和非线性纯时滞微分系统,进一步还推广到N维纯时滞微分系统,为纯时滞神经网络的研究打下理论基础。

Theory; the spatial meshing theory includes comparative motion, comparative differential and conjugative curved surface; and the application of meshing theory includes gear drive and worm drive. The spatial meshing theory is the main part of the course.

课程的重点讲解内容有曲线的参数方程、切线、法面、弧长、曲率、空间曲线的基本公式、挠率及平面曲线的基本公式等;曲面第一和第二基本公式,法曲率、主方向和主曲率、欧拉公式、短程挠率、欧拉公式和贝特朗公式推广、相对法曲率和相对短程挠率等;刚体的绝对和相对运动速度、相对微分和绝对微分、相对速度和相对微分、轨迹曲面的法曲率和短程挠率等;空间共轭曲面的啮合条件、诱导法曲率、两类界限点、等距共轭曲面、空间啮合的二次接触原理等;蜗杆传动的数学模型建立及啮合特性分析方法等。

To investigate the dynamic stability of a two-degree-of-freedom manipulator as a system,differential equations of motion for this system were established on the basis of the Lagrange equation,and perturbed differential equations with period coefficients were derived for the period motion of this system by applying the perturbance theory.

为了研究两自由度机械手系统的动力学稳定性,基于拉格朗日方程给出了它的运动微分方程,并用扰动理论确定系统周期运动具有周期系数的扰动微分方程;根据F loquet理论对该系统扰动微分方程的平衡点的稳定性进行了分析,并用数值方法研究了平衡点失稳后的倍周期分岔过程。

This paper is devoted to discuss the bifurcation of a chemostat with delay and simplified Holling type-IV response function.

关于培养器模型各种类型的方程如常微分方程,偏微分方程和时滞微分方程等已经有了很多结果。

The vertical axis of the switch has a surface of positive first differential, comprised of splines drawn between points if varying distance from a datum plane, and has along the horizontal axis a surface of a positive first differential and negative second differential, comprised of a combination of splines drawn between points of varying distance from the datum plane.

开关的竖直轴线的表面具有正的一阶微分,其由多个在离基准平面不同距离的点之间绘制的样条构成,并且沿水平轴线具有一个表面,该表面具有正的一阶微分和负的二阶微分,其由一组在离基准平面不同距离的点之间绘制的样条构成。

An algorithm called initial function method for the solution of differential equation with tension is also given.

推导出了不考虑拉伸和考虑拉伸情况的弹性环形变微分方程,导出了求解不考虑拉伸情况的弹性环形变微分方程的差分方程和算法,还给出了可谓之初参数法的求解考虑拉伸情况的弹性环形变微分方程的算法。

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