高阶导数

Based on Bezier curve continuance of first－order and second－order derivative, the characteristic vector equation of two Bezier curve is presented in point of intersection. The algorithm is not only of high accuracy with all of the interpolated points being on the curve theoretically, but also of very high speed in the real－time interpolation processes. The interpolation velocity does not change and the segment tolerance of interpolation can be control by selecting the parameter in cerement rationally every time.

为保证两段Bezier曲线在连接点处一阶导数、二阶导数连续，导出了两段Bezier曲线特征向量应满足的关系方程，Bezier插补法不仅在理论上可使所有的插补点落在曲线上，而且实时插曲补速度高，每次插补时可合理地选择参数增量，能使插补速度保证不变，也可控制弓高误差。

From equations eliminated some unknown function and its derivative, are contained only one unknown function with constant coefficient of linear differential equations.

从方程组中消去一些未知函数及其各阶导数，得到只含有一个未知函数的高阶常系数线性微分方程 9。

ADAMS. According to a function with STEP5 has features of continuous first and second derivative,the higher degree of approximation,etc.,we test and verify feasibility of fore-and-aft movement and turning gait of the robot. Thus a solution of the Snake-like robot motion under the ADAM...

ADAMS软件对蛇形机器人进行了从样机模型建立到运动学仿真与分析等一系列研究；并根据STEP5函数具有一阶与二阶导数连续、较高的逼近程度等特性验证了蛇形机器人前后移动和左右转弯步态可行性；找到了一种在ADAMS环境下求解机器人运动的方法，简化了理论计算，提高了设计效率。

In Chapter 2, starting from the basic fractional ordinary differential equations,weapply a high order approximation of fractional derivative advanced by Lubich to frac-tional differential equation, construct a high numerical difference scheme to solve thefractional differential equation, present error analysis of the algorithms theoretically,and prove the consistency ,convergency and stability.

接下来的第二章中，首先从基本的分数阶常微分方程出发，对Lubich提出的一个关于分数阶导数的高阶近似，将其应用于分数阶微分方程，构造高阶数值差分格式来进行分数阶微分方程的数值求解，并在理论上给出这一算法的误差分析，证明了它的相容性，收敛性和稳定性。

In Chapter 4, we consider more complex fractional nonlinear differential equation,also using the high order approximation presented by Lubich to construct correspond-ing numerical scheme and giving the error analysis of the algorithms.

在第四章中，进一步的考虑更复杂的非线性分数阶常微分方程，同样利用的是Lubich提出分数阶导数的高阶近似，构造相应的数值格式，并给出这一算法的误差分析，即相容性，收敛性和稳定性的证明。

This paper is the continuance of that of Lewalle (2001). Lewalle has made use of Gaussian wavelet to obtain the N-S equations with flexion as fundamental quantity in the infinite domain. In that work, Lapalace operator has been degraded to one-order operator. Moreover the resulted N-S equations take the form of diffusion equations with local bilinear mutual interaction kernel.

本文是Lewalle工作的继续，Lewalle利用高斯子波，得到了以弯曲度为基本量的无穷域中N-S方程，此时Lapalace算子降低为一阶导数，并且N-S方程变形为具有局部化双线性相互作用的扩散方程的形式。

The linear extrapolation technique was the most practical and suitable method because of its relative high correlation with a wide range of chlorophyll content, relative simple algorithm, relative high sensitivity to chlorophyll at high or low content and application to more wider bandwidth spectra.

四点线性内插法计算的红边位置往往偏大，最大一阶导数法与叶绿素含量的关系存在着明显的不连续性，拉格朗日内插法、倒高斯模型法在一定程度上存在着对高叶绿素含量的饱和现象，多项式拟合法对拟合波段区间、最高项次及光谱分辨率等比较灵敏而导致结果不够稳定，而线性外推法计算出的红边位置对叶绿素含量最为敏感，预测的准确度最高，且计算相对比较简单，并能适用于较宽波段的遥感数据。

Padé approximation is an effective rational approximation.Using the first derivative of Gaussian function as basic wavelet,Pad conversion is used to obtain its rational fraction approximation.

采用高斯函数一阶导数作为基本小波，用Padé变换获得其有理分式逼近，利用开关电流技术实现小波滤波器可获得小波变换所需的基本小波及其膨胀小波。

In model experiments, we find that the deviation of the first derivative calculated by Fourier transform is very large to comparing with the theoretical derivative, but the fitting effect of the derivative of anomalies calculated by cosine transform is very good. The calculation accuracy of data are all very high except that errors of several data on the boundary are large because of the residual Gibbus effect induced by finite truncation of gravity anomalies. Errors are -009%～5%.

模型实验中发现，用Fourier变换计算的一阶导数与理论导数偏差很大，而余弦变换计算的导数与理论异常导数拟合效果非常好，除边界几个数据因重力异常的有限截断产生的吉布斯效应残留使误差较大外，数据的计算精度均很高，误差为-009%～5%。

By analyzing, an adaptive mode of linear filter based on DCT is given out. The curves of the vertical second derivative of gravity anomaly are matched well with those of the academic second derivative, and the calculating precision is much higher.

通过分析给出了基于DCT的合适的线性滤波方式，滤波后的重力异常垂向二阶导数与理论二阶导数拟合效果好，具有较高的计算精度。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。