四次函数

高斯曲率为已给四次函数的旋转曲面

Rotational Surface With Given Gauss Curvature Function of the Fourth Order

四次函数连续性线性微分方程的解法及其推广

The Solution of the Continuance Linear Differential Equation that Coefficient Contain Four Number of Times Function

四次函数实零点的完全判据和正定条件

The complete criterion of roots of quartic functions and the positive definite condition of a quartic function

乘波构型的源流场选用常用的锥形流场，前缘曲线在底面的投影用一个四次函数来描述，流线追踪生成下表面，对上表面进行局部等熵膨胀设计。

Cone flow field is used here as the generating flow field . The projection of the leading-edge on the base surface is defined using a forth-order function . The lower surface is produced tracing streamlines and isentropic expansion is done in some part of upper surface .

论证了两曲面的交线为空间曲线，其方程为一元四次隐函数关系式；

It is proved that the intersecting line of the two curved surface is space curve , and the equation is quartic implicit function with one unknown .

使四次样条函数为C2连续可提供额外的自由度，用于提高曲面的插值精度和控制曲面的形状。

Reducing the continuity of quartic spline interpolation surface to C2 can provide an additional degree of freedom , which can improve the interpolation accuracy and control the shape of the surface .

提出一组带两个形状参数，的四次多项式基函数，它是带一个形状参数的三次Bernstein基函数的扩展。

A class of 4-degree polynomial basis function with two shape parameters , is presented , which is the extension of the cubic Bernstein with one shape parameter , and a cubic B é zier curve with two shape parameters , is defined based on it .

给出四次多项式调配函数，它是三次非均匀B-样条函数的扩展；

A class of polynomial blending functions of degree four is presented , which is an extension of the cubic non-uniform B-spline curve .

四次样条函数由于本身的两个缺点而被人们忽视了其重要的应用价值，人们普遍认为偶数次样条曲线曲面不适合曲线曲面插值问题。

Since the two shortcomings of quartic spline function , its important applications have been ignored . And it is generally agreed that the even spline curves and surfaces are not suitable for curve and surface interpolation problem .

四次样条函数的两个缺点：一是连续性方程对应的不是三对角矩阵；二是样条函数的断点不在数据点处。

The quartic spline function has two shortcomings : ( 1 ) The continuity equation is not the corresponding tri-diagonal matrix . ( 2 ) The breakpoint of spline function is not in the positions of data points .

为了探讨各种剪滞翘曲位移模式的合理性，分别选取二次抛物线、三次抛物线、四次抛物线及余弦函数等翘曲位移模式进行计算；

In order to discuss the rationality of various warping displacement modes , second-degree parabola , cubic parabola , fourth-degree parabola and cosine function are selected respectively .

本文建议用四次多项式应力函数根据少数测点数据及地表边界条件对地应力场进行趋势分析。

Stress function in 4th power polynomial is proposed in the paper for trend analysis of residual stress field according to the measured datum of a few points and boundary conditions of the rock surface .