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1·In this paper, we discuss when a quartic equation has no real roots, and obtain a necessary and sufficient condition on a quartic equation which has no real roots.

本文讨论了一元四次方程无实根的一些充分、必要条件，并得到了一元四次方程无实根的一个充要条件。

2·The qualitative theory of ordinary differential equations and numerical simulation method are employed to investigate the kink waves of a nonlinear quartic equation.

用微分方程定性理论结合数值模拟方法研究了一类非线性四阶波动方程的纽结波。

3·Given the velocity ratio of S-to P-waves, the depth of reflector and the offset, the horizontal distance between source and the converting point can be determined by solving a quartic equation.

如果我们已知介质中横波与纵波速度的比值、水平界面的埋藏深度和炮检距，炮点到共转换点的水平距离就可以通过解一个四次方程求出。

4·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.

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；

5·The method of qualitative analysis of differential equation and bifurcation is employed to study two classes of quartic systems.

用微分方程定性分析方法和分支方法研究两类四次系统。

6·Section I describes the numerical solution of first order matrix linear differential equation using the cubic matrix spline function and quartic matrix spline function.

第一节介绍了三次矩阵样条函数方法和四次矩阵样条函数方法逼近一阶矩阵线性微分方程的数值解。

7·The solar equation table of the Dayan Calendar is a mathematical table of equally quartic difference, and it reflects Yi Xing's profound understanding about the solar motion.

《大衍历》日躔表是一份四次差分相等的数表，反映一行对太阳运动复杂性的深刻认识。