四次方程

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。

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 .

用一元四次方程精确解的解析公式，研究飞机扰动运动特征方程的求解方法，并讨论计算机编程中应注意的若干问题。

This paper studies out the solving method of characteristic equation of disturbance motion by using the exact solution of quartic equation , and discusses some problems needing attention in computer programming .

一元四次方程2种根式求解算法的精度分析

Accurate Analysis of Two Root Algorithms on Solving Quartic Equation

况且，在平衡计算中常常发生比四次方程还高的高次方程。

Moreover equations of degree higher than quartic often arise in equilibrium calculations .

对于一般的各向异性媒质，给出了四次方程系数的简明算式，该算式完全适用于磁化等离子体、磁化铁氧体等回旋媒质。

Straightforward expression of coefficients is given , which is useful for anisotropic media such as magnetized plasma and magnetized ferrite .

基于四次方程的三角解研究非球对称动态黑洞的类视界面

Use the Trigonometric Function Solutions of Fourth Order Equations to Study the Event Horizon of Non-sphere Symmetric and Non-stationary Black Hole

本文用四次方程代替常用的几个二次方程曲线的回转体，来描述对称裂交的大形变过程。

In the paper , large deformation of symmetry fission has been described by a biquadratic surface revolution instead of several quadratic equations .

文中导出确定倾斜界面转换点的两个方程，即四次方程和迭代方程；

Two equations , namely a quadruplicate equation and an iteration equation , are deduced , which are used to determine conver - sion points in the slant interface .

然后根据四次方程的系数判定给定的五个位置存在布氏点的个数，最后求出各个解。

First of all , a quartic equation is obtained by using the rigid tody displacement matrices and some theories of higher algebra according to given five positions of coupler .

对一类非线性系统的局部稳定控制问题，首先证明一个四次方程实根判定定理，由此给出一类四次型定号的条件和一类系统局部稳定的充分条件。

In this paper , the local stabilization problem of a class of nonlinear control systems is discussed . A theorem concerning the roots of quartic algebraic equations is proved .

我们通过分析这两个一元四次方程的根，来枚举两个圆环面的所有位置关系，并给出每种位置关系的等价条件。

By analyzing the roots of the two quartic equations , we can enumerate all kinds of position relationship between two tori and present the equivalent condition of every kind of position relationship .

介绍了二次曲线族的定义和分类，并举例说明了它在求二次曲线的方程、解二元二次方程组及解一元四次方程中的应用。

In this article , the author introduces the definition and the classification of the family of quadric curve , and illustrates its applications with examples in solving the equation of quadric curve , the groups of binary quadratic equation and one variable equation of four times .

《授时历》在计算方法上也有创新，例如三次插内插法、四次多项式方程、球面三角法等数学方法的使用。

It also made innovations in terms of calculation methods ; for instance ， the use of mathematical approaches like cubic interpolation ， polynomial equations to the 4th order and spherical trigonometry .

应用四元二次方程回归旋转正交实验设计，探讨浸提次数，浸提剂倍数，浸提温度和浸提时间对硒多糖浸提率的影响。

By means of quaternion-square regression-rotation orthogonal experimental design , we probed into the effect on the extraction rate by times , water , temperature and time .

应用多尺度微扰理论研究了弱耦合非简谐参数的经典和量子四次非谐振子，得到了四次非简谐运动方程的经典和量子二阶解。

Classical and quantum oscillators of quartic anharmonicity are solved analytically up to the second power of ( weak-coupling constant ) by using the multiple-scale perturbation theory .