(1) A complete quartic polynomial consists of 15 terms.

(2) 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.

(3) 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.

(4) The curvilinear equation of quartic polynomial is used to simulate the boundary of the pile hole to improve the presumption of previous research results which are not well suitable.

(5) In chapter two, using piecewise quartic polynomial as kernel function, we give analytical convolution solutions for points, line segments, arcs, quadratic Bezier curves and triangle segments.

(6) Two algorithms on solving quartic equation are introduced, and their accuracies and stabilities in numerical computation are analyzed in this paper.

(7) In fact, this rational quartic spline is the successful generalization of quartic polynomial spline.

(8) At first, this paper presents two - dimensional quartic convolution interpolation to smooth digital terrain.

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

(10) The qualitative theory of ordinary differential equations and numerical simulation method were employed to investigate the kink waves of a nonlinear quartic wave equation.

(11) It provides a framework for both linear programming and quartic programming.

(12) 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.

(13) 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.

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

(15) The intersection of two right circular cylinders is usually quartic curve.

(16) This paper proposes a piecewise geometric approach to parametrize a kind of quartic implicit algebraic surface.

(17) The applied interpolation method adopts quintic spline and derivatives generation approach for discrete points by using quartic polynomial, which can better meet the needs of high-accuracy machining.

(18) An optimum range of process pressures has been obtained through the combined analysis of test results plus quartic curve fits.