Topic
Quintic function
About: Quintic function is a research topic. Over the lifetime, 1677 publications have been published within this topic receiving 26780 citations.
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TL;DR: The existence of non-degenerate RRMF quintics is newly demonstrated through a constructive process, involving simple algebraic constraints on the coefficients of two quadratic complex polynomials that are sufficient and necessary for any PH quintic to admit a rational rotation-minimizing frame.
30 citations
TL;DR: In this paper, a non-uniform rational B-spline interpolation algorithm with compensatory parameter to minimize feedrate fluctuation and contour error is presented. But the algorithm is not suitable for high speed precision machining of a part.
Abstract: The high-speed precision machining of a part requires minimal feedrate fluctuation and contour error, and parametric spline interpolations have proven to be superior over linear and circular interpolations. However, parametric spline interpolations may result in large feedrate fluctuation due to an inaccurate mapping between the spline parameter u and the displacement S. This paper presents a non-uniform rational B-spline interpolation algorithm with compensatory parameter to minimize feedrate fluctuation and contour error. Since the cubic or quintic polynomials expressing the u-S mapping are acquired, they can be calculated by two consecutive interpolation points with the continuity condition. Thus, the parameter u can be calculated quickly and accurately by substituting the desired displacement S into the cubic or quintic polynomials. Simulation shows that the feedrate fluctuation of the proposed algorithm is much smaller than that of Taylor interpolation algorithms and Feed correction algorithm.
30 citations
TL;DR: Two direct algebraic methods are used to solve a fourth-order dispersive cubic–quintic nonlinear Schrodinger equation, which is used to describe the propagation of optical pulse in a medium exhibiting a parabolic nonlinearity law.
30 citations
TL;DR: In this article, a sufficient condition of a quintic harmonic polynomial parametric surface being a minimal surface was proposed, and several new models of minimal surfaces with shape parameters were derived from this condition.
Abstract: In this paper, quintic parametric polynomial minimal surface and their properties are discussed. We first propose the sufficient condition of quintic harmonic polynomial parametric surface being a minimal surface. Then several new models of minimal surfaces with shape parameters are derived from this condition. We also study the properties of new minimal surfaces, such as symmetry, self-intersection on symmetric planes and containing straight lines. Two one-parameter families of isometric minimal surfaces are also constructed by specifying some proper shape parameters.
29 citations
TL;DR: In this article, the problem of finding power integral bases in algebraic number fields is equivalent to solving the corresponding index form equations, and an efficient enumeration algorithm is described to solve completely index form equation in quintic fields with Galois group S5.
Abstract: The problem of determining power integral bases in algebraic number fields is equivalent to solving the corresponding index form equations. As is known (cf. Győry [25]), every index form equation can be reduced to an equation system consisting of unit equations in two variables over the normal closure of the original field. However, the unit rank of the normal closure is usually too large for practical use. In a recent paper Győry [27] succeeded in reducing index form equations to systems of unit equations in which the unknown units are elements of unit groups generated by much fewer generators. On the other hand, Wildanger [32] worked out an efficient enumeration algorithm that makes it feasible to solve unit equations even if the rank of the unit group is ten. Combining these developments we describe an algorithm to solve completely index form equations in quintic fields. The method is illustrated by numerical examples: we computed all power integral bases in totally real quintic fields with Galois group S5.
29 citations