scispace - formally typeset
Search or ask a question
Topic

Quintic function

About: Quintic function is a research topic. Over the lifetime, 1677 publications have been published within this topic receiving 26780 citations.


Papers
More filters
Journal ArticleDOI
TL;DR: This paper introduces L p piecewise polynomial parametric splines of degree 3 or 5 which smoothly interpolate data points and shows how interesting it can be to be able to change the partition associated to the data points in order to obtain convexity properties when possible.

21 citations

Proceedings ArticleDOI
01 Aug 2016
TL;DR: An interpolation method based on quintic non-uniform rational B-spline(NURBS) is proposed to construct curves when to plan the trajectory of manipulators with respect to three objectives, time optimal, energy optimal and smoothness optimal, and shows that quintic NURBS curve can get high-order continuous trajectories and NSGA-II algorithm can provide an effective approach to get the perfect Pareto solutions.
Abstract: In this paper an interpolation method based on quintic non-uniform rational B-spline(NURBS) is proposed to construct curves when to plan the trajectory of manipulators with respect to three objectives, time optimal, energy optimal and smoothness optimal. The mathematical model of quintic NURBS curve is set up to gain high-order continuous trajectories with endpoint configuration parameters can be specified, and a fast and elitist multi-objective genetic algorithm (NSGA-II) is adopted to optimize the trajectory of manipulators aims to get a series of Pareto optimal solutions under the three objectives. Through the simulation with six-degree of freedom robot shows that quintic NURBS curve can get high-order continuous trajectories and NSGA-II algorithm can provide an effective approach to get the perfect Pareto solutions for quintic NURBS curve. By constructing a average fuzzy membership function, a potential optimal solution can be selected from Pareto optimal set, then the high-order continuous optimal trajectory can be obtained.

21 citations

Journal ArticleDOI
TL;DR: In this paper, the axial compression makes the lateral displacements coupled with the torsional displacement (Φ) when warping is concerned, and the resulting twelve-order differential equation is customarily solved by finite element method assuming independent cubic shape functions for Y, Z and Φ.
Abstract: To approximate a tube building by thin-walled Vlasov beam, it is unreasonable to neglect the axial force due to dead and live loads. The axial compression makes the lateral displacements (Y, Z) coupled with the torsional displacement (Φ) when warping is concerned. The resulting twelve-order differential equation is customarily solved by finite element method assuming independent cubic shape functions for Y, Z and Φ. It is pointed out here that the displacement functions are not completely independent. Indeed, if one takes the static solutions of the governing ordinary differential equations as shape functions, for the same number of degrees of freedom, one can approximate the Vlasov beam by quintic polynomials plus six hyperbolic-trigonometric functions. For static problems without distributed force, the resulting stiffness equation is exact. For dynamic problems, the resulting finite element converges rapidly.

21 citations

Journal ArticleDOI
TL;DR: In this article, a family of cyclic quartic fields arising from the covering of modular curves X1 (16) -XO(16) was studied and an integral basis and a fundamental system of units were found.
Abstract: We study a family of cyclic quartic fields arising from the covering of modular curves X1(16) -XO(16). An integral basis and a fundamental system of units are found. It is shown that a root of the quartic polynomial we construct is a translate of a cyclotomic period by an integer of the quadratic subfield of the quartic field. Recently, 0. Lecacheux [9, 10] and H. Darmon [4] showed how to use coverings of modular curves to obtain cyclic extensions of Q. In particular, they were able to give a geometric construction of a family of cyclic quintic fields discovered by E. Lehmer [11]. The covering X1 (N) --* X0(N) (for N > 2) has degree q$(N)/2 and group (Z/NZ) X /{I 1 }. For the quintic case, they took N = 25, which gave a cyclic covering of degree 10, then took the subcovering of degree 5. An important ingredient in the construction was the fact that XO(25) has genus 0. This also occurs for N = 1, ..., 10, 12, 13, 16, 18. These all give trivial or quadratic coverings except for N = 7, 9, 13, 16, 18. The values N = 7, 9, 18 yield cubic extensions and can be shown to yield the family of polynomials X3 aX2 (a + 3)X 1, namely the "simplest cubic fields" [17]. (However, it should be remarked that every cyclic cubic extension of Q comes from a polynomial of this form if a is allowed to be rational. Similarly, we are guaranteed that the quadratic extensions obtained from the coverings mentioned above correspond to polynomials of the form X2 aX 1 with a rational.) The case N = 13 is treated by Lecacheux [9]. It might be suspected that the sextic fields she obtains are the same as the "simplest sextics" constructed by M.-N. Gras [6]. However, these latter fields were found by taking the fixed field of an element of order 6 in PGL2(Q) = Aut(Q(X)). Therefore, they come from a covering of curves of genus 0. But X1 (13) has genus 2. Alternatively, these sextic fields must be different because the discriminants of the quadratic, and cubic, subfields are different. In the present paper, we study the case N = 16. As above, it might be hoped that this case would give a geometric construction of the quartic fields studied Received March 14, 1990; revised October 22, 1990. 1980 Mathematics Subject Classification ( 1985 Revision). Primary 1 I R 16. Research supported in part by N.S.F. ? 1991 American Mathematical Society 0025-5718/91 $1.00 + $.25 per page

21 citations

Journal ArticleDOI
TL;DR: In this article, a cubic-quintic complex Ginzburg-Landau equation (CQGLE) with third-order dispersion (TOD) was derived to model the propagation of ultrashort optical solitons in optical fibers.

21 citations


Network Information
Related Topics (5)
Differential equation
88K papers, 2M citations
88% related
Eigenvalues and eigenvectors
51.7K papers, 1.1M citations
87% related
Boundary value problem
145.3K papers, 2.7M citations
86% related
Partial differential equation
70.8K papers, 1.6M citations
85% related
Bounded function
77.2K papers, 1.3M citations
85% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202397
2022254
2021109
2020104
201993
201893