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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28 Jun 2018
TL;DR: The objective of this articles is to conclude curvature information of quintic trigonometric Bezier curves with the goal of approximating roads’ maximum speed and estimating the maximum allowed speed.
Abstract: This paper describes a new function called quintic trigonometric Bezier curve that has the potential to estimate the maximum driving speed allowed for safe driving on roads. The shape parameters present in this trigonometric Bezier function gives more flexibility for users in designing highways. Since the curves do interpolate the points, small changes in shape parameters will affect the curvature of the curve, therefore creating a bigger difference towards speed estimation. The objective of this articles is to conclude curvature information of quintic trigonometric Bezier curves with the goal of approximating roads’ maximum speed and estimating the maximum allowed speed.
14 citations
TL;DR: In this paper, the singular point and singular close orbits were applied to study the Hopf, homoclinic loop and heteroclinical loop bifurcation of a perturbed cubic Hamiltonian system under Z4-equivariant quintic perturbation.
Abstract: This paper is concerned with the number and distribution of limit cycles of a perturbed cubic Hamiltonian system which has 5 centers and 4 saddle points. The singular point and singular close orbits’ stability theory and perturbation skills of differential equations are applied to study the Hopf, homoclinic loop and heteroclinic loop bifurcation of such system under Z4-equivariant quintic perturbation. It is found that the perturbed system has at least 16 limit cycles bifurcated from the focus. Further, at least 14 limit cycles with three different distributions appear in the heteroclinic loops bifurcation.
14 citations
TL;DR: Extreme binary self-dual quintic codes are constructed in lengths 60 and 70 by a randomized algorithm and are shown to be cyclic when the component codes are cyclic of odd length coprime to 5.
14 citations
TL;DR: In this article, the existence and first order Lagrange condition of an open loop control were proved for stochastic nonlinear Schrodinger equations with the critical quintic and cubic nonlinearities in dimensions one and two.
Abstract: We study optimal control problems for stochastic nonlinear Schrodinger equations in both the mass subcritical and critical case. For general initial data of the minimal
$$L^2$$
regularity, we prove the existence and first order Lagrange condition of an open loop control. In particular, these results apply to the stochastic nonlinear Schrodinger equations with the critical quintic and cubic nonlinearities in dimensions one and two, respectively. Furthermore, we obtain uniform estimates of (backward) stochastic solutions in new spaces of type
$$U^2$$
and
$$V^2$$
, adapted to evolution operators related to linear Schrodinger equations with lower order perturbations. These estimates yield a new temporal regularity of (backward) stochastic solutions, which is crucial for the tightness of approximating controls induced by Ekeland’s variational principle.
14 citations
TL;DR: In this article, the coupled cubic-quintic nonlinear Schrodinger equations describing the effects of quintic non-linearity on the ultrashort optical pulse propagation in non-Kerr media were investigated.
Abstract: Under investigation in this paper are the coupled cubic–quintic nonlinear Schrodinger equations describing the effects of quintic nonlinearity on the ultrashort optical pulse propagation in non-Kerr media. Lax pair of the equations is obtained via the Ablowitz–Kaup–Newell–Segur scheme and the corresponding Darboux transformation is constructed. One-, two- and three-soliton solutions are presented and an infinite number of conservation laws are also derived. The features of solitons are graphically discussed: (i) head-on and overtaking elastic collisions of the two solitons; (ii) periodic attraction and repulsion of the bounded states of two solitons; (iii) energy-exchanging collisions of the three solitons.
14 citations