Quintic function

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

Threefolds from Solutions of a Partial Differential Equation

Abstract: Several types of complex algebraic threefolds are constructed. They are based on solutions of a second-order linear partial differential equation. The solutions are related to a one-parameter family of polynomials associated with configurations of real lines in the plane. Some of the polynomials produce hypersurfaces with many singularities. Particular cases of quintic and sextic threefolds are analyzed. The construction of Calabi–Yau threefolds is based on special types of the line configurations.

On Polynomial Differential Equations of Duffing Type

Abstract: The exact and explicit general periodic solution of polynomial differential equations of Duffing type is calculated as a power law of the cosine function. In doing so the solution of all Duffing equations of three terms like the cubic, quintic and heptic equations may be easily expressed in a straightforward fashion.

The Unified Transform Method to Initial-Boundary Value Problem for a Coupled Cubic–Quintic Nonlinear Schrödinger System

Abstract: In this study, we consider a coupled cubic–quintic nonlinear Schrodinger (CCQNLS) system, which is an important model in fiber-optic communication since this system can be used to describe the effect of quintic nonlinearities on the propagation of ultrashort optical soliton pulses in non-Kerr media. We solved the initial-boundary value problem of the CCQNLS system on the half-line by virtue of the unified transform method. And we manifest that the solution of the CCQNLS system can be represented by the unique solution of a $$3\times 3$$ matrix Riemann–Hilbert problem formulated in the complex $$\lambda $$ -plane. Furthermore, we demonstrate that a slice of spectral functions are not independent of each other, but rather to satisfy a paramount relations (so-called global relationship).

Quintic polynomial trajectory planning method for industrial robot

Abstract: The invention discloses a quintic polynomial trajectory planning method of an industrial robot. According to the method, based on the start-stop displacement, speed and acceleration information of a trajectory, by means of the speed trend of S-shaped trajectory planning, the interpolation time of quintic polynomial trajectory planning is deduced, and a quintic polynomial trajectory planning model is further determined. According to the quintic polynomial trajectory planning method, the quintic polynomial trajectory planning model is determined based on the speed running trend of S-shaped trajectory planning, so that the situation that the quintic polynomial curve shape is unstable and likely to twist is solved, the monotonicity of a speed variation in the planning process is ensured, the conditions of large convexity and reversing are unlikely to occur, it is ensured that the planned trajectory can satisfy intrinsic motion parameter restraints of the robot at every moment from the starting point and ending point of the trajectory, and the planning curve is smoother and the trajectory running process is stabler compared with common trapezoidal planning and S-shaped planning models.