Quintic function

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

Positivity conditions for quartic polynomials

Abstract: Simple necessary and sufficient conditions that a quartic polynomial f(z) be non-negative for z greater than or equal to 0 or a is less than or equal to z and z is less than or equal to b are derived, and illustrated geometrically. The geometry provides considerable insight and suggests various approximations and computational simplifications. The theory is applied to monotone quintic spline interpolations, giving necessary and sufficient conditions and an algorithm for monotone Hermite quintic interpolation.

Attractors for damped quintic wave equations in bounded domains

Abstract: The dissipative wave equation with a critical quintic nonlinearity in smooth bounded three dimensional domain is considered. Based on the recent extension of the Strichartz estimates to the case of bounded domains, the existence of a compact global attractor for the solution semigroup of this equation is established. Moreover, the smoothness of the obtained attractor is also shown.

Optimal Polynomial Control of Seismically Excited Linear Structures

Abstract: In this paper, an optimal nonlinear control law that is polynomial in terms of the states of the system is proposed for limiting the peak response of seismic-excited buildings. A performance index that is quadratic in control and polynomial of an arbitrary order of the states is considered. The performance index is minimized based on the solution of the Hamilton-Jacobi-Bellman equation. The resulting controller is a summation of polynomials of different orders, i.e., linear, cubic, and quintic, among others. Gain matrices for different parts of the controller are calculated easily by solving matrix Riccati and Lyapunov equations. Extensive simulation results indicate that the new optimal polynomial controller consumes less energy in reducing the peak response quantities; however, it may use bigger peak control force than the linear controller. When the earthquake intensity exceeds the design one, the optimal polynomial controller is capable of exerting larger control forces thus achieving a higher reducti...

New Exact Envelope Traveling Wave Solutions of High-Order Dispersive Cubic-Quintic Nonlinear Schrödinger Equation

Abstract: Using trial equation method, abundant exact envelope traveling wave solutions of high-order dispersive cubic-quintic nonlinear Schrodinger equation, which include envelope soliton solutions, triangular function envelope solutions, and Jacobian elliptic function envelope solutions, are obtained. To our knowledge, all of these results are new. In particular, our proposed method is very simple and can be applied to a lot of similar equations.