We provide a generalization of Halanay’s inequality, where the decay rate is constant but gain multiplying delayed term time varying. While usual conditions require to be strictly larger than an upper bound on gain, our less restrictive results allow times when can exceed rate. This allows us prove asymptotic stability in significant cases that were not amenable previous Lyapunov function const...

Abstract For studying the evolution of transverse deflection an extensible beam derived from connection mechanics, we investigate initial boundary value problem nonlinear equation with linear strong damping term, weak and source term. The key idea our analysis is to describe invariant manifold via Nehari manifold. To establish results global well-posedness solution, consider at three different ...

We prove the time-asymptotic stability of composite waves consisting superposition a viscous shock and rarefaction for one-dimensional compressible barotropic Navier-Stokes equations. Our result solves long-standing problem first mentioned in 1986 by Matsumura Nishihara [28]. The same authors introduced it officially as an open 1992 [29] was again described very challenging 2018 survey paper [2...

Abstract. Maximum likelihood (ML) estimation based on bivariate record data is considered as the general inference problem. Assume that the process of observing k records is repeated m times, independently. The asymptotic properties including consistency and asymptotic normality of the Maximum Likelihood (ML) estimates of parameters of the underlying distribution is then established, when m is ...

In this paper we develop an asymptotic theory for estimation based on signed ranks in the ARMA model when the innovation density is symmetrical. We provide two classes of estimators and we establish their asymptotic normality with the help of the asymptotic properties for serial signed rank statistics. Finally, we compare our procedure to the one of least-squares, and we illustrate the performa...

Star formation can be triggered by compression from shock waves. In this study, we investigated the interaction of hydrodynamic shocks with Bonnor–Ebert spheres using 3D hydrodynamical simulations self-gravity. Our indicated that cloud evolution primarily depends on two parameters: speed and initial radius. Stronger compress clouds more efficiently, when central region becomes gravitationally u...

This work addresses some asymptotic behavior of solutions to stochastic convective Brinkman–Forchheimer (SCBF) equations perturbed by multiplicative Gaussian noise in two and three dimensional bounded domains. Using a weak convergence approach Budhiraja Dupuis, we establish the Laplace principle for strong solution SCBF suitable Polish space. Then, Wentzell–Freidlin type large deviation is deri...

The combined use of Variable Geometry Turbine (VGT) and Exhaust Gas Recirculation (EGR) gives us an opportunity to reduce emissions, without compromising the need to generate more power. In the present work, a multivariable approach is used to tackle the EGR-VGT actuator control problem. A linear multivariable controller is designed using Lyapunov’s Indirect Method, based on the Jacobian matrix...