Notwithstanding recent claims by Richard et al., there is no linear hydrodynamic instability of axisymmetrically stable disks in the local limit. We prove this by means of an exact stability analysis of an unbounded incompressible flow having constant stratification and constant shear.

It is shown that every small-time locally controllable system in the plane can (locally) be asymptotically stabilized by employing locally Hölder continuous feedback laws, as essentially was conjectured by E. Sontag. An explicit algorithm for the construction of such feedback laws is given.

ABSTRACT. When the zero solution of an almost periodic differential system is uniform-asymptotically stable, it is shown that the zero solution is diminishingly asymptotically stable and totally asymptotically stable. Generalization of the above theorem to bounded solutions and functional differential equations with finite time-lag are obtained by the same method. The techniques used in the pro...

This research develops the SVEIHQR model to simulate spread of COVID-19 with vaccination, implementation health protocols, and treatment. The population is divided into twelve subpopulations, resulting in a mathematical form system differential equations variables. From model, we obtain disease-free equilibrium point, endemic basic reproduction number (R0). point locally asymptotically stable w...

FAST TCP is important for promoting dataintensive applications since it can cleverly react to both packet loss and delay for detecting network congestion. This paper provides a continuous time model and extensive stability analysis of FAST TCP congestion-control mechanism in bufferless Optical Burst Switched Networks (OBS). The paper first shows that random burst contentions are essential to st...

We establish the existence and robustness of layered, time-periodic solutions to a reaction-diffusion equation in a bounded domain in Rn, when the diffusion coefficient is sufficiently small and the reaction term is periodic in time and bistable in the state variable. Our results suggest that these patterned, oscillatory solutions are stable and locally unique. The location of the internal laye...

A nonlinear observer for estimation of the longitudinal velocity, lateral velocity, and yaw rate of a vehicle, designed for the purpose of vehicle side-slip estimation, is modified and extended in order to work for different road surface conditions. The observer relies on a road-tire friction model and is therefore sensitive to changes in the adhesion characteristics of the road surface. The fr...