The photoinduced oxidation of tetra(N-methyl-4-pyridyl)porphyrinmanganese(III) has been achieved in homogeneous solution. The manganese porphyrin was used as an electron donor in a three-component system with tris-(2,2'-bipyridine)ruthenium(II) as the photosensitizer and chloropentaamminecobalt(III) as the electron acceptor. The photooxidized manganese porphyrin is unstable in aqueous solution,...

We prove nonlinear stability for finite amplitude perturbations of plane Couette flow. A bound of the solution of the resolvent equation in the unstable complex half-plane is used to estimate the solution of the full nonlinear problem. The result is a lower bound, including Reynolds number dependence, of the threshold amplitude below which all perturbations are stable. Our result is an improvem...

In this paper, we have proposed Euler’s modified method for solving the six coupled system of non-linear ordinary differential equations (ODEs), which are aroused in the reduction of stratified Boussinesq equations. This method can also be called as revised Euler’s modified method for solving two simultaneous ODEs. We have obtained the numerical solutions on stable and unstable manifolds. The e...

An SIR epidemic model with pulse birth and standard incidence is presented. The dynamics of the epidemic model is analyzed. The basic reproductive number R∗ is defined. It is proved that the infection-free periodic solution is global asymptotically stable if R∗ < 1. The infection-free periodic solution is unstable and the disease is uniform persistent if R∗ > 1. Our theoretical results are conf...

This paper is concerned with the stability problem of a linear integro-differential system with distributed delay in the diagonal terms. We establish some explicit conditions for the zero solution of the system to be asymptotically stable. In particular, as the delay parameter increases monotonously under certain conditions, the zero solution switches finite times from stability to instability ...

Stable power processes are never guaranteed. An assortment of unstable behaviors wrecks power apparatus, including mechanical vibration, malfunctioning control apparatus, unstable fluid flow, unstable boiling of liquids, or combinations thereof. A necessary condition for stable reactor power is that the reactor distortion accompanying a temperature rise decreases the reactivity, thus slowing an...

The dynamics of structurally stable heteroclinic cycles connecting fixed points with one-dimensional unstable manifolds under the influence of noise is analyzed. Fokker-Planck equations for the evolution of the probability distribution of trajectories near heteroclinic cycles are solved. The influence of the magnitude of the stable and unstable eigenvalues at the fixed points and of the amplitu...

In the present paper we obtain a closed form expression for the squared H⊥ 2 norm of a partial fraction expansion with repeated unstable poles. We also obtain a closed form expression for the squared H2 norm of a partial fraction expansion with repeated stable poles. As an application we use the H⊥ 2 result to extend the closed form solution of the discretetime linear time invariant (LTI) signa...

Abstract We reconsider the one-step replica-symmetry-breaking (1RSB) solutions of two random combinatorial problems: k-XORSAT and k-SAT. We present a general method for establishing the stability of these solutions with respect to further steps of replica-symmetry breaking. Our approach extends the ideas of Ref. [1] to more general combinatorial problems. It turns out that 1RSB is always unstab...

A delayed feedback control framework for stabilizing unstable periodic orbits of linear periodic time-varying systems is proposed. In this framework, act-and-wait approach is utilized for switching a delayed feedback controller on and off alternately at every integer multiples of the period of the system. By analyzing the monodromymatrix of the closed-loop system, we obtain conditions under whi...