Stability Criteria for SIS Epidemiological Models under Switching Policies

We study the spread of disease in an SIS model. The model considered is a time-varying, switched model, in which the parameters of the SIS model are subject to abrupt change. We show that the joint spectral radius can be used as a threshold parameter for this model in the spirit of the basic reproduction number for time-invariant models. We also present conditions for persistence and the existence of periodic orbits for the switched model and results for a stochastic switched model

Viability problem with perturbation in Hilbert space

This paper deals with the existence result of viable solutions of the differential inclusion $$\dot{x}(t) \in f(t,x(t)) + F(x(t))$$ $$x(t) \in K \quad \text{on } [0,T],$$ where $K$ is a locally compact subset in separable Hilbert space $H,$ $(f(s,\cdot))_s$ is an equicontinuous family of measurable functions with respect to $s$ and $F$ is an upper semi-continuous set-valued mapping with compact values contained in the Clarke subdifferential $\partial_{c} V(x)$ of an uniformly regular function $V.

Investigation of the Coupling Potential by means of S-matrix Inversion

We investigate the inelastic coupling interaction by studying its effect on the elastic scattering potential as determined by inverting the elastic scattering $S$-matrix. We first address the effect upon the real and imaginary elastic potentials of including excited states of the target nucleus. We then investigate the effect of a recently introduced novel coupling potential which has been remarkably successful in reproducing the experimental data for the $^{12}$C+$^{12}$C, $^{12}$C+$^{24}$Mg and $^{16}$O+$^{28}$Si reactions over a wide range of energies. This coupling potential has the effect of deepening the real elastic potential in the surface region, thereby explaining a common feature of many phenomenological potentials. It is suggested that one can relate this deepening to the super-deformed state of the compound nucleus, $^{24}$Mg.Comment: 12 pages with 3 figure

Impulsive Fractional Differential Inclusions Involving the Caputo Fractional Derivative

Mathematics Subject Classification: 26A33, 34A37.In this paper, we establish sufficient conditions for the existence of solutions for a class of initial value problem for impulsive fractional differential inclusions involving the Caputo fractional derivative. Both cases of convex and nonconvex valued right-hand side are considered. The topological structure of the set of solutions is also considered

Black hole mass and angular momentum in topologically massive gravity

We extend the Abbott-Deser-Tekin approach to the computation of the Killing charge for a solution of topologically massive gravity (TMG) linearized around an arbitrary background. This is then applied to evaluate the mass and angular momentum of black hole solutions of TMG with non-constant curvature asymptotics. The resulting values, together with the appropriate black hole entropy, fit nicely into the first law of black hole thermodynamics.Comment: 20 pages, references added, version to appear in Classical and Quantum Gravit

The high partial wave phenomenon of spin changing atomic transitions

The collisional transition between two highly excited atomic states with different spin is investigated theoretically. Taking helium-like n1S − n3P as an example, it is found that the transition is driven in the highly ion-ized Fe ion purely by exchange, and the cross section becomes increasingly dominated by partial waves of high orbital angular momentum as the scattering energy increases. Whereas for the near-neutral Li ion the transition is dominated by channel coupling in low partial waves. Analytical bench-marks and numerical methods are developed for the accurate calculation of the exchange integral at high angular momentum. It is shown how the partial wave and energy dependence of the collision strength for high n spin changing transitions in the highly ionized ion is related to the overlap of the extended atomic orbitals.</p

Photodegradation of 2-naphthol Using Nanocrystalline TiO2

The kinetics of the photocatalytic degradation of 2-naphthol has been investigated in aqueous suspensions of titanium dioxide (TiO2) under a variety of conditions, which is essential from application point of view. The degradation was studied using different parameters such as types of TiO2, catalyst concentration, substrate concentration, reaction pH and in the presence of different electron acceptors such as hydrogen peroxide (H2O2), potassium bromate (KBrO3) and potassium persulphate (K2S2O8) besides molecular oxygen. The degradation rates were found to be strongly influenced by all the above parameters. The photocatlyst ″Degussa P-25″ was found to be more efficient as compared with other photocatalysts. The results indicate the process follows Langmuir-Hinshelwood-type kinetics and inference is made of the reaction taking place on the semiconductor particle surface. An analysis of Total Organic Carbon (TOC) showed that a complete mineralization of 2-naphthol can be easily achieved.The kinetics of the photocatalytic degradation of 2-naphthol has been investigated in aqueous suspensions of titanium dioxide (TiO2) under a variety of conditions, which is essential from application point of view. The degradation was studied using different parameters such as types of TiO2, catalyst concentration, substrate concentration, reaction pH and in the presence of different electron acceptors such as hydrogen peroxide (H2O2), potassium bromate (KBrO3) and potassium persulphate (K2S2O8) besides molecular oxygen. The degradation rates were found to be strongly influenced by all the above parameters. The photocatlyst ″Degussa P-25″ was found to be more efficient as compared with other photocatalysts. The results indicate the process follows Langmuir-Hinshelwood-type kinetics and inference is made of the reaction taking place on the semiconductor particle surface. An analysis of Total Organic Carbon (TOC) showed that a complete mineralization of 2-naphthol can be easily achieved