On global stability of an HIV pathogenesis model with cure rate

In this paper, applying both Lyapunov function techniques and monotone iterative techniques, we establish new sufficient conditions under which the infected equilibrium of an HIV pathogenesis model with cure rate is globally asymptotically stable. By giving an explicit expression for eventual lower bound of the concentration of susceptible CD4⁺ T cells, we establish an affirmative partial answer to the numerical simulations investigated in the recent paper [Liu, Wang, Hu and Ma, Global stability of an HIV pathogenesis model with cure rate, Nonlinear Analysis RWA (2011) 12 : 2947–2961]. Our monotone iterative techniques are applicable for the small and large growth rate in logistic functions for the proliferation rate of healthy and infected CD4⁺ T cells. Copyright © 2014 John Wiley & Sons, Ltd.     

Investigation of void formation beneath thin AlN layers by decomposition of sapphire substrates for self-separation of thick AlN layers grown by HVPE

Void formation at the interface between thick AlN layers and (0 0 0 1) sapphire substrates was investigated to form a predefined separation point of the thick AlN layers for the preparation of freestanding AlN substrates by hydride vapor phase epitaxy (HVPE). By heating 50–200 nm thick intermediate AlN layers above 1400 °C in a gas flow containing H₂ and NH₃, voids were formed beneath the AlN layers by the decomposition reaction of sapphire with hydrogen diffusing to the interface. The volume of the sapphire decomposed at the interface increased as the temperature and time of the heat treatment was increased and as the thickness of the AlN layer decreased. Thick AlN layers subsequently grown at 1450 °C after the formation of voids beneath the intermediate AlN layer with a thickness of 100 nm or above self-separated from the sapphire substrates during post-growth cooling with the aid of voids. The 79 μm thick freestanding AlN substrate obtained using a 200 nm thick intermediate AlN layer had a flat surface with no pits, high optical transparency at wavelengths above 208.1 nm, and a dislocation density of 1.5×10⁸ cm⁻².     

Observation of mechanically induced luminescence from microparticles

We have invented a new device based on atomic force microscopy that measures the emission from a single microparticle by force direct application using the AFM probe, and successfully observed emission in the region of the elastic deformation, friction, and destructive deformation.     

Global dynamics of a delayed SIRS epidemic model with a wide class of nonlinear incidence rates

In this paper, by constructing Lyapunov functionals, we consider the global dynamics of an SIRS epidemic model with a wide class of nonlinear incidence rates and distributed delays $\int^{h}_{0} p(\tau)f(S(t),I(t-\tau)) \mathrm{d}\tau$ under the condition that the total population converges to 1. By using a technical lemma which is derived from strong condition of strict monotonicity of functions f(S,I) and f(S,I)/I with respect to S??0 and I>0, we extend the global stability result for an SIR epidemic model if R ₀>1, where R ₀ is the basic reproduction number. By using a limit system of the model, we also show that the disease-free equilibrium is globally asymptotically stable if R ₀=1.     

Global stability for a multi-group SIRS epidemic model with varying population sizes

In this paper, by extending well-known Lyapunov function techniques to SIRS epidemic models, we establish sufficient conditions for the global stability of an endemic equilibrium of a multi-group SIRS epidemic model with varying population sizes which has cross patch infection between different groups. Our proof no longer needs such a grouping technique by graph theory commonly used to analyze the multi-group SIR models.