Lyapunov functions for SIR and SIRS epidemic models

In this paper, we construct a new Lyapunov function for a variety of SIR and SIRS models in epidemiology. Global stability of the endemic equilibrium states of these systems is established.     

Differential mixed variational inequalities in finite dimensional spaces

In this paper, we introduce and study a class of differential mixed variational inequalities in finite dimensional Euclidean spaces. Under various conditions, we obtain linear growth and bounded linear growth of the solution set for the mixed variational inequalities. Moreover, we present some conclusions which enrich the literature on the mixed variational inequalities and generalize the corresponding results of [4]. In particular we prove existence theorems for weak solutions of a differential mixed variational inequality in the weak sense of Carathéodory by using a result on differential inclusions involving an upper semicontinuous set-valued map with closed convex values. Also by employing the results from differential inclusions we establish a convergence result on Euler time-dependent procedure for solving initial-value differential mixed variational inequalities.     

Controlling the Pore Sizes and Related Properties of Inverse Opal Scaffolds for Tissue Engineering Applications

Inverse opal scaffolds are finding widespread use in tissue engineering and regenerative medicine. Herein, the way in which the pore sizes and related physical properties of poly(D ,L ‐lactide‐co‐glycolide) inverse opal scaffolds are affected by the fabrication conditions is systematically investigated. It is found that the window size of an inverse opal scaffold is mainly determined by the annealing temperature rather than the duration of time, and the surface pore size is largely determined by the concentration of the infiltration solution. Although scaffolds with larger pore or window sizes facilitate faster migration of cells, they show slightly lower compressive moduli than scaffolds with smaller pore or window sizes.     

Positive solutions for singular boundary value problems with sign changing nonlinearities depending on x′ via index theory

Using the theory of fixed point index, this article discusses the existence of positive solutions for singular second-order boundary value problems, where f may be singular at x?=?0 and x′=0, and f may change sign.     

An intersection theorem for set-valued mappings

Given a nonempty convex set X in a locally convex Hausdorff topological vector space, a nonempty set Y and two set-valued mappings T: X ? X, S: Y ? X we prove that under suitable conditions one can find an x ∈ X which is simultaneously a fixed point for T and a common point for the family of values of S. Applying our intersection theorem, we establish a common fixed point theorem, a saddle point theorem, as well as existence results for the solutions of some equilibrium and complementarity problems.     

Polymer‐free,low tension graphene mechanical resonators

Graphene resonators are fabricated using a polymer‐free, direct transfer method onto metal reinforced holey carbon grids. The resonators are distinguished by the absence of organic residues and excellent crystallinity. The normal mode frequencies are measured using a Fabry–Perot technique; resonance curves indicate highly linear behaviour but very little built‐in strain, which is consistent with device geometry examined by atomic force microscopy. We conclude that the oscillators' restoring force is due instead to graphene's intrinsic bending rigidity; our measurements indicate a value of approximately 1.0 eV, consistent with previous theoretical and experimental work. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Evidence for an isomeric 3/2- state in 53Co

The fragmentation of a 550MeV/u primary beam of ⁵⁸Ni on a ⁹Be target has been used to measure time- and energy-correlated γ decays following the implantation of event-by-event discriminated secondary fragments into a ⁹Be stopper plate. A new isomeric γ decay with T _1/2 = 14( ) ns and E _γ = 646.2(2) keV is observed and attributed to the decay of the yrast 3/2^- state in ⁵³ ₂₇Co₂₆ . This short-lived isomeric state has been populated by means of nuclear reactions during the stopping process of the secondary fragments. The experimental findings are discussed in the framework of large-scale spherical shell model calculations in conjunction with isospin symmetry-breaking residual interactions for the A = 53 , T _z = ±1/2 mirror nuclei ⁵³Co and ⁵³Fe .     

Lyot filter based multiwavelength fiber ring laser actively mode-locked at 10 GHz using an electroabsorption modulator

A multiwavelength fiber ring laser comprising of a Lyot filter and hybrid gain medium is presented. A wavelength channel spacing of 100 GHz is achieved by appropriate tuning of the Lyot filter length. Four wavelength channels are simultaneously mode-locked at 10 GHz using an electroabsorption modulator. We highlight how the intra-cavity modulator can affect the stability of the mode-locked laser spectrum when used in conjunction with a Lyot filter. We show that, due its reduced polarization sensitivity, an electroabsorption modulator significantly improves the stability of the mode-locked laser spectrum when compared to using a Mach-Zehnder modulator.