On exact solutions to epidemic dynamic models

In this study, we address an SIR (susceptible-infected-recovered) model that is given as a system of first order differential equations and propose the SIR model on time scales which unifies and extends continuous and discrete models. More precisely, we derive the exact solution to the SIR model and discuss the asymptotic behavior of the number of susceptibles and infectives. Next, we introduce an SIS (susceptible-infected-susceptible) model on time scales and find the exact solution. We solve the models by using the Bernoulli equation on time scales which provides an alternative method to the existing methods. Having the models on time scales also leads to new discrete models. We illustrate our results with examples where the number of infectives in the population is obtained on different time scales.     

Two-component organogelators: combination of Nε-alkanoyl-L-lysine with various N-alkanoyl-L-amino acids: additional level of hierarchical control

Synthesis of two-component organogelation system was performed very easy and concise manner from N^ε-palmitoyl-L-lysine ethyl ester and N^ε-miristoyl-L-lysine ethyl ester in which they were used as base component and N-lauroyl-L-amino acids (amino acids:, alanine, leucine and phenylalanine as acid components.). And their organogelation properties were examined in different pharmaceutical fluids such as liquid paraffin, fatty acid ethyl, and isopropyl esters. In this way, gelation efficiency was ascertained variations of alkanoyl moieties and combination of different amino acids in the gelator structures. Characterization of gelators was performed via thermal measurement such as Tg and gel–sol enthalpy change; SEM and FTIR as optical methods.     

Removal of Pb2+ and Cd2+ ions from aqueous solutions using guanidine modified hydrogels

In this study, experimental measurements have been made on the batch adsorption of cadmium and lead ions from aqueous solutions using poly(guanidine modified 2‐acrylamido‐2‐methylpropan sulfonic acid/acrylic acid/N‐vinylpyrrolidone/2‐Hydroxyethyl methacrylate), P(AMPSG/AAc/NVP/HEMA) hydrogels. The guanidyl end group bearing AMPSG monomer was synthesized from the reaction of AMPS and guanidine. The hydrogels were prepared by UV‐curing technique. The morphology of the dry H10‐hydrogel sample was examined by SEM. The influence of the uptake conditions, such as pH, functional monomer per cent, contact time, initial feed concentration, and foreign metal ions on the metal ion binding capacity of hydrogel, was also tested. The selectivity of the hydrogel toward the different metal ions tested was Hg(II) > Pb(II) > Au(III) > Cd(II). The adsorption isotherm models were applied to the experimental data, and it was seen that the Langmuir isotherm model was the best fit for the adsorption of Cd(II) and Pb(II) ions on P(AMPSG/AAc/NVP/HEMA) hydrogel. It was found that adsorbed lead and cadmium ions on P(AMPSG/AAc/NVP/HEMA) hydrogel can be effectively desorbed by acid leaching and the regenerated P(AMPSG/AAc/NVP/HEMA) hydrogel can be reused almost five times less without any loss of adsorption capacity. Copyright © 2009 John Wiley & Sons, Ltd.     

A location-routing problem for the conversion to the “click-and-mortar” retailing: The static case

The static conversion from brick-and-mortar retailing to the hybrid click-and-mortar business model is studied from the perspective of distribution logistics. Retailers run warehouses and brick-and-mortar stores to meet the demand of their walk-in customers. When they decide to operate on the Web as an e-tailer, also click-and-mortar stores are needed which can serve both walk-in and online customers. While the distance between home and the nearest open store is used as a proxy measure for walk-in customers, a quality of service (QoS) guarantee for online customers is timely delivery of their orders. We describe and solve a static location-routing based problem for companies that embrace the clicks-and-bricks strategy in their retail operations. An augmented Lagrangian relaxation method embedded in a subgradient optimization procedure generates lower bounds, whereas a heuristic method finds feasible solutions. The performance of the Lagrangian-based solution method is tested on a number of randomly generated test problems.     

Replica-molded high-Q polymer microresonators

Ultrahigh-Q microtoroids on a chip are applied as replication masters to demonstrate replica-molded high-Q microresonator arrays. Replica Q factors are nearly material loss limited, affirming the integrity of the replication process, and are as high as 5 x 10(6), or nearly a factor of 40 greater than previous polymer-based devices. Because the molding process is nondestructive, both the master and the molds can be reused. Additionally, by using a novel optical polymer (Vicast), we demonstrate storage of high-Q microresonators in the mold for weeks, providing a method to preserve the whispering-gallery Q factor.     

Temperature dependence of the lattice parameters in the S1G and S2G phases of HxBPA

The temperature dependence of the monoclinic lattice constants in the two smectic phases, S¹_G and S²_G, of HxBPA, has been obtained from X-ray diffraction data, in the temperature range 300 K < T < 240 K. The variation of b (unique axis) is consistent with the chain ordering in the S²_G phase indicated by Raman and NMR measurements.