The numerical solution of problems in calculus of variation using Chebyshev finite difference method

The Chebyshev finite difference method is used for finding the solution of the ordinary differential equations which arise from problems of calculus of variations. Our approach consists of reducing the problem to a set of algebraic equations. This method can be regarded as a non-uniform finite difference scheme. Some numerical results are also given to demonstrate the validity and applicability of the presented technique. The method is easy to implement and yields very accurate results.     

Momentum and heat transfer over a continuously moving surface with a parallel free stream in a viscoelastic fluid

The flow and heat transfer characteristics for a continuous moving surface in a viscoelastic fluid are investigated. Constitutive equations of viscoelastic fluid obey the second‐grade model. Analytic expressions to velocity and temperature have been developed by employing homotopy analysis method. The criterion to the convergence of the solution is properly discussed. Furthermore, the values of skin friction coefficient and the local Nusselt number have been computed and discussed. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

Partial functional differential equation with an integral condition and applications to population dynamics

In this work we consider a semilinear functional partial differential equation with an integral condition. We apply the method of semidiscretization in time, to establish the existence and uniqueness of solutions. We also study the continuation of the solution to the maximal interval of existence. Finally we give examples to demonstrate the applications of our results.     

Effects of Hall current and heat transfer on rotating flow of a second grade fluid through a porous medium

The effects of Hall current and heat transfer on the rotating flow of a second grade fluid past a porous plate with variable suction are examined. The medium considered is porous and suction and external flow velocities vary periodically. The plate is assumed to be at a higher temperature than the fluid. The influences of the Hall parameter and porosity of the medium have been seen and discussed on the velocity and temperature profiles. Moreover, these influences have also been seen on the drag and lateral stress. Finally, the obtained solutions are also compared with the previous studies in the literature and found quite agreement.     

Impact of Various Parameters Over the Adsorption of Polyvinylpyrrolidone onto Kaolin

The adsorption of water-soluble polymer, polyvinylpyrrolidone having molecular mass 9.1 ± 1.43 × 10³Kg mole^?1 on kaolin has been investigated. The effect of different parameters like pH, molecular mass of polymer and pre-heat treatment on the adsorption of PVP has been deliberated. The 20.7% decrease in adsorption in pH ranging from 2–10 have been found, which was an indication of the fact that with the increase in pH the kaolin surfaces sites charge amount and ultimately sign changes. Maximum adsorption was observed at pH 5.6 that was also molecular mass dependent. By increasing the pretreatment temperature, the amount of polymer adsorbed was also increased. However, above the specific temperature adsorption of PVP was decreased and attributed to decrease in specific surface area of kaolin.     

Magnetohydrodynamic flow of a Sisko fluid in annular pipe: A numerical study

This paper presents a numerical study for the unsteady flow of a magnetohydrodynamic (MHD) Sisko fluid in annular pipe. The fluid is assumed to be electrically conducting in the presence of a uniform magnetic field. Based on the constitutive relationship of a Sisko fluid, the non‐linear equation governing the flow is first modelled and then numerically solved. The effects of the various parameters especially the power index n, the material parameter of the non‐Newtonian fluid b and the magnetic parameter B on the flow characteristics are explored numerically and presented through several graphs. Moreover, the shear‐thinning and shear‐thickening characteristics of the non‐Newtonian Sisko fluid are investigated and a comparison is also made with the Newtonian fluid. Copyright © 2009 John Wiley & Sons, Ltd.     

Understanding and tuning the catalytic bias of hydrogenase

When enzymes are optimized for biotechnological purposes, the goal often is to increase stability or catalytic efficiency. However, many enzymes reversibly convert their substrate and product, and if one is interested in catalysis in only one direction, it may be necessary to prevent the reverse reaction. In other cases, reversibility may be advantageous because only an enzyme that can operate in both directions can turnover at a high rate even under conditions of low thermodynamic driving force. Therefore, understanding the basic mechanisms of reversibility in complex enzymes should help the rational engineering of these proteins. Here, we focus on NiFe hydrogenase, an enzyme that catalyzes H(2) oxidation and production, and we elucidate the mechanism that governs the catalytic bias (the ratio of maximal rates in the two directions). Unexpectedly, we found that this bias is not mainly determined by redox properties of the active site, but rather by steps which occur on sites of the proteins that are remote from the active site. We evidence a novel strategy for tuning the catalytic bias of an oxidoreductase, which consists in modulating the rate of a step that is limiting only in one direction of the reaction, without modifying the properties of the active site.     

Simultaneous trace-levels determination of Hg(II) and Pb(II) ions in various samples using a modified carbon paste electrode based on multi-walled carbon nanotubes and a new synthesized Schiff base

A modified carbon paste electrode based on multi-walled carbon nanotubes (MWCNTs) and 3-(4-methoxybenzylideneamino)-2-thioxothiazolodin-4-one as a new synthesized Schiff base was constructed for the simultaneous determination of trace amounts of Hg(II) and Pb(II) by square wave anodic stripping voltammetry. The modified electrode showed an excellent selectivity and stability for Hg(II) and Pb(II) determinations and for accelerated electron transfer between the electrode and the analytes. The electrochemical properties and applications of the modified electrode were studied. Operational parameters such as pH, deposition potential and deposition time were optimized for the purpose of determination of traces of metal ions at pH 3.0. Under optimal conditions the limits of detection, based on three times the background noise, were 9.0 × 10⁻⁴ and 6.0 × 10⁻⁴ μmol L⁻¹ for Hg(II) and Pb(II) with a 90 s preconcentration, respectively. In addition, the modified electrode displayed a good reproducibility and selectivity, making it suitable for the simultaneous determination of Hg(II) and Pb(II) in real samples such as sea water, waste water, tobacco, marine and human teeth samples.     

Synthesis of double mesoporous core-shell silica spheres with tunable core porosity and their drug release and cancer cell apoptosis properties

In this work, we demonstrate a simple two-pot approach to double mesoporous core–shell silica spheres (DMCSSs) with uniform size of 245–790 nm, shell thickness of 41–80 nm and surface area and total pore volume of 141–618 m² g^?1 and 0.14–0.585 cc g^?1, respectively. First, solid silica spherical particles were synthesized by the Stöber method and used as a core. Second, a mesoporous shell could be formed around the silica cores by using an anionic surfactant and a co-structure directing agent. It was found that mesopores can be anchored within dense silica cores during mesoporous silica shell formation, synchronously the base group with surfactant assistant can etch the dense silica cores to re-organize new mesostructure, so that double mesoporous core–shell silica sphere (DMCSS) structure can be obtained by a single surfactant-templating step. The spherical size and porosity of the silica cores of DMCSS together with shell thickness can be tuned by controlling Stöber parameters, including the concentrations of ammonia, solvent and tetraethoxysilane and the reaction time. DMCSS were loaded with ketoprofen and thymoquinone, which are an anti-inflammatory and a potential novel anti-cancer drug, respectively. Both drugs showed controlled release behavior from the pores of DMCSS. Drug uptakes within DMCSS were ～27 and 81 wt.% for ketoprofen and thymoquinone, respectively. Furthermore, DMCSS loaded with thymoquinone was more effective in inducing cancer cell apoptosis than uncontained thymoquinone, because of the slow release of the drug from the mesoporous structure.