Conditionally oscillatory half-linear differential equations

We consider a nonoscillatory half-linear second order differential equation (*) $$ (r(t)\Phi (x'))' + c(t)\Phi (x) = 0,\Phi (x) = \left| x \right|^{p - 2} x,p > 1, $$ and suppose that we know its solution h. Using this solution we construct a function d such that the equation (**) $$ (r(t)\Phi (x'))' + [c(t) + \lambda d(t)]\Phi (x) = 0 $$ is conditionally oscillatory. Then we study oscillations of the perturbed equation (**). The obtained (non)oscillation criteria extend existing results for perturbed half-linear Euler and Euler-Weber equations.     

Effects of hydrochloric acid treatment on structure characteristics and C<Subscript>2</Subscript>H<Subscript>4</Subscript> adsorption capacities of Ünye bentonite from Turkey: a combined FT-IR,XRD, XRF,TG/DTA and MAS NMR study

In this study, a bentonite sample from Ünye, Turkey was treated with various HCl solutions (0.1, 1.0 and 5.0 M) at 90 °C during 3 and 6 h. X-ray diffraction (XRD), X-ray fluorescence (XRF), differential thermal analysis (DTA), thermogravimetric analysis (TG), Fourier transform infrared (FT-IR), magic angle spinning nuclear magnetic resonance (²⁹Si and ²⁷Al MAS NMR) and surface area measurement methods were employed in order to investigate the structural and thermal changes occurring as a result of the acid activation. The data for the adsorption of C₂H₄ obtained at 273 K and pressures up to 100 kPa correlated with structural properties of the acid treated bentonite samples. With the increase of both concentration of acid solution and treatment time, the specific surface area values and the retentions of C₂H₄ gas of bentonite samples increased. Bentonite treated with 5.0 M HCl for 6 h adsorbed C₂H₄ most effectively.     

Bioactivity Profiles of Cytoprotective Short-Chain Quinones

Short-chain quinones (SCQs) have been investigated as potential therapeutic candidates against mitochondrial dysfunction, which was largely thought to be associated with the reversible redox characteristics of their active quinone core. We recently reported a library of SCQs, some of which showed potent cytoprotective activity against the mitochondrial complex I inhibitor rotenone in the human hepatocarcinoma cell line HepG2. To better characterize the cytoprotection of SCQs at a molecular level, a bioactivity profile for 103 SCQs with different compound chemistries was generated that included metabolism related markers, redox activity, expression of cytoprotective proteins and oxidative damage. Of all the tested endpoints, a positive correlation with cytoprotection by SCQs in the presence of rotenone was only observed for the NAD(P)H:quinone oxidoreductase 1 (NQO1)-dependent reduction of SCQs, which also correlated with an acute rescue of ATP levels. The results of this study suggest an unexpected mode of action for SCQs that appears to involve a modification of NQO1-dependent signaling rather than a protective effect by the reduced quinone itself. This finding presents a new selection strategy to identify and develop the most promising compounds towards their clinical use.     

Compactly uniform Bochner integrability of random elements

As the concept of uniform integrability has an essential role in the convergence of moments and martingales in the probability theory it is important to study this concept. In the present paper using Bochner integral we define a new type of uniform integrability for sequences of random elements. We give some independent necessary and sufficient conditions for this concept. We also generalize the concepts of strong and statistical convergences to sequences of random elements and we obtain the relationship between these two important concepts of summability theory via this new type of uniform integrability.     

On the sequential order continuity of the <Emphasis Type="Italic">C</Emphasis>(<Emphasis Type="Italic">K</Emphasis>)-space

As shown in [1], for each compact Hausdorff space K without isolated points, there exists a compact Hausdorff P′-space X but not an F-space such that C(K) is isometrically Riesz isomorphic to a Riesz subspace of C(X). The proof is technical and depends heavily on some representation theorems. In this paper we give a simple and direct proof without any assumptions on isolated points. Some generalizations of these results are mentioned.     

Fermionic approach to soliton equations

In this paper we exploit the algebraic structure of the soliton equations and find solutions in terms of fermion particles. We show how determinants arise naturally in the fermionic approach to soliton equations. We write the τ-function for charged free fermions in terms of determinants. Examples of how to get soliton, rational and dromion solutions from τ-functions for the various soliton equations are given.     

Unification of calculus on Time Scales with mathematica

In 1990 Hilger defined the Time Scale Calculus which is the unification of discrete and continuous analysis in his PhD. In 2005 Yantir and Ufuktepe showed delta derivative with Mathematica[5]. In this study we give many computations of Time Scale Calculus with Mathematica such as the numerical and symbolic computation of forward jump operator and delta derivative for a particular time scale, graphs of functions, and definite integral on a time scale. We also improve and extent the Time Scale package for symbolics computations.     

A membrane-less enzymatic fuel cell with layer-by-layer assembly of redox polymer and enzyme over graphite electrodes

Layer-by-layer (LBL) assembly of alternate osmium redox polymers and glucose oxidase, at anode, and laccase, at cathode, using graphite electrodes form a membrane-less glucose/O(2) enzymatic fuel cell providing a power density of 103 μW cm(-2) at pH 5.5.     

Characterization of nanoporous gold electrodes for bioelectrochemical applications

The high surface areas of nanostructured electrodes can provide for significantly enhanced surface loadings of electroactive materials. The fabrication and characterization of nanoporous gold (np-Au) substrates as electrodes for bioelectrochemical applications is described. Robust np-Au electrodes were prepared by sputtering a gold-silver alloy onto a glass support and subsequent dealloying of the silver component. Alloy layers were prepared with either a uniform or nonuniform distribution of silver and, post dealloying, showed clear differences in morphology on characterization with scanning electron microscopy. Redox reactions under kinetic control, in particular measurement of the charge required to strip a gold oxide layer, provided the most accurate measurements of the total electrochemically addressable electrode surface area, A(real). Values of A(real) up to 28 times that of the geometric electrode surface area, A(geo), were obtained. For diffusion-controlled reactions, overlapping diffusion zones between adjacent nanopores established limiting semi-infinite linear diffusion fields where the maximum current density was dependent on A(geo). The importance of measuring the surface area available for the immobilization was determined using the redox protein, cyt c. The area accessible to modification by a biological macromolecule, A(macro), such as cyt c was reduced by up to 40% compared to A(real), demonstrating that the confines of some nanopores were inaccessible to large macromolecules due to steric hindrances. Preliminary studies on the preparation of np-Au electrodes modified with osmium redox polymer hydrogels and Myrothecium verrucaria bilirubin oxidase (MvBOD) as a biocathode were performed; current densities of 500 μA cm(-2) were obtained in unstirred solutions.     

Comparative Evaluation of Pumice Stone as an Alternative Immobilization Material for 1,3-Propanediol Production from Waste Glycerol by Immobilized Klebsiella pneumoniae

In this study, pumice stone (PS), which is a vastly available material in Turkey, was evaluated as an alternative immobilization material in comparison to other commercially available immobilization materials such as glass beads and polyurethane foam. All immobilized bioreactors resulted in much better 1,3-propanediol production from waste glycerol in comparison to the suspended cell culture bioreactor. It was also demonstrated that the locally available PS material is as good as the commercially available immobilization material. The maximum volumetric productivity (8.5?g?L^?1?h^?1) was obtained by the PS material, which is 220?% higher than the suspended cell system. Furthermore, the immobilized bioreactor system was much more robust against cell washout even at very low hydraulic retention time values.