Homotopy Solution for the Channel Flow of a Third Grade Fluid

The solution for the flow of a third grade fluid bounded by two parallel porous plates is given using homotopy analysis method (HAM). A comparison is made with the exact numerical solution for the various values of the physical parameters. It is found that a proper choice of the auxiliary parameter occurring in HAM solution gives very close results.     

Lead dioxide-coated carbon paste electrodes

Lead dioxide electrodeposited under optimized conditions on carbon paste provides an electroanalytically useful electrode, with an anodic working range extending to 1.9 V. Voltammograms for sulphite are used to study electrode lifetime and reproducibility; calibration graphs are linear up to 10^-3M sulphite in 0.5 M sulphuric acid.     

The micro-volumetric determination of lead with thionalide and its application to the analysis of tin-base and lead-base alloys

The authors have elaborated an exact micro-volumetric method for the determination of lead with thionalide. The method has been successfully applied to the determination of lead in tin-base and lead-base alloys, following the isolation of lead as lead sulphate and its redissolution in ammonium acetate.     

Error estimates on anisotropic elements for functions in weighted Sobolev spaces

In this paper we prove error estimates for a piecewise average interpolation on anisotropic rectangular elements, i.e., rectangles with sides of different orders, in two and three dimensions.

Our error estimates are valid under the condition that neighboring elements have comparable size. This is a very mild assumption that includes more general meshes than those allowed in previous papers. In particular, strong anisotropic meshes arising naturally in the approximation of problems with boundary layers fall under our hypotheses.

Moreover, we generalize the error estimates allowing on the right-hand side some weighted Sobolev norms. This extension is of interest in singularly perturbed problems.

Finally, we consider the approximation of functions vanishing on the boundary by finite element functions with the same property, a point that was not considered in previous papers on average interpolations for anisotropic elements.

As an application we consider the approximation of a singularly perturbed reaction-diffusion equation and show that, as a consequence of our results, almost optimal order error estimates in the energy norm, valid uniformly in the perturbation parameter, can be obtained.

     

Distinct distances between a collinear set and an arbitrary set of points

We consider the number of distinct distances between two finite sets of points in ${\mathbb{R}}^k$, for any constant dimension $k\ge 2$, where one set $P_1$ consists of $n$ points on a line $l$, and the other set $P_2$ consists of $m$ arbitrary points, such that no hyperplane orthogonal to $l$ and no hypercylinder having $l$ as its axis contains more than $O\left(1\right)$ points of $P_2$. The number of distinct distances between $P_1$ and $P_2$ is then

$\Omega \left(min\left\{n^{2∕3}{m}^{2∕3},\frac{n^{10∕11}{m}^{4∕11}}{{log}^{2∕11}m},n^2,m^2\right\}\right).$

Without the assumption on $P_2$, there exist sets $P_1$, $P_2$ as above, with only $O(m+n)$ distinct distances between them.     

Preparation,Characterization and Application of Modified Surfaces with 3,5-Bis(3,5-dinitrobenzoyl-amino) benzoic acid

Summary: The spontaneous adsorption of the dendron 3,5-Bis (3,5-dinitrobenzoylamino) benzoic acid (D-NO₂) onto gold and carbon electrodes produced conductive surfaces with electroactive chemical functions. A comparative electrochemical behavior of both electrodes after dendron immobilization led us to conclude that the self-assembly of D-NO₂ on carbon is faster and stronger. Considering this advantage, the surface of magnetic maghemite nanoparticles (MNPs) was modified using D-NO₂. Firstly, MNPs were modified with APS as silane coupling agent and afterwards, D-NO₂ was covalently attached to the surface, achieving nitro-functionalized MNPs. Subsequently, the immobilization of these modified MNPs onto glassy carbon surfaces was explored to generate a novel platform promising for biosensors development.     

Microwave-assisted regioselective cycloaddition reactions between 9-substituted anthracenes and levoglucosenone

The cycloaddition reactions of 9-substituted anthracenes and levoglucosenone were investigated under microwave irradiation and conventional heating conditions. Considering time, yields, and regioselectivity, microwave technology has proven to be an ideal tool to achieve this chemical transformation. [reaction: see text].     

QCD as a topologically ordered system

We argue that QCD belongs to a topologically ordered phase similar to many well-known condensed matter systems with a gap such as topological insulators or superconductors. Our arguments are based on an analysis of the so-called “deformed QCD” which is a weakly coupled gauge theory, but nevertheless preserves all the crucial elements of strongly interacting QCD, including confinement, nontrivial θ$\theta$ dependence, degeneracy of the topological sectors, etc. Specifically, we construct the so-called topological “BF” action which reproduces the well known infrared features of the theory such as non-dispersive contribution to the topological susceptibility which cannot be associated with any propagating degrees of freedom. Furthermore, we interpret the well known resolution of the celebrated U(1)_A$U{\left(1\right)}_A$ problem where the would be η^′${\eta }^{\prime }$ Goldstone boson generates its mass as a result of mixing of the Goldstone field with a topological auxiliary field characterizing the system. We then identify the non-propagating auxiliary topological field of the BF formulation in deformed QCD with the Veneziano ghost (which plays the crucial role in resolution of the U(1)_A$U{\left(1\right)}_A$ problem). Finally, we elaborate on relation between “string-net” condensation in topologically ordered condensed matter systems and long range coherent configurations, the “skeletons”, studied in QCD lattice simulations.