Best proximity points of non-self mappings

Let A,B be nonempty subsets of a Banach space X and let T:A→B be a non-self mapping. Under appropriate conditions, we study the existence of solutions for the minimization problem min _x∈A ∥x?Tx∥.     

Peracid-induced ring opening of some hexahydro-2H-isoxazolo[2,3-a]pyridines to second-generation cyclic aldonitrones

A study of the stereo- and face selectivity of the cycloaddition reactions of several mono- and disubstituted alkenes with 4-hydroxymethyl-3,4,5,6-tetrahydropyridine 1-oxide has been carried out. The addition reactions have displayed a very high degree of face selectivity in the range 13-48:1. Use of dimethyl methylenemalonate as a protective group in nitrone cycloaddition reactions has been demonstrated. The invertomeric analysis revealed that the bicyclic cycloadducts remain predominantly as the cis-fused isomer, which leads to the formation of synthetically important second-generation cyclic aldonitrones via peracid oxidation. One interesting finding was that treatment of the cycloadducts with two equivalents of peracid afforded the cyclic N-hydroxy lactams, presumably via further oxidation of the aldonitrones. The piperidine ring has been elaborated by cycloaddition reaction of the second-generation nitrones with several alkenes, which in most cases gave the cycloadducts in a stereoselective manner.     

Amenability constants for semilattice algebras

For any finite commutative idempotent semigroup S, a semilattice, we show how to compute the amenability constant of its semigroup algebra ℓ ¹(S). This amenability constant is always of the form 4n+1. We then show that these give lower bounds to amenability constants of certain Banach algebras graded over semilattices. We also give example of a commutative Clifford semigroups G _n whose semigroup algebras ℓ ¹(G _n ) admit amenability constants of the form 41+4(n−1)/n. We also show there is no commutative semigroup whose semigroup algebra has an amenability constant between 5 and 9. N. Spronk’s research was supported by NSERC Grant 312515-05.     

Corrosion inhibition of mild steel in hydrochloric acid by betanin as a green inhibitor

The effect of betanin (2,6-pyridinedicarboxylic acid, 4-(2-(2-carboxy-5-(beta-D-glucopyr-anosyloxy)-2,3-dihydro-6-hydroxy-1H-indol-1-yl)ethenyl)-2,3-dihydro-(S-(R*,R*))) on the corrosion inhibition of mild steel has been investigated in 1 M HCl solution. Weight loss method, potentiodynamic polarization, and electrochemical impedance spectroscopy techniques were applied to study the mild steel corrosion behavior in the absence and presence of different concentrations of betanin under the influence of various experimental conditions. The results obtained showed that betanin is a good “green” inhibitor for mild steel in 1 M HCl solution. Scanning electron microscopy observations of the steel surface confirmed the protective role of the inhibitor. The polarization curves showed that betanin behaves mainly as a mixed-type inhibitor. Maximum inhibition efficiency (98%) is obtained at betanin concentrations of 0.01 M. The results obtained from weight loss, polarization, and impedance measurements are in good agreement.     

Functoriality and uniformity in Hrushovski's groupoid-cover correspondence

The correspondence between definable connected groupoids in a theory T and internal generalised imaginary sorts of T, established by Hrushovski in [“Groupoids, imaginaries and internal covers,” Turkish Journal of Mathematics, 2012], is here extended in two ways: First, it is shown that the correspondence is in fact an equivalence of categories, with respect to appropriate notions of morphism. Secondly, the equivalence of categories is shown to vary uniformly in definable families, with respect to an appropriate relativisation of these categories. Some elaborations on Hrushovki's original constructions are also included.     

Exact Solution of Klein-Gordon Equation for Charged Particle in Magnetic Field with Shape Invariant Method

Based on the shape invariance property we obtain exact solutions of the three-dimensional relativistic Klein Gordon equation for a charged particle moving in the presence of a certain varying magnetic field, and we also show its non-relativistic limit.     

The effect of relative phase on the stability of temporal dark soliton in $${{\mathcal {}}}$$-symmetric nonlinear directional fiber coupler

In this paper, we numerically investigate the effect of relative phase on the stability of dark solitons in \({\mathcal {PT}}\)-Symmetric nonlinear directional coupler (NLDC), by considering gain in the bar and loss in the cross in the range of \(\theta =0^\circ\) to \(180^\circ\). The \({\mathcal {PT}}\)-Symmetric perturbed eigenfunctions are used to study the soliton stability. The results of simulations are shown that in the first half region of the relative phase the soliton is unstable while in the second one, is stable. In the stable region gain and loss cancel each other and also the perturbed eigenfunctions have no effect on solitons while in the unstable region solitons are amplified in the bar and attenuated in the cross except for some small intervals which the roles are changed. The behavior of such perturbation can be interpreted as self all-optical phase soliton switching and optical logic gates.     

A nonstandard Riemann existence theorem

We study elementary extensions of compact complex spaces and deduce that every complete type of dimension is internal to projective space. This amounts to a nonstandard version of the Riemann Existence Theorem, and answers a question posed by Anand Pillay.

     

Synergic effect of Pt-Co nanoparticles and a dopamine derivative in a nanostructured electrochemical sensor for simultaneous determination of <Emphasis Type="Italic">N</Emphasis>-acetylcysteine,paracetamol and folic acid

A carbon paste electrode (CPE) was modified with Pt-Co nanoparticles and 2-(3,4-dihydroxyphenethyl)isoindoline-1,3-dione (3,4-DHPID) and then used for determination of N-acetylcysteine (N-AC) in the presence of paracetamol (PC) and folic acid (FA). The Pt-Co nanoparticles were synthesized by the polyol method and characterized by X-ray diffraction, energy dispersive X-ray analysis and transmission electron microscopy. The modified CPE displays good electrocatalytic activity towards the electrooxidation of N-AC in solution of pH 7.0. It was applied to the determination of N-AC in the presence of PC and FA (with well separated signals peaking at 0.2, 0.55 and 0.86 V vs. Ag/AgCl) by using square wave voltammetry. The peak currents are linearly dependent on the concentrations of N-AC, PC and FA in the respective ranges from 0.07 to 500, 1.0 to 850, and 2.0 to 550 μmol·L^?1, with detection limits of 0.009, 0.6 and 0.8 μmol·L^?1. The modified CPE was applied to the determination of N-AC, PC and FA in (spiked) pharmaceutical and biological samples.

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Graphical abstract Pt-Co nanoparticles and 2-(3,4-dihydroxyphenethyl)isoindoline-1,3-dione were used for modification of a carbon paste electrode which then was used for sensitive determination of N-actylcysteine in the presence of paracetamol and folic acid.

     

Two‐Dimensional Crowding Uncovers a Hidden Conformation of α‐Synuclein

The intrinsically disordered protein (IDP), α‐synuclein (αS), is well‐known for phospholipid membrane binding‐coupled folding into tunable helical conformers. Here, using single‐molecule experiments in conjunction with ensemble assays and a theoretical model, we present a unique case demonstrating that the interaction–folding landscape of αS can be tuned by two‐dimensional (2D) crowding through simultaneous binding of a second protein on the bilayer surface. Unexpectedly, the experimental data show a clear deviation from a simple competitive inhibition model, but are consistent with a bimodal inhibition mechanism wherein membrane binding of a second protein (a membrane interacting chaperone, Hsp27, in this case) differentially inhibits two distinct modules of αS–membrane interaction. As a consequence, αS molecules are forced to access a hidden conformational state on the phospholipid bilayer in which only the higher‐affinity module remains membrane‐bound. Our results demonstrate that macromolecular crowding in two dimensions can play a significant role in shaping the conformational landscape of membrane‐binding IDPs with multiple binding modes.