Solution of nonlinear weakly singular Volterra integral equations using the fractional‐order Legendre functions and pseudospectral method

In this article, our main goal is to render an idea to convert a nonlinear weakly singular Volterra integral equation to a non‐singular one by new fractional‐order Legendre functions. The fractional‐order Legendre functions are generated by change of variable on well‐known shifted Legendre polynomials. We consider a general form of singular Volterra integral equation of the second kind. Then the fractional Legendre–Gauss–Lobatto quadratures formula eliminates the singularity of the kernel of the integral equation. Finally, the Legendre pseudospectral method reduces the solution of this problem to the solution of a system of algebraic equations. This method also can be utilized on fractional differential equations as well. The comparison of results of the presented method and other numerical solutions shows the efficiency and accuracy of this method. Also, the obtained maximum error between the results and exact solutions shows that using the present method leads to accurate results and fast convergence for solving nonlinear weakly singular Volterra integral equations. Copyright © 2015 John Wiley & Sons, Ltd.     

A novel fixed point theorem for the k-Meir-Keeler function

Generalized Meir-Keeler functions are introduced that contain a class of weakly uniformly strict contraction maps. A theorem is proven that assures the existence of a fixed point for the closed k-Meir-Keeler functions and provides a con- structive method to find the points. An advantage of the method is that it is possible to show the existence of a fixed point for functions with domains that are neither complete nor closed.     

Effective Potential in Noncommutative BTZ Black Hole

In this paper, we investigated the noncommutative rotating BTZ black hole and showed that such a space-time is not maximally symmetric. We calculated effective potential for the massive and the massless test particle by geodesic equations, also we showed effect of non-commutativity on the minimum mass of BTZ black hole.     

Three‐dimensional Hemidirected Mixed‐ligand Lead(II) Coordination Polymer, [Pb2(bpa)2(SCN)3(NO3)]n (bpa = 1,2‐di(4‐pyridyl)ethane)

A new 3D hemidirected mixed‐ligand lead(II) coordination polymer with the ligand 1,2‐di(4‐pyridyl)ethane bpa) and the two metal coordinated anions nitrate and thiocyanate, [Pb₂(bpa)₂(SCN)₃(NO₃)]_n ( 1 ), has been synthesized and characterized by CHN elemental analysis, IR‐, ¹H‐ and ¹³C NMR spectroscopy. The single crystal X‐ray data of compound 1 show that the complex is a three‐dimensional coordination polymer with two different Pb atoms with stereoactive electron lone pairs and six‐ and five‐coordinate hemidirected geometries, respectively.     

Selective separation of methanol-water mixture using functionalized boron nitride nanosheet membrane: a computer simulation study

Structural Chemistry - The separation of alcohol-water mixture from each other is one of the significant subjects for scientists in the pharmacy and engineering fields owing to economic savings. In...     

Facile synthesis of PtSnZn nanosheet thin film at oil–water interface by use of organometallic complexes: An efficient catalyst for methanol oxidation and p‐nitrophenol reduction reactions

PtSnZn nanosheet thin film with stable and high activity towards methanol electro‐oxidation was synthesized via a simple reduction of organometallic precursors including [PtCl₂(cod)] (cod = cis,cis‐1,5‐cyclooctadiene) and [Sn(CH₃)₄] complexes, in the presence of [Zn(acac)₂] (acac = acetylacetonate) complex at toluene–water interface. Catalytic activities of PtSnZn nanosheets were investigated in the p‐nitrophenol (p‐Nip) reduction and methanol oxidation reactions. The obtained results demonstrate that PtSnZn nanosheets exhibit a good electrocatalytic performance for methanol oxidation reaction, the catalytic activity of the PtSnZn nanosheets being at least 3.5 times higher than that of Pt nanoparticle thin film. Also, the apparent rate constant obtained for p‐Nip reduction with the PtSnZn nanosheets is at least 2.3 times higher than that for Pt nanoparticle thin film due to the appropriate interaction between platinum, tin and zinc metals and geometric properties of PtSnZn nanosheet thin film. Nanosheets are highly favourable for superior catalytic performances due to their geometric properties. A facile and efficient route was used to synthesize trimetallic alloy thin film at oil–water interface.     

Zn/MCM-41-catalyzed unsymmetrical Hantzsch reaction and the evaluation of optical properties and anti-cancer activities of the polyhydroquinoline products

The three-component Hantzsch condensation of various aryl aldehydes, dimedone, and methyl 3-aminocrotonate was investigated in the presence of MCM-41-supported ZnNO3. The polyhydroquinoline products which were obtained under mild conditions and very easy workup were evaluated for anti-cancer activities against MCF-7, SK-BR-3, and HT-29 of breast and colon cancer cells. The fluorescence emission of some products was also studied and their optical parameters were reported.     

Carbon Nanofiber and Poly[2-(methacryloyloxy) ethyl] Trimethylammonium Chloride Composite as a New Benchmark Carbon-based Electrocatalyst for Sulfide Oxidation

There is an overwhelming desire to develop new sulfide oxidation electrocatalysts that perform at low potentials and exhibit high current density for the removal and efficient sensing of sulfide. This article describes a comparative electrochemical analysis of various commercially available carbon materials and polymer/surfactant composite electrocatalysts for direct electrooxidation of sulfide in an aqueous solution. The composites were prepared from five different carbon materials multiwalled carbon nanotubes, fullerene-C₆₀, graphene, glassy carbon, and carbon nanofibers (CNF) and four different polymers: chitosan, polyvinylidene fluoride, Nafion, and indigenously synthesized poly[2-(methacryloyloxy)ethyl] trimethylammonium chloride (PMTC). The carbon@polymer composites were prepared by a simple ultrasonication technique, and the electrodes were prepared by drop-drying the prepared composite on indium tin oxide (ITO) substrates. The CNF@PMTC showed the highest positive zeta potential that allowed an accumulation of many negatively charged sulfide ions at the CNF@PMTC surface. Cyclic voltammetry was used for the electrooxidation of sulfide in an aqueous solution of tris buffer (0.05 M; pH 8.0) and KNO₃ (0.1 M). The lowest sulfide oxidation peak potential (i. e., −51 mV vs. standard hydrogen electrode) with a high catalytic current response (730 μA/cm²) of the CNF@PMTC-modified ITO electrode among the tested and previously reported carbon-based electrode materials make it ideal for direct sulfide electrooxidation. Taking this and its simple preparation method into account, CNF@PMTC can be considered a benchmark carbon-based electrocatalyst for sulfide oxidation.