Tetrazolo[1,5‐a]quinoline‐4‐carbaldehyde and its Schiff base on mild steel as corrosion inhibitor in 1 M HCl solution: electrochemistry,theoretical and SEM surface analysis

The corrosion inhibition impact of two quinoline derivatives, viz tetrazolo [1,5‐a] quinoline‐4‐carbaldehyde ( TQC ) and (Z) ?5‐methyl‐N‐(tetrazolo [1,5‐a] quinolin‐4‐ylmethylene) thiazol‐2‐amine ( MTQT ), has been examined against mild steel in 1 M HCl solution using conventional weight loss, potentiodynamic polarization, linear polarization, electrochemical impedance spectroscopy, quantum chemical, and scanning electron microscopic studies. The experimental results have showed that TQC and MTQT revealed a good corrosion inhibition and that the inhibition efficiency increases with the increase of concentration of inhibitor to attain 94.54% for TQC and 99.25% for MTQT at 25 ppm. Polarization measurements suggest that TQC and MTQT act as a mixed‐type inhibitor. A synergism between inhibitors can be observed by polarization measurements. Electrochemical impedance spectroscopy measurements show an increase of the transfer resistance with the inhibitor concentration. Adsorption of TQC and MTQT on the mild steel surfaces in 1 N HCl solution follows the Langmuir adsorption isotherm model. Furthermore, quantum chemical calculations have been conducted using B3LYP functional and 6‐31G(d,p) basis set to complement the experimental evidences. Copyright © 2015 John Wiley & Sons, Ltd.     

Exact solutions to magnetogasdynamic equations in Lagrangian coordinates

The Lie group of point transformations, which leave the equations for a simplified model of one dimensional ideal gas in magnetogasdynamics invariant, are used to obtain some exact solutions for the governing system of hyperbolic partial differential equations (PDEs). Similarity variables which reduces the governing system of PDEs into system of ordinary differential equations (ODEs) are determined through the transformations. The resulting ODEs are solved analytically to obtain some exact solutions that exhibits space-time dependence. Further, we study the propagation of weak discontinuity through a state characterized by one of the solutions.     

Proton‐Conducting Magnetic Coordination Polymers

Three isostructural lanthanide‐based two‐ dimensional coordination polymers (CPs) {[Ln₂(L)₃(H₂O)₂]_n ? 2n CH₃OH) ? 2n H₂O} (Ln=Gd³⁺ ( 1 ), Tb³⁺ ( 2 ), Dy³⁺ ( 3 ); H₂L=cyclobutane‐1,1‐dicarboxylic acid) were synthesized by using a low molecular weight dicarboxylate ligand and characterized. Single‐crystal structure analysis showed that in complexes 1 – 3 lanthanide centers are connected by μ₃‐bridging cyclobutanedicarboxylate ligands along the c axis to form a rod‐shaped infinite 1D coordination chain, which is further linked with nearby chains by μ₄‐connected cyclobutanedicarboxylate ligands to form 2D CPs in the bc plane. Viewing the packing of the complexes down the b axis reveals that the lattice methanol molecules are located in the interlayer space between the adjacent 2D layers and form H‐bonds with lattice and coordinated water molecules to form 1D chains. Magnetic properties of complexes 1 – 3 were thoroughly investigated. Complex 1 exhibits dominant ferromagnetic interaction between two nearby gadolinium centers and also acts as a cryogenic magnetic refrigerant having a significant magnetic entropy change of ?ΔS_m=32.8 J kg^?1 K^?1 for ΔH=7 T at 4 K (calculated from isothermal magnetization data). Complex 3 shows slow relaxation of magnetization below 10 K. Impedance analysis revealed that the complexes show humidity‐dependent proton conductivity (σ=1.5×10^?5 S cm^?1 for 1 , σ=2.07×10^?4 S cm^?1 for 2 , and σ=1.1×10^?3 S cm^?1 for 3 ) at elevated temperature (>75 °C). They retain the conductivity for up to 10 h at high temperature and high humidity. Furthermore, the proton conductivity results were correlated with the number of water molecules from the water‐vapor adsorption measurements. Water‐vapor adsorption studies showed hysteretic and two‐step water vapor adsorption (182000 μL g^?1 for 1 , 184000 μL g^?1 for 2 , and 1874000 μL g^?1 for 3 ) in the experimental pressure range. Simulation of water‐vapor adsorption by the Monte Carlo method (for 1 ) confirmed the high density of adsorbed water molecules, preferentially in the interlayer space between the 2D layers.     

On the Lipschitz continuity of certain quasiregular mappings between smooth Jordan domains

We first investigate the Lipschitz continuity of (K,K’)-quasiregular C ² mappings between two Jordan domains with smooth boundaries, satisfying certain partial differential inequalities concerning Laplacian. Then two applications of the obtained result are given: As a direct consequence, we get the Lipschitz continuity of ρ-harmonic (K,K’)-quasiregular mappings, and as the other application, we study the Lipschitz continuity of (K,K’)- quasiconformal self-mappings of the unit disk, which are the solutions of the Poisson equation Δw = g. These results generalize and extend several recently obtained results by Kalaj, Mateljevi? and Pavlovi?.     

A new method for exact solutions of variant types of time‐fractional Korteweg‐de Vries equations in shallow water waves

The current article devoted on the new method for finding the exact solutions of some time‐fractional Korteweg–de Vries (KdV) type equations appearing in shallow water waves. We employ the new method here for time‐fractional equations viz. time‐fractional KdV‐Burgers and KdV‐mKdV equations for finding the exact solutions. We use here the fractional complex transform accompanied by properties of local fractional calculus for reduction of fractional partial differential equations to ordinary differential equations. The obtained results are demonstrated by graphs for the new solutions. Copyright © 2016 John Wiley & Sons, Ltd.     

N-heterocyclic carbene-catalyzed 1,3-dipolar cycloaddition reactions: a facile synthesis of 3,5-di- and 3,4,5-trisubstituted isoxazoles

A first example of organo-N-heterocyclic carbene (NHC) catalyzed click-type fast 1,3-dipolar cycloaddition of nitrile oxides with alkynes was developed for the regioselective synthesis of 3,5-di- and 3,4,5-trisubstituted isoxazoles. Triethylamine (Et(3)N) was employed as an effective base to generate both nitrile oxide and the organo-NHC catalyst in situ. This catalytic approach was used to attach a variety of substituents, including other biologically active fragments, onto the isoxazole ring to selectively design multinucleus structures. Further, we have also optimized the conditions for Cu(I)-free Sonogashira cross-coupling to obtain internal alkynes in high yields, which were subsequently used in cycloaddition. A catalytic cycle is proposed and the remarkable regiocontrol in the formation of isoxazoles was ascribed to a beneficial zwitterion intermediate developed by the interaction of the strongly nucleophilic organo-NHC catalyst with alkyne followed by nitrile oxide.     

Linear or cross-shaped di(cyclopentadienyltitanium) compounds with aryl or heteroaryl spacers

The preparation of hexamethylated and hexabenzylated arylene or heteroarylene bridged dinuclear di(cyclopentadienyltitanium) compounds from the reaction of the corresponding hexachlorides with methyllithium or benzylmagnesium chloride is described. The spacers between the cyclopentadienyl rings consist of one, two or three phenylene groups, a dioctyloxyphenylene group or a 2,2'-bithienylene group. The corresponding hexachlorides and hexaisopropoxides have also been prepared.     

SOME EXACT SOLUTIONS OF 3-DIMENSIONAL ZERO-PRESSURE GAS DYNAMICS SYSTEM

The 3-dimensional zero-pressure gas dynamics system appears in the modeling for the large scale structure formation in the universe. The aim of this paper is to construct spherically symmetric solutions to the system. The radial component of the velocity and density satisfy a simpler one dimensional problem. First we construct explicit solutions of this one dimensional case with initial and boundary conditions. Then we get special radial solutions with different behaviours at the origin.