Modified iteration method for solving fractional gas dynamics equation

This paper is devoted to the time‐fractional gas dynamics equation with Caputo derivative. Fractional operators are very natural tools to model memory‐dependent phenomena. Modified iteration method is proposed to obtain the approximate and analytical solution of the fractional gas dynamics equation. This method is a combined form of the new iteration method and Laplace transform. Modified iteration method really is powerful and simple method compared with other methods. Existence and uniqueness of solution are proven. Numerical results for different cases of the equation are obtained. Copyright © 2016 John Wiley & Sons, Ltd.     

Existence results to a nonlinear p(k)-Laplacian difference equation

In the present paper, by using variational method, the existence of non-trivial solutions to an anisotropic discrete non-linear problem involving p(k)-Laplacian operator with Dirichlet boundary condition is investigated. The main technical tools applied here are the two local minimum theorems for differentiable functionals given by Bonanno.     

Efficient Synthesis of Novel Coumarin‐3‐carboxamides (=2‐Oxo‐2H‐1‐benzopyran‐3‐carboxamides) Containing Lipophilic Spacers

The novel coumarin‐3‐carboxamides (=2‐oxo‐2H‐1‐benzopyran‐3‐carboxamides) 5a – 5g containing lipophilic spacers were synthesized through the Ugi‐four‐component reaction (Scheme 1). The reactions of aromatic aldehydes 1 , 4,4′‐oxybis[benzenamine] or 4,4′‐methylenebis[benzenamine] as diamine 2 , coumarin‐3‐carboxylic acid (=2‐oxo‐2H‐benzopyran‐3‐carboxylic acid; 3 ), and alkyl isocyanides 4 lead to the desired substituted coumarin‐3‐carboxamides 5a – 5g at room temperature with high bond‐forming efficiency. These novel coumarin derivatives exhibit brilliant fluorescence at 544 nm in CHCl₃.     

Vortex‐assisted natural deep eutectic solvent microextraction using response surface methodology optimization for determination of orthophosphate in water samples by molybdenum blue method

A new, rapid, and efficient microextraction technique named vortex‐assisted natural deep eutectic solvent microextraction has been developed for the preconcentration and determination of orthophosphate in real water samples. The method is based on the formation of the phosphomolybdenium blue complex followed by proposed microextraction procedure and subsequent spectrophotometric determination in a microcell. Screening study for the optimal composition of natural deep eutectic solvent was initially performed with different solvents, including choline chloride as hydrogen bond acceptor and different hydrogen bond donors. A ternary mixture of glucose‐choline chloride‐water was used as the most efficient extraction solvent. Response surface methodology based on the central composite design was used to optimize experimental parameters. Under optimal conditions, the calibration graph for orthophosphate determination was linear over the range of 2.0–80.0 µg/L (correlation coefficient of 0.9971) with a detection limit of 0.2 µg/L. The repeatability, reproducibility, and relative error values of the method were below 7%, indicating acceptable precision and accuracy. This approach, using natural deep eutectic solvent as an eco‐friendly solvent with high solubilization power and vortex mixing as an alternative energy source, represents a promising choice for a green separation and preconcentration methodology for determination of orthophosphate in real water samples.     

The converse of Schur’s theorem

Schur’s theorem states that for a group G finiteness of G/Z(G) implies the finiteness of G′. In this paper, we show the converse is true provided that G/Z(G) is finitely generated and in such case, we have |G/Z(G)| ≤ |G′| ^d(G/Z(G)). In the special case of G being nilpotent, we prove |G/Z(G)| divides |G′| ^d(G/Z(G)).     

Selective and Sensitive Determination of Uranyl Ions in Complex Matrices by Ion Imprinted Polymers‐Based Electrochemical Sensor

We report on the design of a UO₂²⁺‐selective electrode based on the use of UO₂²⁺ imprinted polymer nanoparticles (IP‐NPs), and its application for the differential pulse adsorptive cathodic stripping voltammetry determination of uranyl ions. A carbon paste electrode was modified with the IP‐NPs, and differential pulse adsorptive cathodic stripping voltammetry was applied as the detection technique after open‐circuit sorption of UO₂²⁺ ions. The modified electrode responses to UO₂²⁺ was linear in the 0.1 µg L^?1 to 10 µg L^?1 and in the 0.01 mg L^?1 to 10 mg L^?1. The method detection limit of the sensor was 0.03 µg L^?1.     

Highly Efficient Aminolysis of Epoxides Catalyzed by Reusable Zirconyl Triflate,ZrO(OTf)2

Efficient ring opening of epoxides with aromatic amines catalyzed by ZrO(OTf)₂ is reported, and the corresponding β amino (beta-amino acid) alcohols were obtained in high yields in CH₃CN as solvent. The reactions were carried out at room temperature and in the presence of only 1.25 mol% of ZrO(OTf)₂. This catalyst can be reused several times without loss of its activity.     

Magnetite Nanoparticles Immobilized Pectinase: Preparation,Characterization and Application for the Fruit Juices Clarification

In this work, pectinase was immobilized on the surface of silica‐coated magnetite nanoparticles via covalent attachment. The magnetite‐immobilized enzyme was characterized by Fourier transform infrared spectroscopy, X‐ray powder diffraction, scanning electron microscopy and vibrating sample magnetometery techniques. Response Surface Methodology using Minitab Software was applied for statistical designing of operating conditions in order to immobilize pectinase on magnetic nanoparticles. The optimal conditions were obtained at 30 °C and pH 5.5 with 42.97 μl pectinase for 2 h. The immobilization yield was 50.6% at optimized conditions. Compared to the free pectinase, the immobilized pectinase was found to exhibit enhanced enzyme activity, better tolerance to the variation of pH and temperature, and improved storage stability. Both free and immobilized samples reduced the viscosity of apple juice from 1.12 to 0.88 and 0.92 mm²s^?1, respectively, after 30 min at their optimum temperature. Furthermore, the immobilized enzyme could be reused six consecutive cycles and the efficiency loss in viscosity reduction was found to be only 8.16%.     

Gaussian free field in the background of correlated random clusters,formed by metallic nanoparticles

The effect of metallic nano-particles (MNPs) on the electrostatic potential of a disordered 2D dielectric media is considered. The disorder in the media is assumed to be white-noise Coulomb impurities with normal distribution. To realize the correlations between the MNPs we have used the Ising model with an artificial temperature T that controls the number of MNPs as well as their correlations. In the T → 0 limit, one retrieves the Gaussian free field (GFF), and in the finite temperature the problem is equivalent to a GFF in iso-potential islands. The problem is argued to be equivalent to a scale-invariant random surface with some critical exponents which vary with T and correspondingly are correlation-dependent. Two type of observables have been considered: local and global quantities. We have observed that the MNPs soften the random potential and reduce its statistical fluctuations. This softening is observed in the local as well as the geometrical quantities. The correlation function of the electrostatic and its total variance are observed to be logarithmic just like the GFF, i.e. the roughness exponent remains zero for all temperatures, whereas the proportionality constants scale with T ? T _c . The fractal dimension of iso-potential lines (D _f ), the exponent of the distribution function of the gyration radius (τ _r ), and the loop lengths (τ _l ), and also the exponent of the loop Green function x _l change in terms of T ? T _c in a power-law fashion, with some critical exponents reported in the text. Importantly we have observed that D _f (T) ? D _f (T _c ) ~ 1/√ξ(T), in which ξ(T) is the spin correlation length in the Ising model.