Operational Matrix of Fractional Integration Based on the Shifted Second Kind Chebyshev Polynomials for Solving Fractional Differential Equations

This paper is devoted to studying a computational method for solving multi-term differential equations based on new operational matrix of shifted second kind Chebyshev polynomials. The properties of the operational matrix of fractional integration are exploited to reduce the main problem to an algebraic equation. We present an upper bound for the error in our estimation that leads to achieve the convergence rate of O(M ^−κ). Numerical experiments are reported to demonstrate the applicability and efficiency of the proposed method.

     

Sonochemical syntheses of xanthene derivatives using zeolite-supported transition metal catalysts in aqueous media

An efficient green method for the syntheses of biologically active xanthene derivatives by use of zeolite-supported transition metal catalysts is described. A Fe-Cu/ZSM-5 heterogeneous catalyst has the highest activity in the one-pot syntheses with a wide range of aldehydes and cyclic 1,3-diketones, under ultrasonic irradiation in water at ambient temperatures. The three-component condensation in the presence of supported metal catalysts is operationally simple, requires no expensive or toxic reagents, and gives high yields in short reaction times.     

Synthesis and crystal structure of the dinuclear copper(II) Schiff base complex μ‐hydroxido‐μ‐chlorido‐bis{[bis(trans‐2‐nitrocinnamaldehyde)ethylenediamine]chloridocopper(II)} dichloromethane sesquisolvate

Transition metal complexes of Schiff base ligands have been shown to have particular application in catalysis and magnetism. The chemistry of copper complexes is of interest owing to their importance in biological and industrial processes. The reaction of copper(I) chloride with the bidentate Schiff base N,N′‐bis(trans‐2‐nitrocinnamaldehyde)ethylenediamine {Nca₂en, systematic name: (1E,1′E,2E,2′E)‐N,N′‐(ethane‐1,2‐diyl)bis[3‐(2‐nitrophenyl)prop‐2‐en‐1‐imine]} in a 1:1 molar ratio in dichloromethane without exclusion of air or moisture resulted in the formation of the title complex μ‐chlorido‐μ‐hydroxido‐bis(chlorido{(1E,1′E,2E,2′E)‐N,N′‐(ethane‐1,2‐diyl)bis[3‐(2‐nitrophenyl)prop‐2‐en‐1‐imine]‐κ²N,N′}copper(II)) dichloromethane sesquisolvate, [Cu₂Cl₃(OH)(C₂₀H₁₈N₄O₄)₂]·1.5CH₂Cl₂. The dinuclear complex has a folded four‐membered ring in an unsymmetrical Cu₂OCl₃ core in which the approximate trigonal bipyramidal coordination displays different angular distortions in the equatorial planes of the two Cu^II atoms; the chloride bridge is asymmetric, but the hydroxide bridge is symmetric. The chelate rings of the two Nca₂en ligands have different conformations, leading to a more marked bowing of one of the ligands compared with the other. This is the first reported dinuclear complex, and the first five‐coordinate complex, of the Nca₂en Schiff base ligand. Molecules of the dimer are associated in pairs by ring‐stacking interactions supported by C—H…Cl interactions with solvent molecules; a further ring‐stacking interaction exists between the two Schiff base ligands of each molecule.     

An efficient synthesis of substituted 2-iminothiazolidin-4-one and thiadiazoloquinazolinone derivatives

A convenient synthesis of functionalized 2-iminothiazolidin-4-ones and thiadiazoloquinazolinones has been achieved by the reaction of dialkyl acetylenedicarboxylates (DAAD) with 1-pheny-3-pyridin-2-yl-thiourea (1) and 3-amino-2-mercapto-3H-quinazolin-4-one (8), respectively. The starting materials for these processes were prepared from phenyl isothiocyanate, 2-aminopyridine for (1) and anthranilic acid, carbon disulfide, hydrazine for (8). Treatment of these compounds with DAAD resulted in the formation of an intermediate that readily underwent intramolecular cyclization to afford functionalized five membered heterocyclic rings was formed.     

Reductive amination of aldehydes and ketones to their corresponding amines with N-methylpyrrolidine zinc borohydride

A simple and convenient procedure for reductive amination of aldehydes and ketones using N-methylpyrrolidine zinc borohydride (ZBHNMP) as a reducing agent is described. The reactions are carried out with 1 equiv of amine and 1 equiv of aldehyde or ketone using 1 equiv of ZBHNMP in methanol under neutral conditions at room temperature.     

Comparison of theoretical and experimental results for band-gap-graded CZTSSe solar cell

The simulation of CZTSSe solar cells is presented in this paper. The simulation results are in reasonable agreement with the experimental data, indicating the reliability of simulation results. New structure is proposed to increase the functionality of the cell. Improved functional performances are achieved by inserting a P-Silicon (P-Si) layer as back surface field. Simulation results suggest that by inserting this P-Si layer, efficiency of the CZTSSe solar cell increases from 12.6% to 16.59%, which is a significant improvement. For the champion cell J_SC = 36.27 mA/cm², V_OC = 0.625 V and FF = 73.11% has been achieved.     

Thermal width of quarkonium from holography

Nuclear effects in deep inelastic scattering at low $x$ are phenomenologically described changing the typical dynamical and/or kinematical scales characterizing the free nucleon case. In a holographic approach, this rescaling is an analytical property of the computed structure function $F_2(x,Q^2)$ . This function is given by the sum of a conformal term and of a contribution due to quark confinement, depending on IR hard-wall parameter $z_0$ and on the mean square distances, related to a parameter $Q^\prime $ , among quarks and gluons in the target. The holographic structure function per nucleon in a nucleus $A$ is evaluated showing that a rescaling of the typical nucleon size, $z_0$ and $Q^\prime $ , due to nuclear binding, can be reabsorbed in a $Q^2$ -rescaling scheme. The difference between neutron and proton structure functions and the effects of the longitudinal structure functions can also be taken into account. The obtained theoretical results favorably compare with the experimental data.     

Radial basis functions method for solving of a non-local boundary value problem with Neumann’s boundary conditions

In this paper, the problem of solving the two-dimensional diffusion equation subject to a non-local condition involving a double integral in a rectangular region is considered. The solution of this type of problems are complicated. Therefore, a simple meshless method using the radial basis functions is constructed for the non-local boundary value problem with Neumann’s boundary conditions. Numerical examples are included to demonstrate the reliability and efficiency of this method. Also N_e and root mean square errors are obtained to show the convergence of the method.