Homotopy analysis method for MHD viscoelastic fluid flow and heat transfer in a channel with a stretching wall

In this paper, we analyze the flow and heat transfer characteristics of a magnetohydrodynamic (MHD) viscoelastic fluid in a parallel plate channel with a stretching wall. Homotopy analysis method (HAM) is used to obtain analytical solutions of the governing nonlinear differential equations. The analytical solutions are obtained in the form of infinite series and the convergence of the series solution is discussed explicitly. The obtained results are presented through graphs for several sets of values of the parameters, and the salient features of the solutions are analyzed. A comparison of our HAM results (for a special case of the study) with the available results in the literature (obtained by other methods) shows that our results are accurate for a wide range of parameters. Further, we point that our analysis finds application to the study of the haemodynamic flow of blood in the cardiovascular system subject to external magnetic field.     

A Variational Problem for Steady Vortices in a Shear Flow Past an Obstacle

We prove existence of maximizers for a variational problem for a steady vortex anomaly of bounded extent in a shear flow, past an obstacle, in a planar exterior domain. Kinetic energy is maximized subject to the vorticity being a rearrangement of a prescribed function.     

Copper-doped silica cuprous sulfate: A highly efficient heterogeneous nano-catalyst for one-pot three-component synthesis of 1-H-2-substituted benzimidazoles from 2-bromoanilines,aldehydes, and [bmim]N3

A facile and highly efficient one-pot three-component synthesis of 1-H-2-substituted benzimidazole derivatives from readily available substrates catalyzed by copper-doped silica cuprous sulfate (CDSCS) is described. In this method, treatment of diverse 2-bromoanilines, aldehydes, and [bmim]N₃ in DMF at 110 °C in the presence of CDSCS as a highly efficient heterogeneous nano-catalyst affords the corresponding 1-H-2-substituted benzimidazoles in good to excellent yields. The CDSCS is an inexpensive and stable nano-catalyst that could be simply prepared, recovered and reused for many consecutive reaction runs without significant loss of its activity.     

Synthesis,crystal structural study and catalyst active of benzyloxycarbonylmethyl triphenylphosphonium hexabromopalladate (II) in amination of aryl halides and Suzuki cross-coupling reaction

In this study, palladium (II) chloride reacted with the phosphonium salt [PhCH₂COOCH₂P(Ph)₃]Br to give [PhCH₂COOCH₂P(Ph)₃]₂[Pd₂Br₆] (1). The characterization of synthesized compound was performed by elemental analysis, FT-IR, ¹H, ³¹P, ¹³C NMR and also X-ray crystallography. It was found that this compound works as an efficient catalyst for the amination of aryl halides to afford primary amines, the results of which were satisfactory. Furthermore, it was found that the catalyst showed a high activity for Suzuki carbon–carbon cross-coupling of aryl halides and phenylboronic acid. Interestingly, the catalyst can be recovered from the reaction mixture and recycled four consecutive runs without any significant loss in activity.     

Synthesis of fused hydroxy dihydropyrroles and unexpected dihydropyrazine and dihydroquinoxaline derivatives based on heterocyclic ketene aminals

The one-pot four-component synthesis of highly functionalized fused hydroxyl dihydropyrroles and dihydropyrazines from readily available diamines, 1,1-bis (methylsulfanyl)-2-nitroethene, phenylglyoxal monohydrates, and C-H acids have been developed. This strategy provides an efficient, catalyst-free approach for easy access to various new hydroxyl-dihydropyrrole and dihydropyrazine rings in good to high yields. The products were confirmed by ¹H and ¹³C NMR, IR, mass, and X-ray crystal structure analyses.     

Extremal principle based on the linear subdifferential

An extremal principle in the vein of Mordukhovich is proved based on the linear generalized gradient.     

A rapid and convenient synthesis of gem-bis(dithiocarbamate) derivatives from primary aliphatic amines,carbon disulfide,and aromatic aldehydes using boron trifluoride-diethyl etherate

An efficient route for the synthesis of gem-bis(dithiocarbamate) derivatives is developed using dithiocarbamic acid salts generated from primary aliphatic amines and CS₂. The method offers high yields, employs mild reaction conditions, and demonstrates excellent functional group compatibility. The structures of the products were confirmed spectroscopically and by X-ray analysis.     

Calmness of Set-Valued Mappings Between Asplund Spaces and Application to Equilibrium Problems

The paper deals with the calmness of two classes of nonconvex set-valued mappings in Asplund spaces and its application to equilibrium problems. Its main part is devoted to establish new sufficient conditions for calmness, which are derived in terms of coderivatives and w* boundaries of normal cones to constraint sets. In order to achieve this goal, a new concept so-called “sequential normal smoothness” for the sets in Asplund spaces is introduced and compared with two well-known notions of convexity and semismoothness. Finally, the results are applied to prove necessary optimality conditions for nonparametric equilibrium problems under new weak constraint qualifications.