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.     

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.     

Constrained and unconstrained rearrangement minimization problems related to the <Emphasis Type="Italic">p</Emphasis>-Laplace operator

In this paper we consider an unconstrained and a constrained minimization problem related to the boundary value problem

$$ - {\Delta _p}u = f{\text{ in }}D,{\text{ }}u = 0{\text{ on }}\partial D$$

. In the unconstrained problem we minimize an energy functional relative to a rearrangement class, and prove existence of a unique solution. We also consider the case when D is a planar disk and show that the minimizer is radial and increasing. In the constrained problem we minimize the energy functional relative to the intersection of a rearrangement class with an affine subspace of codimension one in an appropriate function space. We briefly discuss our motivation for studying the constrained minimization problem.

     

Synthesis, characterization and electrochemical properties of two new calix[4]arene derivatives bearing two ferrocene imine or ferrocene amine units at the upper rim

A novel calix[4]arene derivative with two ferrocenyl Schiff-base groups at the upper rim 3 has been synthesized from 5,17-diformyl-25,27-dipropoxy-26,28-dihydroxy calix[4]arene and 4-ferrocenylaniline via condensation reaction. Reduction of 3 with sodium borohydride led to calix[4]arene derivative 4 with two amino ferrocenyl groups at the upper rim. The ferrocenyl Schiff-base calix[4]arene and its corresponding reduced amine have been purified and characterized by elemental analysis,¹H NMR, FTIR, Mass and UV-vis spectral data. Electrochemical properties of compounds 3 and 4 have been investigated. Cyclic voltammograms of 3 and 4 show reversible redox couples of ferrocene/ferrocinium at E_1/2=0.401 V and 0.346 V, respectively. Electrochemical studies show these redox active compounds electrochemically recognize trivalent lanthanides La³⁺ and Ce³⁺ and divalent Pb²⁺ and Cu²⁺cations. With ferrocenyl Schiff-base calix[4]arene 3 an anodic shift as large as 130 mV is observed on addition of one equivalent of Ce³⁺ ion. Also extraction properties of compound 4 towards some metal cations have been described. It has been observed that compound 4 has a good selectivity for metal cations Fe³⁺, Cu²⁺, Pb²⁺ and Cd²⁺ against Ni²⁺ and Co²⁺.     

Thulium(III) Ions Monitoring by a Novel Thulium(III) Microelectrode Based on a S‐N Schiff Base

This study presents for the first time development of a highly selective and sensitive thulium(III) micro‐sensor. Theoretical calculations were conducted on a S‐N Schiff base [thiophene‐2‐carbaldehyde‐(7‐methyl‐1,3‐benzothiazol‐2‐yl) hydrazone] (TCMH) in order to obtain a clue about the tendency of TCMH to Tm(III) and some other metal ions. Then, TCMH was used as a membrane‐active component to prepare a Tm(III)‐selective polymeric membrane microelectrode. In line with the resulting data, the electrode exhibits a Nernstian response toward Tm(III) ions for a very wide concentration range (1.0×10^?11–4.0×10^?6 M) with a detection limit of 1.0×10^?11 (ca. 1.5 ppt) and a very fast response time in the whole concentration range (<5 s). In addition, the results showed that the certain microelectrode could be applied in the pH range of 4.0–11.0 with a usage of more than one month without any considerable potential divergence.     

Complementary formulation for plate vibration problems

Zusammenfassung Das Problem der schwingenden Platte wird mit Hilfe des Hamiltonischen Prinzips und des komplementären Prinzips formuliert. Es wird gezeigt, dass das komplementäre Prinzip auf drei Bewegungsgleichungen an Stelle einer einzigen führt. Die Randbedingungen werden bei der rechteckigen Platte für beide Formulierungen des Problems angegeben. Für die Eigenfrequenzen der freien Rechteckplatte ergibt sich mit dem komplementären Prinzip eine deutliche Verbesserung gegenüber dem Hamiltonischen Prinzip bei Behandlung mit dem Ritzschen Verfahren.