Existence of Continuous Eigenvalues for a Class of Parametric Problems Involving the $(p,2)$-Laplacian Operator

We discuss a parametric eigenvalue problem, where the differential operator is of \((p,2)\)-Laplacian type. We show that, when \(p\neq 2\), the spectrum of the operator is a half line, with the end point formulated in terms of the parameter and the principal eigenvalue of the Laplacian with zero Dirichlet boundary conditions. Two cases are considered corresponding to \(p>2\) and \(p<2\), and the methods that are applied are variational. In the former case, the direct method is applied, whereas in the latter case, the fibering method of Pohozaev is used. We will also discuss a priori bounds and regularity of the eigenfunctions. In particular, we will show that, when the eigenvalue tends towards the end point of the half line, the supremum norm of the corresponding eigenfunction tends to zero in the case of \(p>2\), and to infinity in the case of \(p < 2\).

     

Copper-doped silica cuprous sulfate (CDSCS) as a highly efficient heterogeneous nano catalyst for synthesis of 3,5-disubstituted isoxazoles

A facile and highly efficient protocol for 1,3-dipolar cycloaddition of in situ generated nitrile oxides with terminal alkynes catalyzed by copper-doped silica cuprous sulfate (CDSCS) as a new and convenient heterogeneous nano catalyst is described. In this protocol, ‘click’ cycloaddition of various structurally diverse alkynes and imidoyl chlorides in the presence of CDSCS and NaHCO₃ in a solution of i-PrOH/H₂O (1:1, V/V) furnishes the corresponding 3,5-disubstituted isoxazoles in good to excellent yields at room temperature. CDSCS was approved as a chemically and thermally stable nano catalyst that can be recovered and reused for many consecutive trials without considerable decline in its reactivity.     

Synthesis,X-ray crystal structure and DFT studies of cobalt(II) and vanadium(V) complexes with N,N,O-tridentate aroyl-hydrazone based ligand

A new aroyl-hydrazone, 2-pyridine carboxaldehyde-derived hydrazone ligand and its cobalt(II) (1) and vanadium(V) (2) complexes were prepared. The structures of these compounds were investigated using elemental analysis, spectral (IR, UV), and X-ray diffraction measurements. The electrochemical properties of the complexes were studied by cyclic voltammetry. The hydrazone ligand acted as tridentate and coordinated to vanadium and cobalt via N-imine, N-pyridine, and O-benzohydrazide atoms. The Co(II) complex crystallizes in the monoclinic system, space group P2₁/c, and has a binuclear structure. Chloride ions behave as the linking bridge and a tridentate hydrazine ligand HL and water as the terminal capping ligands. The central Co(II) ion has distorted octahedral geometry. The vanadium(V) complex crystallizes in the monoclinic crystal system, space group P2₁/n, and can be described as having highly distorted trigonal-bipyramidal coordination. The geometries and electronic properties of the complexes were also obtained using DFT and TD-DFT calculations.     

CuI-catalyzed thioarylation of active methylene compounds with in situ generated benzenethiols: Preparation of α-thioaryl-β-dicarbonyls and 4-thioaryl-5-pyrazolones

In this paper, a one-step copper-catalyzed procedure for oxidative coupling of active methylene compounds including cyclic β-diketones, cyclic β-ketoesters and 5-pyrazolone with benzenethiols is described. Benzenethiols are in situ generated in the reaction mixture from aryl halides and thiourea as sulfur transfer reagent. α-Thioaryl compounds are obtained in excellent yields and in short reaction time via the process which is free from the foul smell of thiols.     

C-H activation in bithiazole ring with thallium(III) ion

Two novel organometallic complex of 2,2′-dimethyl-4,4′-bithiazole (dm4bt) ligand (L) with formula [Tl(dm4bt)₂(NO₃)(H₂O)] (1) and [Tl(dm4bt)₂(NO₃)(DMSO)] (2) have been synthesized and structurally characterized by elemental analysis, FT-IR, ¹H NMR spectra and X-ray crystallography. These complexes also display the first transoid conformation in bithiazole ligands in which C-H bond activation in bithiazole ring is observed with Tl(III) ion.     

Correlation between macrovoid formation and the ternary phase diagram for polyethersulfone membranes prepared from two nearly similar solvents

The morphological structure of membranes prepared from two nearly similar systems consisting of water/N,N-dimethylacetamide (DMAc)/polyethersulfone (PES) and water/N-methyl-2-pyrrolidone (NMP)/polyethersulfone (PES) has been studied. The morphology of the prepared membranes showed that both systems exhibit an instantaneous liquid–liquid demixing that leads to the formation of macrovoids in the resulting structures. Nevertheless, the resulting macrovoid structures were contrary to the generally accepted concepts concerning macrovoid formation. The membranes morphologies showed that in spite of better miscibility between water and DMAc, which must promote the formation of channel- and finger-like structures, more sponge-like structures were observed in membranes prepared from the water/DMAc/PES system compared to those prepared from the water/NMP/PES system. To find the source of this unexpected phenomenon, the complete ternary phase diagrams consisting of theoretical binodal curves, vitrification boundaries, and gelation boundaries were constructed for both systems and it was shown that gelation process occurs earlier in the water/DMAc/PES system compared to the other system, which inhibits the growth of macrovoids in this system.     

Fluidized-bed Fenton-like oxidation of a textile dye using natural magnetite

Degradation of Acid Orange 7 (AO7) as a model azo dye was investigated in a recirculating pilot fluidized-bed reactor by a Fenton-like process using natural magnetite (NM) and potassium persulfate (K₂S₂O₈). Scanning electron microscopy was performed to characterize the magnetite sample. The heterogeneous Fenton-like process (NM/\({\text{S}}_{2} {\text{O}}_{8}^{2 - }\)) is a modified method owing to its enhanced mass transfer. It can be operated reliably and simply by reducing the produced iron oxide sludge in the conventional Fenton process. Degradation efficiency (DE %) of AO7 by NM/ \({\text{S}}_{2} {\text{O}}_{8}^{2 - }\) process was affected by operational parameters. The DE % of 75 % was obtained for the AO7 treatment (15 mg/L) at the desired conditions, such as pH 5, 0.2 mM \({\text{S}}_{2} {\text{O}}_{8}^{2 - }\), and 0.5 g/L NM after 120 min of reaction time. The dye degradation rate in all the experiments followed the pseudo-second-order kinetic with high correlation coefficients (R ² ≥ 0.98). The low released iron concentration, successive reusability at milder pH and the recirculation mode with the proper mixing are the significant advantages of the NM/\({\text{S}}_{2} {\text{O}}_{8}^{2 - }\) process.     

Electrochemical and photo-assisted electrochemical treatment of the pesticide imidacloprid in aqueous solution by the Fenton process: effect of operational parameters

Research on Chemical Intermediates - The aim of this study was to compare the degradation efficiency (DE%) of imidacloprid as a model pesticide by electro-Fenton (EF) and photoelectro-Fenton...     

Poly(<Emphasis Type="Italic">n</Emphasis>-octyl methacrylate) viscosity index improver: Kinetic study via on-line <Superscript>1</Superscript>H-NMR technique

The free radical solution polymerization of n-octyl methacrylate has been studied in benzene-d ₆ in the presence of 2,2′-azobisisobutyronitrile as thermal initiator. An on-line nuclear magnetic resonance spectroscopy was applied to record the reaction data and to determine the monomer conversion at different times during the polymerization reaction. Effect of monomer and initiator concentration as well as reaction temperature on polymerization rate was studied. The order of the reaction with respect to initiator (0.45) was consistent with the classical kinetic rate equation, while the order of reaction with respect to monomer (1.87) was much greater than unity. An overall activation energy (E _a = 53.8 kJ/mol) was obtained over the temperature range 328?338 K. Also, the efficiency of the synthesized poly(n-octyl methacrylate) for improving the viscosity index of the lube oil was investigated.     

Irreversible electrowetting on thin fluoropolymer films

A study was conducted to investigate electrowetting reversibility associated with repeated voltage actuations for an aqueous droplet situated on a silicon dioxide insulator coated with an amorphous fluoropolymer film ranging in thickness from 20 to 80 nm. The experimental results indicate that irreversible trapped charge may occur at the aqueous-solid interface, giving rise to contact angle relaxation. The accumulation of trapped charge was found to be related to the applied electric field intensity and the breakdown strength of the fluoropolymer. On the basis of the data, an empirical model was developed to estimate the amount of trapped charge in the fluoropolymer as well as the voltage threshold for the onset of irreversible electrowetting.