The effect of fractional calculus on the formation of quantum-mechanical operators

In this paper, the deformation of the ordinary quantum mechanics is formulated based on the idea of conformable fractional calculus. Some properties of fractional calculus and fractional elementary functions are investigated. The fractional wave equation in 1 + 1 dimension and fractional version of the Lorentz transformation are discussed. Finally, the fractional quantum mechanics is formulated; infinite potential well problem, density of states for the ideal gas, and quantum harmonic oscillator problem are discussed.     

Some remarks on the Hodge conjecture for abelian varieties

We show how the classical Hodge conjecture for the middle cohomology of an abelian variety is equivalent to the general Hodge conjecture for the middle cohomology of a smooth ample divisor in the abelian variety. This is best suited to abelian varieties with actions of imaginary quadratic fields.     

Substituted quinolinones. 31. Some new pyrano[3,2‐c]quinoline‐3‐carboxamides and their antioxidant activity

1‐Ethyl‐4‐hydroxy‐2‐oxo‐1,2‐dihydroquinoline‐3‐carbaldehyde ( 1 ) was annulated using malonic acid and/or its ethyl ester to furnish pyrano[3,2‐c]quinoline‐3‐carboxylic acid 2 and its ester 3 . Interconversions between acid 2 and ester 3 were successfully carried out. The anticipated pyrano[3,2‐c]quinoline‐3‐carboxamides 5–12 were conveniently attained via condensation of ester 3 with the proper amine. Surprisingly, treatment of ester 3 with dimethylformamide (DMF) in acidic media led to the carboxamide 5 . All attempts to convert ester 3 to its corresponding acid hydrazides by interaction with the proper hydrazine derivative led to formation of pyrazolidinediones 15 and 17 . Ester 3 underwent cyclo‐condensation with malononitrile dimer affording pyrido[3′,4′:5,6]pyrano[3,2‐c]quinoline derivative 18 . The new compounds revealed significant antioxidant effect, which suggests that most of them are possible potent antioxidant agents.     

Air‐assisted liquid–liquid extraction coupled with dispersive liquid–liquid microextraction and a drying step for extraction and preconcentration of some phthalate esters from edible oils prior to their determination by GC

In this work, a new, cheap, simple, fast, and low organic solvent consuming procedure is proposed for isolation, enrichment, and gas chromatographic determination of some phthalate esters in edible oils. The method is based on a combination of air‐assisted liquid–liquid extraction and dispersive liquid–liquid microextraction followed by a drying step under N₂ gas. Several experimental parameters affecting both extraction and preconcentration steps were investigated and optimized. Under the optimum conditions for the proposed method, wide linear ranges (0.05–800 μg/L) and low detection limits (0.007–0.023 μg/L) were observed. The ranges of enrichment factors and extraction recoveries were 68–340 and 14–68%, respectively. Eventually, the target analytes were successfully determined in different edible oils using the proposed method.     

One-pot,solvent-free and efficient synthesis of 2,4,6-triarylpyridines catalyzed by nano-titania-supported sulfonic acid as a novel heterogeneous nanocatalyst

Nano titania-supported sulfonic acid (n-TSA) has found to be a highly efficient, eco-friendly and recyclable heterogeneous nanocatalyst for the solvent-free synthesis of 2, 4, 6-triarylpyridines through one-pot three-component reaction of acetophenones, aryl aldehydes and ammonium acetate. This reported method illustrates several advantages such as environmental friendliness reaction conditions, simplicity, short reaction time, easy work up, reusability of catalyst and high yields of the products. One new compound is reported too. Furthermore, the catalyst could be recycled after a simple work-up, and reused at least six times without substantial reduction in its catalytic activity.     

Shape control of nanostructured TiO2 using a Schiff base ligand via sol–gel hydrothermal method

Employing a Schiff base ligand in a hydrothermal sol–gel method for preparation of TiO₂ nanostructures was studied. The as-prepared products were characterized by X-ray diffraction, scanning electron microscopy, transmission electron microscopy, Fourier transform infrared spectrum, electron dispersive X-ray spectroscopy and ultraviolet–visible spectroscopy. It is shown that in the controlled reaction conditions, a Schiff base ligand containing hard atoms is capable of driving the growth mechanism in a way that anisotropic shapes of TiO₂ nanostructures are formed. Considering the structure of the Schiff base ligand, the possible growth mechanism of TiO₂ nanostructures is proposed. The optical studied as well as calculated molecular orbital structure of ligand by density functional theory is done.     

Synthesis of diaryl thioethers from aryl halides and potassium thiocyanate

An efficient palladium catalyst was synthesized using nicotine, benzyl chloride and palladium chloride. The structure of this catalyst was characterized and it was then used for the synthesis of diaryl sufides. A variety of diaryl thioethers were synthesized under relatively mild reaction conditions. This protocol avoids foul‐smelling thiols via cross‐coupling of aryl halides with potassium thiocyanate and all substrates give the corresponding products in good to excellent yields in the presence of low amounts of the catalyst. Copyright © 2014 John Wiley & Sons, Ltd.     

One-pot synthesis of novel polysubstituted furopyran derivatives via pseudo seven-component reaction (6 + 1) of isocyanides with bisarylidene Meldrum's acid containing ether groups

In the present study, a group of polysubstituted furopyran derivatives possessing ether spacer groups were synthesized under good-to-exceptional yields via cycloaddition of bisarylidene Meldrum's acid derivatives (1 mmol) with isocyanides (6 mmol) within dichloromethane (CH₂Cl₂) for 3 to6 hours at room temperature with no assistance from any type of catalysts. The structure of the products was then confirmed by Fourier Transform-infrared spectroscopy, ¹H-nuclear magnetic resonance spectroscopy, ¹³C-nuclear magnetic resonance spectroscopy, and elemental analysis. Moreover, the 5c , 5d , and 5f compounds exhibited favorable pharmaceutical behavior as antibacterial.     

Selective aerobic photocatalytic oxidation of benzyl alcohol over spherical structured WO<Subscript>3</Subscript>/TiO<Subscript>2</Subscript> nanocomposite under visible light irradiation

TiO₂/WO₃ nanocomposite with nanodisk morphology was prepared and successfully used as a photocatalyst. The nanocomposite was obtained via sonochemical and hydrothermal methods, using pomegranate juice as a capping agent. The products were characterized by FE-SEM imaging, BET, EDAX spectroscopy, X-ray diffraction, DRS, and FT-IR spectroscopy. TiO₂/WO₃ nanocomposite showed high sensitivity to absorb visible light in compared to TiO₂. In an optimized condition, the yield of the aerobic photocatalytic oxidation of benzyl alcohol derivatives reached to 65% for the TiO₂/WO₃ nanocomposite, while the conversion percent of the derivatives was less than 8% and 50% on the TiO₂ and WO₃ nanoparticles, respectively. Experimental results were supported by density functional theory (DFT) calculations. The DFT results in several solvents of different dielectric constants, confirmed the strong dependence of light absorption and photocatalytic activity to adsorption energy of the substrates on the surface of the nanoparticles (E_ad). In addition, the theoretical results showed an inverse correlation between the adsorption energy of benzyl alcohol and its conversion percent, accordance to the experimental trend.

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