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.     

FP-LMTO method to calculate the structural,thermodynamic and optoelectronic properties of SixGe1−xC alloys

The structural and electronic properties of the ternary Si_xGe_1?xC alloys have been calculated using the full-potential linear muffin-tin-orbital (FP-LMTO) method based on density functional theory within both local density approximation (LDA) and generalised gradient approximation (GGA). The calculated equilibrium lattice constants and bulk moduli are compared with previous results. The concentration dependence of the electronic band structure and the direct and indirect band gaps are investigated. Using the approach of Zunger and co-workers, the microscopic origins of the band gap bowing are investigated also. Moreover, the refractive index and the optical dielectric constant for Si_xGe_1?xC are studied. The thermodynamic stability of the alloys of interest is investigated by means of the miscibility. This is the first quantitative theoretical prediction to investigate the effective masses, optical and thermodynamic properties for Si_xGe_1?xC alloy, and still awaits experimental confirmations.     

New fundamental relation of hyperrings

We prove that θ^∗${\theta }^{\ast }$ as previously defined [Int. J. Contemp. Math. Sci. 5 (2010) 721] is the smallest equivalence relation such that the quotient structure R/θ^∗$R/{\theta }^{\ast }$ is a commutative fundamental ring. We also investigate some properties with respect to the commutative fundamental relation θ^∗${\theta }^{\ast }$ on a hyperring R$R$.     

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.     

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.