Stability analysis for a nonlinear coupled system of fractional hybrid delay differential equations

The main objective of this research work is to establish existence results as well as to study qualitative aspects of the proposed coupled system of fractional hybrid delay differential equations (FHDDEs). Using the hybrid fixed point theory, we establish appropriate results for the existence of at least one solution to our problem. The powerful tools of functional analysis and dynamical systems are applied to derive different kinds of stability analysis. These include Ulam-Hyers (UH), generalized Ulam-Hyers (GUH), Ulam-Hyers-Rassias (UHR), and generalized Ulam-Hyers-Rassias (GUHR). In order to provide the authenticity of the our results, an illustrative example is given to wind up the present research work.     

Effect of cooling speed on structure and properties of rapidly solidified Pb–25wt.% Sn alloy

The effect of cooling speed on structure, hardness, mechanical and electrical transport properties of rapidly solidified Pb–25wt.% Sn alloy have been investigated. A single roller melt spinning technique with linear speeds 15.7 and 31.7 m/s, was used for the preparation of specimens. The results showed that a lower cooling speed increased the precipitation of Sn in a Pb-matrix phase as compared with the higher cooling speed. This decomposition behavior decreased the electrical resistivity and increased the internal friction, thermal diffusivity and Vickers microhardness of the lower cooling speed as compared with those of the higher cooling speed.     

On the proximinality of compact operators over spaces of measurable functions

The main results in this paper are, the characterization of all the σfinite positive measures μ and v, for which K(L₁(μ, L₁(v)) proximinal in K(L₁(μ, L₁(v)) all the a-finite positive measures fi and v, for which K(L_∞(μ), L_∞(v)) is proximinal in L(L_∞μ)), L_v(v)) and all the compact Hausdorff spaces Q, for which K(C(Q), L_∞(μ)) is proximinal in L(C(Q), :_∞(μ))     

Glycerol: A Promising Benign Solvent for Catalyst‐free One‐pot Multi‐component Synthesis of 1H‐Pyrozolo[1,2‐b]phthalazine‐5,10‐diones and 2H‐Indazolo[2,1‐b]phthalazine‐triones Under Controlled Microwaves Irradiation

A simple green and efficient one‐pot multi‐component synthesis of 1H‐pyrozolo[1,2‐b]phthalazine‐5,10‐diones and 2H‐indazolo[2,1‐b]phthalazine‐triones has been developed utilizing one‐pot multi‐component reaction of aromatic aldehydes, active methylene reagents, phthalic anhydride, and hydrazine hydrate or alternatively phthalhydrazide in glycerol without catalyst under controlled microwave heating. The current synthetic protocol offers several advantages such as excellent yields, high EcoScale and atom economy, simple working up reactants and products, and the absence of hazardous catalysts or solvents.     

Multicomponent access to novel proline/cyclized cysteine tethered monastrol conjugates as potential anticancer agents

The versatility of multicomponent Biginelli’s reaction is exploited in the development of proline and cyclized cysteine tethered conjugates of monastrol, a kinesin Eg5 inhibitor. Ten new conjugates are synthesized focusing on structural replacement of the ester moiety (C-5 position) of the monastrol backbone with amino acid based amide moieties. On cytotoxic evaluation, conjugate 24 has shown promising in vitro cytotoxic activity against leukemia. Molecular docking studies revealed that the conjugates 19 and 24 exhibit better interaction at kinesin Eg5 receptor compared to monastrol. Moreover, computational calculations and predictions of important molecular properties suggest that these new amino acid based conjugates could be further improved to provide potential anticancer agents.     

Subdiffraction resolution in total internal reflection fluorescence microscopy with a grating substrate

We propose a fluorescence surface imaging system that presents a power of resolution beyond that of the diffraction limit without resorting to saturation effects or probe scanning. This is achieved by depositing the sample on an optimized periodically nanostructured substrate in a standard total internal reflection fluorescence microscope. The grating generates a high-spatial-frequency light grid that can be moved throughout the sample by changing the incident angle. An appropriate reconstruction procedure permits one to recover the fluorescence amplitude from the images obtained for various incidences. Simulations of this imaging system show that the resolution is not limited by diffraction but by the period of the grating.     

A novel method of nanocrystal fabrication based on laser ablation in liquid environment

Metal nanoparticles can be prepared by a novel technique that consists of the laser ablation of a solid target immersed in a water solution of a metal salt. Silicon was chosen as the most adequate target to synthesize silver and gold nanoparticles from a water solution of either AgNO₃ or HAuCl₄. The influence of both the silver nitrate concentrations and the irradiation time of the Si target on the optical properties of the Au and Ag nanoparticles have been investigated. The crystalline nature of the metal nanoparticles has been determined by X-ray diffraction (XRD). Average size and particle size distribution have been measured by means of TEM. The absorbance spectra show the characteristic band of the surface resonant plasmon of silver and gold nanoparticles.     

Metal-free,PTSA catalyzed facile synthesis of β-ketoacetal from β-chlorocinnamaldehyde

A toluene solution of β-chlorocinnamaldehyde and dihydroxy alcohols in the catalytic presence of para-toluenesulphonic acid (PTSA) yield the β-ketoacetal in good to outstanding amount. The catalyst (PTSA), first selectively protect the aldehydic group to form the β-chloroacetal and the subsequent dechlorination by H₂O result the β-ketoacetal. Significant transformation was achieved with electron donating substituent attached at the para-position of cinnamaldehyde. The selective formation of β-keto-1,3-acetal was also obtained with a mixture of 1, 2- and 1, 3- diol. The present reaction consists of a metal-free, economical, robustly feasible, sizeable functional group tolerance and high yield properties. Moreover, the use of different dihydroxy alcohols made this process more benign and valuable towards the metal-free development of ketones. First, of its kind, a rare and unusual multitasking nature of PTSA is observed.     

A new thermal study of the reaction of 6‐azidopyridones with different amines and hydrazines

Reacting of 6‐azidopyridone derivatives 1 with o‐phenylenediamine ( 2a ) in chloroform at room temperature afforded the new azidopyridones 3 . However, its fusion with 2a,b at 100–110°C gave the interesting pyrido[2,3‐b][1,5]diazepines 4a,b . Alternatively, compound 4a could also be obtained by heating azidopyridones 3 at 100–110°C. When compound 1 was allowed to react with hydrazines 7a‐d at room temperature it gave the corresponding azido compounds 8a‐d . Fusion of 1 with phenylhydrazine ( 7d ) at 140–160°C afforded the new aminopyridones 10 . The 6‐azidopyridones 1 could also be converted to the corresponding 6‐alkylaminopyridones 15a‐d by reaction with an excess of alkylamines at room temperature.