Vieta–Fibonacci wavelets: Application in solving fractional pantograph equations

In this paper, the Vieta–Fibonacci wavelets as a new family of orthonormal wavelets are generated. An operational matrix concerning fractional integration of these wavelets is extracted. A numerical scheme is established based on these wavelets and their fractional integral matrix together with the collocation technique to solve fractional pantograph equations. The presented method reduces solving the problem under study into solving a system of algebraic equations. Several examples are provided to show the accuracy of the method.     

Formation of PdNiZn thin film at oil‐water interface: XPS study and application as Suzuki‐Miyaura catalyst

Nanosheet of PdNiZn and nanosphere of PdNiZn/reduced‐graphene oxide (RGO) with sub‐3 nm spheres have been successfully synthesized through a facile oil‐water interfacial strategy. The morphology and composition of the films were determined by X‐ray diffraction (XRD), X‐ray photoelectron spectroscopy (XPS), transmission electron microscopy (TEM), scanning electron microscopy (SEM), energy dispersive analysis of X‐ray (EDAX) and elemental mapping. In the present study, we have developed a method to minimize the usage of precious Pd element. Due to the special structure and intermetallic synergies, the PdNiZn and PdNiZn/RGO nanoalloys exhibited enhanced catalytic activity and durability relative to Pd nanoparticles in Suzuki‐Miyaura C‐C cross‐coupling reaction. Compared to classical cross‐coupling reactions, this method has the advantages of a green solvent, short reaction times, low catalyst loading, high yields and reusability of the catalysts.     

Silica-Polyethyleneglycols/N 2 O 4 Complexes as Heterogeneous Nitrating and Nitrosating Agents

Silica-chloride was reacted with different quantities of H(OCH 2 CH 2 ) n OH (n = 2-4) to furnish silica-based linear polyethylene glycols and cyclic polyethylene glycolic ethers. The N 2 O 4 complex of silica-tetraethylene glycolic ether ( III ) was selected and used as a stable, cheap, and heterogeneous silica-based reagent for the selective mono- and dinitration of phenols and nitrosation of thiols.     

Simultaneous formation of platinum‐based nanocatalysts and degradation of dyes at oil/water interface: Comparative morphological and kinetic studies

To decrease the water pollution of textile industries with a large amount of toxic and non‐biodegradable colored dye effluents, an efficient technique is required to safely remove harmful pollutants. In this paper, the reaction between azo dyes and NaBH₄ catalyzed by nanoparticles (NPs) thin films has been studied. We report insitu degradation of methyl orange (MO) and methyl red (MR) by using Pt‐based thin films monitored by UV–Vis spectroscopy. We have synthesized different thin films such as Pt, PtPd, PtFeFe₂O₃, PtNi and PtAu films from Pt organometallic precursor in the MO and MR medium (dye degradation and NPs formation is happened simultaneously) and activity of these films were compared in the complete degradation of MO and MR dyes. Rate constants for the catalyzed reactions have been determined. PtPd NPs thin film has shown the highest rate constant for the degradation of MO and MR within only a few seconds due to its well‐ordered structure. Furthermore, the effect of presence of MO on the morphology of NPs was investigated.     

Effect of the External Mirror Feedback Strength in the Dynamics and Spectrum of the Injected Semiconductor Lasers

We analytically investigate the effect of an external mirror on the stability of an injected semiconductor laser, the latter treated as injected damped oscillators. In the studied configuration, the injected semiconductor laser with an external mirror is under the influence of a chaotic oscillating optical signal that is generated by a similar semiconductor master laser. We derive our results in terms of the damping rate and resonance frequency. We show that the external mirror can eliminate the unstable modes of the injected laser at low frequencies. Furthermore, the mirror can enhance the damping of the oscillation modes of the injected semiconductor laser; consequently, the driven response of the injected laser may have a broad spectrum, even wider than that of the chaotic driving signal. We also show results for the bandwidths of the injection amplitude and phase increment as functions of the injection rate and feedback strength of the external mirror. In addition, we use bifurcation and time-series curves to describe the dynamical behavior of the injected laser. We identify the feedback strength of injected laser, relative to that of the master laser, which induces synchronization between the injected-laser oscillation modes and the master laser.     

Copper(I) complex covalently anchored on graphene oxide as an efficient and recyclable catalyst for Sonogashira reaction

In this study, the organosilane‐functionalized graphene oxide as a stabilizer was prepared by a facile one‐step silylation approach. [Cu(PPh₃)₃Cl] complex was successfully immobilized onto the graphene oxide surface through coordination interaction with organosilane ligand spacers. The supported catalyst showed enhanced catalytic performance toward Sonogashira reaction of aryl halides with phenylacetylene in water solvent compared with the homogeneous analogues, and it could be readily recycled and reused several times without discernible loss of its activity.