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.     

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.     

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.     

1-Methylimidazolium tetrafluoroborate [Hmim][BF4]: an efficient acidic ionic liquid catalyst for insertion of α-diazo compounds into the N–H bonds of amines

The reusable acidic ionic liquid, 1-methylimidazolium tetrafluoroborate [Hmim][BF₄], was found to be an effective catalyst for the insertion of α-diazoacetate into the N–H bonds of amines. The corresponding products were obtained in good yields and short reaction times via a simple procedure. The catalyst could be recycled and reused without any noticeable decrease in its activity.     

Divalent manganese,cobalt, copper and cadmium complexes of (Z)‐N‐benzoyl‐N′‐(1H‐1,2,4‐triazol‐3‐yl)carbamimidothioic acid: Preparation,characterization, computational and biological studies

In this work, (Z)‐N‐benzoyl‐N′‐(1H‐1,2,4‐triazol‐3‐yl)carbamimidothioic acid and its Mn(II), Co(II), Cu(II) and Cd(II) complexes were introduced for the first time. This carbonyl thiourea ligand was prepared by the reaction of 1H‐1,2,4‐triazol‐3‐amine with benzoyl isothiocyanate. The structural elucidation of these compounds was performed using elemental analysis and spectral and magnetic measurements. Octahedral structures of all complexes, except Cd(II) complex with a tetrahedral geometry, were confirmed by applying DFT structural optimization. The thermal decomposition behaviour of metal complexes of carbonyl thiourea ligand is discussed. The calculation of kinetic parameters for prepared complexes (E_a, A, ΔH*, ΔS* and ΔG*) of all thermal degradation stages has been evaluated using two comparable approaches. Antimicrobial and ABTS‐antioxidant studies indicated potent activity of Cd(II) complex compared with the other investigated compounds. The cytotoxic activity of the prepared compounds was investigated in vitro. The results indicated potent activity of Mn(II) complex against both HePG2 (liver carcinoma) and MCF‐7 (breast carcinoma) cancer cells.     

Silver chloride supported on Vitamin B1 -Organometallic magnetic catalyst: synthesis,density functional theory study and application in A3-coupling reactions

A highly efficient Fe₃O₄@VitB₁–Ag(I) magnetic catalyst has been obtained using surface modification of Fe₃O₄. To this end, silver chloride was immobilized on Fe₃O₄ nanoparticles via vitamin B₁ biomolecules. The synthesized biocompatible magnetic catalyst was applied in an A³-coupling reaction in the presence of aldehyde, amine and phenyl acetylene under solvent-free conditions and afforded the desired products in excellent yields. Also, interactions between metal and ligand in the Fe₃O₄@VitB₁–Ag(I) were studied using theoretical calculations.     

Copper nanoclusters as peroxidase mimetics and their applications to H2O2 and glucose detection

Copper nanoclusters (Cu NCs) are found to possess intrinsic peroxidase-like activity for the first time. Similar to nature peroxidase, they can catalyze the oxidation of 3,3′,5,5′-tetramethylbenzidine by H₂O₂ to produce a nice blue color reaction. Compared with horseradish peroxidase, Cu NCs exhibits higher activity near neutral pH, which is beneficial for biological applications. The increase in absorbance caused by the Cu NCs catalytic reaction allows the detection of H₂O₂ in the range of 10 μM to 1 mM with a detection limit of 10 μM. A colorimetric method for glucose detection was also developed by combining the Cu NCs catalytic reaction and the enzymatic oxidation of glucose with glucose oxidase. Taking into account the advantages of ultra-small size, good stability, and high biocompatibility in aqueous solutions, Cu NCs are expected to have potential applications in biotechnology and clinical diagnosis as enzymatic mimics.     

Enantioselective Diethylzinc Addition to Aromatic Aldehydes Catalyzed by Novel Ti(IV) Complex of Three-Dentate Chiral Sulfonamide Ligands

The synthesis of several novel three-dentate sulfonamide alcohol ligands is described, starting from camphorsulfonyl chloride. The influence of temperature and ligand structure on the asymmetric addition of dietylzinc to aromatic aldehydes has been studied. Enantioselectivities up to 76% have been obtained.