Property (X) for Second-Order Nonlinear Differential Equations of Generalized Euler Type

In this paper the generalized nonlinear Euler differential equation t²k(tu′)u″ + t(f(u)+ k(tu′))u′ + g(u) = 0 is considered. Here the functions f(u), g(u) and k(u) satisfy smoothness conditions which guarantee the uniqueness of solutions of initial value problems, however, no conditions of sub(super) linearity are assumed. We present some necessary and sufficient conditions and some tests for the equivalent planar system to have or fail to have property (X⁺), which is very important for the existence of periodic solutions and oscillation theory.     

Complete hom-Lie superalgebras

Abstract

In this article, we investigate some basic results on complete hom-Lie superalgebras. In particular, we present some sufficient conditions for a hom-Lie superalgebra to be a complete hom-Lie superalgebra. Making use of these conditions, we build a family of complete hom-Lie superalgebras.     

Spectroscopic studies,structural characterization and electrochemical studies of two cobalt (III) complexes with tridentate hydrazone Schiff base ligands: Evaluation of antibacterial activities,DNA‐binding,BSA interaction and molecular docking

Co(III) complexes of tridentate Schiff base ligands derived from N‐(2‐hydroxybenzylideneamino)benzamide (H ₂ L ¹ ) and 2‐(2‐hydroxybenzylidene)hydrazine‐1‐carboxamide ( H ₂ L ² ) were synthesized and characterized using IR, Raman, ¹H–NMR and UV–Vis spectroscopies. X‐ray single crystal structures of complexes 1 and 2 have also been determined, and it was indicated that these Co(III) complexes are in a distorted octahedral geometry. The cyclic voltammetry (CV) of the complexes indicates an irreversible redox behavior for both complexes 1 and 2 . The antibacterial effects of the synthesized compounds have been tested by minimum inhibitory concentration and minimum bactericidal concentration methods, which suggested that the metal complexes exhibit better antibacterial effects than the ligands against Gram‐positive bacteria. The effects of the drug (drug  =  ligands and complexes) on bovine serum albumin (BSA) were examined using circular dichroism (CD) spectropolarimetry, and it was revealed that the BSA (BSA, as a carrier protein) secondary structure changed in the presence of the drug. Interaction of the drug with calf‐thymus DNA (CT‐DNA) was investigated by UV–Vis absorption, fluorescence emission, CV and CD spectroscopy. Binding constants were determined using UV–Vis absorption. The results indicated that the studied Schiff bases bind to DNA, with the hyperchromic effect and non‐intercalative mode in which the metal complexes are more effective than ligands. Furthermore, molecular docking simulation was used to obtain the energetic and binding sites for the interaction of the complexes with Mycobacterium tuberculosis enoyl‐acyl carrier protein reductase (InhA), and results showed that complex 1 has more binding energy.     

The reduction of 4‐nitrophenol and 2‐nitroaniline by palladium catalyst based on a KCC‐1/IL in aqueous solution

KCC‐1/IL/Pd NPs can used as an excellent support for the synthesis of highly sparse homogeneous catalyst. KCC‐1 has high surface area that was functionalized with ionic liquid phase acting as the strong performers so that the Pd catalyst was well‐dispersed without aggregation on the framework of the KCC‐1/IL. This nano catalyst was specified by TGA, XRD, TEM, SEM, FT‐IR, and ICP. For reduction of 2‐nitroaniline and 4‐nitrophenol used from the KCC‐1/IL/Pd NPs as a green catalyst that showed excellent catalytic activities. Compared with the traditional substrate, KCC‐1 substantially increases protection and the accessibility of the nanoparticle sites due to its three dimensional hierarchical structure.     

Ultrasound-assisted dehydrogenation of 5-acetyl-3,4-dihydropyrimidin-2(1H)-ones

In this study, various 5-acetyl-3,4-dihydropyrimidin-2(1H)-ones were synthesized and the dehydrogenation of these compounds by potassium peroxydisulfate in aqueous acetonitrile under thermal and sono-thermal conditions were investigated. Whereas the effect of the nature of 4-substituent influences the rate of reaction, the application of sonic waves decreases drastically the time of thermal reaction.     

On generalized symmetric Finsler spaces

In this paper, we study generalized symmetric Finsler spaces. We first study some existence theorems, then we consider their geometric properties and prove that any such space can be written as a coset space of a Lie group with an invariant Finsler metric. Finally we show that each generalized symmetric Finsler space is of finite order and those of even order reduce to symmetric Finsler spaces and hence are Berwaldian.     

Kinetic and thermodynamic properties of the aerial oxidation of hydroquinone in developer solutions

The aerial oxidation kinetics of hydroquinone in a freshly prepared developer solution at different temperatures and pHs has been studied. The activation parameters, Ea, ΔG# , ΔS# , ΔH# and enthalpy of formation of activated complex, ΔHfo(X# ), are determined. The large negative value of free energy of activation ΔG# proves that hydroquinone extremely tends to be oxidized by air at optimum temperature (20℃) and optimum pH (10.5) and converts to the activated complex semiquinone. It was also found that if the pH of the developer solution is increased from 9.3 to 10.5 the reaction rate will increase by a factor of 2.     

Application of the β-cyclodextrin supramolecules as a green accelerator hosts in one-step preparation of highly functionalised rhodanine scaffolds

β-Cyclodextrin (β-CD) supramolecule was found to be a convenient, green and economical tool in one-pot synthesis of rhodanine scaffolds as a highly efficient mediating agent in aqueous media in which the reaction accelerated to complete in 15 min and room temperature. In this work, amines reacted with equimolar ratio of CS₂ (not excess ratio of CS₂) and then with activated acetylenes in the presence of β-CD in aqueous media.