Uniqueness theorems related to weighted sharing of two sets

Using the notion of weighted sharing of sets, we study the uniqueness problem of meromorphic functions sharing two finite sets. Our results are inspired from an article due to J. F. Chen (Open Math., 15 (2017), 1244–1250)

Automatic estimation of mechanical properties from fractographs using optimal anisotropic diffusion and Voronoi tessellation

With the advent of materials informatics there is a high demand of establishing automatic structure-property correlationship of materials which is a popular research topics due to the advancement of image processing and pattern recognition algorithms. Therefore, in this work, an attempt is made to estimate mechanical properties (i.e. yield strength and ductility) of AISI 304LN stainless steel from the SEM images of fracture surfaces obtained from tensile tests carried out at different strain rates using image processing techniques. As the void morphologies of fracture surfaces change systematically with the change in strain rates, the automatic detection of voids and geometrical features estimation from detected voids from the obtained are key goals of this present study. Therefore, in this work, a novel method of optimal anisotropic diffusion technique along with contrast limited adaptive histogram equalization (CLAHE), Otsu's optimal thresholding and morphological thinning operation are applied over the fractographs for edge enhancement, overcoming inhomogeneous illumination, edge segmentation and thinning, respectively, to detect voids, automatically. Then, Voronoi tessellation technique, which is a geometrical texture analysis, is utilized on these edge images of fractographs to extract four features viz. Voronoi edges, mean area, mean elongation and mean perimeter of Voronoi polygons where the linear correlation values (R2) with mechanical properties are found in the range of 0.90–0.99. A high linear correlation of features (i.e. 0.97–0.99) with the ductility is noticed as ductility is a geometrical parameter measured during fracture

Aluminium complex as an efficient catalyst for the chemo-selective reduction of amides to amines

We report an efficient protocol for the catalytic chemo-selective reduction of tert-amides with pinacolborane (HBpin) to afford the corresponding amines in high yields using aluminium complexes [κ2-{Ph2P(X)NC9H6N}Al(Me)2] [X = S (2a), Se (2b)] as pre-catalysts at room temperature. The aluminium complexes were prepared from the reaction of [Ph2P(X)NC9H6N] [X = S (1a), Se (1b)] and trimethylaluminium in toluene. The solid-state structure of complex 2b is established. Tertiary amides with a wide array of electron-withdrawing and electron-donating functional groups were easily converted to the desired products through the selective cleavage of the amides' CO bond by aluminium hydride as an active species. A kinetic study of the catalytic reaction is also reported

Aluminium alkyl complexes supported by imino-phosphanamide ligand as precursors for catalytic guanylation reactions of carbodiimides

Herein, we report the synthesis, characterisation, and application of three aluminium alkyl complexes, [κ2-{NHIRP(Ph)NDipp}AlMe2] (R = Dipp (2a), Mes (2b); tBu (2c), Dipp = 2,6-diisopropylphenyl, Mes = mesityl, and tBu = tert-butyl), supported by unsymmetrical imino-phosphanamide [NHIRP(Ph)NDipp]- [R = Dipp (1a), Mes (1b), tBu (1c)] ligands as molecular precursors for the catalytic synthesis of guanidines using carbodiimides and primary amines. All the imino-phosphanamide ligands 1a, 1b and 1c were prepared in good yield from the corresponding N-heterocyclic imine (NHI) with phenylchloro-2,6-diisopropylphenylphosphanamine, PhP(Cl)NHDipp. The aluminium alkyl complexes 2a, 2b and 2c were obtained in good yield upon completion of the reaction between trimethyl aluminium and the protic ligands 1a, 1b and 1c in a 1:1 molar ratio in toluene via the elimination of methane, respectively. The molecular structures of the protic ligands 1b and 1c and the aluminium complexes 2a, 2b and 2c were established via single-crystal X-ray diffraction analysis. Complexes 2a, 2b and 2c were tested as pre-catalysts for the hydroamination/guanylation reaction of carbodiimides with aryl amines to afford guanidines at ambient temperature. All the aluminium complexes exhibited a high conversion with 1.5 mol% catalyst loading and broad substrate scope with a wide functional group tolerance during the guanylation reaction. We also proposed the most plausible mechanism, involving the formation of catalytically active three-coordinate Al species as the active pre-catalyst. © 2022 The Royal Society of Chemistry

Neosilyllithium‐Catalyzed Hydroboration of Alkynes and Alkenes in the Presence of Pinacolborane (HBpin)

We report here a novel protocol for the hydroboration of alkynes and alkenes, which in the presence of neosilyllithium (LiCH2SiMe3) (5 mol %) and pinacolborane efficiently results in the formation of corresponding alkenyl and alkyl boronate ester products in good yields. The electron-donating and electron-withdrawing substituents on the aromatic rings of alkynes and alkenes converted smoothly to the desired products. When we extended the scope of reactivity to various aliphatic alkynes and styrenes using similar conditions, the alkenyl and alkyl boronate ester products were again formed in good yields. We also performed intramolecular and intermolecular reactions to check the reactivity of different functional groups on the phenyl ring. Experimental investigations and DLPNO-CCSD(T) calculations reveal mechanistic insights from the LiCH2SiMe3-catalyzed alkyne hydroboration. © 2021 Wiley-VCH Gmb