The discussion in this paper gives several theorems and lemmas on the Sums of Squares of consecutive Carol Numbers. These theorems are proved by using the definition of carol numbers and mathematical induction method. Here the matrix form and the recursive form of sum of squares of consecutive Carol numbers is also given. The properties of the Carol numbers are also derived.
This work involves synthesis of some new heterocyclic compounds including 1, 3-diazetine. The new Schiff bases [VI] ad derived from 3-((5-hydrazinyl-4-phenyl-4H-1, 2, 4-triazol-3-yl) methyl)-1H-indole [V] which was synthesized by refluxing 5-((1H-indol-3-yl) methyl)-4-phenyl-4H-1, 2, 4-triazole-3-thiol [IV] with hydrazine hydrate in absolute ethanol and this amino compound [V] condensation with different aromatic aldehydes in absolute ethanol to yielded a new Schiff bases [VI] ad. N-acyl compounds [VII] ad were synthesized by addition reaction of acetyl chloride to imine group of Schiff bases in dry benzene. The new diazetine derivatives [VIII] ad synthesized by the reaction of N-acyl compounds [VII] ad with sodium azide in dimethylformamid
... Show MoreAddition chloro acetyl isothiocyanate (C3H2ClNOS) with 3-Aminoaceto phenone (C8H9NO) to prepare a fresh Ligand [N-(3-acetyl phenyl carbamothioyl)-2-chloroacetamide](L). The ligand (L) behaves as bidentate coordinating through O and S donor with metal ions, the general formula of all complexes [M(L)2(Cl)2](M+2 = Manganese(II), Cobalt(II), Cadmium(II) and Mercury(II)). Compounds were investigation by Proton-1, Carbon -13 NMR spectra (ligand (L) only), Element Microanalysis for C, N, H, O, S, Fourier-transform infrared, UV visible, Conductance
Abstract Ternary Silver Indium selenide Sulfur AgInSe1.8S0.2 in pure form and with a 0.2 ratio of Sulfur were fabricated via thermal evaporation under vacuum 3*10-6 torr on glasses substrates with a thickness of (550) nm. These films were investigated to understand their structural, optical, and Hall Characteristics. X-ray diffraction analysis was employed to examine the impact of varying Sulfur ratios on the structural properties. The results revealed that the AgInSe1.8S0.2 thin films in their pure form and with a 0.2 Sulfur ratio, both at room temperature and after annealing at 500 K, exhibited a polycrystalline nature with a tetragonal structure and a predominant orientation along the (112) plane, indicating an enhanced de
... Show MoreIn this communication, introduce the split Mersenne and Mersenne-Lucas hybrid quaternions, also obtaining generating functions and Binet formulas for these hybrid quaternions and investigating some properties among them.
This study describes preparation a new series of tetra-dentate N2O2 dinuclear complexes Cr(III), Co(II)and Cu(II) of the Schiff base 2-[5-(2-hydroxy-phenyl)-1,3,4-thiadiazol-2-ylimino]-methyl-naphthalen-1-ol], (LH2) derived from 1-hydroxy-naphthalene-2-carbaldehyde with 2-amino-5-(2-hydroxy-phenyl)-1,3,4-thiadiazole. These ligands were characterized by FT-IR, UV-Vis, Mass spectra, elemental analysis, and 1H-NMR. All prepared complexes have been characterized by conductance measurement, magnetic susceptibility, electronic spectra, infrared spectrum, thermal Analysis (TGA), and metal analysis by atomic absorption. The stoichiometry of metal to ligand, magnetic susceptibility, and electronic spectra measurements show an octahedral geom
... Show MoreThis work is based on the synthesis of Cobalt(II) and Cadmium(II) mixed-ligands compounds obtained from the reaction of N'-(4-methylsulfanyl-benzoyl)-hydrazine carbodithioic acid methyl ester as a ligand and using ethylendiamine (en), 2,2'-bipyridine (bipy) or 1,10-phenanthroline (phen) as a co-ligand. The synthesis of ligand (HL) was based on multi-steps synthetic procedure. The reaction of 4-methylsulfanyl-benzoyl chloride with hydrazine gave 4-methylsulfanyl-benzoic acid hydrazide. This compound was reacted with carbon disulfide and potassium hydroxide in methanol to yield N'-(4-methylsulfanylbenzoyl)-hydrazine potassium thiocarbamate, which upon reaction with methyl iodide resulted in the formation of the ligand. A range of physico-chem
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