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.
Addition 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
on this research is to study the effect of nickel oxide substitution on the pure phases superconductor Tl0.5Pb0.5Ba2Can-1Cun-xNixO2n+3-δ (n=3) where x=(0,0.2,0.4,0.6,0.8.and 1.0). The specimens in this work were prepared with used procedure of solid state reaction with sintering temperature 8500C for 24 h .we used technical (4-prob)to calculated and the critical temperature Tc . The results of the XRD diffraction analysis showed that the structure for pure and doped phases was tetragonal with phases high-Tc phase (1223),(1212) and low-Tc phase (1202) and add
... Show MoreNew 2-Mercaptobenzimidazole derivatives were synthesized. 4,5-disubsitituted 1,2,4-Triazole compounds 1b-2c were synthesized from 2-(benzylthio) benzimidazole compound a, which was then reacted with (NaH) in dioxane at a temperature of (0-5 C°) to produce the salt of compound a. Then the salt was reacted with ethyl chloro acetate to yield Ethyl 2-(benzylthio) benzimidazole acetate compound b. Compound b was converted to triazole derivatives by two pathways. The first pathway was reacting compound b with semicarbazide, thiosemicarbazide and phenylsemicarbazide in DMSO as a solvent to gain compounds 1b-3b, which were then
... Show MoreIn this work, polynomials and the finite q-exponential operator are constructed. The operator is used to combine an operator proof of the generating function with its extension, Mehler's formula with its extension and Roger's formula for the polynomials . The generating function with its extension, Mehler's formula with its extension and Rogers formula for Al-Salam-Carlitz polynomials are deduced by giving special values to polynomials .
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 MoreIn this work , the ligand [N-(4-Methoxybenzoyl amino)-thioxomethyl] Methionine acid has been synthesized by the reaction of 4- Methoxybenzoyl isothiocyanate with methionine acid . The metal complexes were prepared through the reaction of metals chlorides of Co(II) , Ni(II), Cu(II), Zn(II) and Cd(II) in ethanol as solvent . The ligand (MbM) and its metal complexes have been characterized by elemental analysis (CHNS), IR, 1H-13CNMR and UV- Vis spectra, magnetic susceptibility measurements, molar conductivity, melting points and atomic absorption. The metal-ligand ratio was determined by mole ratio method. The suggested structures for the Co(II), Ni(II), Cd(II) and Zn(II) complexes are tetrahedral geometry and the Cu(II) complex
... Show More