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.
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 Moreرضًٍ ْزا انجذث رذضٛش ٔرشخٛض انهٛكبَذ انجذٚذ [KL [: - رفبػم ٍي ذضشًان K [4-{N-(5-methylisoxazol-3-yl) sulfamyl} phenyl carbamodithioate] عهفبيٛثٕكغبصٔل يغ ثُبئٙ كجشٚزٛذ انكبسثٌٕ ثٕجٕد ْٛذسٔكغٛذ انجٕربعٕٛو رذذ انزظؼٛذ االسجبػٙ ) نًذح اسثغ عبػبد ( ٔثئعزؼًبل انًٛثبَٕل كًزٚت نُٛزج انهٛكبَذ انًزكٕس اَفب رى رشخٛض انهٛكبَذ انًذضش ثبعزؼًبل طٛف االشؼخ رذذ انذًشاء ، ً طٛف االشؼخ فٕق انجُفغجٛخ - انًشئٛخ ، طٛف انشٍَٛ انُٕ٘ٔ انًغُبطٛغٙ نهجشٔرٌٕ أنهكبس
... Show MoreThis 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 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 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
... Show MoreA new azo (LH) ligand was prepared by coupling reaction between, diazonium salt of Sulfamethoxazole, and 8-hydroxyquinoline in a process called diazotization process resulting in azo-ligand [4-((8-hydroxyquinolin-7-yl)- N(4-methylisoxazol-3-yl) benzene sulfonamide]. The azo ligand was identified by using spectroscopic techniques to detect and characterize the formation of ligand and complexes of Ni2+, Pt4+, Pd2+, and Rh3+ metal ions, and to determine the chelating behavior of ligand and also its bind position. All complexes have a [1:1] [M-ligand] ratio and all complexes are nonelectrolytes and most of the complexes have octahedral geometry, while Pd2+complex gave square planer geometry and Ni2+ complex indicate tetrahedral geometry. Therma
... Show MoreNew ligand of N-(pyrimidin-2-yl carbamothioyl)acetamide was synthesized and its complexes with (VO(II), Mn (II), Cu (II), Zn (II), Cd (II) and Hg (II) are formed with confirmation of their structures on the bases of spectroscopic analyses. Antimicrobial activity of new complexes are studied against Gram positive S. aureus and Gram negative E. coli, Proteus, Pseudomonas. The octahedral geometrical structures are proved depending on the outcomes from the preceding procedures. Keywords: pyrimidin-2-amine, acetyl isothiocyanate, complexes, Antimicrobial activity
New ligand of N-(pyrimidin-2-yl carbamothioyl)acetamide was synthesized and its complexes with (VO(II), Mn (II), Cu (II), Zn (II), Cd (II) and Hg (II) are formed with confirmation of their structures on the bases of spectroscopic analyses. Antimicrobial activity of new complexes are studied against Gram positive S. aureus and Gram negative E. coli, Proteus, Pseudomonas. The octahedral geometrical structures are proved depending on the outcomes from the preceding procedures
The (E)-4-chloro-N-(2-(dimethylamino)ethyl)-5-((8-hydroxy quinolin-5-yl)diazenyl)-2-methoxybenzamide azo ligand (L) has been synthesized through the reaction of diazonium salt for 5-amino-4-chloro-N-(2-(dimethylamino) ethyl)-2-methoxybenzamide with 8-hydroxyquinoline and identified azo ligand (L) using spectroscopic studies (FTIR, UV-Vis, 1H and 13CNMR, mass), and micro-elemental analysis (C.H.N). Metal chelates of Co(II), Ni(II), Cu(II), as well as Zn(II) have been completed as well as characterized using mass spectra, flame atomic absorption, elemental analysis (C.H.N), infrared, UV-Vis spectroscopy, as well as conductivity, magnetic measurements. The metal-to-ligand ratio in all complexes, as determined by analytical data, was 1:2 and ex
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