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.
Both traditional and novel techniques were employed in this work for magnetic shielding evaluation to shed new light on the magnetic and aromaticity properties of benzene and 12 [n]paracyclophanes with n = 3–14. Density functional theory (DFT) with the B3LYP functional and all-electron Jorge-ATZP and x2c-TZVPPall-s basis sets was utilized for geometry optimization and magnetic shielding calculations, respectively. Additionally, the 6-311+G(d,p) basis set was incorporated for the purpose of comparing the magnetic shielding results. In addition to traditional evaluations such as NICS/NICSzz-Scan, and 2D-3D σiso(r)/σzz(r) maps, two new techniques were implemented: bendable grids (BGs) and cylindrical grids (CGs) of ghost atoms (Bqs). BGs a
... Show MoreA New ligand, N-(2-oxo-1,2- Dihydropyrimidin-4- ylcarbamothioyl) Acetamide (DPA) was prepared by reaction of iso thiosyanate derivative with Cytosine. The ligand has been characterized through elemental analysis, H1 NMR, C13NMR, FT-IR, and UV Visible spectra, such ligand’s transition metal complexes have been characterized through conductivity measurement, FT-IR, UV Visible spectra and magnetic susceptibility, all the complexes of this ligand are solid crystal and molar ratio (2:1) (ligand: metal). The form of molecular for these complexes octa hedral. The general formula [M(DPA)2Cl2], where M+2 = (Mn, Co, Ni, Cu, Zn, Cd, Hg).
The synthesis of ligands with N2S2 donor sets that include imine, an amide, thioether, thiolate moieties and their metal complexes were achieved. The new Schiff-base ligands; N-(2-((2,4-diphenyl-3-azabicyclo[3.3.1]nonan-9-ylidene)amino)ethyl)-2-((2-mercaptoethyl)thio)-acetamide (H2L1) and N-(2-((2,4-di-p-tolyl-3-azabicyclo[3.3.1]nonan-9-ylidene)amino)ethyl)-2-((2-mercaptoethyl)thio) acetamide (H2L2) were obtained from the reaction of amine precursors with 1,4-dithian-2-one in the presence of triethylamine as a base in the CHCl3 medium. Complexes of the general formula K2<
A new ligand [4-chloro-N-(1,5-dimethyl-3-oxo-2-phenyl-2,3- dihydro-1H-pyrazol-4-ylcarb amothioyl) benzamide] (CAP) was synthesized by reaction of P-ChloroBenzoyl isothio cyanate with 4- aminoantipyrine,The ligand was characterized by micro elemental analysis C.H.N.S.,FT-IR,UV-Vis and1H13CNMR spectra, some transition metals complex of this ligand were prepared and characterized by FT-IR, UV-Vis spectra, conductivity measurements, magnetic susceptibility and atomic absorption. From the obtained results the molecular formula of all prepared complexes were [M(CAP)2(H2O)2]Cl2(M+2 =Mn, Co, Ni, Cu, Zn, Cd and Hg),the proposed geometrical structure for all complexes were octahedral
A new ligand [ 2-chloro-N- (1,5-dimethyl-3-oxo-2-phenyl-2,3-dihydro -1H-pyrazol- 4-ylcarbamothioyl)acetamide](L) was synthesized by reacting the Chloro acetyl isothiocyanate with 4-aminoantipyrine,The ligand was characterized by(C HNS) elemental microanalysis and the spectral measurements including Uv-Vis ,IR ,1H and13C NMR spectra, some transition metals complex of this ligand were prepared and characterized by Uv-Vis, FT-IR spectra, conductivity measurements, magnetic susceptibility and atomic absorption. From the obtained results the molecular formula of all prepared complexes were [M(L)2(H2O)2]Cl2 (M+2 =Mn, Co, Ni, Cu, Zn, Cd and Hg),the proposed geometrical structure for all complexes were octahedral.
Experimental densities, viscosities η, and refractive indices nD data of the ternary ethanol+ n-hexane + 3-methyl pentane system have been determined at temperatures 293.15,303.15 and 313.15 K and at atmospheric pressure then these properties were calculated theoretically by using mixing rules for densities, viscosities and refractive indices .After that the theoretical data and the experimental data were compared due to the high relative errors in viscosities an equation of viscosity was proposed to decrease the relative errors.
Background: Diabetes mellitus is a major risk factor for chronic periodontitis (CP) and hyperglycemia has an important role in the enhancement of the severity of the periodontitis. It has been reported that the progression of CP causes shifting of the balance between bone formation and resorption toward osteoclastic resorption, and this will lead to the release of collagenous bone breakdown products into the local tissues and the systemic circulation. Cross-linked N-telopeptide of type I collagen (NTx) is the amino-terminal peptides of type I collagen which is released during the process of bone resorption. This study was conducted to determine the effects of nonsurgical periodontal therapy on serum level of NTx in type 2 diabetic patients
... Show MoreOriganum majorana (Majorana hortensis), an evergreen herbaceous plant belonging to the Lamiaceae family, has been well known for being used for gastrointestinal, cardiac, respiratory, rheumatologic and many other illnesses, but in wounds management hasn’t been qualified scientifically yet. The goal of the study was to evaluate the wound healing properties of sterols in n-hexane and phenols in ethyl acetate extract fractions of the Iraqi Origanum majorana L aerial parts by contrasting their wound healing abilities with those of commercially available MEBO ointment in a rat excised wound repair model. At various periods, the size of the wounds was measured and skin tissue samples were taken for histopathology. When compared to positive and
... Show MoreA (k,n)-arc is a set of k points of PG(2,q) for some n, but not n + 1 of them, are collinear. A (k,n)-arc is complete if it is not contained in a (k + 1,n)-arc. In this paper we construct complete (kn,n)-arcs in PG(2,5), n = 2,3,4,5, by geometric method, with the related blocking sets and projective codes.