For a nonempty subset X of a group G and a positive integer m , the product of X , denoted by Xm ,is the set Xm = That is , Xm is the subset of G formed by considering all possible ordered products of m elements form X. In the symmetric group Sn, the class Cn (n odd positive integer) split into two conjugacy classes in An denoted Cn+ and Cn- . C+ and C- were used for these two parts of Cn. This work we prove that for some odd n ,the class C of 5- cycle in Sn has the property that = An n 7 and C+ has the property that each element of C+ is conjugate to its inverse, the square of each element of it is the element of C-, these results were used to prove that C+ C- = An exceptional of I (I the identity conjugacy class), when n=5+4k , k>=0.
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... Show MoreBackground: The association between facial types and dental arches forms has considerable implications in orthodontic diagnosis and treatment planning. The aim was to establish the maxillary and mandibular dental arches width and length in skeletal and dental class II division 1 and class III malocclusion groups, find out the most frequent dental arch form and facial type and the association between them and to check the gender differences. Materials and Methods: Frontal and lateral facial photographs and maxillary and mandibular occlussal photographs for 90 iraqi subjects with age 18-25 years old (45 males and 45 females) divided equally into three groups, the 1st group with class II division 1malocclusion (overjet more than 3mm but less t
... Show MoreNew Schiff base ligand (E)-6-(2-(4-(dimethylamino)benzylideneamino)-2-(4-hydroxyphenyl)acetamido)-3,3- dimethyl-7-oxo-4-thia-1- azabicyclo[3.2.0]heptane-2-carboxylic acid = (HL) was synthesized via condensation of Amoxicillin and 4(dimethylamino)benzaldehyde in methanol. Figure -1 Polydentate mixed ligand complexes were obtained from 1:1:2 molar ratio reactions with metal ions and HL, 2NA on reaction with MCl2 .nH2O salt yields complexes corresponding to the formulas [M(L)(NA)2Cl],where M=Fe(II),Co(II),Ni(II),Cu(II),and Zn(II), A=nicotinamide .
Eight different Dichloro(bis{2-[1-(4-R-phenyl)-1H-1,2,3-triazol-4-yl-κN3]pyridine-κN})iron(II) compounds, 2–9, have been synthesised and characterised, where group R=CH3 (L2), OCH3 (L3), COOH (L4), F (L5), Cl (L6), CN (L7), H (L8) and CF3 (L9). The single crystal X-ray structure was determined for the L3 which was complemented with Density Functional Theory calculations for all complexes. The structure exhibits a distorted octahedral geometry, with the two triazole ligands coordinated to the iron centre positioned in the equatorial plane and the two chloro atoms in the axial positions. The values of the FeII/III redox couple, observed at ca. −0.3 V versus Fc/ Fc+ for complexes 2–9, varied over a very small potential range of 0.05 V.
... Show MoreIt reflects the gross domestic product in any country total output of goods and services by the size of the country's citizens and foreign residents during the period of the year and reflect the contribution of the commodity sectors of the economy and the distribution and service in the composition of output. And gross domestic product in Iraq as an indicator dominated in the composition of oil output, along with the contribution of the service sector, as the gross domestic product is the output of a yield lien and subjected GDP in Iraq to a series of declines succession due to vibrations of the oil market during the economic blockade on the one hand and stop imported production inputs, lack of arriving in commodity s
... Show MoreThis paper focuses on developing a self-starting numerical approach that can be used for direct integration of higher-order initial value problems of Ordinary Differential Equations. The method is derived from power series approximation with the resulting equations discretized at the selected grid and off-grid points. The method is applied in a block-by-block approach as a numerical integrator of higher-order initial value problems. The basic properties of the block method are investigated to authenticate its performance and then implemented with some tested experiments to validate the accuracy and convergence of the method.
Innovative various Schiff bases and their Co(II), Ni(II) and Cu(II) and Hg(II) compounds made by the condensation of 4-amino antipyrine with derived aminobenzoic acid (2-aminobenzoic acid, 3-aminobenzoic acid, and 4-aminobenzoic acid ) have been prepared by conventional approaches. These complexes were described by magnetic sensibility analysis, FT-IR spectra, and molar-conductance and elemental analysis. Analytical values appeared which the mixed-ligand complexes presented ratio about 2:1 (ligand: metal) with the chelation 4 or 6. The prepared compounds offered a good effect on the organisms; bacteria Staphylococcus-aurous, Escherichia-coli and fungi C. albicans, A. niger. Also, the biological products signalize which the mixed compl
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