In this paper the centralizing and commuting concerning skew left -derivations and skew left -derivations associated with antiautomorphism on prime and semiprime rings were studied and  the commutativity of Lie ideal under certain conditions were proved.

Low conversion copolymerization of N-vinyl-2-pyrrolidon M.W = (111.14) VP (monomer-1) has been conducted with acrylic acid AA and methymethacrylate MMA in ethanol at 70ºC , using Benzoyl peroxide BPO as initiator . The copolymer composition has been determined by elemental analysis. The monomer reactivity ratios have been calculated by the Kelen-Tudos and Finman-Ross graphical procedures . The derived reactivity ratios (r1 , r2 ) are : (0.51 , 4.85) for (VP / AA ) systems and (0.34 , 7.58) for (VP , MMA) systems , and found the reactivity ratios of the monomer AA , MMA is mor than the monomer VP in the copolymerization of (VP / AA) and (VP /MMA) systems respectly . The reactivity ratios values were used for microstructures calculation.

The acidity of spent lubricant was treated using sodium hydroxide solution. The effect of three variables on the treatment have been studied . These are mixing time rangingfrom 5-35 minutes, NaOH to lubricant weight ratio ranging from  0.25-1.25 and weight percentage  of NaOH ranging from  2-6 % .

The experimental design of Box-Wilson method is adopted to find a useful relationship between the three controllable variables and the lowering in the acidity of the spent lubricant. Then the effective variables and interactions are identified using the statistical analysis(F-test) of  three variable fractional design. The mathematical model is well represented  by a second order polynomial.

By

The research demonstrates new species of the games by applying separation axioms via  sets, where the relationships between the various species that were specified and the strategy of winning and losing to any one of the players, and their relationship with the concepts of separation axioms via  sets have been studied.

The study aimed to determine of some Optimum conditions for bioremediation and removing of seven mineral elements included hexavalent chromium, nickel, cobalt, cadmium, lead, iron and copper as either alone or in group by living and heat treated cells of baker’s yeast Saccharomyces cerevisiae. The dried baker's yeast from Aldnaamaya China Company was used in this study. Biochemical tests was used to ensure yeast belonging to S. cerevisiae and then used to remove the mentioned mineral elementes under different conditions which included incubation period, pH, and temperature. It was found that the best of these conditions was 60 minutes for duration of incubation, 6 for pH, 25 ᵒC for temperature. During the study the behavior of living

Novel derivatives of 1-(´1, ´3, ´4, ´6-tetra benzoyl-β-D-fructofuranosyl)-1H- benzotriazole and 1-(´1, ´3, ´4, ´6-tetra benzoyl-β-D-fructofuranosyl)-1H- benzotriazole carrying Schiff bases moiety were synthesised and fully characterised. The protection of D- fructose using benzoyl chloride was synthesized, followed by nucleophilic addition/elimination between benzotria- zole and chloroacetyl chloride to give 1-(1- chloroacetyl)- 1H-benzotriazole. The next step was condensation reaction of protected fructose and 1-(1-chloroacetyl)-1H- benzotriazole producing a new nucleoside analogue. The novel nucleoside analogues underwent a second conden- sation reaction with different aromatic and aliphatic amines to provide new Schiff b

The cross section evaluation for (α,n) reaction was calculated according to the available International Atomic Energy Agency (IAEA) and other experimental published data . These cross section are the most recent data , while the well known international libraries like ENDF , JENDL , JEFF , etc. We considered an energy range from threshold to 25 M eV in interval (1 MeV). The average weighted cross sections for all available experimental and theoretical(JENDL) data and for all the considered isotopes was calculated . The cross section of the element is then calculated according to the cross sections of the isotopes of that element taking into account their abundance . A mathematical representative equation for each of the element