Electronic properties such as density of state, energy gap, HOMO (the highest occupied molecular orbital) level, LUMO (the lowest unoccupied molecular orbital) level and density of bonds, as well as spectroscopic properties like infrared (IR), Raman scattering, force constant, and reduced masses for coronene C₂₄, reduced graphene oxide (rGO) C₂₄O₅and interaction between C₂₄O₅and NO₂gas molecules were investigated. Density functional theory (DFT) with the exchange hybrid function B3LYP with 6-311G** basis sets through the Gaussian 09 W software program was used to do these calculations. Gaussian view 05 was em

الوصف New complexes of Cu (ll), Ni (II)„Co (II), and Zn (ll) with 2-amino-5-p-Flouro Phenyl 1, 3, 4-Thiadiazole have been synthesized. The products were isolated, studied and characterized by physical measurements, ie,(FT-IR)„UV-Vis and the melting points were determined. The new Schiff base (L) has been used to prepare some complexes. The prepared complexes were identified and their structural geometry were suggested

A new ligand ( 4- methoxy benzoyl ) carbamothioyl ) Glycine (MCG) is synthesized by reaction of (4- methoxy benzoyl isothiocyanate) with Glycine(1:1). It is characterized by micro elemental analysis (C.H.N.S.), FT-IR, (UV-Vis) and 1H and 13CNMR spectra. Some metals ions complexes of this ligand were prepared and characterized byFT-IR,UV-Visible spectra, conductivity measurements, magnetic susceptibility and atomic absorption. From results obtained, the following formula [M(MCG)2] where M2+ = Mn, Co, Ni, Cu, Zn, , Cd and Hg, the proposed molecular structure for these complexes as tetrahedral geometry, except copper complex is has square planer geometry.

A new ligand [N-(3-acetylphenylcarbamothioyl)-4-methoxybenzamide](MAA) was synthesized by reaction of 4-methoxybenzoylisothiocyanate with 3-aminoacetophenone,The ligand was characterized by elemental microanalysis C.H.N.S, FT-IR, UV-Vis and 1H,13CNMR spectra, some transition metals complexes of this ligand were prepared and characterized by FT-IR, UV-Vis spectra, conductivity measurements, magnetic susceptibility and atomic absorption, From obtained results the molecular formula of all prepared complexes were [M(MAA)2(H2O)2]Cl2 (M+2 =Mn, Co, Ni, Cu, Zn, Cd and Hg),the proposed geometrical structure for all complexes were octahedral

The necessary optimality conditions with Lagrange multipliers  are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time  and the final state  are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.