A complexified adjoint representations of the complexification Lie algebras associated with the special orthogonal group SO(3) and special linear group SL(2,₵)  have been obtained. A new representation of their tensor product is naturally arisen and computed in details.

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.

In this work, some of new 2-benzylidenehydrazinecarbothioamide derivatives have been prepared by condensation of thiosemicarbazide and different substituted aromatic benzaldehydes in presence of glacial acetic acid to give compounds (1-6), these compounds have characterized by its physical properties and spectroscopic methods. This work also included theoretical study to prove the ability of these compounds as corrosion inhibitors; The program package of Gaussian 09W with its graphical user interface GaussView 5.0 had used for this purpose; the methods of Density Functional Theory (DFT) with basis set of 6-311G (d,p) / hybrid function of B3LYP and semiempirical method of PM3 have been used, the study included theoretical simulation

In this work, some of new 2-benzylidenehydrazinecarbothioamide derivatives
have been prepared by condensation of thiosemicarbazide and different substituted
aromatic benzaldehydes in presence of glacial acetic acid to give compounds (1-6),
these compounds have characterized by its physical properties and spectroscopic
methods. This work also included theoretical study to prove the ability of these
compounds as corrosion inhibitors; The program package of Gaussian 09W with its
graphical user interface GaussView 5.0 had used for this purpose; the methods of
Density Functional Theory (DFT) with basis set of 6-311G (d,p) / hybrid function of
B3LYP and semiempirical method of PM3 have been used, the study included
t

In the partition theory, there is more then one form of representation of dedication, most notably the Abacus diagram, which gives an accurate and specific description. In the year 2019, Mahmood and Mahmood presented the idea of merging more than two plans, and then the following question was raised: Is the process of separating any somewhat large diagram into smaller schemes possible? The general formula to split e-abacus diagram into two or more equal or unequal parts was achieved in this study now.

3-(4-hydroxyphenyl)-2-(3-(4-nitrobenzoyl) thioureido) propanoic acid (HNP) a new ligand was synthesized by reaction of Tyrosine with (4-Nitrobenzoyl isothiocyanate) by using acetone as a solvent. The prepared ligand (HNP) has been characterized by elemental analysis (CHNS), infrared (FT-IR), electronic spectral (Ultraviolet visible) and(1H,13C-Nuclear Magnetic Resonance) spectra. Some Divalent metal ion complexes of (HNP) were prepared and spectroscopic studies by Fourier transform infrared (FTIR), electronic spectral(UV-Vis), molar conductance, magnetic susceptibility and atomic absorption. The results measured showed the formula of six prepared complexes were [M (HNP)2] (M+2 = Manganese, Cobalt, Nickel, Znic, Cadmium and Mercury),from the

Viscosities (η) and densities (ρ) of atenolol and propranolol hydrochloride in water and in concentrations (0.05 M) and (0.1 M) aqueous solution of threonine have been used to reform different important thermodynamic parameters like apparent molal volumes fv partial molal volumes at infinite dilution fvo , transfer volume fvo (tr), the slop Sv , Gibbs free energy of activation for viscous flow of solution ΔG*1,2 and the B-coefficient have been calculated using Jones-Dole equation. These thermodynamic parameters have been predicted in terms of solute-solute and solute-solvent interaction.

In this research, the preparation of bidentate Schiff base was carried out via the condensation reaction of both the salicylaldehyde with 1-phenyl-2,3-dimethyl-4-amino-5-oxo-pyrazole to form the ligand (L). The mentioned ligand was used to prepare complexes with transition metal ions Mn(II), Co(II), Ni(II), Cu(II) and Zn(II). The resulting complexes were separated and characterized by FTIR and UV-Vis spectroscopic technique. Elemental analysis for Carbon, Hydrogen and Nitrogen elements, electronic spectra of the ligand and complexes were obtained, and the magnetic susceptibility tests were also achieved to measure the dipole moments. The molar conductivities were also measured and determination of chlorine content in the complexes and

       Our work included a synthesis of three new imine derivatives—1,3-thiazinan-4-one, 1,3-oxazinan-6-one and 1,3-oxazepin-4,7-dione—which contained an adamantyl fragment. These were produced via the condensation of the Schiff`s base (E)-N-(adamantan-1-yl)-1-(3-aryl)methanimine with 3-mercaptopropanoic acid; 3-chloropropanoic acid; and maleic, citraconic anhydride, respectively. These new imines were prepared via the condensation of adamantan-1-ylamine and 3-nitro-, 3-bromobenzaldehyde in n-BuOH. We obtained a good yield of products. FTIR, ¹H NMR spectroscopy and C.H.N.S analysis were used to diagnostic the products. The molecular structure of (E)-N-(adamantan-1-yl