The purpose of this work is to determine the points and planes of 3-dimensional projective space PG(3,2) over Galois field GF(q), q=2,3 and 5 by designing a computer program.

The investigation of determining solutions for the Diophantine equation  over the Gaussian integer ring for the specific case of  is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.

Background: The isatin molecule is present in many natural substances, including plants and animals, and is used to prepare compounds with various biological activities. Objectives: To synthesize a new series of isatin derivatives with the expectation that they will have antimicrobial activity. Methods: Thiazole Schiff bases were synthesized from various Mannich bases of isatin to evaluate their antimicrobial properties. Initially, Mannich bases (2a–e) were synthesized by reacting isatin with formaldehyde and different secondary amines. Subsequently, they were treated with 2-aminothiazole to yield the final compounds (3a–e). Spectroscopic characterization was done via FT-IR and 1H-NMR. The antimicrobial screening was conducted o

     In this research, new Schiff base is derived from chitosan O-nitrobenzyldehyde and its complexes were synthesized. All compounds were characterized by FT-IR, UV-Visible, TGA, DTA, TG and molar conductivity with melting point. The results showed that Schiff base was coordinated via  nitrogen atom azomethine with the center metal ions Co+2,Ni+2 and Cu+2 behaving monodentate ligand and forming complexes with molecular formula [M(L)Cl2H2O] The tetrahedral geometrical was suggested for all prepared complexes based on the characterization data for all techniques.   +2,Cu+2, Ni+2M = Co   

A new Mannich base ligand was prepared by reacting the 2-chloro.-N-(5-mercapto-1, 3, 4-thiadazol -2-yl) acetamide and Piperidine in the presence (formaldehyde) (L) ligand. A series of ligand complexes were prepared from (L) with the metal ion Co (II), Ni (II), Cu (II), Pd (II), Pt (IV), and Au (III). Various spectroscopic techniques such as C.H.N.S, FTIR, UV-VIS, , ¹HNMR, ¹³CNMR, Magnetic moment, and molar conductivity successfully characterize the obtained compounds. The M: L ratio was determined using the molar ratio method in solution. All prepared compounds' antibacterial and antifungal activity was studied against two types of bacteria and one type of fungi at a rate of 0.02M. The standard ΔH°

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.

2,2'-(1-(3,4-bis(carboxydichloromethoxy)-5-oxo-2,5-dihydrofuran-2-yl)ethane-1,2-diyl)bis(oxy)bis(2,2-dichloroacetic acid) a derivative of L-ascorbic acid was prepared by reaction of L-ascorbic acid with trichloroacetic acid (1:4) ratio, in the presence of potassium hydroxide. A series of new metal complexes of this ligand were prepared by a reaction with the chlorides of Cd(II), Co(II), Ni(II), Cu(II) and Zn(II). The new ligand and its complexes were identified by C.H.N., IR, UV-visible spectra, Thermogravimetric analysis (TGA), as well as 1H, 13C-NMR and Mass spectra for ligand L. The complexes were also identified by molar conductance, atomic absorption, magnetic susceptibility and X-ray diffraction for Cu (II) complex. FT-IR spectra

Two series of bent core mesogen containing 1,2,4-traizole ring [X]a-e and [XI]a-e were synthesized by many steps starting from esterification of isophthalic acid with methanol to yield diester compound [I] which was converted to their acid hydrazide [II] and the acid hydrazide reacted with ammonium thiocyanate or phenyl isothiocyanate to yield compounds [III] and [IV] , respectively . Then cyclization by 4% NaOH to yielded 1,2,4 traizole-3- thiol compounds [V] and [VI], respectively, afterword adding hydrazine hydrate to yield compounds [VII] and [VIII] .These compounds condensated with different substituted aldehyde to give new Schiff bases[X]a-e and [XI]a-e,respectively. The synthesized compounds were characterized by melting points ,