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 potential use of zinc oxide and other metal oxide nanoparticles in biomedical are gaining interest in the scientific and medical communities, largely due to the physical and chemical properties of these nanomaterials. The present work revealed the effect of zinc oxide nanoparticles (ZnONPs) on the total salivary peroxidase enzyme activity of human saliva in comparison to de-ionized water. Materials and methods: Forty eight unstimulated saliva samples were collected from dental students/University of Baghdad 18-22 years. Then measure the total salivary peroxidase activity first without any addition to human saliva as a control, second with dilution the saliva with de-ionized water, and third with zinc oxide nanoparticles in c

We have studied the effect of applying an external magnetic field on the characteristics of iron oxide (IO) nanoparticles (NPs) synthesized by pulsed laser ablation in dimethylformamide (DMF). The NPs synthesized with and without applying of magnetic field were characterized by Fourier transformation infrared spectroscopy (FT-IR), UV–Vis absorption, scanning electron microscope (SEM), atomic force microscope (AFM), and X-ray diffraction (XRD). SEM results confirmed that the particle size was decreased after applying magnetic field.

This study including synthesis of some new Schiff bases compounds [1‐6] from the reaction of Sulfamethoxazole drug with some aromatic aldehydes in classical Schiff base method then treatment Schiff  bases with succinic anhydride to get oxazepines rings [7-11]These derivatives were characterized by melting point, FT‐IR, ¹H NMR and mass spectra. Some of synthesized compounds were evaluated in vitro for their antibacterial activities against three kinds of pathogenic strains Staphylococcus aureus, Escherichia coli

In this work, lanthanium (III) complexes were synthesized using by Schiff base ligand (L) derived from benzaldehyde and o-aminoaniline with five amino acids (AA) from glycine (Gly), L-alanine (Ala), L-valine (Val), L-asparagine (Asp) and DL- phenylalanine (Phe). The Schiff base ligand has been characterized by elemental analysis, (MASS, FTIR, 1HNMR, 13CNMR, UV-VIS) electronic spectra. The structures of the new complexes have been described of analysis of elements, molar conductivity, (UV-Vis electronic, FTIR, mass) spectra also magnetic moment. The molar conductivity values of the complexes indicat this every of complexes are electrolytes and other analytical studies reveal octahedral geometry for La (III) ion. The Schiff base ligand, five

A new set of metal complexes by the general formula [M(P)2(H2O)2]Cl2 has been prepared through the interaction of the new Ligand [N1, N4-bis(4-methoxyphenyl)succinamide] (P) derived from succinyl chloride with p-anisidine with the transition metal ions [Cu(II), Mn(II), Cd(II), Co(II) and Ni(II)]. Compounds diagnosed by TGA, 1 H, 13CNMR and Mass spectra (for (P)), Fourier-transform infrared and Electronic spectrum, Magnetic measurement, molar conduct, (%M, %C, %H, %N). These measurements indicate that (P) is associated with the metal ion in a bi-dentate fashion by nitrogen atoms (the amide group), and the octahedral composition of these complexes is suggested. Staphylococcus Aureus (+) and Escherichia Coli (–) were studied for the antibact

The synthesis, characterization and mesomorphic properties of two new series of triazine-core based liquid crystals have been investigated. The amino triazine derivatives were characterized by elemental analysis, Fourier transforms infrared (FTIR), 1HNMR and mass spectroscopy. The liquid crystalline properties of these compounds were examined by differential scanning calorimetry (DSC) and polarizing optical microscopy (POM). DSC and POM confirmed nematic (N) and columnar mesophase textures of the materials. The formation of mesomorphic properties was found to be dependent on the number of methylene unit in alkoxy side chains.

4-[(2-hydroxy-4,6-dimethylphenyl)diazenyl]-1,5-dimethyl-2-phenyl-1H-pyrazol-3(2H)-one has been readied by combination the diazonium salt of 4-aminoantipyrine with 3,5-dimethylphenol. Spectral studies ( FTIR, UV-Vis, 1H and 13CNMR) and microelemental analysis (C.H.N) are use to identified of the ligand. Complexes of some transition metals were performed as well depicted. The formation of complexes were characterized by using atomic absorption of flame, elemental analysis, infrared and UV-Vis spectral process as well conductivity and magnetic quantifications. Nature of compounds produced have been studied followed the mole ratio and continuous contrast methods, Beer's law followed during a concentration scope (1×10-4 - 3×10-4 M/L). height m

The Ligand 2-(4-nitrophenyl azo)-2,4-dimethylphenol derived from 4-nitroaniline and 2,4-dimethylphenol was synthesized. The prepared ligand was identified by FT-IR and UV-Vis spectroscopic techniques. Treatment of the ligand with the following metal ions ( CuII , ZnII ,CdII and HgII) in aqueous ethanol with a 1:2 M:L ratio. Characterization of these compounds has been done on the basis of FT-IR and UV-Vis, as well as magnetic susceptibility and conductivity measurements. On the basis of physicochemical data tetrahedral geometries were assigned for the complexes.

The present work involved preparation of new substituted and unsubstituted and poly imides (1-17) using reaction of acryloyl chloride with different amides (aliphatic ,aromatic) in the presence of a suitable solvent and amount tri ethyl amine (Et3N) with heating – the structure confirmation of all polymers were proved using FT-IR,1H-NMR,C13NMR and UV spectroscopy ,thermal analysis (TG) for some polymers confirmed their thermal stabilities . Other physical properties including softening and melting points, PH and solubility of the polymers were also measured