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.

A progression of Polyaniline (PANI) and Titanium dioxide (TiO₂) nanoparticles (NPs) were prepared by an in-situ polymerization strategy within the sight of TiO₂ NPs. The subsequent nanocomposites were analyzed using Fourier-transform infrared spectra (FTIR), X-ray diffraction (XRD), Scanning Electron Microscopy (SEM), and Energy Dispersive X-Ray Analysis (EDX) taken for the prepared samples. PANI/TiO₂ nanocomposites were prepared by various compound materials (with H₂SO₄ 0.3 M and without it, to compare the outcome of it) by the compound oxidation technique using ammonium persulfate (APS) as oxidant within the sight of ultrafine grade powder of TiO₂ cooled in an ice bath.

Transition metal complexes of Co(II), Ni(II), Cu(II), and Zn(II) with 2-(4-antipyrine azo)-4-nitroaniline derived from 4-aminoantipyrine and 4-nitroaniline were synthesized. Characterization of these compounds has been done on the basis of elemental analysis, electronic data, FT-IR, UV-Vis and 1HNMR, as well as magnetic susceptibility and conductivity measurements. The nature of the complexes formed were studied following the mole ratio and continuous variation methods, Beer's law obeyed over a concentration range (1×10-4 - 3×10-4 M). High molar absorbtivity of the complex solutions were observed. From the analytical data, the stoichiometry of the complexes has been found to be 1:2 (metal:ligand). On the basis of physicochemical data octa

The complexes of the 2-hydroxy-4-Nitro phenyl piperonalidene with metal ions Cr(III), Ni(II), Pt(IV) and Zn(II) were prepared in ethanolic solution. These complexes were characterized by spectroscopic methods, conductivity, metal analyses and magnetic moment measurements. The nature of the complexes formed in ethanolic solution was study following the molar ratio method. From the spectral studies, monomer structures proposed for the nickel (II) and Zinc (II) complexes while dimeric structures for the chromium (III) and platinum (IV) were proposed. Octahedral geometry was suggested for all prepared complexes except zinc (II) has tetrahedral geometry, Structural geometries of these compounds were also suggested in gas phase by using

The formation and structural investigation of three new Mannich bases are reported. The synthesis of these compounds was accomplished via a multicomponent one-pot reaction using CaCl2 as a catalyst. The reaction of the benzaldehyde, m-bromoaniline and cyclohexanone or 4-methylcyclohexanone resulted in the formation of L1 and L3, respectively. The synthesis of L2 was achieved by mixing benzaldehyde, o-bromoaniline and cyclohexanone. The isolated compounds were characterised using a range of analytical and spectroscopic techniques. These include; NMR (1H and 13C-NMR), ESMS, FTIR, electronic spectroscopy, microanalyses and melting points. The NMR data for L1 and L2 indicated the presence of one isomer in solutions, on the NMR time scale. How

This work include synthesized and characterization the compound [I] by reaction 1,4-phenylenediamine with chloro acetic acid then this compound reaction with methanol in present sulfuric acid to synthesized ester compound [II] after that reaction with hydrazine hydrate to synthesized acide hydrazide [III] and the later compound reaction with substituted acetophenone[IV]n to synthesized substituted acetophenone hydrazones[V-XI]. In addition synthesized4-formylpyrazole derivatives [XIIXVIII] via cyclisation substituted acetophenone hydrazones [V-XI] with Vilsmeier-Haack reagent DMF/POCl3. The compounds characterized by melting points, FTIR, 1HNMR and mass spectroscopy. The mesomorphic behavior studied by using polarized optical microscopy and

   This study, which is considered the first of its kind in the world and the Arab homeland, was carried out in the laboratory of mushroom production belonging to the Medicinal Plant Unit/ College Of Agricultural Engineering Sciences/ University of  Baghdad during the period from July 21, 2016, to December 30, 2018, aiming to isolate and purify the mycelium of the wild isolation in addition to the genetic and morphological identification of the mushroom Agaricus bellaniae. The obtained pure isolation was tagged in the American National Center for Biotechnology Information (NCBI) with symbol MF987843.1, thus Iraq would be the second country in the world in which the mushroom is grown following the United States of America. The

The non static chain is always the problem of static analysis so that explained some of theoretical work, the properties of statistical regression analysis to lose when using strings in statistic and gives the slope of an imaginary relation under consideration.  chain is not static can become static by adding variable time to the multivariate analysis the factors to remove the general trend as well as variable placebo seasons to remove the effect of seasonal .convert the data to form exponential or logarithmic , in addition to using the difference repeated d is said in this case it integrated class d. Where the research contained in the theoretical side in parts in the first part the research methodology ha