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.

Complexes of (Co2+, Ni2+, Cu2+, Zn2+, Cd2+ and Hg2+) with the ligand Ethyl cyano (2-methyl carboxylate phenyl azo acetate) (ECA) have been prepared and characterized by FTIR, (UV-Visible), Atomic absorption spectroscopy, Molar conductivity measurements and magnetic moments measurements. The following general formula has been suggested for the prepared complexes [M(ECA)2]Cl2 where M = (Co2+, Ni2+, Cu2+ ,Zn2+, Cd2+, Hg2+) and the geometry is octahedral.

compound [1] was formed from the reaction of benzoin and benzaldehyde in the presence of ammonia, which was reacted with sodium hydride in DMF to obtain imidazole salt. This salt was reacted with adipoyl chloride to give compound [2]. Acid hydrazide derivative [3] was obtained from the reaction of compound [2] with hydrazine hydrate. After that Shiff bases [4-9] have been synthesized from the reaction of compound [3] with different aromatic aldehydes. These new formed compounds were diagnosed by 13C-NMR, 1H-NMR for some of them (in Ahl-Albate University in Jordan) and FT-IR spectroscopy (In Baghdad University). All of the prepared products have been studied their biological activities toward two kinds of bacteria. These products show

    Heat exchanger is an important device in the industry for cooling or heating process. To increase the efficiency of heat exchanger, nanofluids are used to enhance the convective heat . transfer relative to the base fluid. - Al2O3/water nanofluid is used as cold stream in the shell and double concentric tube heat exchanger counter current to the hot stream basis oil. These nanoparticles were of particle size of 40 nm and it was mixed with a base fluid (water) at volume
concentrations of 0.002% and 0.004%. The results showed that each of Nusselt number and overall heat transfer coefficient increased as nanofluid concentrations increased. The pressure drop of nanofluid increased slightly than the base fluid because

Nonsteroidal anti-inflammatory drugs (NSAIDs) are drugs that help reduce inflammation, which often helps to relieve pain. In this research new ibuprofen oxothiazolidnone derivatives were synthesized from the reaction of Schiff base derivatives of Ibuprofen with mercapto acetic acid VI a-c, to improve the potency and to decrease the drug's potential side effects, a new series of 4-thiazolidinone derivatives of ibuprofen was synthesized VI a-c . The characterizations of the compounds were identified by using FTIR, 1HNMR technique and by measuring the physical properties.

Mixed ligand metal complexes are synthesized from oxalic acid with Schiff base, and the Schiff base was obtained from trimethoprim and acetylacetone. The synthesized complexes were of the type [M(L1)(L2)], where the metal, M, is Ni(II), Cu(II), Cr(III), and Zn(II), L1 corresponds to the trimethoprim ((Z)-4-((4-amino-5-(3,4,5-trimethoxybenzyl)pyrimidine-2-yl)imino)pentane-2-one) as the first ligand and L2 represent the oxalate anion ( ) as a second ligand. Characterization of the prepared compounds was performed by elemental analysis, molar conductivity, magnetic measurements, 1H-NMR, 13C-NMR, FT-IR, and Ultraviolet-visible (UV-Vis) spectral studies. The recorded infrared data is reinforced with density functional theory (DFT) calcul

Mixed ligand metal complexes are synthesized from oxalic acid with Schiff base, and the Schiff base was obtained from trimethoprim and acetylacetone. The synthesized complexes were of the type [M(L1)(L2)], where the metal, M, is Ni(II), Cu(II), Cr(III), and Zn(II), L1 corresponds to the trimethoprim ((Z)-4-((4-amino-5-(3,4,5- trimethoxybenzyl)pyrimidine-2-yl)imino)pentane-2-one) as the first ligand and L2 represent the oxalate anion (𝐶􀬶𝑂􀬶 􀬶􀬿) as a second ligand. Characterization of the prepared compounds was performed by elemental analysis, molar conductivity, magnetic measurements, 1H-NMR, 13C-NMR, FT-IR, and Ultraviolet-visible (UV-Vis) spectral studies. The recorded infrared data is reinforced with density functional th

Introduction. Chemotherapy with Cabazitaxel (CBZ) is a typical first-line treatment option for naïive castration-resistant prostate cancer resistant to docetaxel. On the other hand, Cabazitaxel's therapeutic success is constrained by chemoresistance and side effects.

Aim. To assess whether 6 alpha-ethylchenodeoxycholic acid (6-ECDCA), a selective agonist for bile acid receptors will enhance the efficacy of CBZ in androgen-independent prostate cancer cells.

Materials and methods. The 3-(4,5-Dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) viability assay was used to assess the cytotoxicity of 6-ECDCA and CBZ medicines or t