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.

The aim of this research is to prepare a set of complexes with the general formula [M(HMB)n] , where M=VO (II) , Cr(III) and Cu(II) while  n=2,3,2 respectively resulting from the reaction of anew ligand [N'-(2-hydroxy-3-methoxybenzyl)-4-methylbenzohydrazide] (HMB) derived from the reaction of the tow substances (4-methylbenzohydrazide  and 2-hydroxy-3-methoxy benzaldehyde) with metal ions. The prepared compounds were identified by several spectroscopic methods such as Infrared, Nuclear Magnetic Resonance and Electronic Spectra. From the results of the measurements, it was suggested that the prepared complexes have different geometries such as square planar (Cu), square pyramidal (VO) and octahedral (Cr). DFT simulations backed up

In the present study, a novel ligand (L) made of 2-hydroxynaphthaldehyde and 3-hydrazone-1,3-dihydro-indole-2-one(3-[(3-hydroxynaphthalen-2-yl-ethylidene)-hydrazono]-1,3-dihydro-indol-2-one). The ligand was characterized by FTIR, UV-vis, mass, 1H-NMR, 13C-NMR, and CHN elemental analysis. New complexes of this ligand were created by treating methanol and a drop of DMF solution of the produced ligand with the hydrated metal salts of Mn(II), Co(II), Ni(II), Cu(II), and Zn(II) in a molar ratio of 2:1 (L:M). As a result, complexes have been emerged and identified FTIR, UV-vis, C.H.N., chloride-containing, molar conductance, magnetic susceptibility, and atomic absorption. The characterization result for each complex indicated complexes wi

Objective: Evaluation of the poly ether keton keton polymer (PEKK) coating material on the commercial pure titanium disks (CP Ti) with or without laser surface structuring. Design: In vitro experimental study of PEKK polymer coated material on the CP Ti disks with or without laser surface structuring. Materials and methods: coating the surface of the commercial pure titanium (CP Ti) disks with PEKK polymer was performed via using frictional mode CO2 laser, then the samples disks analyzed by using FESEM. Results: the FESEM reveal good adherence and distribution of the PEKK coated material over the CP Ti substrate by using the frictional mode CO2 laser at 2 watt and 6 ms pulse duration. Conclusion: the frictional mode CO2 laser considered an

Abstract:

Background: Retinol binding protein 4 (RBP4), an adipokine that participate in a lipid metabolism or insulin resistance through a complex regulatory network. Recently, RBP4 was reported to be associated with many cardiovascular diseases (CVDs) risk factors in patients of type 2 diabetes mellitus (T2DM). This study aims to study the correlation of  serum RBP4 with some markers of glycemic control, dyslipidemia, hypertension and obesity in T2DM Iraqi patients.

Subjects and Methods: one hundred fifty participants were enrolled in this coss-sectional study, 120 of participants were T2DM patients and 30 were apparently healthy individuals to serve as control gro