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 magnetic properties of a pure Nickel metal and Nickel-Zinc-Manganese ferrites having the chemical formula Ni_0.1(Zn_0.4Mn_0.6)_0.9Fe₂O₄ were studied. The phase formation and crystal structure was studied by using x-ray diffraction which confirmed the formation of pure single spinel cubic phase with space group (Fd3m) in the ferrite. The samples microstructure was studied with scanning electron microstructure and EDX. The magnetic properties of the ferrite and nickel metal were characterized by using a laboratory setup with a magnetic field in the range from 0-500 G. The ferrite showed perfect soft spinel phase behavior while the nickel sample showed higher magnetic loss an

The paper discusses the structural and optical properties of In 2 O 3 and In 2 O 3-SnO 2 gas sensor thin films were deposited on glass and silicon substrates and grown by irradiation of assistant microwave on seeded layer nucleated using spin coating technique. The X-ray diffraction revealed a polycrystalline nature of the cubic structure. Atomic Force Microscopy (AFM) used for morphology analysis that shown the grain size of the prepared thin film is less than 100 nm, surface roughness and root mean square for In 2 O 3 where increased after loading SnO 2 , this addition is a challenge in gas sensing application. Sensitivity of In 2 O 3 thin film against NO 2 toxic gas is 35% at 300 o C. Sensing properties were improved after adding Tin Oxi

Introduction: Implant stability is usually measured with resonance frequency analysis (RFA) and damping capacity assessment (DCA). This study aimed to measure primary and secondary stabilities using 3 devices that are based on these methods, namely; RFA (Osstell^®) and DCA (Periotest^® and AnyCheck^®) to assess the correlations of the measurements obtained by these devices and the correlations between implant stability and insertion torque. Material and Methods: This observational prospective study included 35 dental implants. The implant stability was measured using the 3 devices. Mann–Whitney U

A new optoelectronic flow injection method is proposed for the determination of ferrous ions (Fe ²⁺ ) based on thiocyanate complexation to form a deep-red FeSCN ²⁺ complex.

Thin films of GexS1-x were fabricated by thermal evaporating under vacuum of 10-5Toor on glass substrate. The effect of increasing of germanium content (x) in sulfide films on the electrical properties like d.c conductivity (σDC), concentration of charge carriers (nH) and the activation energy (Ea) and Hall effect were investigated. The measurements show that (Ea) increases with the increasing of germanium content from 0.1to0.2 while it get to reduces with further addition, while charge carrier density (nH) is found to decrease and increase respectively with germanium content. The results were explained in terms of creating and eliminating of states in the band gap

Thin films of ZnSxSe1-x with different sulfide content(x)
(0, 0.02, 0.04, 0.06, 0.8, and 0.1), thickness (t) (0.3, 0.5, and 0.7 μm) and annealing temperature (Ta) (R.T 373 and 423K) were fabricated by thermal evaporating under vacuum of 10-5 Toor on glass substrate. The results show that the increasing of sulfide content (x)and annealing temperature lead to decrease the d.c conductivity σDC of and concentration of charge carriers (nH) but increases the activation energy (Ea1,Ea2), while the increasing of t increases σDC and nH but decrease (Ea1,Ea2). The results were explained in different terms

Fe3O4:Ce thin films were deposited on glass and Si substrates by Pulse Laser Deposition Technique (PLD). Polycrystalline nature of the cubic structure with the preferred orientation of (311) are proved by X-ray diffraction. The nano size of the prepared films are revealed by SEM measurement. Undoped Iron oxide and doped with different concentration of Ce films have direct allowed transition band gap with 2.15±0.1 eV which is confirmed by PL Photoluminescence measurements. The PL spectra consist of the emission band located at two sets of peaks, set (A) at 579±2 nm , and set (B) at 650 nm, respectively when it is excited at an excitation wavelength of 280 nm at room temperature. I-V characteristics have been studied in the dark and under v