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 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

Infertility is one of the types of diseases that occur in the reproductive system. Obesity is a state that can be occurred due to excessive fats, the progression in obesity stage results in a change in adipose tissue and the development of chronic inflammation, endocrine glands disorders and women’s reproductive system, and also increase the infection with covid-19. The study aimed to investigate the effect of the obesity, lipid-profile, and IL-6 on hormones-dysregulation in infertile-women with COVID-19 complications. The current study included 70 samples: 50 infertility-women-with-covid-19-infected, 20 healthy-women/control, the ages of both patients and healthy subjects were selected within the range 18-34 years. Levels of FBS, LH,

Two different composite materials were prepared by stir casting method of AA 6061 alloy as a matrix reinforced with two addition different ceramic materials Al₂O₃ and B₄C of grain size   20 µm by 2.5, 5, 7.5 and10% in weight. The composite material with aluminum alloy as a matrix possesses a unique mechanical properties such as: high specific strength and hardness, low density, and high resistance to corrosion and friction wear. This composite is widely used in automotive parts space and marine applications.

Pin-on-disc technique was used to calculate the wear rate for each addition of Al₂O₃ and B₄C particles. Rockwell hardness test and

Forty five wound specimens were collected from patients suffering from wound infections and taken from various hospitals in Ibb city, Yemen. The study was to determine synergic antibacterial activity of between mountain honey and Argemone mexicana plant. Isolation, identification of bacterial isolates and antibiotic sensitivity test were done. Agar-disc and agar-well diffusion method were carried to determine antibacterial activity of honey, Argemone mexicana plant and a mixture of them against bacterial isolates. Out of 45 specimens, 29 (64.4%) gave positive cultures. Staphylococcus aureus was the predominant bacterial pathogens with percentage (72.4%) followed by Pseudomonas aeruginosa (17.2%) and Staphylococcus epidermidis (10.4%).

Wellbore stability is considered as one of the most challenges during drilling wells due to the
reactivity of shale with drilling fluids. During drilling wells in North Rumaila, Tanuma shale is
represented as one of the most abnormal formations. Sloughing, caving, and cementing problems
as a result of the drilling fluid interaction with the formation are considered as the most important
problem during drilling wells. In this study, an attempt to solve this problem was done, by
improving the shale stability by adding additives to the drilling fluid. Water-based mud (WBM)
and polymer mud were used with different additives. Three concentrations 0.5, 1, 5 and 10 wt. %
for five types of additives (CaCl2, NaCl, Na2S

In this research, rabbit femurs were implanted with CP Ti screws coated with a combination of CaCO₃ and nanohydroxyapatite, and the effect on osseointegration was assessed using histological and histomorphometric examination at 2 and 6 weeks. CaCO₃ and nanohydroxyapatite were combined with the EPD to coat the surfaces of the CP Ti screws. The femurs of five male rabbits were implanted with coated and uncoated implant screws. Healing time was divided into two groups (2 and 6 weeks). After 2 and 6 weeks of implantation, the histological examination revealed an increase in the growth of bone cells for coated screws, and the histomorphometric analysis revealed an increase in the percentage of ne

The presented work shows a preliminary analytic method for estimation of load and pressure distributions on low speed wings with flow separation and wake rollup phenomena’s. A higher order vortex panel method is coupled with the numerical lifting line theory by means of iterative procedure including models of separation and wake rollup. The computer programs are written in FORTRAN which are stable and efficient.

      The capability of the present method is investigated through a number of test cases with different types of wing sections (NACA 0012 and GA(W)-1) for different aspect ratios and angles of attack, the results include the lift and drag curves, lift and pressure distributions along the wing s

This paper investigates the effect of magnetohydrodynamic (MHD) of an incompressible generalized burgers’ fluid including a gradient constant pressure and an exponentially accelerate plate where no slip hypothesis between the burgers’ fluid and an exponential plate is no longer valid. The constitutive relationship can establish of the fluid model process by fractional calculus, by using Laplace and Finite Fourier sine transforms. We obtain a solution for shear stress and velocity distribution. Furthermore, 3D figures are drawn to exhibit the effect of magneto hydrodynamic and different parameters for the velocity distribution.