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 study was extraction of jojoba oil using different solvents. A mixture of waterhexane and water-ethanol are used as solvents to extract jojoba oil in a batch extraction process and compared with a pure solvent extraction process. The effects of particle size of crushed seeds, solvent-to-water ratio and time on jojoba oil extraction were investigated. The best recovery of oil was obtained at the boiling temperature of the solvent and four hour of extraction time. When seed particle size was 0.45 mm and a pure ethanol was used (45% yield of oil extraction), whereas, it was 40% yield of oil at 25% water-hexane mixture. It was revealed that the water-ethanol and water-hexane mixtures have an effect on the oil extraction yield. T

Prostheses are used as an alternative to organs lost from the body. Flex-Foot Cheetah is considered one of the lower limb prostheses used in high-intensity activities such as running. This research focused on testing two samples of Flex-Foot Cheetah manufactured of two various materials (carbon, glass) with polyester and compare between them to find the foot with the best performance in running on the level of professional athlete. In the numerical analysis, the maximum principal stress, maximum principal elastic strain, strain energy; finally, the blade total deformation were calculated for both feet. In experimental work, the load-deflection test was done for foot to calculate the bending the results were very close to

     The process of stocks evaluating considered as a one of challenges for the financial analysis, since the evaluating focuses on define the current value for the cash flows which the shareholders expected to have. Due to the importance of this subject, the current research aims to choose Fama & French five factors Model to evaluate the common stocks to define the Model accuracy in Fama& French for 2014. It has been used factors of volume, book value to market value, Profitability and investment, in addition to Beta coefficient which used in capital assets pricing Model as a scale for Fama & French five factors Model. The research sample included 11 banks listed in Iraq stock market which have me

The wear behavior of alumina particulate reinforced A332 aluminium alloy composites produced by a stir casting process technique were investigated. A pin-on-disc type apparatus was employed for determining the sliding wear rate in composite samples at different grain size (1 µm, 12µm, 50 nm) and different weight percentage (0.05-0.1-0.5-1) wt% of alumina respectively. Mechanical properties characterization which strongly depends on microstructure properties of reinforcement revealed that the presence of ( nano , micro) alumina particulates lead to simultaneous increase in hardness, ultimate tensile stress (UTS), wear resistances. The results revealed that UTS, Hardness, Wear resistances increases with the increase in the percentage of

This investigation was undertaken to evaluate the effectiveness of using Hydrated lime as a (partial substitute) by weight of filler (lime stone powder) with five consecutive percentage namely (1.0, 1.5, 2.0, 2.5, 3.0) % by means of aggregate treatment, by introducing dry lime on dry and 2–3% Saturated surface aggregate on both wearing and binder coarse. Marshall design method, indirect tensile test and permanent deformation under repeated loading of Pneumatic repeated load system at full range of temperature (20, 40, 60) C0 were examined The study revealed that the use of 2.0% and 1.5 % of dry and wet replacement extend the pavement characteristics by improving the Marshall properties and increasing the TSR%. Finally, increase permanent

This study is an approach to assign the land area of  Kirkuk city [ a city located in the northern of Iraq, 236 kilometers north of  Baghdad  and 83 kilometers  south of  Erbil [ Climatic atlas of  Iraq, 1941-1970  ]  into different  multi zones by using Satellite image and Arc Map10.3,  zones of different traffic noise pollutions. Land zonings process like what achieved in this paper will help and of it’s of a high interest point for the future of Kirkuk city especially urban

Now-a-days the Flexible AC Transmission Systems (FACTS) technology is very effective in improving the power flow along the transmission lines and makes the power system more flexible and controllable. This paper deals with the most robust type of FACTS devices; it’s a Unified Power Flow Controller (UPFC). Many cases have been taken to study how the system behaves in the presence and absence of the UPFC under normal and contingency conditions. The UPFC is a device that can be used to improve the bus voltage, increasing the loadability of the line and reduce the active and reactive power losses in the transmission lines, through controlling the flow of real and reactive power. Both the magnitude and the phase angle of th

The electrochemical behavior of carbon steel in water sweetening station in Libya has been studied in the range of ( 293–333 ^oC) using weight loss technique. Measurements were carried out over a range of Reynolds number (5000 – 25000).An apparatus was designed for studying the corrosion process in the turbulent regime, which is of industrial significance. It was found that The corrosion rate of carbon steel in water sweetening station is under diffusion control and increases with increasing Reynolds number. On the other hand the variation of corrosion rate with temperature in the range of (293–333 ^oC) was found to follow Arrhenius equation and the activation energy approximately the same except at low Reynolds

This study intends to examine the content of photo coverage related to the Gulf Cup (Gulf 25) as presented by Iraqi photojournalists on Instagram between 02/01/2023 and 27/01/2023. Utilizing content analysis, the two researchers employed the survey method to evaluate 674 digital photos posted by seven photojournalists specializing in this sporting event, which concluded with the Iraqi team's victory in the city of Basra.
Key findings from the study include:
1. The Category "Photos from the Gulf Cup matches" predominated, accounting for 291 instances or 42.794% of the total.
2. Photojournalists exhibited a keen interest in capturing images of attending fans and documenting celebrations surrounding th