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 develop qualitative workouts based on certain sensory perceptions for the development of offensive basketball abilities and to determine their impact on female pupils. Several findings, based on the au-thor's extensive expertise instructing basketball materials and our closeness to the sample, revealed deficits in some sensory perceptions “in the game of basketball”, which impair the accuracy of passing the ball to the best team-mate. It also affects the pace of dribbling and the difficulty of selecting the op-timal moment and distance to fire. Therefore, the researcher designs qualita-tive activities based on many sensory experiences, including distance, speed, force, and direction shift. In addition, the

The experimental proton resonance data for the reaction P+48Ti have been used to calculate and evaluate the level density by employed the Gaussian Orthogonal Ensemble, GOE version of RMT, Constant Temperature, CT and Back Shifted Fermi Gas, BSFG models at certain spin-parity and at different proton energies. The results of GOE model are found in agreement with other, while the level density calculated using the BSFG Model showed less values with spin dependence more than parity, due the limitation in the parameters (level density parameter, a, Energy shift parameter, E1and spin cut off parameter, σc). Also, in the CT Model the level density results depend mainly on two parameters (T and ground state back shift energy, E0), which are app

The hydrodynamics behavior of gas - solid fluidized beds is complex and it should be analyzed  and understood due to its importance in the design and operating of the units. The effect of column inside diameter and static bed height on the minimum fluidization velocity, minimum bubbling velocity, fluidization index, minimum slugging velocity and slug index have been studied experimentally and theoretically for three cylindrical columns of 0.0762, 0.15 and 0.18 m inside diameters  and 0.05, 0.07 and 0.09 m static bed heights .The experimental results showed that the minimum fluidization and bubbling velocities had a direct relation with column diameter and static bed height .The minimum slugging velocity had an

The solution gas-oil ratio is an important measurement in reservoir engineering calculations. The correlations are used when experimental PVT data from particular field are missing. Additional advantages of the correlations are saving of cost and time.
This paper proposes a correlation to calculate the solution gas -oil ratio at pressures below bubble point pressure. It was obtained by multiple linear regression analysis of PVT data collected from many Iraqi fields.
In this study, the solution gas-oil ratio was taken as a function of bubble point pressure, stock tank oil gravity, reservoir pressure, reservoir temperature and relative gas density.
The construction of the new correlation is depending on thirty seven PVT reports th

The aim of this research is to estimate the parameters of the linear regression model with errors following ARFIMA model by using wavelet method depending on maximum likelihood and approaching general least square as well as ordinary least square. We use the estimators in practical application on real data, which were the monthly data of Inflation and Dollar exchange rate obtained from the (CSO) Central Statistical organization for the period from 1/2005 to 12/2015. The results proved that (WML) was the most reliable and efficient from the other estimators, also the results provide that the changing of fractional difference parameter (d) doesn’t effect on the results.

The present study dealt with the removal of methylene blue from wastewater by using peanut hulls (PNH) as adsorbent. Two modes of operation were used in the present work, batch mode and inverse fluidized bed mode. In batch experiment, the effect of peanut hulls doses 2, 4, 8, 12 and 16 g, with constant initial pH =5.6, concentration 20 mg/L and particle size 2-3.35 mm were studied. The results showed that the percent removal of methylene blue increased with the increase of peanut hulls dose. Batch kinetics experiments showed that equilibrium time was about 3 hours, isotherm models (Langmuir and Freundlich) were used to correlate these results. The results showed that the (Freundlich) model gave the best fitting for adsorption capacity. D