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 simulation of passively Q-switching is four non – linear first order differential equations. The optimization of passively Q-switching simulation was carried out using the constrained Rosenbrock technique. The maximization option in this technique was utilized to the fourth equation as an objective function; the parameters, γa, γc and β as were dealt with as decision variables. A FORTRAN program was written to determine the optimum values of the decision variables through the simulation of the four coupled equations, for ruby laser Q–switched by Dy +2: CaF2.For different Dy +2:CaF2 molecules number, the values of decision variables was predicted using our written program. The relaxation time of Dy +2: CaF2, used with ruby was

This paper contains studying of the Evaluation for the Petrophysical Properties of
Yamama Formation in Ratawi Field which occurs in about 70 km to the west of
Basrah city in Mesopotamia zone (Zubair subzone). The study includes a
petrophysical evaluation and (3 Dimensions) geological model for each unit
especially the three hydrocarbon units comprising the Yamama Formation in (5)
boreholes which are Rt-3, Rt-4, Rt-5, Rt-6 and Rt-7 distributed on the crest and
flanks of the Ratawi structure that are carried out in the present study. The
formation's boundaries were determined using well logs, available core intervals and
by Petrophysical data and it is found that it can be subdivided into three main
reservoir uni

This research seeks to explore the impact of notifications on enhancing user engagement with websites, primarily through user subscriptions and their interaction with notifications on these websites. The significance of this study lies in its implications for crafting compelling headlines that capture users' attention, streamline their access to journalistic content, and align with the objectives and editorial policies of news websites. It sheds light on the factors influencing users' preferences for specific notifications and their engagement with content based on their individual interests, motivations, and the satisfaction derived from such interactions.
The researcher has reached several key findings, inc

In this paper, we study and investigate the quark anti-quark interaction mechanism through the annihilation process. The production of photons in association with interaction quark and gluon in the annihilation process. We investigate the effect of critical temperature, strength coupling and photons energy in terms of the quantum chromodynamics model theory framework. We find that the use of large critical temperature Tc =134 allows us to dramatically increase the strength coupling of quarks interaction. Its sensitivity to decreasing in photons rate with respect to strength coupling estimates. We also discuss the effect of photons energy on the rate of the photon , such as energies in range (1.5 to 5 GeV).The photons rate increases

     In this study, a preliminary economic feasibility study of the project of wind power at the site of Al-Shehabi (Wasit-Iraq) was conducted using measured wind data at altitudes of 10, 30, 50 and 52 m per 10 minutes. For the purpose of comparison, data from NASA were used at the same location at 50 m height. The lowest unit cost of electricity from wind energy was found to be 0.028 $/Kwh and 0.0399 $/Kwh by using the standard methodologies of Levelized Cost of Energy (LCOE) equation and Net Present Value (NPV) procedure, respectively. Furthermore, RETScreen software was used to perform the economic prefeasibility study of a proposed wind farm. The study concludes that this site is economically feasible if a wind fa