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.

In this paper, the Monte-Carlo simulation method was used to compare the robust circular S estimator with the circular Least squares method in the case of no outlier data and in the case of the presence of an outlier in the data through two trends, the first is contaminant with high inflection points that represents contaminant in the circular independent variable, and the second the contaminant in the vertical variable that represents the circular dependent variable using three comparison criteria, the median standard error (Median SE), the median of the mean squares of error (Median MSE), and the median of the mean cosines of the circular residuals (Median A(k)). It was concluded that the method of least squares is better than the

In this paper a comparison of the experimental of evacuated tube solar water heater systems with and without mirror flat reflector. The aim of using the reflector to improve thermal efficiency, and the data gathered which are (temperature, solar irradiation and time) for three days were compared. the results from compared data the temperature lower increase in evacuated tube solar water heater system without reflector than the temperature increase in evacuated tube solar water heater system with reflector .The results show (53, 39, 35) % for three days respectively that the evacuated tube solar water heater system with reflector has higher thermal efficiencies than the results (47, 28, 30) % for three days respectively thermal efficiencies

Background: For decades, the use of naturally accessible materials in treating human disease has been widespread. The goal of this study was to determine the anti-fungal effectiveness /of the lemongrass essential oil (LGEO) versus Candida albicans (C. albicans) adhesion to polymethylmethacrylate (PMMA) materials. Material and methods: LGEO's anti-fungal activity was tested against C. albicans adhesion using the following concentration of LGEO in PMMA monomer (2.5 vol. %, 5 vol. % LGEO) selected from the pilot study as the best two effective concentrations. A total of 40 specimens were fabricated for the candida adherence test and were subdivided into four equal groups: negative control 0 vol. % addition, experimental with 2.5 vol. % and

Single phase capacitor-run induction motors (IMs) are used in various applications such as home appliances and machine tools; they are affected by the sags or swells and any fault that can lead to disturb the supply and make it produce rms voltage below or above the rated motor voltage, which is 220V. A control system is designed to regulate the output voltage of the converter irrespective to the variation of the load and within a specific range of supply voltage variation. The steady-state equivalent circuit of the Buck-Boost chopper type AC voltage regulator, as well as the analysis of this circuit are presented in this paper. Switching device for the regulator is an IGBT Module. The proposed chopper uses pulse width modulation (PWM) c

     Titanium dioxide nanotube arrays (TiO2 NTAs) were successfully decorated with nanoclusters of cobalt by an electrochemical deposition method. This Co-TiO2 NTAs nanostructure exhibited high compatibility with aluminum chloride\ chloroacetamide (an ionic liquid) and calcium chloride dihydrate\ acetamide (a deep eutectic solvent), leading to significant improvements in the electrochemical properties of the system. Significantly, this led to a discernible augmentation in both potential and current values, concomitant with a decrease in internal resistance. The presence of cobalt facilitated a faster transfer of electric charge, enhancing the overall efficiency of the system. Moreover, the incorporation of cobalt exhibited a ben

This study aimed to evaluate the surface changes of commercial pure Titanium disks (CP Ti) and the Ti 13Nb 13 Zr (Alloy) with a zigzag pattern of laser surface treatment. In vitro, experimental study of CNC Laser treatment on the CP Ti and Alloy disks. Texturing the surfaces of CP Ti and Alloy disks via CNC laser, the sample disks were analyzed using surface roughness, wettability and FESEM. The FESEM revealed a proper increase in the surface texturing and roughness on macro and micro measures without crack formation or dramatic change of the core substance of the CP Ti and Alloy disks. The CNC laser is an effective and suitable method for surface texturing CP Ti and Alloy for dental implantology. Keywords: Commercial pure Titanium;