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.

Academic achievement is a professional standard for measuring student levels in the first stages. Therefore, any indication of the level of achievement makes us in an attempt to employ students in evening schools. The researcher has developed a closed questionnaire of (36) paragraphs. A total of (164) male and (24) female students were chosen from evening schools. The result of this research revealed that the number of students was a reason for the low level of their achievement, the lack of laboratories, educational methods, and techniques of the most prominent problems confirmed by students in these schools. In addition, to support educational institutions with their necessary needs. The most important conclusion in this research is th

In the present study, 1-ethyl -3-methyllimidazolium acetate ionic liquid is introduced for extractive desulfurization of Iraqi kerosene (1622ppm) and compared with 1-ethyl -3- methyllimidazolium tetrafloroborate. The effect of ionic liquid/ fuel ratio (1/9, 1/4, 1/2), temperature (25, 30,40oC), stirring speed (300,450rpm) and time (10, 30, 90, 180, 360 min) were studied. Sulfur compound analysis was performed using X-Ray fluorescence. The ionic liquid with acetate anion (OAc) showed better performance than tetrafloborate (BF4). The maximum extraction efficiency was 32% achieved at 1/2 IL/Fuel and 40oC after 90min. The oxidation step using hydrogen peroxide (8ml/200ml), catalyzed by acetic acid (2ml) and followed by ionic liquid extraction h

The goal of this experimental study is to determine the effects of different parameters (Flow rate, cuttings density, cuttings size, and hole inclination degree) on hole cleaning efficiency. Freshwater was used as a drilling fluid in this experiment. The experiments were conducted by using flow loop consist of approximately 14 m (46 ft) long with transparent glass test section of 3m (9.84 ft.) long with 4 inches (101.6 mm) ID, the inner metal drill pipe with 2 inches (50.8 mm) OD settled with eccentric position positive 0.5. The results obtained from this study show that the hole cleanings efficiency become better with high flow rate (21 m3/hr) and it increase as the hole inclination angles increased from 60 to 90 degree due to dominated

Objectives Bromelain is a potent proteolytic enzyme that has a unique functionality makes it valuable for various therapeutic purposes. This study aimed to develop three novel formulations based on bromelain to be used as chemomechanical caries removal agents. Methods The novel agents were prepared using different concentrations of bromelain (10–40 wt. %), with and without 0.1–0.3 wt. % chloramine T or 0.5–1.5 wt. % chlorhexidine (CHX). Based on the enzymatic activity test, three formulations were selected; 30 % bromelain (F1), 30 % bromelain-0.1 % chloramine (F2) and 30 % bromelain-1.5 % CHX (F3). The assessments included molecular docking, Fourier-transform infrared spectroscopy (FTIR), viscosity and pH measurements. The efficiency

     This research examines the quantitative analysis to assess the efficiency of the transport network in Sadr City, where the study area suffers from a large traffic movement  for the variability of traffic flow and intensity at peak hours as a result of inside traffic and outside of it, especially in the neighborhoods of population with  economic concentration.                                                           &n

The aim of this study is to utilize the electromembrane extraction (EME) system as a manner for effective removal of zinc from aqueous solutions. A novel and distinctive electrochemical cell design was adopted consisting of two glass chambers, a supported liquid membrane (SLM) housing a polypropylene flat membrane infused with 1-octanol and a carrier. Two electrodes were used, a graphite as anode and a stainless steel as cathode. A comprehensive examination of several influential factors including the choice of carrier, the applied voltage magnitude, the initial pH of the donor solution, and the initial concentration of zinc was performed, all in a concerted effort to ascertain their respective impacts on the efficiency of zinc elim

This study depicts the removal of Manganese ions (Mn²⁺) from simulated wastewater by combined electrocoagulation/ electroflotation technologies. The effects of initial Mn concentration, current density (C.D.), electrolysis time, and different mesh numbers of stainless steel screen electrodes were investigated in a batch cell by adopting Taguchi experimental design to explore the optimum conditions for maximum removal efficiency of Mn. The results of multiple regression and signal to noise ratio (S/N) showed that the optimum conditions were Mn initial concentration of 100 ppm, C.D. of 4 mA/cm², time of 120 min, and mesh no. of 30 (wire/inch). Also, the relative significance of each factor was attained by the analysis

This study depicts the removal of Manganese ions (Mn2+) from simulated wastewater by combined electrocoagulation/ electroflotation technologies. The effects of initial Mn concentration, current density (C.D.), electrolysis time, and different mesh numbers of stainless steel screen electrodes were investigated in a batch cell by adopting Taguchi experimental design to explore the optimum conditions for maximum removal efficiency of Mn. The results of multiple regression and signal to noise ratio (S/N) showed that the optimum conditions were Mn initial concentration of 100 ppm, C.D. of 4 mA/cm2, time of 120 min, and mesh no. of 30 (wire/inch). Also, the relative significance of each factor was attained by the analysis of variance (ANO

In this research study the effect of irradiation by (CW) CO2 laser on some optical properties of (Cds) doping by Ni thin films of (1)µm thickness has been prepared by heat evaporation method. (X-Ray) diffraction technique showed the prepared films before and after irradiation are ploy crystalline hexagonal structure, optical properties were include recording of absorbance spectra for prepared films in the range of (400-1000) nm wave lengths, the absorption coefficient and the energy gap were calculated before and after irradiation, finally the irradiation affected (CdS) thin films by changing its color from the Transparent yellow to dark rough yellow and decrease the value absorption coefficient also increase the value of energy gap.