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 study, the photodegradation of Congo red dye (CR) in aqueous solution was investigated using Au-Pd/TiO₂ as photocatalyst. The concentration of dye, dosage of photocatalyst, amount of H₂O₂, pH of the medium and temperature were examined to find the optimum values of these parameters. It has been found that 28 ppm was the best dye concentration. The optimum amount of photocatalyst was 0.09 g/75 mL of dye solution when the degradation percent was ~ 96 % after irradiation time of 12 hours, while the best amount of hydrogen peroxide was 7μl/75 mL of dye solution at degradation percent ~97 % after irradiation time of 10 hours, whereas pH 5 was the best value to carry out the reaction at the highest deg

The uptake of Cd(II) ions from simulated wastewater onto olive pips was modeled using artificial neural network (ANN) which consisted of three layers. Based on 112 batch experiments, the effect of contact time (10-240 min), initial pH (2-6), initial concentration (25-250 mg/l), biosorbent dosage (0.05-2 g/100 ml), agitation speed (0-250 rpm) and temperature (20-60ºC) were studied. The maximum uptake (=92 %) of Cd(II) was achieved at optimum parameters of 60 min, 6, 50 mg/l, 1 g/100 ml, 250 rpm and 25ºC respectively.

Tangent sigmoid and linear transfer functions of ANN for hidden and output layers respectively with 7 neurons were sufficient to present good predictions for cadmium removal efficiency with coefficient of correlatio

Corrosion resistance of metals is one of the most important topics for researchers. In this work, epoxy-TiO2 nanocomposite has been developed for protection of 6061AL alloy. The dip-coating technique used to deposit the coating on 6061 Al alloy substrate. Different concentrations of TiO2 NPs (1,3,5 )Wt% have been used to study the corrosion behavior in 3.5% NaCl medium. Also, 200,150 and 100 mm/min dipping speeds have been employed for 1%wt TiO2 to show their effects on coating layer and corrosion rate. Characterization of coated surfaces were investigated by AFM, FESEM andEDS,while theelectrochemical measurementswas using to evaluate protective nature of the coating. The results have shown that the corrosion rate has decreased with

Dyes are extensively water-soluble and toxic chemicals. The disposing of wastewater rich with such chemicals has severely impacted surface water quality (rivers and lakes). In the current study, an anionic dye, methyl orange, were extracted from wastewater fluids using bulk liquid membranes supplemented with an anionic carrier (Aliquat 336 (QCI)). Parameters including solvent type (carbon tetrachloride and chloroform), membrane stirring speed (100-250 rpm), mixing speed of both phases (50-100 rpm), The feed pH (2-12) and implemented temperature (35-60 °C) were thoroughly analyzed to determine the effect of such variables on extraction effectiveness. Furthermore, the effect of methyl orange (10-50 ppm) in the feed stage and NaOH (0

This study aimed to explore the relationship between cyberbullying and levels of pessimism and optimism among female university students, emphasizing the significance of these variables in students' psychological well-being. The research problem was identified in the increasing rates of cyberbullying among female students and its negative impact on optimism and pessimism, alongside the lack of effective counseling programs addressing this issue. The study sample consisted of 30 third-year students from the College of Physical Education and Sports Sciences for Women during the academic year 2023--2024. The participants were deliberately selected through a lottery method. The researchers employed the descriptive survey method as it suited the

Authors in this work design efficient neural networks, which are based on the modified Levenberg - Marquardt (LM) training algorithms to solve non-linear fourth - order three -dimensional partial differential equations in the two kinds in the periodic and in the non-periodic - Periodic. Software reliability growth models are essential tools for monitoring and evaluating the evolution of software reliability. Software defect detection events that occur during testing and operation are often treated as counting processes in many current models. However, when working with large software systems, the error detection process should be viewed as a random process with a continuous state space, since the number of faults found during testin