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 aqueous extract of (Typha domingensis Pers.) pollen grain (qurraid) to know its ability to manufacture silver nanoparticles. Qurraid is a semi-solid yellow food substance, sold in Basra markets and eaten by the local population. It is made from the pollen of the T.  domingensis Pers. plant after being pressed and treated with water vapor. The Gas chromatography–mass spectrometry (GC-MS) reaction was done to identify the active compounds of qurraid aqueous extract. The ability of the aqueous extract of qurraid to manufacture silver nanoparticles was tested, and the construction of silver nanoparticles was inferred by the reaction mixture's color, which ranged from yellow to dark brown. The synthesi

In this study, vegetable tanned leather waste of cow (VTLW-C) is used as adsorbent for removing methyl violet 10B dye from aqueous solution. The VTLW-C adsorbent was characterized by FTIR and SEM in order to evaluate its surface properties before using in adsorption experiments. Batch adsorption method was applied to study the effect of different factors such as weight of leather waste, time of shaking, and starting concentration of methyl violet 10B dye. Different isothermal models such as Langmuir, Freundlich, Temkin and Dubinin-Radushkevich (D–R) were used to analyze the experimental data. Kinetic study proceeds using (PFO) kinetic model and (PSO) kinetic model. The results showed better agreement with the Freundlich model; this means

The present study utilised date palm fibre (DPF) waste residues to adsorb Congo red (CR) dye from aqueous solutions. The features of the adsorbent, such as its surface shape, pore size, and chemical properties, were assessed with X-ray diffraction (XRD), BET, Fourier-transform infrared (FTIR), X-ray fluorescence (XRF), and field emission scanning electron microscope (FESEM). The current study employed the batch system to investigate the ideal pH to adsorb the CR dye and found that acidic pH decolourised the dye best. Extending the dye-DPF waste mixing period at 25°C reportedly removed more dye. Consequently, the influence of the starting dye and DPF waste quantity on dye removal was explored in this study. At 5 g/L dye concentration, 48% d

Hydrogen sulfide removal catalyst was prepared chemically by precipitation of zinc bicarbonate at a controlled pH. The physical and chemical catalyst characterization properties were investigated. The catalyst was tested for its activity in adsorption of H₂S using a plant that generates the H₂S from naphtha hydrodesulphurization and a unit for the adsorption of H₂S. The results comparison between the prepared and commercial catalysts revealed that the chemical method can be used to prepare the catalyst with a very good activity.

It has observed that the hydrogen sulfide removal over zinc oxide catalyst follows first order reaction kinetics with activation energy of 19.26 kJ/mole and enthalpy and e

The azo dye brilliant reactive red K-2BP (λmax = 534 nm) is widely used for coloring textiles because of its low-cost and tolerance fastness properties. Wastewaters treatment that contains the dye by conventional ways is usually inadequate due to its resistance to biological and chemical degradation. During this study, the continuous reactor of an advanced oxidation method supported the use of H₂O₂/sunlight, H₂O₂/UV, H₂O₂/TiO₂/sunlight, and H₂O₂/TiO₂/UV for decolorization of brilliant reactive red dye from the effluent. The existence of an optimum pH, H₂O₂ concentration, TiO₂ concentration, and d

Aim: The study designed to evaluate the Geno-protective effect of green tea extract against genotoxicity induced by metronidazole and tinidazole. Methods: Thirty-six mice were used, For each experiment, The animals divided into 6 groups: Group I- Negative control administered distilled water; Group II-Healthy mice treated with metronidazole alone, Group III- Healthy mice treated with tinidazole alone; Group IV- Healthy mice administered green tea extract alone Group V- Healthy mice treated with metronidazole, followed by green tea extract administration, Group VI- Healthy mice treated with tinidazole, followed by administration of green tea extract. Results: treatment with Tinidazole significantly increase total chromosomal aberration (0.18

   In this study, the circulating fluidized bed was used to remove the Tetracycline from wastewater utilizing a pistachio shell coated with ZnO nanoparticles. Several parameters including, Tetracycline solution flowrate, initial static bed height, Tetracycline initial concentration and airflow rate were systematically examined to show their effect on the breakthrough curve and the required time to reach the adsorption capacity and thus draw the fully saturated curve of the adsorbent. Results showed that using ZnO nanoparticles will increase the adsorbent surface area and pores and as a result the adsorption increased, also the required time for adsorbent saturation increased and thus the removal efficiency may be achieved at mi

Cadmium is one of the heavy metal found in the wastewater of many industries. The electrocoagulation offers many advantages for the removal of cadmium over other methods. So the removal of cadmium from wastewater by using electrocoagulation was studied to investigate the effect of operating parameters on the removal efficiency. The studied parameters were the initial pH, initial concentration, and applied voltage. The study experiments were conducted in a batch reactor with  with two pairs of aluminum electrodes with dimension  and 2mm in thick with 1.5 cm space between them. The optimum removal was obtained at pH =7, initial concentration = 50 mg/L, and applied voltage = 20 V and it was 90%.