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.

Soil improvement has developed as a realistic solution for enhancing soil properties so that structures can be constructed to meet project engineering requirements due to the limited availability of construction land in urban centers. The jet grouting method for soil improvement is a novel geotechnical alternative for problematic soils for which conventional foundation designs cannot provide acceptable and lasting solutions. The paper's methodology was based on constructing pile models using a low-pressure injection laboratory setup built and made locally to simulate the operation of field equipment. The setup design was based on previous research that systematically conducted unconfined compression testing (U.C.Ts.). Th

Zinc Oxide nanoparticles were prepared using pulsed laser ablation process from a pure zinc metal placed inside a liquid environment. The latter is composed of acetyltrimethylammonium bromide (CTAB) of 10−3 molarity and distilled water. A Ti:Sapphire laser of 800 nm wavelength, 1 kHz pulse repetition rate, 130 fs pulse duration is used at three values of pulse energies of 0.05 mJ, 1.11 mJ and 1.15 mJ. The evaluation of the optical properties for the obtained suspension was applied through ultraviolet–visible absorption spectroscopy test (UV/VIS). The result showed peak wavelengths at 210 nm, 211 nm and 213 nm for the three used pulse energies 0.05 mJ, 1.11 mJ and 1.15 mJ respectively. This indicates a blue shift,

Background: Due to the complicated and time-consuming physiological procedure of bone healing, certain graft materials have been frequently used to enhance the reconstruction of the normal bone architecture. However, owing to the limitations of these graft materials, some pharmaceutical alternatives are considered instead.  Chitosan is a biopolymer with many distinguishing characteristics that make it one of the best materials to be used as a drug delivery system for simvastatin. Simvastatin is a cholesterol lowering drug, and an influencer in bone formation process, because it stimulates osteoblasts differentiation, bone morphogenic protein 2, and vascular endothelial growth factor. Objectives: histological, histochemical and histomorp

Fire incidences are classed as catastrophic events, which mean that persons may experience mental distress and trauma. The development of a robotic vehicle specifically designed for fire extinguishing purposes has significant implications, as it not only addresses the issue of fire but also aims to safeguard human lives and minimize the extent of damage caused by indoor fire occurrences. The primary goal of the AFRC is to undergo a metamorphosis, allowing it to operate autonomously as a specialized support vehicle designed exclusively for the task of identifying and extinguishing fires. Researchers have undertaken the tasks of constructing an autonomous vehicle with robotic capabilities, devising a universal algorithm to be employed

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