In this work, a weighted H lder function that approximates a Jacobi polynomial which solves the second order singular Sturm-Liouville equation is discussed. This is generally equivalent to the Jacobean translations and the moduli of smoothness. This paper aims to focus on improving methods of approximation and finding the upper and lower estimates for the degree of approximation in weighted H lder spaces by modifying the modulus of continuity and smoothness. Moreover, some properties for the moduli of smoothness with direct and inverse results are considered.

      Land surface temperature (LST) is crucial for determining the region's environmental quality because a significant temperature rise causes disasters, which cause environmental imbalance, reducing biodiversity and hastening desertification. In this study, remote sensing and geographic information systems were used to estimate the change in the LST of Babylon, Iraq, using two satellite images taken 20 years apart (2002, 2022). The temperature was extracted using a specific mathematical model in ArcMap10.8 software. The findings demonstrated a significant variation in temperatures and the concentration in various regions of Babylon between 2002 and 2022 and the relationship between LST and Normalized difference

     The Rock Wool Board (RWB) is widely used in the building exterior insulation all over world. As polymer affects hardening of plate, meaning it acted as a basic binder in this work and gave a smooth texture, ease of carrying and workmanship in different sizes and shapes. PVA was studied at the rates of PVA %4, %5, %6.66, %10, %20, results showed that 6.66% is the best percentage, through tensile and bending tests, this percentage was use with polyurethane with rates of PU 1, 0.5, 0.333, 0.25, 0.2 It is found that the ratio 0.333 is the best ratio to give good mechanical properties of bending, tensile and elongation. This percentage was fixed on different percentages of polymer (PU/PVA) as %2.5, %5, %10, %15, %20 and examinations

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

      In this paper, the interplay among four population species is offered. The system consists of two competitive prey, predator and super predators. The application of the hypothesis of the Sotomayor theorem for local bifurcation around every equilibrium point is adopted. It is detected that the transcritical bifurcation could occur near most of the system's equilibrium points, while saddle-node and pitchfork bifurcation can not be accrued at any of them. Further, the conditions that guarantee the accruing Hopf bifurcation are carried out. Finally, some numerical analysis is illustrated to confirm the analytical results.