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.

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

Background: The healing process involves the restoration of the body’s structural integrity. The extracellular matrix, blood cells, cytokines, and growth factors are all involved in this dynamic, intricate, multicellular process. Hemostasis, the inflammatory phase, the proliferative phase, and the maturation phase are all included. Opuntia ficus-indica oil (OFI) and Punica grantum (PGS) oil are extensively used natural treatments that are regarded as advantageous for their sedative, spasmolytic, and anti-inflammatory properties, as well as for angiogenesis promotion, fibroblast increase, collagen production and deposition, and extracellular-matrix remodeling. Materials and methods: Twenty-four New Zealand rab

This work investigates experimentally the effect of using a skirt with a square foundation of 100 mm width resting on dry gypseous soil (i.e., loose soil with 33% relative density), and subjected to an inclined load. Previous works did not study the use square skirted foundation rested on gypseous soil and subjected to inclined load. The investigated soil was brought from Tikrit city with 59% gypsum content. Standard physical and chemical tests on selected soil were carried out. Model laboratory tests were carried out to determine the effect of using a skirt with a square foundation on the load-settlement behavior of gypseous soil and subjected to inclined load with various Skirt depth (Ds) to foundation width (B) ratio

      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.