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.

The solution gas-oil ratio is an important measurement in reservoir engineering calculations. The correlations are used when experimental PVT data from particular field are missing. Additional advantages of the correlations are saving of cost and time.
This paper proposes a correlation to calculate the solution gas -oil ratio at pressures below bubble point pressure. It was obtained by multiple linear regression analysis of PVT data collected from many Iraqi fields.
In this study, the solution gas-oil ratio was taken as a function of bubble point pressure, stock tank oil gravity, reservoir pressure, reservoir temperature and relative gas density.
The construction of the new correlation is depending on thirty seven PVT reports th

Indexes of topological play a crucial role in mathematical chemistry and network theory, providing valuable insights into the structural properties of graphs. In this study, we investigate the Resize graph of G2(3), a significant algebraic structure arising from the exceptional Lie group (G2) over the finite field F3. We compute several well-known topological indices, including the Zagreb indices, Wiener index, and Randić index, to analyze the graph's connectivity and complexity. Our results reveal intricate relationships between the algebraic structure of G2(3) and its graphical properties, offering a deeper understanding of its combinatorial and spectral characteristics. These findings contribute to the broader study of algebraic graph t

سرطان البنكرياس هو مرض ذو معدل وفيات مرتفع، ولا يزال التشخيص المبكر لسرطان البنكرياس يمثل تحديًا. يظل معدل البقاء النسبي لمدة 5 سنوات أقل من 8%، والاستراتيجيات العلاجية غير فعالة في زيادة معدلات بقاء المريض على قيد الحياة. في خلايا سرطان البنكرياس، ارتبطت مقاومة العلاج بالتغيرات الجينية التي تؤدي إلى ظهور مسارات خلوية شاذة؛ ولذلك، هناك ما يبرر ايجاد استراتيجيات جديدة لعلاج هذا المرض. هنا، سعينا لاستكشاف

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