A method for Approximated evaluation of linear functional differential equations is described. where a function approximation as a linear combination of a set of orthogonal basis functions which are chebyshev functions .The coefficients of the approximation are determined by (least square and Galerkin’s) methods. The property of chebyshev polynomials leads to good results , which are demonstrated with examples.

The region is defined by the spatial dimension, which consists of a set of stabilizers (towns and villages). The concept of the territory requires conditions on the nature of functional relations and the mutual influence of the regions within the region. Any territory must be based on the interdependence and interaction between the mother city and its surrounding countryside and cities, and when the interdependence is strong and the interaction is clear, it helps to define the territory. The regions are divided on different bases. There are geographically or national homogeneous regions, and there are cultural regions that want to preserve their culture in terms of language or religion. There are administrative regions to manage

From a health standpoint, fluoride (F) is a vital element for humans. It had harmful effects on numerous organs when consumed in high dosages. Fluoride poisoning has been linked to liver damage. The purpose of this study was to see how sodium fluoride (Naf) affected liver function and the glycemic index in adult male albino rats. Fourteen (14) adult male Wistar albino rats were randomly and evenly divided into two groups and given the following treatments for thirty (30) days: G1 Group (Control group), were given distilled water and fed a balanced diet, G2 rats were administered water that contained 100 ppm Naf. The animals were fasted for 8-12 hours before being anesthetized and blood samples were taken by heart puncture technique

From a health standpoint, fluoride (F) is a vital element for humans. It had harmful effects on numerous organs when consumed in high dosages. Fluoride poisoning has been linked to liver damage. The purpose of this study was to see how sodium fluoride (Naf) affected liver function and the glycemic index in adult male albino rats. Fourteen (14) adult male Wistar albino rats were randomly and evenly divided into two groups and given the following treatments for thirty (30) days: G1 Group (Control group), were given distilled water and fed a balanced diet, G2 rats were administered water that contained 100 ppm Naf. The animals were fasted for 8-12 hours before being anesthetized and blood samples were taken by heart puncture technique

Well integrity is a vital feature that should be upheld into the lifespan of the well, and one constituent of which casing, necessity to be capable to endure all the interior and outside loads. The casing, through its two basic essentials: casing design and casing depth adjustment, are fundamental to a unique wellbore that plays an important role in well integrity. Casing set depths are determined based on fracturing pressure and pore pressure in the well and can usually be obtained from well-specific information. Based on the analyzes using the improved techniques in this study, the following special proposition can be projected: The selection of the first class and materials must be done correctly and accurately in accordance with the

Well integrity is a vital feature that should be upheld into the lifespan of the well, and one constituent of which casing, necessity to be capable to endure all the interior and outside loads. The casing, through its two basic essentials: casing design and casing depth adjustment, are fundamental to a unique wellbore that plays an important role in well integrity. Casing set depths are determined based on fracturing pressure and pore pressure in the well and can usually be obtained from well-specific information. Based on the analyzes using the improved techniques in this study, the following special proposition can be projected: The selection of the first class and materials must be done correctly and accurately in accordance with

Background/objectives: Inflammatory mediators such as prostaglandin E2 (PGE2) and nitric oxide (NO) are key indicators of pulp response to mechanical trauma. However, the influence of cavity depth on their release dynamics remains unclear. This study aimed to evaluate the effects of different cavity depths—moderate (without pulp exposure) and deep (with pulp exposure)—on the release of PGE2 and NO in the pulp tissue of rat mandibular incisors at two time intervals (3 and 9 h).Methods: In total, 40 male Wistar rats were divided into two main groups (n = 20) based on cavity depth. A split-mouth design was used, with cavities of different depths prepared on the left mandibular incisors, leaving the right incisors without cavities as