The research aims to find approximate solutions for two dimensions Fredholm linear integral equation. Using the two-variables of the Bernstein polynomials we find a solution to the approximate linear integral equation of the type two dimensions. Two examples have been discussed in detail.

Background: Orthodontic force is considered to stimulate cells in the periodontium to release many mediators such as cytokines which play a responsible role for periodontal and alveolar bone remodeling, bone resorption and new bone deposition. Aim of this study was carried out to estimate changes of the (interleukin-one beta, tumor necrosis factor – alpha and C-reactive protein) levels in unstimulated whole saliva during the leveling stage of orthodontic tooth movement. Materials and methods: The sample consisted of thirty adult patients (12 males and 18 females) with ages ranges (19-23) years. Each sample had Class I and Class II malocclusion dental classification and required bilateral extraction of their maxillary first premolars, und

This research studies the effect of adding micro, nano and hybrid by ratio (1:1) of (Al2O3,TiO2) to epoxy resin on thermal conductivity before and after immersion in HCl acid for (14 day) with normality (0.3 N) at weight fraction (0.02, 0.04, 0.06, 0.08) and thickness (6mm). The results of thermal conductivity reveled that epoxy reinforced by (Al2O3) and mixture (TiO2+Al2O3) increases with increasing the weight fraction, but the thermal conductivity (k) a values for micro and Nano (TiO2) decrease with increasing the weight fraction of reinforced, while the immersion in acidic solution (HCl) that the (k) values after immersion more than the value in before immersion.

In this paper, a polymer-based composite material was prepared by hand Lay-up method consisting of epoxy resin as a base material reinforced by magnesium oxide powder once and silicon dioxide powder again and with different weight ratios (3, 6, 9 and 12) wt %. The three-point bending test was performed in normal conditions and after immersion in sulfuric acid. The results showed that the bending value decreased with the increase of the weighted ratio of the reinforcement material (MgO, SiO2). The Bending of samples reinforced by SiO2 was found to be less than the bending of samples reinforced by particles (MgO). For example, the bending of the SiO2 sample (0.32 mm) at the weighted ratio (3%) and for the MgO (0.18mm) sample at the weight

Biosorption of lead, chromium, and cadmium ions from aqueous solution by dead anaerobic biomass (DAB) was studied in single, binary, and ternary systems with initial concentration of 50 mg/l. The metal-DAB affinity was the same for all systems. The main biosorption mechanisms were complexation and physical adsorption of metallic cations onto natural active functional groups on the cell wall matrix of the DAB. It was found that biosorption of the metallic cations onto DAB cell wall component was a surface process. The main functional groups involved in the metallic cation biosorption were apparently carboxyl, amino, hydroxyle, sulfhydryl, and sulfonate. These groups were part of the DAB cell wall structural polymers. Hydroxyle groups (–O

In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal meth