The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.

Abstract

 This research deals will the declared production planning operation in the general company of planting oils, which have  great role in production operations management who had built mathematical model for correct non-linear programming according to discounting operation during raw materials or half-made materials purchasing operation which concentration of six main products by company but discount included just three products of raw materials, and there were six months taken from the 1^st half of 2014 as a planning period has been chosen . Simulated annealing algorithm  application on non-linear model which been more difficulty than possible solution when imposed restric

Resin-modified glass ionomer cement tends to shrink due to polymerization of the resin component. Additionally, they are more prone to syneresis and imbibition during the setting process. This in vitro study evaluates the impact of chitosan, a biopolymer that is, both biomaterial and biocompatible, on the strength of dentin bonding and compares it with ACTIVA Bio-ACTIVE Restorative. The present study was aimed to assess the impact of including chitosan into Fuji II on the shear bond strength between. the restoration material and tooth dentin,

The effects of nutrients and physical conditions on phytase production were investigated with a recently isolated strain of Aspergillus tubingensis SKA under solid state fermentation on wheat bran. The nutrient factors investigated included carbon source, nitrogen source, phosphate source and concentration, metal ions (salts) and the physical parameters investigated included inoculum size, pH, temperature and fermentation duration. Our investigations revealed that optimal productivity of phytase was achieved using wheat bran supplemented with: 1.5% glucose. 0.5% (NH4)2SO4, 0.1% sodium phytate. Additionally, optimal physical conditions were 1 × 105 spore/g substrate, initial pH of 5.0, temperature of fermentation 30˚C and fermentation dura

Abstract: Background: Staphylococcus aureus is Gram-positive bacteria that lives as a normal flora in living organisms but can be pathogenic to humans. Although a relatively unspectacular, nonmotile coccoid bacterium, S. aureus is a dangerous human pathogen in both community-acquired and nosocomial infections. Due to the increasing emergence of new strains of this antibiotic-resistant bacteria, it has become essential to approach different methods to control this pathogen. One of these methods is the antimicrobial photodynamic inactivation process using a low-level laser, in this paper, the Photodynamic effects of Rose Bengal and LLLL on the virulence factors of S.aureus were evaluated.

In wide range of chemical, petrochemical and energy processes, it is not possible to manage without slurry bubble column reactors. In this investigation, time average local gas holdup was recorded for three different height to diameter (H/D) ratios 3, 4 and 5 in 18" diameter slurry bubble column. Air-water-glass beads system was used with superficial velocity up to 0.24 m/s. the gas holdup was measured using 4-tips optical fiber probe technique. The results show that the axial gas holdup increases almost linearly with the superficial gas velocity in 0.08 m/s and levels off with a further increase of velocity. A comparison of the present data with those reported for other slurry bubble column having diameters larger than