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.

The Boltzmann equation has been solved using (EEDF) package for a pure sulfur hexafluoride (SF6) gas and its mixtures with buffer Helium (He) gas to study the electron energy distribution function EEDF and then the corresponding transport coefficients for various ratios of SF6 and the mixtures. The calculations are graphically represented and discussed for the sake of comparison between the various mixtures. It is found that the various SF6 – He content mixtures have a considerable effect on EEDF and the transport coefficients of the mixtures

The purpose of this paper is to find the best multiplier approximation of unbounded functions in    –space by using some discrete linear positive operators. Also we will estimate the degree of the best multiplier approximation in term of modulus of continuity and the averaged modulus.

Tau-P linear noise attenuation filter (TPLNA) was applied on the 3D seismic data of Al-Samawah area south west of Iraq with the aim of attenuating linear noise. TPLNA transforms the data from time domain to tau-p domain in order to increase signal to noise ratio. Applying TPLNA produced very good results considering the 3D data that usually have a large amount of linear noise from different sources and in different azimuths and directions. This processing is very important in later interpretation due to the fact that the signal was covered by different kinds of noise in which the linear noise take a large part.

Derivative spectrophotometry is one of the analytical chemistry techniques used
in the analysis and determination of chemicals and pharmaceuticals. This method is
characterized by simplicity, sensitivity and speed. Derivative of Spectra conducted
in several ways, including optical, electronic and mathematical. This operation
usually be done within spectrophotometer. The paper is based on form of a new
program. The program construction is written in Visual Basic language within
Microsoft Excel. The program is able to transform the first, second, third and fourth
derivatives of data and the return of these derivatives to zero order (normal plot).
The program was applied on experimental (trial) and reals values of su

In this paper we estimate the coefficients and scale parameter in linear regression model depending on the residuals are of type 1 of extreme  value distribution for the largest values . This can be regard as an improvement for the studies with the smallest values . We study two estimation methods ( OLS  & MLE ) where we resort to Newton – Raphson (NR) and Fisher Scoring methods to get MLE estimate because the difficulty of using the usual approach with MLE . The relative efficiency criterion is considered beside to the statistical inference procedures for the extreme value regression model of type 1 for largest values . Confidence interval , hypothesis testing for both scale parameter and regression coefficients

In this paper, a procedure to establish the different performance measures in terms of crisp value is proposed for two classes of arrivals and multiple channel queueing models, where both arrival and service rate are fuzzy numbers. The main idea is to convert the arrival rates and service rates under fuzzy queues into crisp queues by using graded mean integration approach, which can be represented as median rule number. Hence, we apply the crisp values obtained to establish the performance measure of conventional multiple queueing models. This procedure has shown its effectiveness when incorporated with many types of membership functions in solving queuing problems. Two numerical illustrations are presented to determine the validity of the