In this paper, our aim is to study variational formulation and solutions of 2-dimensional integrodifferential equations of fractional order. We will give a summery of representation to the variational formulation of linear nonhomogenous 2-dimensional Volterra integro-differential equations of the second kind with fractional order. An example will be discussed and solved by using the MathCAD software package when it is needed.

Samarium ions (Sm +3), a rare-earth element, have a significant optical emission within the visible spectrum. PMMA samples, mixed with different ratios of SmCl3.6H2O, were prepared via the casting method. The composite was tested using UV-visible, photoluminescence and thermogravimetric analysis (TGA). The FTIR spectrometry of PMMA samples showed some changes, including variation in band intensity, location, and width. Mixed with samarium decreases the intensity of the CO and CH2 stretching bands and band position. A new band appeared corresponding to ionic bonds between samarium cations with negative branches in the polymer. These variations indicate complex links between the Sm +3 ion and oxygen in the ether group. The optical absorption

In this paper the method of singular value decomposition  is used to estimate the ridge parameter of ridge regression estimator which is an alternative to ordinary least squares estimator when the general linear regression model suffer from near multicollinearity.

Accurate predictive tools for VLE calculation are always needed. A new method is introduced for VLE calculation which is very simple to apply with very good results compared with previously used methods. It does not need any physical property except each binary system need tow constants only. Also, this method can be applied to calculate VLE data for any binary system at any polarity or from any group family. But the system binary should not confirm an azeotrope. This new method is expanding in application to cover a range of temperature. This expansion does not need anything except the application of the new proposed form with the system of two constants. This method with its development is applied to 56 binary mixtures with 1120 equili

The Assignment model is a mathematical model that aims to express a real problem facing factories and companies which is characterized by the guarantee of its activity in order to make the appropriate decision to get the best allocation of machines or jobs or workers on machines in order to increase efficiency or profits to the highest possible level or reduce costs or time To the extent possible, and in this research has been using the method of labeling to solve the problem of the fuzzy assignment of real data has been approved by the tire factory Diwaniya, where the data included two factors are the factors of efficiency and cost, and was solved manually by a number of iterations until reaching the optimization solution,

Is in this research review of the way minimum absolute deviations values ​​based on linear programming method to estimate the parameters of simple linear regression model and give an overview of this model. We were modeling method deviations of the absolute values ​​proposed using a scale of dispersion and composition of a simple linear regression model based on the proposed measure. Object of the work is to find the capabilities of not affected by abnormal values by using numerical method and at the lowest possible recurrence.

This research is considered one of the important researches in Maysan Governorate, as it focuses on the construction of helicopter airport project in the oil fields of the Maysan Oil Company, where the oil general companies in Maysan Governorate suffer from the cost of transporting the foreign engineering experts and the governing equipment of sustaining oil industry from Iraq's international airports to oil fields and vice versa. Private international transport companies transport foreign engineering from the oil fields to Iraqi airports and vice versa, and other international security companies take action to provide protection for foreign engineering experts during transportation. Hence, this process is very costly.

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The nuclear structure included the matter, proton and neutron densities of the ground state, the nuclear root-mean-square (rms) radii and elastic form factors of one neutron ²³O and ²⁴F halo nuclei have been studied by the two body model of  within the harmonic oscillator (HO) and Woods-Saxon (WS) radial wave functions. The calculated results show that the two body model within the HO and WS radial wave functions succeed in reproducing neutron halo in these exotic nuclei. Moreover, the Glauber model at high energy has been used to calculated the rms radii and reaction cross section of these nuclei.

A modified Leslie-Gower predator-prey model with a Beddington-DeAngelis functional response is proposed and studied. The purpose is to examine the effects of fear and quadratic fixed effort harvesting on the system's dynamic behavior. The model's qualitative properties, such as local equilibria stability, permanence, and global stability, are examined. The analysis of local bifurcation has been studied. It is discovered that the system experiences a saddle-node bifurcation at the survival equilibrium point whereas a transcritical bifurcation occurs at the boundary equilibrium point. Additionally established are the prerequisites for Hopf bifurcation existence. Finally, using MATLAB, a numerical investigation is conducted to verify the va