In this paper, Touchard polynomials (TPs) are presented for solving Linear Volterra integral equations of the second kind (LVIEs-2k) and the first kind (LVIEs-1k) besides, the singular kernel type of this equation. Illustrative examples show the efficiency of the presented method, and the approximate numerical (AN) solutions are compared with one another method in some examples. All calculations and graphs are performed by program MATLAB2018b.

In this research, Haar wavelets method has been utilized to approximate a numerical solution for Linear state space systems. The solution technique is used Haar wavelet functions and Haar wavelet operational matrix with the operation to transform the state space system into a system of linear algebraic equations which can be resolved by MATLAB over an interval from 0 to . The exactness of the state variables can be enhanced by increasing the Haar wavelet resolution. The method has been applied for different examples and the simulation results have been illustrated in graphics and compared with the exact solution.

The main work of this paper is devoted to a new technique of constructing approximated solutions for linear delay differential equations using the basis functions power series functions with the aid of Weighted residual methods (collocations method, Galerkin’s method and least square method).

A new method based on the Touchard polynomials (TPs) was presented for the numerical solution of the linear Fredholm integro-differential equation (FIDE) of the first order and second kind with condition. The derivative and integration of the (TPs) were simply obtained. The convergence analysis of the presented method was given and the applicability was proved by some numerical examples. The results obtained in this method are compared with other known results.

Most of the known cases of strong gravitational lensing involve multiple imaging of an active galactic nucleus. The properties of lensed active galactic nuclei make them promising systems for astrophysical applications of gravitational lensing. So we present a simple model for strong lensing in the gravitational lensed systems to calculate the age of four lensed galaxies, in the present work we take the freedman models with (k curvature index =0) Euclidian case, and the result show a good agreement with the other models.

     Twosimple, sensitive,accurate, and precise spectrophotometric methods have been developed for the determination of chlorpromazine – HCl in pure form and pharmaceutical formulation. The first method involved treatment of cited drug with a measured excess of permanganate in acid medium and the unreacted oxidant was measured at 525 nm. The second method involves the reaction  of the drug with potassium permanganate in the presence of sodium hydroxide to produce a bluish – green  colored manganite which is measurable at 610nm. All the experimental variables affecting the development of the manganite ions were investigatedand conditions were optimized. Working linearity ranges were 5-45 µg.mL-1an

The aim of this paper is to present the numerical method for solving linear system of Fredholm integral equations, based on the Haar wavelet approach. Many test problems, for which the exact solution is known, are considered. Compare the results of suggested method with the results of another method (Trapezoidal method). Algorithm and program is written by Matlab vergion 7.

The object of the presented study was to monitor the changes that had happened in the main features (water, vegetation, and soil) of Al-Hammar Marsh region. To fulfill this goal, different satellite images had been used in different times, MSS 1973, TM 1990, ETM+ 2000, 2002, and MODIS 2009, 2010. A new technique of the unsupervised classification called (Color Extracting Technique) was used to classify the satellite images. MATLAP programming used the technique and separated Al-Hammar Marsh from other water features (rivers, irrigated lands, etc.) when calculated the changes in the water content of the study region. ArcGIS 9.3 (arcMAP, arcToolbox) were used to achieve this work and calculate area of each class.

Antibiotics present the greatest threat to soil and aquatic ecosystems among the different therapeutic groups of medicines (which include prescription drugs and treatments for cancer). The strongest drugs, antibiotics, have been utilized to stop the growth of microorganisms or eradicate them. Using high-performance liquid chromatography technology with fluorescence detection, the amounts of levofloxacin and tetracycline in the wastewater from three hospitals (Medical City, AlKindi, and Al-Yarmouk) were determined. Levofloxacin and tetracycline were chosen in this study because they are the most important water pollutants. These antibiotic residues were separated and measured using a gradient elution technique on a reverse-phase C18 co