In this paper, we describe the cases of marriage and divorce in the city of Baghdad on both sides of Rusafa and Karkh, we collected the data in this research from the Supreme Judicial Council and used the cubic spline interpolation method to estimate the function that passing through given points as well as the extrapolation method which was applied for estimating the cases of marriage and divorce for the next year and comparison between Rusafa and Karkh by using the MATLAB program.

The Wang-Ball polynomials operational matrices of the derivatives are used in this study to solve singular perturbed second-order differential equations (SPSODEs) with boundary conditions. Using the matrix of Wang-Ball polynomials, the main singular perturbation problem is converted into linear algebraic equation systems. The coefficients of the required approximate solution are obtained from the solution of this system. The residual correction approach was also used to improve an error, and the results were compared to other reported numerical methods. Several examples are used to illustrate both the reliability and usefulness of the Wang-Ball operational matrices. The Wang Ball approach has the ability to improve the outcomes by minimi

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.

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.

An experimental study is conducted to investigate the effect of heat flux distribution on the boiling safety factor of its cooling channel. The water is allowed to flow in a horizontal circular pipe whose outlet surface is subjected to different heat flux profiles. Four types of heat flux distribution profiles are used during experiments: (constant distribution profile, type a, triangle distribution profile with its maximum in channel center, type b, triangle distribution profile with its maximum in the channel inlet, type c, and triangle distribution profile with its maximum in the channel outlet, type d). The study is conducted using heat sources of (1000 and 2665W), water flow rates of (5, 7 and 9 lit/min). The water

Atherosclerosis is the most common causes of vascular diseases and it is associated with a restriction in the lumen of blood vessels. So; the study of blood flow in arteries is very important to understand the relation between hemodynamic characteristics of blood flow and the occurrence of atherosclerosis.

looking for the physical factors and correlations that explain the phenomena of existence the atherosclerosis disease in the proximal site of LAD artery in some people rather than others is achieved in this study by analysis data from coronary angiography as well as estimating the blood velocity from coronary angiography scans without having a required data on velocity by using some mathematical equations and physical laws. Fif

Solutions of dyes Rhodamine 6G (Rh6G) and Coumarin480(C480) were prepared at five concentrations (1x10-3, 5x10-4, 1x10-4, 5x10-5 and1x10-5) mol/l, the mixing was stirred to obtain on a homogenous solution, the(poly methyl-methacrylate) (PMMA) was solved by chloroform solvent with certain ratio, afterward (PMMA+Rh6G) and (PMMA+C480) thin films were prepared by casting method on glass block which has substrate with dimensions (7.5 x2.5)cm2, the prepared samples were left in dark place at room temperature for 24 hours to obtain uniform and homogenous thin films. UV-VIS absorption spectra, transmission spectra and fluorescence spectra were done to measure linear refractive index and linear absorption coefficient. The nonlinear optical proper

lar water heating systems with heat pipes of three diameter groups of 16, 22 and 28.5 mm. The first and third groups had evaporator lengths of 1150, 1300 and 1550 mm. The second group had an additional length of 1800 mm. all heat pipes were of fixed condenser length of 200 mm. Ethanol at 50% fill charge ratio of the evaporator volume was used as the heat pipes working fluid. Each heat pipe condenser section was inserted in a storage tank and the evaporator section inserted into an evacuated glass tube of the Owens- Illinois type. The combined heat pipe and evacuated glass tube form an active solar collector of a unique design.
The resulting ten solar water heating systems were tested outdoors under the meteorological conditions of Bag