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.

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.

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 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.

In This research a Spectroscopic complement and Thermodynamic properties for molecule PO2 were studied . That included a calculation of potential energy . From the curve of total energy for molecule at equilibrium distance , for bond (P-O), the degenerated of bond energy was (4.332eV) instate of the vibration modes of ( PO2 ) molecule and frequency that was found active in IR spectra because variable inpolarization and dipole moment for molecule. Also we calculate some thermodynamic parameters of ( PO2 ) such as heat of formation , enthalpy , heat Of capacity , entropy and gibb's free energy Were ( -54.16 kcal/mol , 2366.45 kcal/mol , 10.06 kcal /k/mol , 59.52 k

Friction Stir Welding (FSW) is one of the most effective solid states joining process and has numerous potential applications in many industries. A FSW numerical tool, based on ANSYS F.E software, has been developed. The amount of the heat gone to the tool dictates the life of the tool and the capability of the tool to produce a good processed zone. Hence, understanding the heat transfer aspect of the friction stir welding is extremely important for improving the process. Many research works were carried out to simulate the friction stir welding using various softwares to determine the temperature distribution for a given set of welding conditions. The objective of this research is to develop a finite element sim

Back ground: This in vitro study was carried out to investigate the effect of post space regions (coronal, middle and apical), Time and the mode of polymerization (dual, self-cured) of the cements used on the bond strength between translucent fiber post and root dentin by using push-out test. Materials and Methods: Forty eight extracted mandibular first premolars (single root) were instrumented with ProTaper Universal system files (for hand use) and obturated with gutta percha for ProTaper and AH26® root canal sealer following the manufacturer instructions, after 24 hours post space was prepared using FRC postec® plus drills no.3 creating 8 mm depth post space. The prepared samples were randomly divided into two main groups (24 samples ea

This investigation was undertaken to evaluate the effectiveness of using Hydrated lime as a (partial substitute) by weight of filler (lime stone powder) with five consecutive percentage namely (1.0, 1.5, 2.0, 2.5, 3.0) % by means of aggregate treatment, by introducing dry lime on dry and 2–3% Saturated surface aggregate on both wearing and binder coarse. Marshall design method, indirect tensile test and permanent deformation under repeated loading of Pneumatic repeated load system at full range of temperature (20, 40, 60) C0 were examined The study revealed that the use of 2.0% and 1.5 % of dry and wet replacement extend the pavement characteristics by improving the Marshall properties and increasing the TSR%. Finally, increase permanent