In this research, the study of thermal treating by laser, plasma glow discharge and tubular furnace on Ti-6Al-4V alloy coated with hydroxyapatite by methods of dip coating and electrophoretic deposition .A group of samples was coated by dip coating and another group was coated by electrophoretic deposition. The first group was treated by pulse laser 10 (mJ) as energy for samples from both coating with uniform distributed pulses on every single sample surface, The second thermal treating was made by plasma glow discharge in a locally made system with argon atmosphere, 600 Volt , and 6 cm distance between the electrodes, The third treating was made by tubular furnace in air atmosphere and 400 °C for 1 hour duration. T

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

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.

This research aims to numerically solve a nonlinear initial value problem presented as a system of ordinary differential equations. Our focus is on epidemiological systems in particular. The accurate numerical method that is the Runge-Kutta method of order four has been used to solve this problem that is represented in the epidemic model. The COVID-19 mathematical epidemic model in Iraq from 2020 to the next years is the application under study. Finally, the results obtained for the COVID-19 model have been discussed tabular and graphically. The spread of the COVID-19 pandemic can be observed via the behavior of the different stages of the model that approximates the behavior of actual the COVID-19 epidemic in Iraq. In our study, the COV

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.

Incremental forming is a flexible sheet metal forming process which is performed by utilizing simple tools to locally deform a sheet of metal along a predefined tool path without using of dies. This work presents the single point incremental forming process for producing pyramid geometry and studies the effect of tool geometry, tool diameter, and spindle speed on the residual stresses. The residual stresses were measured by ORIONRKS 6000 test measuring instrument. This instrument was used with four angles of (0º,15º,30º, and 45º) and the average value of residual stresses was determined, the value of the residual stress in the original blanks was (10.626 MPa). The X-ray diffraction technology was used to measure the residual stresses

After Hamdallah and his success on the realization of this manuscript (a letter in detail what was said in the parents of the Prophet  Ibn Kamal Pasha (d. 940 e) study and investigation I will review some of the results reached in the realization of this manuscript:
1. The hadiths mentioned in this manuscript are mostly placed or weak.
2 - We are not entitled to speak about the silence of the law for saying Almighty ﭽ ﮮ ﮯ ﮰ ﮱ ﯓ ﯔ ﯕ ﯖ ﯗ ﯘ ﯙ ﭼ Table: 101.
3 in which harm to our Holy Prophet  وله تع ﮂ ﮃ ﮄ ﮅ ﮆ ﮈ ﮉ ﮊ ﮋ ﮌ ﮍ ﮎ ﭼ parties: 57.
4 Because the parents of the Prophet  of the people of the period ordered them to God for the Almighty ﭽ ﯨ ﯩ ﯪ ﯫ ﯬ

Inherent fluctuations in the availability of energy from renewables, particularly solar, remain a substantial impediment to their widespread deployment worldwide. Employing phase-change materials (PCMs) as media, saving energy for later consumption, offers a promising solution for overcoming the problem. However, the heat conductivities of most PCMs are limited, which severely limits the energy storage potential of these materials. This study suggests employing circular fins with staggered distribution to achieve improved thermal response rates of PCM in a vertical triple-tube heat exchanger involving two opposite flow streams of the heat-transfer fluid (HTF). Since heat diffusion is not the same at various portions of the PCM unit,