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.

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.

Background: Tobacco smoking and tuberculosis (TB) are two major public health problems; Associations between smoking and tuberculosis including death from tuberculosis have been reported , A reduction in smoking could be expected to have a significant impact on TB incidence and prevalence .
Objectives: to assess the effect of smoking on tuberculosis.
Methods: This study was conducted from June 2011 to June 2012 in 200 patients, adult ( aged 17 years and more), newly diagnosed patients of pulmonary tuberculosis, at the chest and Respiratory Disease Specialized Center in Baghdad. Demographic data, presenting symptoms, data on smoking, and recurrence of disease were compared. Information on smoking status, tobacco smoking was collecte

The present research aims at identifying the impact of S.N.I.P.S strategy on the achievement of fifth grade students in natural geography

For the purpose of verifying the objective of the research, the researcher put the following zero hypothesis: There is no statistically significant difference at the level of (0.05) between the mean score of experimental group who study according to the (S.N.I.P.S) strategy, and the mean score of control group who study according to the traditional method in the achievement test.

In order to verify the validity of this null hypothesis, the researcher adopted the experimental method. Two groups of (60) fifth grade literary students were collecte

The study aims at showing the effect of basil oil on the sensory properties of the laboratory biscuits. the results show the sensory valuation before and after the storage. the (A4) equation exceeds 15% of T exchange (3 , 4 , 5 g. basil 19 , 55 g . fats )in most of the studied sensuous qualities. Then, the (A5) equation of 20% exchange percentage (4.60g. basil oil + 18.40g. fats). Then, the (A3) equation of 10% exchange percentage (2.30g. basil oil + 20.70g. fats). Then the (A2) equation of 5% exchange percentage (1.5g. basil oil + 21.85g. fats). Finally, the control equation (A1) received the lower value of sensuous evaluation and general acceptance. Abstract differences also appeared at denotation level 0.05 between the (A2)