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 work in this paper involves the planning, design and implementation of a mobile learning system called Nahrain Mobile Learning System (NMLS). This system provides complete teaching resources, which can be accessed by the students, instructors and administrators through the mobile phones. It presents a viable alternative to Electronic learning. It focuses on the mobility and flexibility of the learning practice, and emphasizes the interaction between the learner and learning content. System users are categorized into three categories: administrators, instructors and students. Different learning activities can be carried out throughout the system, offering necessary communication tools to allow the users to communicate with each other

This article introduces a novel procedure to detect an approximate solution to Fredholm fractional integro-differential equations with linear type (LFFIDE) defined using Caputo fractional derivative. The new procedure approximates the solution using three types of polynomials: Laguerre polynomials, Hermite polynomials, and Legendre polynomials, thereafter transforming the problem into a linear programming problem. The approximate solutions are compared using testing examples to examine the efficiency of the suggested approach. Also, a comparison with the other methods using the same polynomials illustrates The effectiveness and consistency of the proposed technique. Finally, the error analysis of the proposed technique and convergent are di

To assess the feasibility of using a faecal occult blood test (FOBT) kit as a screening tool for periodontal disease. Additionally, the study aimed to evaluate the test's sensitivity and specificity while exploring the influence of factors like age, sex and the number of teeth on its performance.

This paper is concerned with combining two different transforms to present a new joint transform FHET and its inverse transform IFHET. Also, the most important property of FHET was concluded and proved, which is called the finite Hankel – Elzaki transforms of the Bessel differential operator property, this property was discussed for two different boundary conditions, Dirichlet and Robin. Where the importance of this property is shown by solving axisymmetric partial differential equations and transitioning to an algebraic equation directly. Also, the joint Finite Hankel-Elzaki transform method was applied in solving a mathematical-physical problem, which is the Hotdog Problem. A steady state which does not depend on time was discussed f

 In the present work a theoretical analysis depending on the new higher order . element in shear deformation theory for simply supported cross-ply laminated plate is developed. The new displacement field of the middle surface expanded as a combination of exponential and trigonometric function of thickness coordinate with the transverse displacement taken to be constant through the thickness. The governing equations are derived using Hamilton’s principle and solved using Navier solution method to obtain the deflection and stresses under uniform sinusoidal load. The effect of many design parameters such as number of laminates, aspect ratio and thickness ratio on static behavior of the laminated composite plate has been studied. The

  Acinetobacter baumannii (A. baumannii ) is considered a critical healthcare problem for patients in intensive care units due to its high ability to be multidrug-resistant to most commercially available antibiotics. The aim of this study is to develop a colorimetric assay to quantitatively detect the target DNA of A. baumannii based on unmodified gold nanoparticles (AuNPs) from different clinical samples (burns, surgical wounds, sputum, blood and urine). A total of thirty-six A. baumannii clinical isolates were collected from five Iraqi hospitals in Erbil and Mosul provinces within the period from September 2020 to January 2021. Bacterial isolation and biochemical identification of isolates