In this paper we use non-polynomial spline functions to develop numerical methods to approximate the solution of 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of these method, and to compare the computed results with other known methods.

In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal meth

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 research study is important since it establishes predicted rates for various nervous system functional indicators.In terms of performing the skill of Dribbling in basketball for young players in Baghdad Governorate in order to reach scientific results that serve researchers, coaches, and players uniformly. The study's goal is to create predictive equations for specific functional indicators of the nervous system in relation to the Dribbling skill performance of young basketball players in Baghdad Governorate. The researchers used a descriptive approach with a survey method on (8) youth basketball league clubs in Baghdad Governorate for the 2022-2023 sports season, totaling (96) players . Three tests were used to measure the nervous sy

In this research the Empirical Bayes method is used to Estimate the affiliation parameter in the clinical trials and then we compare this with the Moment Estimates for this parameter using Monte Carlo stimulation , we assumed that the distribution of the observation is binomial distribution while the distribution with the unknown random parameters is beta distribution ,finally we conclude that the Empirical bayes method for the random affiliation parameter is efficient using Mean Squares Error (MSE) and for different Sample size .

The purpose of this research is to demonstrate the effectiveness of a program to address the problem of mixing similar letters in the Arabic language for students in the second grade of primary and to achieve the goal of the research. The researcher followed the experimental method to suit the nature of this research and found that there are statistically significant differences between the tribal and remote tests, The effectiveness of the proposed educational program. At the end of the research, the researcher recommends several recommendations, the most important of which are: 1 - Training students to correct pronunciation of the outlets, especially in the first three stages of primary education (primary) and the use of direct training

Abstract  

  In this work, two algorithms of Metaheuristic algorithms were hybridized. The first is Invasive Weed Optimization algorithm (IWO) it is a numerical stochastic optimization algorithm and the second is Whale Optimization Algorithm (WOA) it is an algorithm based on the intelligence of swarms and community intelligence. Invasive Weed Optimization Algorithm (IWO) is an algorithm inspired by nature and specifically from the colonizing weeds behavior of weeds, first proposed in 2006 by Mehrabian and Lucas. Due to their strength and adaptability, weeds pose a serious threat to cultivated plants, making them a threat to the cultivation process. The behavior of these weeds has been simulated and used in Invas

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.

Vaginal biopsies and smears were collected from ten adult local healthy goats. Routine histological methods were carried out on vaginal biopsies and then stained with PAS stain. The smears were stained with Methylene blue. All samples were inspected under light microscope. The present study found that many constituents of the wall of the vagina, which have an important functional role, were absent; among these were the vaginal glands, goblet cells, muscularis mucosa, and lymphatic nodules. On the other hand, vagina showed special compensatory histological mechanisms, namely, the deep epithelial folds, the well-developed germinated stratum basale, the apparent basement membrane, and the profuse defensive cells, such as neutrophils, m