This paper is dealing with non-polynomial spline functions "generalized spline" to find the approximate solution of linear Volterra integro-differential equations of the second kind and extension of this work to solve system of linear Volterra integro-differential equations. The performance of generalized spline functions are illustrated in test examples

     This work is devoted to define new generalized gamma and beta functions involving the recently suggested seven-parameter Mittag-Leffler function, followed by a review of all related special cases. In addition, necessary investigations are affirmed for the new generalized beta function, including, Mellin transform, differential formulas, integral representations, and essential summation relations. Furthermore, crucial statistical application has been realized for the new generalized beta function.  

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.

This study, which was conducted in the city of Mosul, through collected 1200 samples from the stool of patients with diarrhea attending hospitals and private clinics for the period from the beginning of January 2019 to the end of December 2019, those whose ages ranged from less than a year-60 year, and for both sexes and by reality 700 samples stool for males and 500 samples stool for females. Samples were collected in clean, sterile, and sealed 40ml plastic bottles. Patient information is noted, name of the parasite, history, sex, age, address. The result showed that climate and temperature have a significant effect on increase the incidence of intestinal parasites through the direct effect on the increase in infection rate. This effect wa

Experimental and numerical investigations of the centrifugal pump performance at non-cavitating and cavitating flow conditions were carried out in the present study. Experiments were performed by applying a vacuum to a closed-loop system to investigate the effects of the net positive suction head available (NPSHa), flow rate, water temperature and pump speed on the centrifugal pump performance. Accordingly, many of the important parameters concerning cavitation phenomenon were calculated. Also, the noise which is accompanied by cavitation was measured. Numerical analysis was implemented for two phase flow (the water and its vapor) using a 2-D simulation by ANSYS FLUENT software to investigate the internal flow of centrifugal pump under c

This quasi-experimental study investigated generative AI (GenAI) tools—Copilot for chemistry and GitHub Copilot for mathematics—on academic achievement and sustainable professional development among 160 undergraduates (40 experimental/control per department) at the University of Baghdad’s Ibn Al-Haitham College of Education for Pure Sciences (2024–2025). Non-random assignment controlled for covariates. Pre/post validated tests (α ≥ .85; 15 MCQ + 5 essay items) measured outcomes. ANOVA revealed significant gains for experimental groups (p < .001, η2 = .41, Cohen’s d = 0.72 [95% CI: 0.45–0.98]). Chemistry excelled in affective domains; mathematics in cognitive/skills. Findings affirm GenAI’s domain-specific efficacy, prov

This quasi-experimental study investigated generative AI (GenAI) tools—Copilot for chemistry and GitHub Copilot for mathematics—on academic achievement and sustainable professional development among 160 undergraduates (40 experimental/control per department) at the University of Baghdad’s Ibn Al-Haitham College of Education for Pure Sciences (2024–2025). Non-random assignment controlled for covariates. Pre/post validated tests (α ≥ .85; 15 MCQ + 5 essay items) measured outcomes. ANOVA revealed significant gains for experimental groups (p < .001, η2 = .41, Cohen’s d = 0.72 [95% CI: 0.45–0.98]). Chemistry excelled in affective domains; mathematics in cognitive/skills. Findings affirm GenAI’s domain-specific effica

Rheumatoid arthritis and periodontitis use analogous effector destructive procedures, in that the inflammatory cells and pro-inflammatory cytokines that drive chronic bone erosion in RA and chronic periodontal destruction in Periodontitis are alike. Periodontitis (PD) has appeared as a hazard factor in a number of health situations as rheumatoid arthritis (RA). To determine the effect of anti-tumor necrosis factor alpha biological treatment (methotrexate and Enbrel or infliximab) on periodontal status of patients having rheumatoid arthritis with periodontitis in comparison to those having periodontitis without rheumatoid arthritis and control healthy subjects and to determine the serum levels of anti-cyclic citrullinated peptide (ACCP) in t