In this paper, we describe the cases of marriage and divorce in the city of Baghdad on both sides of Rusafa and Karkh, we collected the data in this research from the Supreme Judicial Council and used the cubic spline interpolation method to estimate the function that passing through given points as well as the extrapolation method which was applied for estimating the cases of marriage and divorce for the next year and comparison between Rusafa and Karkh by using the MATLAB program.

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.

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

Background: Neutrophils destroy pathogens via phagocytosis. Neutrophils are effective innate and acquired immunity phagocytes. Low-density neutrophils are distinct neutrophil phenotypes linked to several systemic and infectious diseases. To our knowledge, low-density neutrophil phagocytosis in periodontitis has not been examined. Opsonized and non-opsonized fluorescent beads mixed with low-density neutrophils were gated and analyzed by flow cytometry to count cells that consumed at least one bead.

Aims of the Study: To estimate the potential impact of antibody (Ab)-labeled and non-labeled phagocytosis capacity of low-d

This paper presents an analytical study for the magnetohydrodynamic (MHD) flow of a generalized Burgers’ fluid in an annular pipe. Closed from solutions for velocity is obtained by using finite Hankel transform and discrete Laplace transform of the sequential fractional derivatives. Finally, the figures are plotted to show the effects of different parameters on the velocity profile.

As material flow cost accounting technology focuses on the most efficient use of resources like energy and materials while minimizing negative environmental effects, the research aims to show how this technology can be applied to promote green productivity and its reflection in attaining sustainable development. In addition to studying sustainability, which helps to reduce environmental impacts and increase green productivity, the research aims to demonstrate the knowledge bases for accounting for the costs of material flow and green productivity. It also studies the technology of accounting for the costs of material flow in achieving sustainable development and the role of green productivity in achieving sustainable development. According