In this article, we investigate a mathematical fractional model of tuberculosis that takes into account vaccination as a possible way to treat the disease. We use an in-host tuberculosis fractional model that shows how Macrophages and Mycobacterium tuberculosis interact to knowledge of how vaccination treatments affect macrophages that have not been infected. The existence of optimal control is proven. The Hamiltonian function and the maximum principle of the Pontryagin are used to describe the optimal control. In addition, we use the theory of optimal control to develop an algorithm that leads to choosing the best vaccination plan. The best numerical solutions have been discovered using the forward and backward fractional Euler

     We have presented the distribution of the exponentiated expanded power function (EEPF) with four parameters, where this distribution was created by the exponentiated expanded method created by the scientist Gupta to expand the exponential distribution by adding a new shape parameter to the cumulative function of the distribution, resulting in a new distribution, and this method is characterized by obtaining a distribution that belongs for the exponential family. We also obtained a function of survival rate and failure rate for this distribution, where some mathematical properties were derived, then we used the method of maximum likelihood (ML) and method least squares developed  (LSD)

importumt educational institution as (kindergartens) need teachers which qualified ownes modalities in their education for children , as Marzanu method in a way of learning and own methods of crisis management, because the teachers that own those styles of learning ginekindergarten children knowledge and the childrenIeaving based on theMeaing and knowledge and integration of their information, And teachers that earn methods of crisis management provide for the children of the kindergarten security within the educational institution which in turn affect the growth and development of the Child and then abilities, health physical, mental, psychological …etc.., The aims of the current research have identified to recognize: 1- the dimension

This research aims primarily to highlight personal tax exemptions A comparative study with some Arab and European regulations. And by conducting both theoretical comparative analyses. Most important findings of the study is the need to grant personal and family exemptions that differ according to the civil status of the taxpayer (single or married). In other words, the exemption increases as the number of family members depend on its social sense. Also taking into account some incomes that require a certain effort and looking at the tax rates, it is unreasonable for wages to be subject to the same rates applied to commercial profits.      

We have studied Bayesian method in this paper by using the modified exponential growth model, where this model is more using to represent the growth phenomena. We focus on three of prior functions (Informative, Natural Conjugate, and the function that depends on previous experiments) to use it in the Bayesian method. Where almost of observations for the growth phenomena are depended on one another, which in turn leads to a correlation between those observations, which calls to treat such this problem, called Autocorrelation, and to verified this has been used Bayesian method.

The goal of this study is to knowledge the effect of Autocorrelation on the estimation by using Bayesian method. F

In this study, a mathematical model for the kinetics of solute transport in liquid membrane systems (LMSs) has been formulated. This model merged the mechanisms of consecutive and reversible processes with a “semi-derived” diffusion expression, resulting in equations that describe solute concentrations in the three sections (donor, acceptor and membrane). These equations have been refined into linear forms, which are satisfying in the special conditions for simplification obtaining the important kinetic constants of the process experimentally.