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 can understand interior design as a series of interconnected human principles and goals formed by science and knowledge to build a human product that reveals or gives meaning to things، and this can be presented through ecology as a system concerned with environmental aspects and as part of interior design، seeking to achieve aesthetic and functional values، in an interactive form between spaces The interior and its occupants are within an environmental balance full of life، and the ecological interior design attaches great importance to the embodiment of spiritual aspects in the internal environment، in addition to emphasizing the importance of protecting the environment and preserving resources through saving in its use and usi

              The purpose of this project is to build a scientific base and computational programs in an accelerator design work. The transfer of group of laws in alinear accelerator cavity to computer codes written in Fortran power station language is inorder to get a numerical calculation of an electromagnetic field generated in the cavities of the linear accelerator. The program in put contains mainly the following, the geometrical cavity constant, and the triangular finite element method high – order polynomial. The out put contains vertical and horizontal components of the electrical field together with the electrical and the magnetic field intensity. 

A study worthy of study and objective analysis of the relationship of formal synthesis and innovative effectiveness in the design of modern women's fabrics, which deals with the first chapter the problem of research based on the following questions: (What role of innovative thinking in the formal synthesis of women's clothing designs Modern)

   The research objectives included the following:

1 - defines the concept of innovative thinking and its effectiveness in design

2 - Reveal the role of innovative thinking in the formal synthesis of the designs of modern women's fabrics

   The theoretical framework which included the following parts:.

1 - Innovative thinkin

In light of the intellectual and technological progress within the current developments of time, as well as the emergence of digital tools and means of display and communication, which had a major role in the shifts of the time of globalization in various commercial and economic fields, as well as areas of transferring the design image and its stages of development to customers and the convergence of views between the customer and the interior designer, which are the most important pillars of the design process As a whole, and accordingly, there is an urgent need for a process of intellectual balance between them through digital tools from the technical side and through social media from the intellectual side. Customer comments via socia

The Mesopotamian soil is muddy and fertile, and so from ancient eras Iraqis used mud in their building, settlements and architecture in different methodologies according to the nature and the function of the building that was either in its pure form or by mixing it with other materials such as straw . also as raw bricks in different ways either for the whale building or parts of it, or for the finishing parts such as roofing for instance. In this research these different forms and methodologies will permeate through out a chosen examples of historical building, rural buildings and settlements and ancient buildings as well as some current uses of mud in the structures and building in standing cities, this in order to conclude some

     The goal of this research is to solve several one-dimensional partial differential equations in linear and nonlinear forms using a powerful approximate analytical approach. Many of these equations are difficult to find the exact solutions due to their governing equations. Therefore, examining and analyzing efficient approximate analytical approaches to treat these problems are required. In this work, the homotopy analysis method (HAM) is proposed. We use convergence control parameters to optimize the approximate solution. This method relay on choosing with complete freedom an auxiliary function linear operator and initial guess to generate the series solution. Moreover, the method gives a convenient way to guarantee the converge

In this paper, a method based on modified adomian decomposition method for solving Seventh order integro-differential equations (MADM). The distinctive feature of the method is that it can be used to find the analytic solution without transformation of boundary value problems. To test the efficiency of the method presented two examples are solved by proposed method.