The problem of Bi-level programming is to reduce or maximize the function of the target by having another target function within the constraints. This problem has received a great deal of attention in the programming community due to the proliferation of applications and the use of evolutionary algorithms in addressing this kind of problem. Two non-linear bi-level programming methods are used in this paper. The goal is to achieve the optimal solution through the simulation method using the Monte Carlo method using different small and large sample sizes. The research reached the Branch Bound algorithm was preferred in solving the problem of non-linear two-level programming this is because the results were better.

Several efforts have been made to study the behavior of Total Electron Content (TEC) with many types of geomagnetic storm, the purpose of this research is to study the disturbances of the ionosphere through the TEC parameter during strong, severe and great geomagnetic storms and the validity of International Reference Ionosphere IRI model during these kinds of storms. TEC data selected for years 2000-2013 (descending solar cycle 23 to ascending cycle 24), as available from koyota Japan wdc. To find out the type of geomagnetic storms the Disturbance storm time (Dst) index was selected for the years (2000-2013) from the same website. Data from UK WDC have been taken for the solar indices sunspots number (SSN), radio flux (F10.7) and ionosp

Background: The frontal sinus area can be used as a diagnostic aid to recognize mouth breather subjects. The aims of this study were to determine the gender difference in each group, to compare the frontal sinus area between mouth breather and nasal breather group, and to verify the presence of correlation between the frontal sinus area and the cephalometric skeletal measurements used in this study. Materials and Methods: Cephalometric radiographs were taken for 60 adults (30 mouth breathers and 30 nasal breathers) age range (18-25), for each group 15 males and 15 females, in the orthodontic clinic in the college of Dentistry at Baghdad University. The control group (nasal breather) with skeletal class I and ANB angle ranged between 2-4º,

In this paper we present a study on Peristaltic of fractional generalized Maxwell viscoelastic fluid through a porous medium. A modified Darcy-Brinkman model is utilized to simulate the flow of a generalized Maxwell fluid in a porous medium in an inclined channel with slip effect. The governing equation is simplified by assuming long wavelength and low Reynolds number approximations. The numerical and approximate analytical solutions of the problem are obtained by a semi-numerical technique, namely the homotopy perturbation method. The influence of the dominating physical parameters such as fractional Maxwell parameter, relaxation time, amplitude ratio, permeability parameter, Froude number, Reynolds number and inclination of channel on

In this paper, we illustrate how to use the generalized homogeneous -shift operator  in generalizing various well-known q-identities, such as Hiene's transformation, the q-Gauss sum, and Jackson's transfor- mation. For the polynomials , we provide another formula for the generating function, the Rogers formula, and the bilinear generating function of the Srivastava-Agarwal type. In addition, we also generalize the extension of both the Askey-Wilson integral and the Andrews-Askey integral.

This paper discusses reliability of the stress-strength model. The reliability functions 𝑅1 and 𝑅2 were obtained for a component which has an independent strength and is exposed to two and three stresses, respectively. We used the generalized inverted Kumaraswamy distribution GIKD with unknown shape parameter as well as known shape and scale parameters. The parameters were estimated from the stress- strength models, while the reliabilities 𝑅1, 𝑅2 were estimated by three methods, namely the Maximum Likelihood,  Least Square, and Regression.

 A numerical simulation study a comparison between the three estimators by mean square error is performed. It is found that best estimator between

. Mesopotamian art is thase mployed all around him into forms for artistic purposes and different con not at ions help him to understand the world around him and customized for their interests

The mural architectural art has distinguished traits that made it promote to the rank of the prominent arts that have been employed  by the Mesopotamian human to relate to the world  the heroic deeds and exploits  of that civilization ,that formed greatest and most splendid wonderful works that still illustrious and outstanding  till nowadays .The mural  architectural  art of pottery and glazed considered one of the most ancient wonders  of Mesopotamian creation in Old Iraq .The best quintessence of mural

The exploitation of all available resources and benefiting from them is one of the most important problems facing the decision makers at the present time. In order to exploit these resources, it is necessary to organize the conflicting objectives, which is the main work in the project management, which enables the development of a plan that decision makers can use to shorten the total completion time and reduce the total cost of the project. Through the use of modern scientific techniques, and therefore the researcher using the critical path method using the technology of programming goals to find more efficient ways to make appropriate decisions where the researcher worked to solve the problems in the construction of the Departm

he assignment model represents a mathematical model that aims at expressing an important problem facing enterprises and companies in the public and private sectors, which are characterized by ensuring their activities, in order to take the appropriate decision to get the best allocation of tasks for machines or jobs or workers on the machines that he owns in order to increase profits or reduce costs and time As this model is called multi-objective assignment because it takes into account the factors of time and cost together and hence we have two goals for the assignment problem, so it is not possible to solve by the usual methods and has been resorted to the use of multiple programming The objectives were to solve the problem of