In this work, nonlinear diabetes controlled model with and without complications in a population is considered. The dynamic behavior of diabetes in a population by including a constant control is studied and investigated. The existence of all its possible fixed points is investigated as well as the conditions of the local stability of the considered model are set. We also find the optimal control strategy in order to reduce the number of people having diabetes with complications over a finite period of time. A numerical simulation is provided and confirmed the theoretical results.

In this paper, we will study and prove the existence and the uniqueness theorems
of solutions of the generalized linear integro-differential equations with unequal
fractional order of differentiation and integration by using Schauder fixed point
theorem. This type of fractional integro-differential equation may be considered as a
generalization to the other types of fractional integro-differential equations
Considered by other researchers, as well as, to the usual integro-differential
equations.

The research aims to evaluate the suppliers at Diyala general electric industries company conducted in an environment of uncertainty and fuzzy where there is no particular system followed by the company, and also aims to use the problem of traveling salesman problem in the process of transporting raw materials from suppliers to the company in a fuzzy environment. Therefore, a system based on mathematical methods and quantity was developed to evaluate the suppliers. Fuzzy inference system (FIS) and fuzzy set theory were used to solve this problem through (Matlab) and the problem of the traveling salesman in two stages was also solved by the first stage of eliminating the fuzzing of the environment using the rank function method, w

In this work, the relationship between the ionospheric parameters (Maximum Usable Frequency (MUF), Lowest Usable Frequency (LUF) and Optimum working Frequency (OWF)) has been studied for the ionosphere layer over the Iraqi zone. The capital Baghdad (44.42^oE, 33.32^oN) has been selected to represent the transmitter station and many other cities that spread over Iraqi region have represented as receiver stations. The REC533 communication model considered as one of the modern radio broadcasting version of ITU has been used to calculate the LUF parameter, while the MUF and OWF ionospheric parameters have been generated using ASAPS international communication model which represents one of the most advanced  and

This paper aims to study the fractional differential systems arising in warm plasma, which exhibits traveling wave-type solutions. Time-fractional Korteweg-De Vries (KdV) and time-fractional Kawahara equations are used to analyze cold collision-free plasma, which exhibits magnet-acoustic waves and shock wave formation respectively. The decomposition method is used to solve the proposed equations. Also, the convergence and uniqueness of the obtained solution are discussed. To illuminate the effectiveness of the presented method, the solutions of these equations are obtained and compared with the exact solution. Furthermore, solutions are obtained for different values of time-fractional order and represented graphically.

  The search is an application for one of the problems of mathematics in the computer; as providing construction and design of a major program to calculate the inverse permutations of the symmetric group Sn , where 1 ≤ n ≤ 13; using some of the methods used in the Number Theory by computer . Also the research includes design flow chart for the main program and design flow chart for the program inverse permutations and we give some illustrative examples for different symmetric groups and their inverse permutations.

The Amarah Oil field structure was studied and interpreted by using 2-D seismic data obtained from the Oil  Exploration company. The study is concerned with Maysan Group Formation (Kirkuk Group) which is located in southeastern Iraq and belongs to the Tertiary Age. Two reflectors were detected based on synthetic seismograms and well logs (top and bottom Missan Group). Structural maps were derived from seismic reflection interpretations to obtain the location and direction of the sedimentary basin. Two-way time and depth maps were conducted depending on the structural interpretation of the picked reflectors to show several structural features. These included three types of closures, namely two anticlines extended in the directions of

       This study introduces a series of single and pile group model tests subjected to lateral loads in . multilayered sand from Karbala, Iraq. The aim of this study is to investigate: the performance of the pile groups subjected to lateral loads; in which the pile batter inclination angle is changed; the effect of pile spacing (s/d) ratio, the influence of using different number of piles and pile group configuration. Results revealed that the performance of single negative (Reverse) Battered piles with inclination of 10° and 20° show a gain of 32% and 76 % in the ultimate lateral capacity over the regular ones. For pile groups, the use of a combination of regular, negative and positive battered piles in

Trichomonas vaginalis is a causative agent of trichomoniasis , one of the most common non-viral sexually transmitted disease (STD) over all the world, especially in immunocompromised women such as pregnant. Wet smear and Giemsa stain are the current methods used in hospital to diagnosis trichomoniasis. DNA based diagnosis is still to be validated to diagnose the local isolates, the objective of the present study was to compare the conventional methods of disease diagnosis with the DNA-based method to diagnose Trichomonas incidence in local isolates. In the present study, 105 samples were collected from outpatient women (18-45 years) of Maternity hospital in Mosul who showed a classical presentation of Trichomonas

In this article, we define and study a family of modified Baskakov type operators based on a parameter . This family is a generalization of the classical Baskakov sequence. First, we prove that it converges to the function being approximated. Then, we find a Voronovsky-type formula and obtain that the order of approximation of this family is . This order is better than the order of the classical Baskakov sequence  whenever . Finally, we apply our sequence to approximate two test functions and analyze the numerical results obtained.