This study presents a mathematical model describing the interaction of gut bacteria in the participation of probiotics and antibiotics, assuming that some good bacteria become harmful through mutations due to antibiotic exposure. The qualitative analysis exposes twelve equilibrium points, such as a good-bacteria equilibrium, a bad-bacteria equilibrium, and a coexisting endemic equilibrium in which both bacteria exist while being exposed to antibiotics. The theory of the Sotomayor theorem is applied to study the local bifurcation around all possible equilibrium points. It’s noticed that the transcritical and saddle-node bifurcation could occur near some of the system’s equilibrium points, while pitchfork bifurcation cannot be accrued at

Abstract:

The current research included " Diagnosis of the reality of the gap for the requirements of Business Continuity Management System According to International Standard (ISO 22301: 2012) in Midland Refineries Company (Daura Refinery) " , for development of an administrative system for Business Continuity is considered a priority in the present day, and in the light of the organizations dependence on computers and information technology in work and communication with others . the international legitimacy (represented by the international organization for standardization (ISO)) remains the basis for matching and commitment , and the importance of the application of Business Continuity Management Syst

Recently, there has been a notable surge in interest surrounding entrepreneurial orientation and strategic entrepreneurship. These concepts are particularly relevant due to their modern characteristics that aid in adapting to the environment. They also play a crucial role in improving production, service, and technological processes to sustain value, minimize competition, and drive ongoing enhancements, ultimately leading to a position of leadership within public companies. Therefore, the primary focus of this research was to examine the influence of entrepreneurial orientation on achieving strategic entrepreneurship. This influence is further mediated by the presence Iraqi Ministry of Agric

     The importance of this research is due to its importance goals, Which are about the attempt of researchers to investigate the probability of depending on businesses^, environments to transform organizations^, performance in away that enhance the leading  role of organizations  in their environments , and through views of a number of the staff working in the foundation of technical institutes in Mosul.  .

     After deciding the methodology of the study that ,in one hand ,performs the goals of the study , and achieving a suitable theoretical framework to present the concepts of businesses^, environments and the leadin

Table tennis is considered one of the fast base sports that the player needs to have the speed of performance and awareness, especially in straight forward and back strikes, which is an important offensive skills, and the player success depends on his perception speed to the point of the fall of the ball in the arena of his competitor. But there is no way to measure cognitive processing speed. Therefore, the researchers sought to design a test that measures this ability to ensure its scientific evaluation, and then establish standard scores for this test for the players of the specialized school of table tennis, to help evaluate them objectively and move away from subjective estimates when evaluating and developing measuring instruments in

It is known that life is as series of variety of difficult problems that individual looks
forward to overcome so as to achieve adaptation and to reach the desired aims .The transition
of the students from the school stage to the stage of the university is actually regarded a
dramatic change where students face when they enter university life that differs from what
they lived in secondary school.
The executive functions are considered the main element that participate in solving the
problems of high orders , because it involves the mental abilities that assist individual to
think and initiative as well as solving problems .
These functions include operational planning and the activated memory and inhibition of
q

The aim of the study is to study the quality of services in a sample of the municipalities of Baghdad governorate and identify the deviations in their operations and provide solutions to address the causes of deviations. The research field aims at the same activity related to municipal services and their quality and analysis using some tools for continuous improvement to identify the authorities responsible for the delay and quality of services. In the future, the importance of research is shown by the use of these tools and their use and their application to the data of the directorates (sample of the study) to diagnose and treat problems, especially that they include statistical methods that are clear and easy to understand the

Tensile strength is a critical property of Hot Mix Asphalt (HMA) pavements and is closely related to distresses such as fatigue cracking. This study aims to evaluate methods for assessing fatigue cracking in Asphalt Concrete (AC) mixes. In order to achieve optimum density at different binder contents, the mixes were compressed using a gyratory compactor. Tensile strength was assessed using the Indirect Tensile (IDT) and Semi-Circular Bend (SCB) tests. The results showed that the tensile strength measured by the SCB test was consistently higher than that measured by the IDT test at 25 °C. In addition, the SCB test showed a stronger correlation between increasing binder content and tensile strength. For binder contents ranging from 4