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

The current paper highlights an important character represented by the American president John Tyler 1841 – 1845, who is considered the tenth American president. The importance of this paper lies in identifying his personality in terms of his upbringing and the political activities he practiced before assuming the presidency and his most significant internal achievements, which showed his decisions as a president. He was fully prepared to support national policies since they do not exceed the authorities of the states. With his achievements in the foreign policy, he was capable to draw and define the features of the American foreign relations that were in harmony with the general situation in the United States of America at that time.

The Sunnah of the Prophet has a great impact in building human behavior, and the formation of Islamic thought, has worked to spread science in all of Egypt, as it carried to the people of the eternal prophecy of the love of science, it was a source of knowledge and civilization. It is a generous source, a rich source of the Islamic nation, always tender, and renewed benefit, which is not only a source of legislation and language but is a source of guidance for thought and guidance of behavior, and the Hadith The importance is obvious In the integration of Islam, and show aspects of human integration in the personality of Mustafa , and the Muslims are interested in talking - collected and codification -, and made the effort of the cent

The aim of the research is to identify the reality of strategic planning in the National Insurance Company and its importance in building institutional work and to identify the requirements that enable this company to successfully implement strategic planning and the obstacles that limit its application and then achieve the marketing objectives of this company. This study started from the fact that there is a problem represented by the main question that was stated.                                            &nbsp

         Bringing about urban, economic, and social changes in rural areas similar to those occurring in urban areas aims to reduce urban-rural disparities by providing services in those areas, decentralizing the management of these services, expanding citizen participation in local governance (decentralized administration), and achieving comprehensive development, developing and empowering localities, and keeping pace with new transformations and their impacts on the functions of the center and localities. In fact, the lack of clarity of the role of local government in planning and managing services has hindered development plans, and declined the level of services in rural areas, and has negative

Abstract                                                    

           The research aims to investigate the existence of correlations and influence between agricultural insurance risk management and economic development in the National Insurance Company with farmers, as agriculture is one of the leading branches of the national economy, ensuring food security and eliminating poverty to ensure sustainable ec

The research dealt with its forefront a definition of the aspects of the study and its variables, the explosive capacity and its relationship to the scoring of football for the halls and highlights the importance of these variables, and the problem of the research consisted that some players fail to score Amie because of the weak power of shots or the slow scoring, so the researchers saw studying this problem and knowing the extent of the influence of the explosive strength During the performance of the skill of scoring with five football, the study aimed to identify the relationship between the explosive strength and the skill of scoring with five football. Researchers assume that there is a statistically significant relationship between t

Abstract:
Rabi’a tribe lived on the land of Euphrates since the first century of the
Christ. Then that land becomes her homeland. The Persians tried many times
to drive her away from that land, but with out result.
In the course of time Rabi’a become more knowledgeable of Persia.
This tribe proved her love and sanctification to the land of Euphrates, in the
battle of Dhyqar.
Rabi’a converted to Islam quickly and helped the Muslims to conquer
Iraq with a big number of fighters in many battles like al- Qadisyyah. That
influenced the anger of Mudriat Arab tribes who were their old enemies.
Mudriat tribes did their efforts to reduce the importance of Rabi’a because of
some its branches were among of t