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

Central banks around the world typically use various financial indicators to evaluate performance. In Iraq, the indicators used by central banks to evaluate the performance of banks are of great importance to ensure that the banks operating within the Iraqi banking system comply with the regulatory and legal requirements issued by the Central Bank of Iraq or the Ministry of Finance. Given the need to study the profitability indicator to ensure its ability to evaluate the performance of specialized banks in Iraq, these banks carry out their banking activities and businesses through capital funded by the government. The use of profitability indicators in evaluating the performance of specialized banks provides information about the profitabil

The purpose of this research highlight the achievement of the effectiveness of small and medium enterprises dimensions and conformable to analyze the relationship between business strategies and human resources management strategies , and launched search of a dilemma thought provoking fundamental questions revolve around the search is the lack of appropriate strategies in these enterprises to help them continuity and permanence in business and markets , as these enterprises lack the human resources management strategies appropriate , as well as business strategies that make them withstand the changes in the market environment is changing and volatile . It was to

Prison and imprisonment  
And their impact on the strengthening of power
In the Qur'anic perspective

This study is targeting the new developed materials and techniques and how they were affected by the scientific and technological developments that contributed to revelated new and varied developed materials and techniques. And from the artist’s formulation by using the materials and techniques and through its embodiment and sensor the values, artistic and aesthetic standards by breaking from the familiar in aesthetic contemporary way.
The studies on questioning what’s the role of The New Developed Materials and Techniques in exposing the aesthetic of the art work?

This study is to show the aesthetic of the art work through the new developed materials and techniques. Which was based on descriptive analyzing method and hig

Dealing with this study to find a link principle in the construction of the system and disorder to the promise of the principles and concepts of intellectual and philosophical form and content in the act of interior design of the halls education in the Ministry of Labor and Social Affairs , which leads to a reaction design objective and functionally and to increase the strength of the effect on users of the coaches and trainers . As it informs the side cognitive and developmental study of the design of the interior spaces . So it was the goal of research in the detection of the nature of the system and disorder with Focus indicators and the type of regulations and privacy and what constitutes the framework of knowledge in order to explai

The Risks Faced by Britain in their Areas of Influence at the Beginning of the Twentieth Century Drove her to the Alliance with the State of European such as France, and Contributed to the Tireless and made by the British and French Politicians in the Consolidation of Friendly Relations between the two Countries Efforts and Strengthened Cooperation in a Positive Way to Visit the king of Britain's Edward VII to France, Offset by Visit French President Loubet to Britain in the Same Year, those Negotiations Bore Fruit between the two Countries for Reaching a Contract Arbitration and Decisiveness between Britain and France Treaty on the Fourteenth of November 1903, Promised that Treaty First Step that Paved the Way for a General Agreement be