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

 Several studies have indicated an unprecedented increase in the number of Arab youth who watch music videos. It is also a custom in Arab countries to broadcast songs at their happy parties such as weddings, engagements and birthdays. We see that guests and party owners interact by dancing and singing with the songs, while the viewership rates of Arab music videos have reached millions on YouTube. The researcher decided to study the image of women through the lyrics of these songs, due to their importance in shaping the image of women in the minds of young people and shaping the (self-image) of young women. Twenty songs were selected from the most watched songs on YouTube for the year 2024, and it was found that the negative qualities of t

سعي المجتمع العراقي منذ أكثر من نصف قرن مضى لإعادة استثمار عشرات المليارات من الدولارات من الإيرادات النفطية في القطاع الزراعي وهياكله وبنياته التحية، كإنشاء السدود والخزانات المائية واستصلاح الأراضي والمشاريع الإنتاجية الحيوانية والنباتية وبطاقات كادت تقترب او تتجاوز حاجز طلب السكان من الأغذية والمنتوجات الزراعية التي تغذي الصناعة الا ان الزيادة السكانية وتحسن مستوى الدخل النفطي شكلا انتقالا جدي

The grammar structure transforms from its fundamental field to another field that takes new dimensions, and is used in another way in speech that differs from the first one, because the formula basis of the name(Faael) in speech is a (distorted characteristic), and the distorted characteristic indicates the stability and the necessity of the characterized. as this characteristic has changed from its use as a distorted characteristic which was established by the elders. to a use that differs from the first and cannot be overlooked to achieve a new purpose, to be used as plural

Prepositions have a key function, which is to associate parts of a sentence, called letters In addition, it adds the meanings of the verbs to the names, ie reached by them, and called by the coffin characters Qualities..

          I chose to search for the meaning of the preposition "from" in Surat Maryam to know its meanings in terms of originality and expansion, so the title of the research (the meanings of preposition "from" in terms of originality and expansion in Surat Maryam model(

Time crosses one of the most important principles that are agreed upon in contracts, because the temporal dimension has a significant impact on all contract provisions and is not limited to a certain group of them. French and Arab legal jurists alike called for this dimension to be given special attention. That is the term of the contract term; To try to limit the temporal elements, clarify their provisions and distinguish between them, but in the Arab world it did not receive the same attention that it received in the West.

The theatrical view reflects various connotations and intellectual and aesthetic implications, as the view includes a symbolic geometric, architectural and archetypal connotation suggestive of reality and nature, as theatrical art is the woman that reflects reality, specifically the significance of the theatrical view that reveals to us the philosophical, aesthetic and cognitive dimensions of theatrical trends, so the research came with the methodological framework, which It included the research problem (what is the significance of the scene as a symbolic system in the Iraqi theatrical performance), the importance of the research and the need for it, the research objective, the limits of the research and the most important terms.
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This research seeks to study the role of military bases in activating defense diplomacy, with a focus on studying the case of France in the African continent, which relied on its military bases as a tool to implement its foreign policy. The research explains the concept of defense diplomacy and its relationship to military bases as an effective tool to strengthening bilateral relations between the state's parties. The research focuses on studying the effectiveness of military bases as a tool for activating French defense diplomacy, and studying the goals that French foreign policy seeks to achieve through its intervention or presence in the African continent. In addition to the geopolitical reasons that prompted France to move to

The business environment is witnessing tremendous developments in the field of production and technology, which requires the development of production methods to go in line with these developments and the increasing competition, which has gone beyond the economic aspects to extend to the environmental aspects, as economic units tended to adopt a cleaner production strategy and through what they achieve by producing environmentally friendly products and achieving economic efficiency. Reducing costs, providing a safe and clean environment for workers, and reducing waste from production operations.