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

يهدف هذا العمل الى بيان طبيعة العلاقة بين الادارة بالتجوال والتجديد الاستراتيجي ، ومدى تأثير المتغير المستقل في المتغير التابع. تضمنت فقرات الاستبانة بوصفه الأداة الرئيسة لجمع البيانات ثلاث جوانب اساسية، تضمن الاول البيانات الشخصية للمستجيبين، فيما تضمن الجانب الثاني الفقرات الخاصة بمتغير الادارة بالتجوال من خلال خمسة ابعاد، فيما اشتمل الجانب الثالث على فقرات التجديد الاستراتيجي عبر تناول اربعة ابعاد. ي

This study came to discuss the subject of industries dependent on petrochemical industries in Iraq (plastic as a model) during the period 2005–2020, and the study concluded that the plastic industries contribute to areas of advancement and progress and opportunities to deal efficiently with the challenges posed by the new variables, the most important of which is the information revolution. communications and trade liberalization, and this is what contributes to the competitiveness of these industries. And because the petrochemical industry in Iraq has an active role in establishing plastic industrial clusters and clusters of micro, small, and medium industries by providing the necessary feedstock for these industries in various fields

The whole world and the Arab world, especially an important part of this international system, is undergoing a radical transformation at all levels. This mosaic of political, economic, social and military relations and alliances, whether based on the special interests of the major Powers or on the basis of mutual interests, The major transformations to social, economic, political and military conflict and these transformations still bear more surprises, at all levels, nothing remains constant, all changed, relations changed and alliances changed and loyalties fell and the principles of the M changed and the spectacular imperial economies collapsed and the will of the masses was no longer fixed.

This study we have made a subject of fanny podcast in electronic media, as a new way to express different issues by the public, This study focuses started on how to address social issues in Alegria by ANAS TINA vidéo on the youtube network , you are to know the trends of young amateur about the various issues dealt with as well as the most important methods used to convince browsers.
The researcher used the survey method based on studying 10 episodes videos of blogger ANAS TINA.
The result of the study found that the most important issues are the abduction of children, teaching in Algeria; women in Algeria, The negative aspects of the issues addressed have been established in order to direct public opinion and awareness of ph

     The control function of important functions in the system of government for several reasons , perhaps the most important of the magnitude of spending and spending in one of the tools adopted in the implementation of the control function.                               

        Perhaps the most prominent stages of the development budget in terms of setup and use in the budget programs and performance , as specialized literature  show its importance in strengthening financial and operationl

When exercising their authority in the jurisprudence, judges are subject to a set of restrictions that they must adhere to, as they do not want their jurisprudence to be accepted and welcomed by law practitioners in general, and legal scholars in particular, and in contrast to it, the arrows of criticism and defamation will extend to that jurisprudence, and then they will have to reverse them . Perhaps the most important of those restrictions imposed on judges is their observance of justice between the parties to the lawsuit through their lack of bias for one of the parties at the expense of the other, in addition to their observance of public order and public morals, as well as their observance of the legal texts that they work under its u

The design fabrics of the most important episodes that are at the core process rhetorical communication, until they became these episodes ample room for research and investigation, and the issue of non-familiar formality is nothing but the result of those relationships Constructivism, which is the result of an effort builders coherent activate the shape and attributes of phenotypic, therefore it will cause him a lot of questions about his and founded the organization in order to activate the speech communication between the product(cloth)and the receiver .On this basis, the research problem identified on imposing the question follows:1. Does the non-familiar formal role in enriching communication discourse of women's fabric designs?2. Ar

In a quick reading of the character of Camille Ben Ziad al-Nekha al-Kufi al-Taabi, one of the most sincere companions of Imam Ali (peace be upon him), he enjoyed great status and status because he was one of the people of his people who lived alongside Imam Ali (peace be upon him) since his tribe migrated from Yemen to Kufa To this end, he became loyal during the reign of Imam Ali (peace be upon him), who is also a member of the delegation coming from Kufa to protest against the actions of the Wali of Kufa during the reign of Caliph Uthman ibn Affan. After the death of Caliph Uthman bin Affan, (Peace and blessings of Allaah be upon him) (Duaa kamil), one of the most famous and important supplications in Islamic history, and each one of u