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 aims to identify the effect of the proposed strategy in accordance with realistic mathematics on the achievement and mathematical Interrelation of third Intermediate students. Two samples were tested from the middle third grade in a school affiliated with the General Directorate of Baghdad- Rusafa, the first for the academic year (2022-2021). The experimental group is (30) students taught according to the proposed strategy, and the control group is (30) students based on the traditional method. To achieve the research objective, the researchers developed a test for achievement consisting of (30) items and a test of sports interconnection composed of (20) items. The results of the stu

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 work aims to show the nature of the relationship between management by walking around  (the independent variable) and strategic renewal (the dependent variable), as well as it shows the effect of the independent variable on the dependent variable. Questionnaire items were considered the main tool for data collection by three basic aspects. The first involved the personal data of the respondents, while the second included items related to management by walking in five dimensions, and the third is strategic renewal items by addressing four dimensions. The tourism sector, while the community has six Excellent grade hotels was taken into account in this wor

In this research entitled "Internal music in the poetry of guidance in the era of Islam and its artistic and semantic implications" dealt with the following:
 Preface, which addressed the importance of internal music in poetry, and its close association with poetry, and the poet himself, to reveal what is touring himself and revolves in his imagination.
 Repetition of all kinds: repetition of letters, repetition of words, and repetition of phrases: It showed what this repetition of strengthening the melody, and linking parts of words within the same house, or the poem, and create a special musical atmosphere to spread a certain significance and to confirm the meanings and accompanied by musical accommodation.
 Anaphysic

Modern communication and media technology has pioneered new horizons and curried out deep changes in the various fields of social life, It effected enormously human communication as well.
Content one Who late the developments which have effected the social relations ،due to the new media ،especially Face book ,will certainly notice the far cry changes of the social relation net which has been effected ,in a way or another ،the accelerated development ،under the appearance of the so called the virtual society .
Face book has embodied the means – communication ,which has become an important turn point in the social communication .
It is the point the present paper tries to expose an discuss by a field study curried on a sam