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 importance of the research lies in knowing the effect of the exercises of the reciprocal method in developing some physical abilities in learning the performance of the players for the effectiveness of the long jump in an economical manner in terms of time and effort and knowing their positive impact and the extent of their impact in creating the required learning for students, and the research aims to prepare reciprocal style exercises in developing some abilities The researchers used the experimental method in the pre and post test for the experimental and control groups to suit the nature of the research, and the research community was identified for the long jump players, the Specialized School for Talent Care in the 2022 sports sea

The possibility of implementing smart mobility in the traditional city: Studying the possibility of establishing an intelligent transportation system in the city center of Kadhimiya

The organization of sporting activities at the local and international levels requires a lot of money, which has increased interest in marketing in the sports field, as it is one of the modern topics that represent the basic knowledge needed by the sports marketer and which represents one of the basic concepts to enhance the benefits and returns of sports clubs. The research problem was the weak awareness of the members of the administrative body of Iraqi sports clubs of the role of sports marketing in the dimensions of competitive superiority and not exploiting them in the optimal way that enables clubs to achieve competitive superiority. The research aims to know the role of sports marketing in competitive superi

 The study aimed to show the jurisprudential impact of the multiplicity of directing the syntactic movement of the Qur’anic readings, and it was based on the inductive, descriptive and analytical approach. , such as the difference in explaining the ruling on washing the feet, and the one who meditates on the Qur’anic readings notices in it a picture of the Qur’anic miracles, and this is what is manifested by the brevity of the speech. Collapse the research, and the research tried to trace the Qur’anic readings, contained in the verses, and the readings were limited to what is related to the explanatory meaning mentioned by the commentators, by clarifying the explanatory relationship between the Qur’anic readings and the me

The economic dimensions of environmental issues are complex and unclear in many cases, there is a kind of confusion in the real relationship between economic growth and environmental regulations. Many of the negative environmental impacts are accompanied by human activities and urban and industrial development in the city, and that many of the projects that did not take into account the environmental factors during the planning and implementation of them can be detrimental, as well as natural environments, archeological sites, historical or scientific value, aesthetic or educational. It also describes the Global Environment Outlook that if current trends continue, population growth, economic growth and consumption patterns, the p

Formed a decoration element Tzeigna important holidays linear, since regulating mechanism of vocabulary and formative elements Btnoatha through activation design with space linear in order to add value expressionistic, and achieve career goals and aesthetic, has promised these diversities and one of the finest artistic achievements that excelled the designer patterned through expertise and skill in the output of the design artwork beautiful image to fit with the importance degree in the field of calligraphy and set the rules, and was questionably basic research problem is the following:
What are the variations in the design of linear motifs Vacations?
In order to solve these problems and to reach the desired outcomes research ai

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.