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

Relying on modern work strategies, such as adopting scientific inductions, consolidates the information in the learner’s memory, develops the skill work of the football player, and raises the efficiency of their motor abilities. From this standpoint, the researcher, who is a teacher at the University of Baghdad, College of Physical Education and Sports Sciences, and follows most of the sports club teams in youth football, believes that there must be From extrapolations through the machine and employing it in the field to serve the skill aspect and benefit from scientific technology in development and making it a useful tool to serve the sports field in football, as the goal of the research was the efficiency of machine extrapolation in de

Factory is trotting home favorite of of Aeidid of Iraqi families since he Amta imparted to the taste of the housewife on the method of processing and preparation and the possibility of using some of the ingredients to raise the nutritional value of meat, sesame and other, but how keep Bz'zajh this product Atne storage

Objectives: The main objective of this study is to examine the crucial role that Russian writers and intellectuals played in catalyzing the 1905 Revolution in Russia. Specifically, the study sought to analyze how their literary works, philosophical ideas, and political writings challenged Tsarist autocracy, depicted the suffering of the masses, and inspired opposition movements. The study aimed to highlight the defiant writings that contributed to the rise of political figures and the eventual overthrow of the repressive regime. Methods: The historical narrative and analytical methods were employed, conducting a comparative analysis of prominent works by renowned authors such as Tolstoy, Gorky, and Chekhov. This analysis focused on

IH Abdul-Abbas, QJ Rashid, M RasimYounus, PalArch's Journal of Archaeology of Egypt/Egyptology, 2021 - Cited by 9

Some responses to ancient grammarians
And contemporary researchers
In monograms

The reform process is a dynamic process going on, especially the administrative and financial reform, which contributes to the work and directing operations towards success and continuous development, which requires determining the validity and the responsibility and the rights and duties of all officials in the school settings (within the formations educational institutions) for the purpose of reducing the administrative and financial corruption, and then ensure management efficient and effective way by taking advantage of the physical, financial and human resources available to achieve the greatest benefit at the lowest cost to the fact that the follow-up performance on an ongoing basis in accordance with the specific of powers

Multimedia is one of the most important elements of modern educational media and must be used in educational websites in order to disseminate knowledge on a large scale and should be used to provide scientific information to all, as the current research tried to explore the possibilities of employing them in the design of educational websites and highlight their role in promoting the scientific aspects of the user. This study included four axes, the first of which was devoted to the introduction which includes the problem of research, its importance, objectives and its objective, temporal and spatial limitations, which were limited to the study of the main pages of Arabic educational websites published in 2019. The second axis contained th

This research sheds light on the contributions of a group of scientific Kurdish scholars in the seventh and eighth Hijri centuries, who devoted themselves to serving science with the bad political and economic conditions at the time, and the research pointed to the flowering of science and how students travel in order to provide them with science, obtain a scientific certificate, then take up The research efforts of the scholars in the two Hijri century mentioned in the science of the Qur’an, whether in the field of recitations, intonation or interpretation, and the research ends with a conclusion in which I mentioned the most important conclusions reached in this research.