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 present study included the physico-chemical parameters of Lesser-Zab river and its effects on Tigris river. Monthly water samples were taken from the two rivers during January to October 1999.There were no signifcant difference in water temperatures. Both rivers were fresh to oligohalin, alkaline and very hard. Close values were determined in total suspended solids in both rivers with little increasing during rainfall period and high discharge. Water was well areated and over saturation was recorded in several occasions. Dissolved oxygen values of Tigris river were influenced by Lesser-Zab. Cations were more dominant than anions in both rivers. In Lesser-Zab, the anions were increased during spring season and declined in summer which t

The research problem lies in the fundamental questions that revolve around the role of each of the tools of promotion, namely advertising, personal sale, public relations, sales promotion, and direct marketing in achieving leadership for business organizations. Research to know the role of promoting the service in the researched company and whether the promotion of the service is qualified to lead the researched company to leadership, and for this purpose formulated research hypotheses of three hypotheses, the first hypothesis says that there is a significant impact relationship between promotion and entrepreneurship. The second hypothesis aimed to determine the role played by promotion in the researched company to achieve unique

Praise be to Allah , the Lord of Heavens , Who revealed His Scripture in plain Arabic, and prayers and peace be upon the Master of all creatures and the chosen one , Muhammad (PBUH).Pushkin was known as a poet in Russia, the sun of its poetry that set, the father of the Russian literature and the founder of its literary language. When he published his poems, trying to express his inner poetic feelings and creative visions, he presented them with creativity and special touch. The reason behind the selection of Pushkin as the subject of this study is that he was affected by Islam and Arabs. For the purpose of this study, the dissertation has been divided into introduction and three chapters; each chapter includes two topics. In the introdu

This experimental study focuses on scouring in box culvert inlets under steady-state conditions and at different percentages of blockage ranging from 0% to 65%, and also looks at the hydraulics of water in the culvert. The investigation shows that the blockage of the culverts has influenced the scouring pattern at the blocked culverts' entrances. Ten experiments were carried out at the laboratory to see how blockage impacts the scouring pattern upstream of a box culvert during steady flow. Both partially blocked and unblocked cases were implemented in this study. The experimental tests were done until the equilibrium scour occurred, which took about 3.5 hours of water flow to reach equilibrium conditions.  The results r

The internet is a basic source of information for many specialities and uses. Such information includes sensitive data whose retrieval has been one of the basic functions of the internet. In order to protect the information from falling into the hands of an intruder, a VPN has been established. Through VPN, data privacy and security can be provided. Two main technologies of VPN are to be discussed; IPSec and Open VPN. The complexity of IPSec makes the OpenVPN the best due to the latter’s portability and flexibility to use in many operating systems. In the LAN, VPN can be implemented through Open VPN to establish a double privacy layer(privacy inside privacy). The specific subnet will be used in this paper. The key and certificate will