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 worsening of environmental problems has led to them being addressed by many entities, the most important of which are the top regulators. Federal Board of supreme audit Office is one of the most important regulators in Iraq. The problem of the research was the fundamental question of the extent to which the Federal Financial Supervisory Office was committed to implementing and exercising environmental control over the audited ones. The refore, the research was based on the main objective of questioning the role of the Federal Financial Supervisory Office in the exercise of environmental control and the compliance of those under its control, by identifying the antosai standards for environmental control, particularly the stand

For Spanish learners who are not immersed in everyday contexts, such as students of Spanish as a foreign language, interaction with native speakers is an enriching experience that allows them to contrast their knowledge in a meaningful way. For its part, understanding the cognitive and grammatical functions of the so-called verbs of change plays an essential role in the development of everyday conversation,including the management of aspects such as dialectal variations.In relation to this important function, the central theme of our proposal is verbs of change. The latter have been the research base of several linguists who highlight, amidst their complex functioning in Spanish, positive communicative bases. By observing these perspecti

The aim of this message to monitor this phenomenon throught the Quran , which is the constitution of the Islamic nation and Hariatha as well as to express kasalah integrity , justice honesty , patience , abd pacr .
We feel this vocabulary to hight athical values advocated by the Quran and the need to build commitment to the orthodox society free of corruption that leads ta a disorder of the human society .
The outcome of the study the researcher found that faith to a number of results was most notably the advent of righteusness in the Holy Quran meaning of comprehensive RPR spacious field and breadth Maadenh .

The Industrial Banks in most countries in the world plays an essential and vital role in developing the industrial sector due to its effective importance in the economic and social development. The research aims to study the ability of the Industrial Bank of Iraq to the growth and development of the mixed industrial sector companies through loans granted to them. In addition, the research seeks to study credit policies pursued by the Industrial Bank of Iraq to finance the mixed industrial sector companies. The data of the research has been collected from the financial statements of the Industrial Banks of Iraq  for the period 2007-2011, and by means of questionnaire distributed to a sample of the mixed industrial sector companies in

This study was conducted to test the hypothesis that the duration of time spent by the student inside the examination rooms answering the all kinds of written ex-amination questions has some kind of a positive effect on the final score he will get from that exam. And if there arc gender differences in this respect. Students and methods: Data on the final examinations of the autumn quarter was gathered on 892 examina-tions conducted at the end of this quarter , this included male participants of 566 and females of 326. Examinations were on twenty different subjects , including all of the first five years of the undergraduate students of Iraqi College of Medicine for the academic year 2002 — 2003 . The scheduled time of the examinations was