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 way used to estimate the fuzzy reliability differs according to the nature of the information of failure time which has been dealt in this research.The information of failure times has no probable distribution to explain it , in addition it has fuzzy quality.The research includes fuzzy reliability estimation of three periods ,the first one from 1986 to 2013,the second one from 2013 to 2033 while the third one from 2033 to 2066 .Four failure time have been chosen to identify the membership function of fuzzy trapezoid represented in the pervious years after taking in consideration the estimation of most researchers, proffional    geologists and the technician who is incharge of maintaining of Mosul Dam project. B

The current research aims to identify the contributions of small income-generating projects in theempowerment of rural women in Nineveh Governorate ,Al-Hamdaniya district, as a simplerandom sample was drawn from the research community of 280 respondents , according to theRobert Mason equation at the level of significance 0.05, so the sample size was 162 respondents,i.e. a percentage 58% collected the necessary data using a questionnaire prepared as a basic toolfor data collection consisting of 20 items distributed on two axes ,and the results of the researchwere analyzed and presented using the spss statistical program, as well as manual analysis usingrepetitions, the weighted mean, the standard deviation, and the percentage weight. And the

The study highlighted the transformation of value systems and educational patterns between past and present, especially with the introduction of modern variables and means, such as mobile phones, the internet, social media, and others. These factors have contributed both positively and negatively to the study. The study highlights the integral role of the school in collaboration with the family in guiding and educating children. It also emphasizes the active role of the school in developing students' abilities and skills, either attracting them to school or vice versa. This includes an examination of the essential skills required in education and their role in achieving a state of psychological well-being and systematically developing child

The aim of this study is to identify the effect of enabling the effectiveness of the work of the audit committees in private commercial banks and to identify the extent of awareness of the importance of empowerment in the work of these committees, especially as it is known that these committees, especially the inspection committees that go to private banks and from various sources including committees of the Central Bank of Iraq Committees of the Securities Commission and finally committees of the external audit offices, through an analysis of the determinants of empowerment in the performance of the most important work of the audit committees, namely: supervising the process of preparing reports, supervising the system of intern

This research is considered a simple attempt and effort which is it first and last target is to point at the procedures of the taxes account that aims to reduce the taxes from the persons and give free to the person who estimates the tax to practice what comes from the competent authorities to describe the person who estimates the tax and not an accountant who practice the accountant procedures which are imposed on him by the annual terms from higher administrations , So he can not evaluate   state of the person who pay the tax , and he might be dissatisfied with his job , because his role can’t  be activated from the general foundation taxes.

And so , this research includes four fields:-

The US invasion of Iraq in 2003 unleashed the repressed national aspirations of the Kurdish people. After the colonial powers, especially Britain, failed to establish a homeland of scattered Kurds in Iraq, Turkey, Syria and Iran, Iraq's Kurds managed to establish a semi-independent state in the north of the country Which lasted decades against the central authority in Baghdad in protest against what they call the forced integration of Kurds in the Iraqi state, and to obtain more rights and privileges as partners in this country. The federal region in the Kurdistan region of Iraq has become a reality, and it is eager not to strengthen its authority in return for the authority of the central government, but to annex other areas inhabited b

             This research aims to apply the Performance Focused Activity Based Costing System in the offices of scientific and advisory services at the University of Technology for the purpose of measuring the cost of services provided by these offices in order to reduce costs. To test the hypothesis of the research, the research was applied in the consulting offices of the University of Technology through the financial statements for the year ending 12/31/2017 of the Scientific and Consulting Services Office of the University of Technology, because the data of these years were issued and audited by the Federal Office of Financial Supervision.

A number of

The aim of the research is to identify the suitability of a patrol model in evaluating the financial performance of Iraqi banks. The financial reports of five Iraqi commercial banks were approved as a sample for research for the period from 2015 to 2020. The most common financial ratios were adopted for the purpose of measuring the five elements of the model, which are capital adequacy, profitability, credit risk, bankal efficiency and liquidity. The results showed the possibility of using the PATROL model in evaluating the performance of Iraqi banks, as it gave a realistic image of the reality of Iraqi banks in terms of high capital adequacy index and high liquidity, as well as fluctuation in profitability index, not to mention the prob

       The study aimed to determine the extent of market knowledge in the companies researched, as if market knowledge is qualified to lead the companies researched to achieve marketing performance , for this purpose, formulated hypotheses of the study in three hypotheses, the first major hypothesis "there is a correlation with significance of market knowledge to improve the marketing performance  , "while the second major hypothesis, "there is a significant moral influence of market knowledge to improve the marketing performance  " these hypotheses targeting to determine the role played by market knowledge in the leadership of companies researched to achieve improvement in marketing perfor