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

تعد الموازنة الأداة الأساسية لتنفيذ أولويات أية دولة، ويتوجب النظر إليها في ضوء المناخ الاجتماعي والسياسي والاقتصادي، لأنها تساعد في توجيه الاقتصاد لتحقيق النمو ورفع مستوى الرفاهية. اعتمدت وزارة المالية في أعداد الموازنة السنوية بعد 9/4/ 2003 أسلوباً مغايراً لما كان معتمداً في العقود الماضية، إذ كانت هناك موازنتين الأولى الموازنة الجارية، والثانية الموازنة الاستثمارية رغم وجود قانون يحتم إصدار موازنة

Abstract

were determine the problem of current research to answer the  question on the consciousness of the Ministry of Agriculture to adopt Staffing  strategy and identify the shortcomings  as the independent variable, represented by the three dimensions (recruitment , selection, placement) and its impact on high performance, as  dependent   variable is described  in  four dimensions (leadership, strategy, structure and processes, culture), in this research were  Used  analytical descriptive  style . This research aims to identify the correlation and impact  of Staffing strategy at high-performance in Ministry of Agriculture , To clarify the relationship between

We have investigated in this research, the contents of the electronic cigarette (Viber) and the emergence of the phenomenon of electronic smoking (vibing) were discussed, although the topic of smoking is one of the oldest topics on which many articles and research have been conducted, electronic smoking has not been studied according to statistical scientific research, we tried in this research to identify the concept of electronic smoking to sample the studied data and to deal with it in a scientific way. This research included conducting a statistical analysis using the factor analysis of a sample taken randomly from some colleges in Bab Al-medium in Baghdad with a size of (70) views where  (КМО) and a (bartlett) tests

This study deals with the impact of leadership styles in its three main dimensions (democratic, autocratic, lenient) as an independent variable of the dimensions of functional combustion (emotional stress, inhumanity, personal achievement). The research sought to achieve a set of goals, the most prominent of which are: studying the reality of the researched organization to identify the leadership patterns used in its management and its impact on the phenomenon of functional combustion, Moreover, knowing the extent of support for these established patterns and their contribution to mitigating the phenomenon of functional combustion in the organization's environment, and testing the impact of these leadership patte

The Iraqi economy has suffered for a long period of inflation because of the Iraq war and the resolutions and the sanctions that were imposed on Iraq, this phenomenon overshadowed at various aspects of the economy including the tax revenue that the State seeks to optimize the total income for the budget, the research covers the years 1990-2010, these years have been divided according to the country's economic variables.

The research  adopted on econometrics analysis that is based on the information and data available on topics and has been using statistical methods to test functions are formulated.

Research concluded that rates of inflation and GDP impact is limited to direct taxation and indirect in current prices a

It is out of question that USA foreign policy has a great superiority and
influence all over the world.
This study deals with all dimensions; aims; and challenges of the American
foreign policy. It aims to answer the following question: within the current changes in
the world, how can the aims of the American foreign policy be realized?

The foreign policy of china is considered an important subject generally, in addition its very significant towards the Middle East specifically. It is the most valued topic, that needs deep academic investigations in order to identify the important factors causes and its consequences, this kind of research provides a proper understanding to the researchers and politicians, it will prove the reasons for China's with the impact to the region, the rivalry with the United States in the coming years

Despite the vast areas occupied by deserts in the world, it is still far from the civilized development and development of the other regions, so they became semi-neglected areas that extend to the hand of urbanization only in specific places and for special purposes, due to the harsh natural conditions surrounding it and to the accuracy The ecological balance in it became the greatest enemy of human beings in the desert areas is the same person who paved the way for increased intervention in the exploitation of natural resources and increase the demand for them to drain seriously affect the impact and still on the environmental and climatic conditions and thus living for the inhabitants of these Areas. The main potential for deve