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

If the sovereignty of the state is reflected in the taxation of its citizens, this sovereignty can not be completed and completed only if it works on its part to collect its debts, whether voluntary or compulsory, and the debt of the debt arises from the will of the individual and the will of the state alone, The existing management of seizure and collection is based on an unequal relationship between the State and the debtor from which the obligation arises. Naturally, this relationship has obligations and rights on both parties. The researcher used a set of studies and previous research, books and other sources related to the subject of research. This was done through the theoretical and practical aspects, which focused on direct and i

In The Name of Allah Most Gracious Most Merciful

In this research, I will deal with the significance of the imperative and the disagreement of the fundamentalists in the general requirement by dividing it into an introduction and two sections. , and the appropriate indication.

This research is concerned with the study of (the dialectic of the familiar and the unfamiliar in Islamic photography), and it consists of four chapters.
If you dealt with the problem of the research subject (the dialectic of the familiar and the unfamiliar in Islamic photography, as it appeared realistic, familiar forms and strange and strange unfamiliar forms represented in many of the main schools of Islamic photography that emerged in Iraq and Persia and then the Ottomans and the However, Islamic painting still retains those previously witnessed and unseen images, which pose themselves forcibly in the form of many questions that must be faced and studied by investigation, observation, extrapolation and conclusion through scientifi

Poor impurity in the right of the patient and the elderly

The tensions and crises and the psychological pressure as well as the rapid changes and great development which is taking place in the present time. And  witnessing community of wars and conflicts that give rise to future concern among members of the community in general and students in particular, as it included the current research a number of chapters, the First chapter contains the research problem, the important goal, then set researcher terminology that has defined and contained in the title of research in the form (concern the future, artistic expression, middle school). The Second chapter included three sections, the first included the nature of adolescence and traits, characteristics and pr

The purpose of this resesrh know (the effectiveness of cooperative lerarning implementation of floral material for calligraphy and ornamentation) To achieve the aim of the research scholar put the two zeros hypotheses: in light of the findings of the present research the researcher concluded a number of conclusions, including: -
1 - Sum strategy helps the learner to be positive in all the information and regulations, monitoring and evaluation during the learning process.
2 - This strategy helps the learner to use information and knowledge and their use in various educational positions, and to achieve better education to increase its ability to develop thinking skills and positive trends towards the article.
In light of this, the