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

This research a study model of linear regression problem of autocorrelation of random error is spread when a normal distribution as used in linear regression analysis for relationship between variables and through this relationship can predict the value of a variable with the values of other variables, and was comparing methods (method of least squares, method of the average un-weighted, Thiel method and Laplace method) using the mean square error (MSE) boxes and simulation and the study included fore sizes of samples (15, 30, 60, 100). The results showed that the least-squares method is best, applying the fore methods of buckwheat production data and the cultivated area of the provinces of Iraq for years (2010), (2011), (2012),

The current study is designed to achieve the goal of early detection of heart disease because it is the main risk of death. Some biomarkers were measured as well as the percentage of the effect of certain risk factors in people with myocardial infarction and heart failure. The study included 40 serum samples from people with heart disease. The effectiveness of the creatine kinase (CK-MB), as well as its temporal and albumin effects, as well as sodium ions in people with myocardial infarction and heart failure, were compared with the control group. as shown below:

-The first group consisted of 25 blood samples from people with myocardial infarction and 15 serum samples from people with heart failure. Blood

God Almighty has imposed on us obligations and set limits on us, and among these obligations is the prayer, which is considered a pillar of Islam. And recently on the statement of its importance, and through extensive explanations, they elaborated on the statement of its pillars, its obligations, its Sunnahs, its rituals, and its bodies, and it is known that the imam in prayer is an important part of the parts of prayer. Whoever assumes this responsibility must be aware of these conditions, the most important of which is jurisprudence in religion, and there has been a disagreement between the jurists, especially the owners of the four schools of thought, about who is qualified to lead the imamate, and this is within many and wide details

There is talk of the Prophet ﷺ proud of his relative, which is the uncle, and the importance of this subject, this search for doctrinal matters related to the two things between us: the interest of the Prophet ﷺ responsible, and also responsible forbidden marriage and marriage as it is forbidden to marry the uncle, and in the uncle language: mother's brother, aunt Her uncle may spend his uncle's nephew, the uncle may embrace his nephew, the uncle shall be the guardian of the little or the small, not to cut off the uncle if he steals from his nephew's money. "

Despite the importance of this term in linguistics and rhetoric ancient and modern literary forms in general, is that it is possible to use in clarifying the foundations of the relationship hidden and manifest between shapes in models art adjacent or successive spatially, as the artwork plastic in general and sculpture in particular consists of formal structure somewhat similar to the structure in any language text and we can decode these blades structure and analyze the implications and come to their meanings and re-read and interpreted under the guidance of the concepts and techniques of neighboring developed primarily for linguistic analysis of texts or launched from their references. This split search to four chapters included the fi

Transportation network could be considered as a function of the developmental level of the Iraq, that it is representing the sensitive nerve of the economic activity and the corner stone for the implementation of development plans and developing the spatial structure.
The main theme of this search is to show the characteristics of the regional transportation network in Iraq and to determine the most important effective spatial characteristics and the dimension of that effect negatively or positively. Further this search tries to draw an imagination for the connection between network as a spatial phenomenon and the surrounded natural and human variables within the spatial structure. This search aiming also to determine the nat

Research summary

The first step towards the goal of coexistence with diversity, we must all recognize each one of us the rights of others regardless of his religion, color, gender, and point of view, and that each one agrees with his partnership with others, and a person’s belonging to a religion or doctrine must be based on conviction and self-motivation, and that the true Sharia prohibits a Muslim To impose on others what they do not believe and believe in, for God Almighty did not give His Prophet this right, so how about others, and it is not surprising for everyone that disharmony and rivalry impede the attempt to advance in society, and it is natural that our enemies take advantage of our division among us,

The provisions of the monkey in Islamic jurisprudence

The movement is considered one of the important factors which attracts the receiver attention in designing artificial works in general, and especially in the advertisements, moreover the subject of the movement in the designing advertisements needs more care and study by the scholars. From this importance and from reaching to the basic streams of the research topic (the effect of the movement in the graphic design) the problem of the research has been set according to the following wonder:

• What is the designing process that establishes the movement in the commercial advertisements designs?

      The researche