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 research deals with financial and supplies support from the rulers and governors of the
Arab cities and Islamic regions to the poor of common people and the poor of their own . The
Islamic Arab community was characterized , since the prophet's era , with great humanistic
features that formed the cultural characteristic which organized individual's economic life .
The prophet , senior Muslims and the rich cared a lot about this side . There was a large
variation in the degrees of wealth and poverty in the Muslim Arab community as a heritage
from the pve – Islamic society where there is no concern about helping the needy and poor .
Thus , the research sheds light on the different forms of help offered by rulers a

The parametric programming considered as type of sensitivity analysis. In this research concerning to study the effect of the variations on linear programming model (objective function coefficients and right hand side) on the optimal solution. To determine the parameter (θ) value (-5≤ θ ≤5).Whereas the result، the objective function equal  zero and the decision variables are non basic، when the parameter (θ = -5).The objective function value increases when the parameter (θ= 5) and the decision variables are basic، with the except of X_24, X₃₄.Whenever the parameter value increase, the objectiv

ABSTRACT
Threw this research to the following:
1 - Know the impact of strategy Puglia in the collection of the rules of the Arabic language
students at the Institute of preparation parameters .
2 - Know the impact of the retention strategy in Puglia collection rules Arabic language
students at the Institute of preparation parameters .
To verify the status Mmermaa Find researcher Elsafreeten following two hypotheses :
1 - There is no statistically significant difference between the average score for the collection
of the fourth grade students at the Institute for the preparation of material parameters who
were studying grammar strategy Puglia and average grades collectible fourth grade
students at the Institu

This study is taken from the doctoral thesis that I prepared in the year 2000 at the University of Bordeaux in France under the title “ Ali bin Abi Talib Imam and Calif “. This thesis was prepared as a continuation of what the French orientalism Louis Massignon wrote about Islam and his student Henry Corbin, who introduced Europeans to Shiism. This study represents the philosophy of dialogue and the unity of the Islamic Emma as one of the most important methods used by Imam Ali.

Imam Ali established the most beautiful, creative, and most complete rules of human dialogue that preserve the unity of the nation’s fabric and preserves human dignity. Imam Ali referred to basic principles foundations to reach this goals, including

The paper deals with the study of the sciences of the Qur’an according to the interpreter, Ayatollah Sayyid Mahmoud al-Talaqani, a religious jihadist figure from Iran. He is the author of the exegesis (Ishraq from Al-Quran), which consists of six parts, which he wrote inside the prisons of the Shah and in exile. Mr. Al-Talaqani agreed with some of the commentators in his positions on the sciences of the Qur’an, and some of them disagreed with others.

In Iraq, the risk of soil pollution by petroleum products increases with the growth of oil exploration, production and shipping large quantities of oil through pipelines over thousands of kilometers. Numerous oil spills have been documented recently in many sites due to damage in the oil industry infrastructures, which have led to soil contamination causing serious environmental hazards and deterioration to the soil and its engineering properties. So, it is essential to investigate the impact of oil leakage through the soil stratum consequently, assessing the eligibility of the contaminated soil for construction projects or identifying the appropriate treatment method. The paper investigates the general behaviour and the associated variatio