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 deals with the poetic image of poets of the eighth century poetic, where they embodied the features of the religious life in which they live, and their impact on the Koranic text in the reflection of the image on their poems, where it becomes clear the ability of the poet at that stage to clarify the aesthetic components of the poetic text; Investigations, singled out the first topic: the analogy, and the second metaphorical picture, and the third: the picture.

The improvement in Direction of Arrival (DOA) estimation when the received signals impinge on Active-Parasitic Antenna (APA) arrays will be studied in this work. An APA array consists of several active antennas; others are parasitic antennas. The responses to the received signals are measured at the loaded terminals of the active element. The terminals of the parasitic element are shorted. The effect of the received signals on the parasites, i.e., the induced short-circuit current, is mutually coupled to the active elements. Eigen decomposition of the covariance matrix of the measurements of the APA array generates a third subspace in addition to the traditional signal and noise subspaces generated by the all-active ante

Is in this research review of the way minimum absolute deviations values ​​based on linear programming method to estimate the parameters of simple linear regression model and give an overview of this model. We were modeling method deviations of the absolute values ​​proposed using a scale of dispersion and composition of a simple linear regression model based on the proposed measure. Object of the work is to find the capabilities of not affected by abnormal values by using numerical method and at the lowest possible recurrence.

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 child realize that the meals time provide golden opportunities to get the attention the child needs. However, many difficulties that may appear about eating food can be avoided, if the family used the right way in dealing with this problem. The study aims, in this case, at searching for the reasons that lies behind the child's obstinacy in eating his food and the attempt to study some variables that is related to the research topic.

The results are summed up as follows:

• The number of the sample children is 3 of both sexes between the ages of 3 to 6 years

And after:

There are many aspects of inference in the Holy Qur’an, whether it is evidence, evidence, argument, authority, or proof.
These expressions or expressions are close in meaning to each other in appearance, but the Qur’an used them all in their exact place, so every word in the Qur’an has its own use that was set for it, and no other word can replace it even if it is close in meaning to it. And these aspects that the Qur’an mentioned as evidence for the aspects of inference in it may come to be mental, textual, or tactile evidence.
The Qur’an exalted the importance of evidence and proof in its religion, and entrusted it with confirming and rejecting the plaintiff’s claim, regardless of its subject matter

This research cancellations in life insurance policies and their impact on the solvency of the insurance companies (Applied Research in the Iraqi general insurance company), The study was descriptive approach in identifying and addressing variables which consists of {cancellations in life insurance} independent variable, the financial solvency of insurance companies as the dependent variable, and for the purpose of achieving the objectives of the research were formulated one hypothesis has been tested in the Iraqi insurance company, the researcher used the financial statements in the collection data needed for the study and information . The research found a number of conclusions highlighted that inflation, as well as economic variables