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

Knowing the nature of the relationship in federal systems lies in studying the political, social, economic and cultural forces, for their role in laying the foundations and the federal system. No matter how important the pillars of that system are, and through this research, we will learn how the political elites were able to crystallize this unique system, until it became one of the political systems that some countries seek to copy and apply its experience.

The first section of this research discussed  the manner of the research from many sides like the problem it faces, importance of it , its targets ,boundaries, the way to collect and get information's and its assumption.

When the second chapter discussed the press – manufacturing and the development ,importance and types of newspapers, also its merits and weaknesses.

The third chapter talked about the scientific side and how to choose an assumption for the research . as it talked also about the apparent honest and stability tests that help in analyzing the research until getting results and so the right assumption for  the research will be chosen.

And finally, the fourth chapter put highlight on the be

The evolution of thought, planning for Urban Communities in the second half of the twentieth century, through several successive stages. He was thought of planning urban communities depends on identifying the general plan for land uses of the project area as a basis for drawing charts the physical, social, economic, and put the general plan for land uses based on the terms of reference set by the number of experts in the ministries and agencies. I have lived cities in the Arab-Muslim region, during the transition period the natural and historic environment, urban, sophisticated balanced ways mentioned in the cultural, social, inspired by the teachings of Islam and the customs and traditions of the Arab social, put forth a set of

research summary

Praise be to Allah، and prayers and peace be upon His Messenger and His chosen one، his family، companions and his family and his family.

After that، this is a study on the question of the claim، as one of the controversial questions that are the mainstay of debates، and I looked at it: the limit of the question of the claim، its importance، its impact، its aspects of corruption، its sections، and the representation of its sections of the fundamentalist controversy;

The research was according to the following plan:

Introduction، in which she mentioned: the importance of the research topic and the reason for its selection، its questions، its l

What is meant by objectives: the purpose, secrets, judgment, and interests that the legislator set for each of its rulings is a doctrine and a law.

Faith is belief with certainty in God Almighty, and what is required of him in his divinity, lordship, names and attributes, belief in his angels, books, messengers, the Last Day and destiny, both good and bad.

And the purposes of faith are the wisdom and secrets contained in the Islamic faith and which achieve human well-being and happiness in the immediate and the future. And that the purposes of belief and faith are the essence of religion, rather it constitutes a basic pillar on which the basis of the intentional consideration as a whole, because the structure of worship i

Any city that has such a market and is organized, organized and established

Mini
And respect
Freedom of expression
Profile.
Conflict resolution and conflict resolution

Political
Which affected the growth of some markets
And religious th
The search for the return of economic and cultural activity and the emigration of some others
Cultural exchange and trade, which in turn
Al-Rifaie
We took the problem that we are experiencing
Menia, the holy city of Karbala in the market organization, has suffered from fierce attacks
Economic and heritage
e
As well as tourism and tourism, as it depends on the abundance of visitors, tourists and residents in terms of needs and motivation
Resource

The study aimed to identify the relationship between the speed and direction of the ball's rotation in the accuracy of the front and rear side longitudinal blow in wheelchair tennis players. The descriptive approach wasused in the manner of correlations to suit the nature of the problem to be studied. The research community identified the 32 players aged18 and over, and the search sample was selected from players with a local classification registered with the 2020 Wheelchair Ground Tennis Federation (2020) in the intentional manner of 8 players, using Smart Tennis Sensor technology to measure the speed and direction of the ball and test the accuracy of the front and rear side longitudinalstraightstrike. She conducted the reconnaissance exp

   Decision-makers in each country work to define a list of internal and external interests, goals and threats to their countries according to the nature of their awareness of these interests, goals and threats. 

  Hence, Iraq is not an exception to this rule, and the process of evaluating its interests and the objectives of its foreign policy is subject to the pattern of awareness of decision-makers and the influencing forces in defining its basic interests, which often witness some kind of difference in defining them, evaluating their importance and determining the size of the threats they face. And among these interests and threats that have witnessed a difference in the assessment of their

Since the beginning of 21^st century, the prices of Agricultural crops have increased. This Increases is accompanied with that increases of crude oil prices and fluctuation of a dollar exchange rate as a dominant currency used in the global trade. The paper aimed to analysis the short run and long run cointegration relationships between prices of some of Agricultural crops imported by Iraq such as wheat and rice crops and both the crude oil prices and the Iraq dinar exchange rate a gained America dollar using ARDL model. The results show the long run equilibrium between they three variable throng the error correction mechanizem. The results also show the significant and economically sound effects of cru