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

A revolution called information revolution has recently invaded the world. It is Currently considered one of the most important properties of development to the countries of the world The criteria provided by computers such as accuracy, speed, time saving Storage and restore have led them to be widely used in economy, industry, agriculture, communications, etc., as well as being the major finder of reengineering the operations of innovation. The use of computers in the preparation of budgets will lead to achieve accuracy. Since, the operation draws upon the statistic and quantity estimations about budget items, the computerized balance sheet may save time and effort of preparing mathematical equations annually. According to the problem o

 The capital in the bank is the important element in establishing it, because it maintains the banking sector in the event of exposure to losses or risks In addition to contributing to the provision of liquidity And protection of depositors' money from potential and unexpected losses. There is also a relationship between the prices of shares and the indicators of the durability of the capital owned, considering that the shares are the components of the bank capital The study limited the indicators of capital to assets and capital to deposits, capital to loans and financial investments Where the most important conclusions are the damage to the detriment of shareholders in contrast to the depositors in the case of increasing the propo

The organization of sporting activities at the local and international levels requires a lot of money, which has increased interest in marketing in the sports field, as it is one of the modern topics that represent the basic knowledge needed by the sports marketer and which represents one of the basic concepts to enhance the benefits and returns of sports clubs. The research problem was the weak awareness of the members of the administrative body of Iraqi sports clubs of the role of sports marketing in the dimensions of competitive superiority and not exploiting them in the optimal way that enables clubs to achieve competitive superiority. The research aims to know the role of sports marketing in competitive superi

        Most vegetation’s are Land cover (LC) for the globe, and there is an increased attention to plants since they represent an element of balance to natural ecology and maintain the natural balance of rapid changes due to systematic and random human uses, including the subject of the current study (Bassia eriophora ) Which represent an essential part of the United Nations system for land cover classification (LCCS), developed by the World Food Organization (FAO) and the world Organization for environmental program (UNEP), to observe basic environmental elements with modern techniques. Although this plant is distributed all over Iraq, we found that this plant exists primarily in the middle

Background: Osteoarthritis (OA) currently seems
inevitable and unavoidable for a large swath of the
population .its etiology relates to a strong ,but
complex ,non mendelian genetic basis ,combined
with mechanical and metabolic factors that cause
molecular alterations the end results of which
affect the whole joint .Glucosamine and
chondrotin sulfate alone or in combination may be
of benefit to a subgroup of individuals who have
knee pain due to OA.
Glucosamine has been shown to alter cartiage turn
over in patients with OA undergoing physical
training
Aim of the study: To find the validity of
glucosamine chondrotin sulfate in treatment of
grade 1 and 2 OA.
Methods: the sample of 280 patients

The current research aims to provide a philosophical and knowledge framework  to explain the issue of organizations dealing with Paradox phenomena by focusing on five main aspects. The first deals with the concept of paradox, and the second aspect deals with the types of forces paradox. While the third aspect regards subject of the philosophy of paradox in organization theory and the fourth side deals with methods of   solving the paradox. Finally, the last side is exposed to the subject of the paradoxes of the three provided by the study (L

The process of granting loans by banks is the confidence they give to their customers, but this trust should not be a cornerstone in granting loans even if granted these loans on the basis of sound banking should involve risks that may be exposed to the bank because of the failure of the client to meet The bank's financial obligations to the bank due to the unexpected economic conditions affecting the customers, which makes them in a state of faltering, which weaken the ability of banks to provide loans, which are the most important sources of revenue and profits, so the problem of non-performing loans is one of the main problems facing most of the banks Which impede the functioning of its work and the reasons that led to the agg

The research deals with the problem of visual pollution, as it is one of the most important urban problems that cities suffer from. The concept of visual pollution has recently emerged to describe the deformation and degradation of the urban environment. Visual pollution is defined as any component of the surrounding environment that is inconsistent and not homogeneous with its natural and human components. The volume of visual pollution has doubled due to the non-compliance with the laws, regulations and controls set by the Municipality of Baghdad by the citizens, and to the weak municipal role that the municipality plays in implementing these laws. Therefore, it has become necessary to know the manifestations of visual pollution and th

Increasing need for day after day to find ways and innovative means of
helping to educate and give children the skills of different kind, has found a
researcher on the subject of hats, six room to give children language skills
through the experience of field reconnaissance conducted on the three
children found that language skills improved, he decided to make these study.
Objectives of the study:
Understand the differences between the experimental group first (the way the
debate) and second (six caps) depending on the test post administration.
to identify the language skills of the second group according to the pre and
post test
Differences between males and females in the second group (Six Hats)
Search T