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

Abstract

The study aims to identify the levels of core competencies dimensions and types of organizational flexibility in the investigated organization, as well as to determine the nature of the relationship and the impact of core competencies dimensions with the process of organizational flexibility. Thus, a number of research questions were presented to express the research problem as follows:

• What is the level of the investigated individuals' awareness to core competencies and organizational flexibility across their dimensions and types in the investigated organization?
• To what extent are core competencies and organizational flexibility available in the Organiz

Pushkin's quotations in Chekhov's works are one of the means of expressing connections between texts, performing the most important constructive role: behind them Chekhov reveals a deep development of the plot-thematic structure, ideas and, more broadly, Pushkin's artistic philosophy.

The scientific relevance of our work is the analysis of the similarities between the literary texts of Pushkin and Chekhov, and touches on quotations in Chekhov's works.

Аннотация

Работа посвящена проблеме функционирования пушкинской традиции в прозе А.П. Чехова . Творчество Чехова занимает уникальное

This paper deals with the role of the clergy in the Church and artists in the emergence of this art, which is represented by an atmosphere of spiritual, aesthetic, artistic, technical and engineering very magnificence and is located in two Find.Chapter One: the stages of stained glass in the Middle AgesThe Architects Goths to get rid of the walls gradually, based Baloctav plane, columns and beams strengthened with the vehicle, as previously mentioned, making the building looks like a glass of excessive use of colored windows building, this art has been known to the art of stained glass And the second chapter: the stages of stained glass in the Middle Ages Department of Winston (Winston) works of stained glass since its inception in the t

The adoption of the concept of preventive war in any country especially in a country like the United States result in a lot of serious consequences, so that pre-emptive military action may alter certain regional arrangements based on the basis of political and security balance, and reduce the incidence of tensions that may worsen a sudden during the application of preventive war, so the concept is applicable to be a risk much more when you face the reality and that because the issues more importantly, it should prepare a detailed and careful study of the post –stage of the use of preventive military action and this requires realy no papers insist or documents discuss this but accurate this field study of the situation thereafter.

This paper addresses the new coloring in the concept of dystopian society as represented by the positive role of one of the characters vs. the passive role of the government and its mutual effect on the people of the society. In addition, it describes how all men in the dystopian society victimize and degrade the other through unlawful acts, like: stealing, rape, and fear, which are the lowest points in a moral decay. However, it offers hope by illustrating a positive sense, as exemplified by the doctor's wife out of Saramago's optimistic view that men may be descended from good women. Accordingly, the paper aims to examine the effect of the government’s role in the lives of the people who have later turned into blind in a dystopian so

It is not long time since globalization has started along with knowledge economy and, communication media and technical information control on the world. As a result serious events appeared like failure in businesses, financial corruption and shortage of administration and control.

In spite of the great efforts held by international organizations and foundations to find organizational frames that adopt independence, que

Artistic formation is an interconnected system of a group of elements and units interconnected with each other in an interwoven fabric, which in turn will be forms with ideas and contents that the artist is keen to convey to the recipient, the formative building includes various types of visual arts, and architecture is in turn a visual art, built from a group Elements and units that show their aesthetic value during the intersection of their building lines and the systems and models of building their external walls, which may be built with a system of incomes and projections or protrusions and pits in their walls, which creates different areas of shade and light during the fall of the sun's rays on them, so their aesthetic value increas

Included a research problem , pointing to deficiencies and neglect in Arabic language teaching in primary and middle school , what makes sense to form your linguistic Bell ( Listening ) is missing , especially grammar, vocabulary endings .

And stressed the importance of research that teaching students the Arabic language is the balance of the next life , and that any defect infects will demolish an important part of their structure and the fact that the theater is a form of human directcommunication , and it`s way is the word this helps students to develop some communication skills , and language the backbone of these skills ,1-      The research sample was identified in all age children ( 6-12 ), which c

Iraqi insurance market need to develop products and to find new insurance policies to cover the damages of the violence and political commotions dangers and to meet the needs of the proposers.                                       

 The global insurance companies recently issued such policies to pay the losses wich caused by the violent political acts of vandalism suffered by the property and investments wich estimated billions of dollars.