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

Current research aims to find out:

1. Effect of using the active learning in the achievement of third grade intermediate students in mathematics.
2. Effect of using of active learning in the tendency towards the study of mathematics for students of third grade intermediate.

In order to achieve the goals of the research, the researcher formulated the following two hypotheses null:

1. There is no difference statistically significant at the level of significance (0.05) between two average of degrees to achievement

Ismailism is of great importance in Islamic history and Islamic political thought. In different countries of the Muslim world today their presence exists and is active but is confused with mystery and secrecy. The most important characteristic of their political ideology is their dependence on the esoteric exegesis, which they have made an intellectual basis for which their most ideas relate, when they make for everything visible and exposed a hidden matter, not only aware of the esoteric exegesis, which only God knows and entrenched in science, and they mean imams or whoever They are called "(esoteric)" as a result of the Ismaili belief in esoteric interpretation and that everything is apparent inward, as well as they called the ((seven

Music and singing are always associated with the movement of society and the emergence of cultural and artistic activities other.
The social and political transformations of the 1930s helped to disseminate the study Music and music in the city of Baghdad and across Iraq This is the beginning of a new era of musical art alongside other arts.
While achieving musical arts A new step was advanced by publishing a technical study among the younger generation they were looking for to contribute to the musical field On the other hand, the city of Baghdad during the period of research many musical and musical performances Egyptian teams have provided many artistic activities and events which have had a significant impact on the development

Recent studies agree that the democratic system in a country can only be established in an atmosphere of political and religious freedom. However, the term democracy and the term freedom have become controversial because their concepts remain multiple and different. Karl Popper is one of the most prominent philosophers in modern Western political thought, and one of the defenders of democracy as opposite to dictatorship. It has defined its function by its ability to restrain the ruling elite and to enforce it to prevent their tendency to tyranny. This can be achieved only in the context of the close relationship between democracy and freedom, so, if there is democracy in the absence of absolute freedom, democracy is a gateway to expandin

في البداية اود الاشارة الى ان فهم حقيقة الازمة هو ذو جانب فني يتعلق بالجينات الوراثية لنظام يملك في احيناته قدرة عالية على تفريخ المشتقات. هذا النظام الذي يزداد عقما وتدميرا يزداد قدرة على خلق النقود الائتمانية/المشتقات، وكلما اقتربنا اكثر من فهم هذا الجانب كلما اسقطت في ايدينا تلك التوصيفات الاكاديمية الجاهزة في نقص الرقابة والاشراف، تركيز المخاطر،....الخ التي تناولتها الكتابات الشائعة في معظم طروحات

The banking industry, as a result of the great challenges it faced, required continuous development of the principles of management, control and mechanisms used. The Basel Committee on Banking Supervision has played a leading role in legalizing many of these developments and has been able to contribute significantly to establishing a common framework for banking supervision, The central role in the various countries of the world is based on coordination between the various regulatory authorities and thinking about finding mechanisms to confront the risks faced by banks, recognizing the importance of the banking sector in the stability of domestic and international banking systems or the danger of this sector in the emergence of F

This paper aims to discuss and analyse the role and importance of implementing industrial Policy to promote industry and enhance economic development in developing countries. The paper discusses the economic justifications for using industrial policy as well as the criticisms leveled against it, for this purpose it analyses the ideas of two different approaches to industrial policy. The first held by the neo-liberals in the USA , who oppose the use of industrial policy and emphasise the role of the market in attaining economic development. The second, represented by many economists who support the use of industrial policy to promote industry and accelerate economic development, they justify their stand by pointing to the negative

Algeria is one of the states that are important to the Ottoman state, because of its geographic location is important to the Mediterranean Sea, as well as the economic resources of the nature of its soil geography and climate,diverse, making it the focus of attention of the Ottomans, along with the van, which has increased the interest of the Ottomans in Algeriais the fall Andalusat the hands of the Spaniardsin1492, and force the Muslims to get out of them, and did not Only Europeans do it, butrushed to the prosecution of Muslims tothe coast of North Africa and seizing control of manyofits ports and cities, prompting the Ottoman state to go forth and back to the barn Muslims,Especially after hehad appealed to the Arabs of the Ottoman sta