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

Encouraging micro-enterprises for comprehensive economic development are crucial to achieve the ambitious vision 2030 of the Kingdom of Saudi Arabia.

 Small and Medium enterprises are inputting around 15.5 per cent to GDP while 33 per cent contribution as a private sector to Saudi Arabia's gross domestic product (GDP). This study aims to identify the most important factors that affect the efficiency of small enterprises in Saudi Arabia. To accomplish this objective, the study was conducted for small projects via the comprehensive inventory method under the supervision of the Institute of Entrepreneurship. A total of 282 questionnaires were collected from entrepreneurs and the differentiation analysis

The last decade of this 20th century provides a wide spread of applications of one of the computer techniques, which is called Fuzzy Logic. This technique depends mainly on the fuzzy set theory, which is considered as a general domain with respect to the conventional set theory. This paper presents in initiative the fuzzy sets theory and fuzzy logic as a complete mathematics system. Here it was explained the concept of fuzzy set and defined the operations of fuzzy logic. It contains eleven operations beside the other operations which related to fuzzy algebra. Such search is considered as an enhancement for supporting the others waiting search activities in this field.

Foreign trade receives a good deal of economists' attention for its active contribution to economic growth, and imports of goods and services that could not be produced locally constitute an important share of the local economy.  Agricultural imports constitute an important share of the total imports due to their role in fulfilling the needs of local markets; however, the agricultural sector in Iraq contributes no more than a limited share of the country's need, which has encouraged the import of a variety of fruits, vegetables and strategic crops and different types of red and white meat. For the sake of identifying the factors affecting the demand on agricultural imports in Iraq, the following factors has been analyzed: th

The current study aims to identify the needs in the stories of the Brothers Grimm. The research sample consisted of (3) stories, namely: 1- The story of the Thorn Rose (Sleeping Beauty) 2- The story of Snow White 3- The story of Little Red Riding Hood. The number of pages analyzed reached (15.5) pages, and to achieve the research objectives, Murray's classification of needs was adopted, which contains (36) basic needs that are further divided into (129) sub-needs. The idea was adopted as a unit of analysis and repetition as a unit of enumeration, Reliability was extracted in two ways: 1- Agreement between the researcher and himself over time, where the agreement coefficient reached 97%. The second was agreement between the researcher and tw

A theoretical analysis of mixing in the secondary combustion chamber of ramjet is presented. Theoretical investigations were initiated to insight into the flow field of the mixing zone of the ramjet combustor and a computer program to calculate axisymmetric, reacting and inert flow was developed. The mathematical model of the mixing zone of ramjet comprises differential equations for: continuity, momentum, stagnation enthalpy, concentration, turbulence energy and its dissipation rate. The simultaneous solution of these equations by means of a finite-difference solution algorithm yields the values of the variable at all internal grid nodes.
The results showed that increasing air mass flow (0.32 to 0.64 kg/s) increases the development o

This research deals with the study of the relationship between the success factors as the independent variable and product strategies as the dependent variable , has reacted to these variables to form the frame , which is the research which centered research problem about the extent to which industrial companies the vision and knowledge of Muslim women survive and develop in the business market , which can be expressed about the extent of awareness of corporate success factors and the use of product strategies and what the relationship between the factors and strategies , while expressing the importance of research to make the focus on the product occupies a paramount importance in the industrial sector companies in relation to t