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

in this paper copper oxide (cuO thin films were prepared by the method of vacum thermal evaporation a pressure.

the bank sect for any country  is very important  because  its represent a major  nerve   to feed a verity economic and finance activities .development any state measure by development  banking  sets and its represent  important  factor to investors attract . and because  important  of this subject ,teen accounting rule is a specialized for it .its related by  Disclosures in the Financial Statements Of Banks and The Similar Institutions, its accredit  by auditing and accounting standard  consul in republic of Iraq.in date 10/28/1998.                      &

The research deals with the problems of improvisation in two basic subjects and applied a samples  and conclusion. The first topic focuses on the concept of improvisation and spontaneity and clarifies the confusion between them. The second topic deals with the foundations and principles on which the actor is based in his artistic preparation for the purpose of developing his improvisational abilities.

The research focuses on clarifying the dimensions of improvisational techniques and its multiplicity in the modern theater. It analyzes the method of improvisation and its use in the construction and composition of the theatrical performance. It deals with two important experiments, such as the experience of the Russian directo

Finance is an essential element when developing any housing policy because of its role in providing funds to institutions concerned with housing lending. Therefore, the research aims to evaluate the financial aid provided by the Central Bank of Iraq in solving the housing crisis through the adoption of the Central Bank of Iraq initiatives to support the financing of the housing sector, and here The importance of the research is highlighted to determine the role of the initiative by drawing an effective strategy aimed at providing the housing sector with the necessary funding. By providing financing to financial institutions directed towards providing real estate credit, and that the percentage of the contribution of the implement

The tax exemption, whether wholly or partially, and for an unlimited duration of the investment or for a limited period of few years, is one of the encouraging things to the flow of foreign capital. And if necessary, impose tax on the profits of the invested capital, the promotion requires that not be discriminatory taxes or payments in the amount of money with the need to avoid double taxation. The tax exemption is granted by the government and the feature according to the law of a natural person or legal entity seeking from the government purports to achieve a set of political goals, economic and  social development. The reduction of taxes or grants partial exemption is one of the factors that encourage attract of direct foreign i

Summary: The study focused on the role of the educational counselor in schools, as an integral part of the educational system that faces multiple challenges and difficulties. In this context, the counselor’s role becomes crucial in attempting to reduce or eliminate such difficulties, in addition to guiding students in an appropriate manner. Methodes: The study employed a descriptive field approach, using interviews and direct observation as tools to examine the actual role performed by school counselors. Results: The study concluded with several key findings, most notably the numerous challenges faced by counselors, including students’ negative behaviors, school dropouts, and the limited administrative support for counselors’ work. Fu

Corrosion of Zn-Ni alloy coatings on stainless steel 316 SS in a chloride-sulfate bath with the addition of either triethanolamine or sucrose was examined. A constant cathode potential was used to deposit zinc-nickel alloys, while cyclic voltammetry and potentio-dynamic polarization were used to measure corrosion. In addition, scanning electron microscopy was utilized to analyse Zn-Ni alloy coating surface layers formed with¬out and with additives. The outcomes discovered that the corrosion resistance of Zn-Ni alloy coat¬ings in 3.5 % NaCl solution was highly influenced by adding triethanolamine or sucrose. Decreasing the Zn:Ni molar ratio led to an increase in corrosion resistance. All Zn-Ni alloy coatings were superior to pure Z