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

Investment in Human is one of the best and most important investments as it is renewed and developed resource over time in comparison with depleted material resources. Human resources is considered the part of the population that could be employed economically to contribute in increasing production energies as it is the support pillar of the society and have great energies that construct the society and raise of nations as well as he is distinguished with characteristics of ambitions to freedom.

Iraq is one of the countries that has large number of population in age of work and production and reduce in age dependent classes (children and old people).This dynamic in population led to step

The aim of the research is to prepare practical volleyball lessons by using the four pillars strategy for middle school students, and to identify the effect of the four pillars strategy in performing the transmission and volleyball skills in the second intermediate students, to assume that the two researchers assume that there are no statistically significant differences between the results of my skill performance tests Sending and preparing tribal and remote volleyball for the experimental and controlled groups, and there are no statistically significant differences between the results of the performance of the transmission and preparation skills of the volleyball between the two experimental and control groups, and the research co

The aim of the current research is to develop the social studies curriculum at the primary stage in light of the standards of the next generation, which was represented in three main dimensions (pivotal ideas, scientific practices, and comprehensive concepts). The researcher designed a tool for the study, which is a content analysis card in the light of (NGSS) standards, based on the previous main dimensions. The descriptive analytical approach was adopted in analyzing the social studies curriculum for the primary stage to determine the degree to which the standards of the next generation are available, as well as to establish the theoretical framework related to the research variables. To develop the social studies curriculum in light o

The grammar structure transforms from its fundamental field to another field that takes new dimensions, and is used in another way in speech that differs from the first one, because the formula basis of the name(Faael) in speech is a (distorted characteristic), and the distorted characteristic indicates the stability and the necessity of the characterized. as this characteristic has changed from its use as a distorted characteristic which was established by the elders. to a use that differs from the first and cannot be overlooked to achieve a new purpose, to be used as plural

The business environment is witnessing tremendous developments in the field of production and technology, which requires the development of production methods to go in line with these developments and the increasing competition, which has gone beyond the economic aspects to extend to the environmental aspects, as economic units tended to adopt a cleaner production strategy and through what they achieve by producing environmentally friendly products and achieving economic efficiency. Reducing costs, providing a safe and clean environment for workers, and reducing waste from production operations.

The negotiation phase is gaining great importance in investment loans due to the magnitude of the amounts awarded and the need to obtain adequate lending guarantees and the development of better conditions, and this requires that negotiating policy with fixed principles that balance between meeting the demands of customers and maintain market share and achieve profits and avoid defaults and losses the bank, and so I have touched Find the concept of investment loans and procedures for granting and the concept of the negotiation process for the granting of loans. The practical side to ensure the preparation of examination form consists of questions commensurate with the methodology developed by the researchers, were directed to the officia