Dyspepsia is a significant public health issue that affects the entire world population. In this work, we formulate and analyze a deterministic model for the population dynamics of Gut bacteria in the presence of antibiotics and Probiotic supplements. All the possible equilibria and their local stability are obtained. The global stability around the positive equilibrium point is established. Numerical simulations back up our analytical findings and show the temporal dynamics of gut microorganisms.

represent websites link support of human communicate and cohesion of cultures different depending on their languages and their environments around, it was the evolution of one of the most important means of communication of services for electronic networks, the Internet active role in containing the world Bbodqh science and knowledge to Taatlaqah cultures from which derives its intellectual and cognitive cupboards continuity and as a link language for each those environmental Altdadat, linguistic, religious, political, economic . We all know that these electronic means difficult promise ring intellectual and mental connectivity for the masses polarized without being of the image as an element Kravekaa supporter of the electronic media an

A numerical investigation has been performed to examine the effect of fluorine concentration on the chain reaction mechanisms and parameters of hydrogen fluoride (HF) chemical laser. The practical difficulties associated with this type of lasers impose that an alternative route might be quite useful. Thus, particular attention was paid to develop a computer program to investigate various processes. The results of this computer simulation program proved their credibility when compared with the little published data. This computer program is called Reaction Rate Simulation Model (RRSM). An entirely new approach to emulate the reaction mechanisms has been followed. The effectiveness of reaction rates in the processes of HF lase

This article examines and proposes a dietary chain model with a prey shelter and alternative food sources. It is anticipated that mid-predators' availability is positively correlated with the number of refuges. The solution's existence and exclusivity are examined. It is established that the solution is bounded. It is explored whether all potential equilibrium points exist and are locally stable. The Lyapunov approach is used to investigate the equilibrium points' worldwide stability. Utilizing a Sotomayor theorem application, local bifurcation is studied. Numerical simulation is used to better comprehend the dynamics of the model and define the control set of parameters.

The exchange rate is the backbone of  any economy in the world, whether  developed or developing, where most countries adopted  many policies, in order to ensure the stability of the exchange rate of the currency, because of its importance as a link between the local economy and the others ,And it contribute in the achievement of internal and external balance and despite the many different factors that affect it, but there is wide consensus on the effectiveness of the role of spending and the currency window in the exchange rate of the Iraqi dinar, especially in the Iraqi economy, effectiveness As the increase in government spending lead to an increase in the supply of money and increase domestic demand and high pr

The research aims to recognize the impact of the training program based on integrating future thinking skills and classroom interaction patterns for mathematics teachers and providing their students with creative solution skills. To achieve the goal of the research, the following hypothesis was formulated: There is no statistically significant difference at the level (0.05) between the mean scores of students of mathematics teachers whose teachers trained according to the proposed training program (the experimental group) and whose teachers were not trained according to the proposed training program (the control group) in Pre-post creative solution skills test. Research sample is consisted of (31) teachers and schools were distribut

Management Representations Letter plays a significant role as an evidence to get conclusions the Auditor is looking for. These conclusions could show the professional opinion of auditor over the fairness and integrity of financial statements for many issues and numbers that management claims, Hereby, the research aims at highlighting the importance of Management Representations Letter and the way of using as an evidence with expressing its meaning and means of application in addition to identify the Responsibility of Auditor on that Letter, This research discusses also the effect of Management Representations Letter on the credibility of financial statement and enhancing the credibility of the submitted reports, From other side, in the t

The aim of the research is to know the effect of a training program based on interactive teaching strategies on achievement and creative problem solving among fourth-grade students in chemistry of the directorate of education Rusafa first, the sample was divided into two groups, one experimental and numbering (29) students and the other control group numbering (30) students. The experimental group underwent the training program in the first semester of the year (2021-2022) and the control one studied according to the usual method. Two tools were built, the first being an academic achievement test consisting of (40) multiple-choice items, and the second a test of creative problem-solving skills in a chemistry subject and consisting o