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.

The role of internal control is based on the effectiveness of the budget through an analysis of the reality of the budget in the research sample as it was studied in the preparation and preparation stages and the implementation stage. The sample showed that the sample did not comply with what is stated in the Ministry of Finance publication of instructions and ceilings. In the process of preparing and resulting from the occurrence of deviations in large proportions both in the discussion of the Ministry of Finance or when implementation as a low rate of implementation and the absence of allocations for some items, although there is a need for them as well as the transfer of large proportions of transfers both up or down and the purpose o

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.

Porous silicon (PS) layers were formed on n-type silicon (Si) wafers using Photo- electrochemical Etching technique (PEC) was used to produce porous silicon for n-type with orientation of (111). The effects of current density were investigated at: (10, 20, 30, 40, and50) mA/cm2 with etching time: 10min. X-ray diffraction studies showed distinct variations between the fresh silicon surface and the synthesized porous silicon. The maximum crystal size of Porous Silicon is (33.9nm) and minimum is (2.6nm) The Atomic force microscopy (AFM) analysis and Field Emission Scanning Electron Microscope (FESEM) were used to study the morphology of porous silicon layer. AFM results showed that root mean square (RMS) of roughness and the grain size of p

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

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 aim of this paper is to introduce the concept of N  and Nβ -closed sets in terms of neutrosophic topological spaces. Some of its properties are also discussed.

Drilling solutions can be considered as an intricate mixture comprising of number of chemical additives which aid specific needs such as controlling the rheological properties and reducing corrosion. Inhibitors are substances that are added in small concentrations to corrosive environment to decrease the corrosion. Their applications can be found in drilling equipments. The effect of adding Zinc Sulphate and Carboxymethyl Cellulose to study their influence on the corrosion of carbon steel in Bentonite mud has been evaluated using Weight Loss Technique. This study focuses on determining rheological properties and corrosion characteristics. Results show CMC and ZnSO₄ work as inhibitors when added to the Bentonite with inhibition