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

Abstract

The term public budget defects became nowadays a chronic, economical phenomenon, almost all the countries weather advanced or development country suffered from it, despite the different visions to economic schools of a thought to accept or reject the deficit in public budget but the prevailed opinion that is needed to rule the role of the state by reducing the public spending which led to continuous deficits in public budget and the consequent upon increase in government borrowing, increase taxes on income and wealth, thus weakening the in contrive for private investment which contributed to the increase of in flationary stagnation, it became a duty to state covered by the lack of financial sources

Abstract Background: Dne of the key component of nasal tipplasty is effecter control of naral tip projection. Several cartilage grafts have been decreased for this purpose each had its own advantage and disadvantage. Aim: To evaluate using of double teostrut graft for controlling of tip projection. Patients and Methods: A total number of 170 patients were subjected to primary and secondary rhino plaster between January 2020 to January 2023. Those patients had double Teostrut banner graft for support of their nasal tip and maintaining tip projection after operation. Results: The follow period was ranging between 6-12 months. The shape of the nose was evaluating by patents vernal analogues scale. The average score for patients satisfaction wa

In this paper Heun method has been used to find numerical solution for first order nonlinear functional differential equation. Moreover, this method has been modified in order to treat system of nonlinear functional differential equations .two numerical examples are given for conciliated the results of this method.

This investigation aimed to explain the mechanism of MFCA by applying this method on air-cooled engine factory which was suffering from high production cost. The results of this study revealed that MFCA is a useful tool to identify losses and inefficiencies of the production process. It is found that the factory is suffering from high losses due to material energy and system losses. In conclusion, it is calculated that system losses are the highest among all the losses due to inefficient use of available production capacity.

Microalgae have been increasingly used for wastewater treatment due to their capacity to assimilate nutrients. Samples of wastewater were taken from the Erbil wastewater channel near Dhahibha village in northern Iraq. The microalga Coelastrella sp. was used in three doses (0.2, 1, and 2g. l^-1) in this experiment for 21 days, samples were periodically (every 3 days) analyzed for physicochemical parameters such as pH, EC, Phosphate, Nitrate, and BOD₅, in addition to, Chlorophyll a concentration. Results showed that the highest dose 2g.l^-1 was the most effective dose for removing nutrients, confirmed by significant differences (p≤0.05) between all doses. The highest removal percentage was

In this paper, The transfer function model in the time series was estimated using different methods, including parametric Represented by the method of the Conditional Likelihood Function, as well as the use of abilities nonparametric are in two methods  local linear regression and cubic smoothing spline method, This research aims to compare those capabilities with the nonlinear transfer function model by using the style of simulation and the study of two models as output variable and one model as input variable in addition t

The efficiency of management is determining factor for the success or failure of agricultural projects generally and Livestock particularly achieving its objectives. Therefore, this research came to diagnose the most important variables that determine the efficiency of management using the probability regression models to measure the probability of management efficient of broilers production projects using  random sample included (60) broilers projects represented 11.6% of Baghdad province (research community) in 2016. After estimating the relationship between the management efficiency (descriptive dependent variable) and the independent variables affecting it (age, educational level, production index (PI), experience). The results