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

 This research provides a new method to study praise poetry that can be used as a course to teach English and Arabic to students in the College of Education. This research answers two questions:

1. Is it possible to examine praise poetry as a tagmeme?
2. Is this analysis of great help in teaching English and Arabic to students in the College of Education?

           The data that will be chosen for the purpose of analysis are two of Shakespeare's sonnets and two of AL Mulik's poems. The sonnets selected for this purpose are 17 and 18. AL Mulik's poems selected for the same purpose are 8 and 9.

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A study of characteristics of the lubricant oils and the physical properties is essential to know the quality of lubricant oils. The parameters that lead to classify oils have been studied in this research. Three types of multi-grades lubricant oils were applied under changing temperatures from 25 ^oC to 78^oC to estimate the physical properties and mixture compositions. Kinematic viscosity, viscosity gravity constant and paraffin (P), naphthenes (N) and aromatics (A) (PNA) analysis are used to predict the composition of lubricants oil. Kinematic viscosity gives good behaviors and the oxidation stability for each lubricant oils. PNA analysis predicted fractions of paraffin (X_P), naphthenes (X_N),

This research provides a new method to study praise poetry that can be used as a course to teach English and Arabic to students in the College of Education. This research answers two questions: Is it possible to examine praise poetry as a tagmeme? Is this analysis of great help in teaching English and Arabic to students in the College of Education? The data that will be chosen for the purpose of analysis are two of Shakespeare's sonnets and two of AL Mulik's poems. The sonnets selected for this purpose are 17 and 18. AL Mulik's poems selected for the same purpose are 8 and 9. Each line in both English and Arabic data is numbered by the researcher herself. Then, those lines are grouped into sentences to facilitat

In this study, generation of elliptical gears with different teeth profiles of crowned involute, double circular arc (DCA), and combined (crowned involute with DCA) has been developed. The resulting mathematical equations have been computerized and feed to CNC end mill machine to manufacture elliptical gear models with different profiles. These models are investigated in plane polariscope to show the resulting stresses under certain load. Comparison of photo-elastic stress results shows that combined elliptical gears with DCA side as a loaded side have a minimum resulting contact stress with a reduction percentage of 40% compare with contact stresses in counterpart elliptical gear of involute profile (which is commonly u

Cams are considered as one of the most important mechanical components that depends the contact action to do its job and suffer a lot of with drawbacks to be predicted and overcame in the design process. this work aims to investigate the induced cam contact and the maximum shear stress energy or (von misses) stresses during the course of action analytically using Hertz contact stress equation and the principal stress formulations to find the maximum stress value and its position beneath the contacting surfaces. The experimental investigation adopted two dimensions photoelastic technique to analyze cam stresses under a plane polarized light. The problem has been numerically simulated using Ansys software version 15 as FE

Objective of the study was to rate and analyze the physical fitness of female students from Iraq and Russia to find similarities, differences and regularities. Sampled for the study were 44 female non-sporting students: 20 students from Pedagogical University in Bagdad; and 24 students from Russian State University of Physical Education, Sport, Youth and Tourism in Moscow. The study was designed to obtain the joints flexibility, coordination, speed-strength and static endurance rates. The Iraqi students were tested with higher coordination abilities than their Russian peers, whilst the latter were ranked higher in the speed-strength, shoulder joints and spine flexibility tests, albeit lower than their Iraqi peers in the hip flexibility test

In this paper, we study the incorporation of the commensalism interaction and harvesting on the Lotka–Volterra food chain model. The system provides one commensal prey, one harvested prey, and two predators. A set of preliminary results in local bifurcation analysis around each equilibrium point for the proposed model is discussed, such as saddle-node, transcritical and pitchfork. Some numerical analysis to confirm the accruing of local bifurcation is illustrated. To back up the conclusions of the mathematical study, a numerical simulation of the model is carried out with the help of the MATLAB program. It can be concluded that the system's coexistence can be achieved as long as the harvesting rate on the second prey population is