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

During of Experimental result of this work , we found that the change of electrical conductivity proprieties of tin dioxide with the change of gas concentration at temperatures 260oC and 360oC after treatment by photons rays have similar character after treatment isothermally. We found that intensive short duration impulse annealing during the fractions of a second leads to crystallization of the films and to the high values of its gas sensitivity.

The primary objective of the present  research is to diagnose the most mportant imensions of quality of work life in a sample of individuals working in the Northern Gas Filling Company in Nynawa. The study sample consisted of 140 employees of the Northern Region Filling Company in even ,Through a questionnaire prepared for this purpose. The study concluded that there are five main factors that are considered to be measure of the quality of working life and are based on their importance: Empowerment, organizational health, internal work environment, motivation, development and training of workers. The study recommended that the organization should payattentio

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In this paper, third order non-polynomial spline function is used to solve 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of this method, and to compare the computed results with other known methods.

Nuclear emission rates for nucleon-induced reactions are theoretically calculated based on the one-component exciton model that uses state density with non-Equidistance Spacing Model (non-ESM). Fair comparison is made from different state density values that assumed various degrees of approximation formulae, beside the zeroth-order formula corresponding to the ESM. Calculations were made for 96Mo nucleus subjected to (N,N) reaction at Emax=50 MeV. The results showed that the non-ESM treatment for the state density will significantly improve the emission rates calculated for various exciton configurations. Three terms might suffice a proper calculation, but the results kept changing even for ten terms. However, five terms is found to give

This investigation reports application of a mesoporous nanomaterial based on dicationic ionic liquid bonded to amorphous silica, namely nano-N,N,N′,N′-tetramethyl-N-(silican-propyl)-N′-sulfo-ethane-1,2-diaminium chloride (nano-[TSPSED][Cl]2), as an extremely effectual and recoverable catalyst for the generation of bis(pyrazolyl)methanes and pyrazolopyranopyrimidines in solvent-free conditions. In both synthetic protocols, the performance of this catalyst was very useful and general and presented attractive features including short reaction times with high yields, reasonable turnover frequency and turnover number values, easy workup, high performance under mild conditions, recoverability and reusability in 5 consecutive runs without lo

The article provides a comparative analysis of comparisons in Russian and Arabic, aimed at identifying their structural, typological, and functional-pragmatic features. The study is based on a systematic approach to the analysis of linguistic means of expressing comparisons in two differ- ent linguistic cultures. The article analyzes the main structural components of comparisons, their classification, and their cognitive and aesthetic functions. The results of the study demonstrate the deep cultural conditioning of comparative constructions and their important role in representing the specific features of the respective linguistic cultures.

The research mainly seeks to predict the amounts of non- oil Iraqi exports which concludes ) Food & Animals , Raw materials and non- tanned Leather and fur , Mineral fuels and Lubricating Oil , Chemical substances and amounts , Manufactured goods , Electrical and non - electrical machines , Supplies and Total non- Oil exports ) by using Markov Chain as one of Statistical approach to forecasting in future . In this search We estimate the transliteration probabilities matrix according to Maximum Likelihood on a data collected from central organization for Statistics and information technology represents an index numbers of non- Oil exports amount in Iraq from 2004 to 2015 depending on 2007 as a basic year . Results shown that trend of index

In this research we have been studied the 3rd order spherical aberration for an optical system consisted of obscured circular aperture with non central circular obscuration through the calculation of point spread function (P.S.F) in presence of the obscuration in the center and comparing the obtained results with that results of moving obscuration far away from the center, where the results showed significant improvement for(P.S.F) value. The study was done of different obscurities ratios in addition to the different 3rd order spherical aberration values (W40=0.25 ,0.5 ,0.75 ,1 ).