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 any of them.
The techniques of fractional calculus are applied successfully in many branches of science and engineering, one of the techniques is the Elzaki Adomian decomposition method (EADM), which researchers did not study with the fractional derivative of Caputo Fabrizio. This work aims to study the Elzaki Adomian decomposition method (EADM) to solve fractional differential equations with the Caputo-Fabrizio derivative. We presented the algorithm of this method with the CF operator and discussed its convergence by using the method of the Cauchy series then, the method has applied to solve Burger, heat-like, and, couped Burger equations with the Caputo -Fabrizio operator. To conclude the method was convergent and effective for solving this type of
... Show MoreAn experiment was carried out in the vegetables field of Horticulture Department / College of Agriculture / Baghdad University , for the three seasons : spring and Autumn of 2005 , and spring of 2007 , to study the type of gene action in some traits of yield and its components in summer squash crosses (4 x 3 = cross 1 , 3 x 7 = cross 2 , 3 x 4 = cross 3 , 3 x 5 = cross 4 , 5 x 1 = cross 5 , 5 x 2 = cross 6). The study followed generation mean analysis method which included to each cross (P1 , P2 , F1 , F2 , Bc1P1 , Bc1P2) , and those populations obtained by hybridization during the first and second seasons. Experimental comparison was performed in the second (Two crosses only) and third seasons , (four crosses) by using RCBD with three repl
... Show MoreThis paper aimed to test random walking through the ISX60 market index for the ability to judge market efficiency at a weak level. The study used Serial Correlation Test, the Runs Test, the Variance Ratio Test, as well as the Rescaled Range Test.The population of the study represents of Iraq Stock Exchange. The study concluded accepting the hypothesis of the study that the returns of the ISX60 market index in the Iraqi market for securities does not follow the random walking in general and as a result the Iraq market for securities is inefficient within the weak level of efficiency and the study recommended need a supervisors work in the Iraqi market for securities to activate all means a which will work to communication with information
... Show MoreThe research aims to evaluate the radioactivity in elected samples of cereals and legume which are wide human consumption in Iraq using Nuclear Track Detectors (NTDs) model CN-85.
The samples were prepared scientifically according to references in this field. After 150 days of exposure, the detector were collected and chemically treated according to scientific sources (etching chemical), nuclear effects have been calculated using the optical microscope.
Radon (222Rn) concentration and uranium (238U) were calculated in unit Bq/m3 and (ppm), the results indicate that the highest concentration of radon and uranium was in yellow corn where the concentration of radon was 137.17×102 Bq/m3 and uranium concentration 2.63 (ppm). The lowest
Low- and medium-carbon structural steel components face random vibration and dynamic loads (like earthquakes) in many applications. Thus a modification to improve their mechanical properties, essentially damping properties, is required. The present study focuses on improving and developing these properties, significantly dampening properties, without losing the other mechanical properties. The specimens used in the present study are structural steel ribbed bar ISO 6935 subjected to heating temperatures of (850, 950, and 1050) ˚C, and cooling schemes of annealing, normalizing, sand, and quenching was selected. The damping properties of the specimens were measured experimentally with the area under the curve for the loadi
... Show MoreIn this paper the effect of thermal annealing on the structural and optical properties of Antimony Selenide (Sb2Se3) is investigated. Sb2Se3 powder is evaporated on clean amorphous glass substrates at room temperature under high vacuum pressure (4.5×10-6 mbar) to form thin films. The structural investigation was done with the aid of X-ray diffraction (XRD) and atomic force microscopy (AFM). The amorphous to polycrystalline transformation of these thin films was shown by X-ray diffraction analysis after thermal annealing. These films' morphology is explained. (UV-Vis ) spectra in ranges from 300 to 1100 nm was used to examine the optical properties of the films .The absorption coefficient and optical energy gap of the investigated films are
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