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

 An edge dominating set    of a graph  is said to be an odd (even) sum degree edge dominating set (osded (esded) - set) of G if the sum of the degree of all edges in X is an odd (even) number. The odd (even) sum degree edge domination number  is the minimum cardinality taken over all odd (even) sum degree edge dominating sets of G and is defined as zero if no such odd (even) sum degree edge dominating set exists in G. In this paper, the odd (even) sum degree domination concept is extended on the co-dominating set E-T of a graph G, where T is an edge dominating set of G.  The corresponding parameters co-odd (even) sum degree edge dominating set, co-odd (even) sum degree edge domination number and co-odd (even) sum degree edge domin

في هذا البحث تم استعمال احد الاساليب التقريبية وهو ما يسمى اسلوب المعدل الموزون للنقاط المقربة (Weighted Average of Rounded Points-WARPing) لتقدير انبعاثات ثاني اوكسيد الكاربون CO_2 في العراق عند استعمال مقدريNadaraya-Watson, Local Linear estimator للفترة الممتدة من عام (1990) ولغاية (2019) ومن ثم المقارنة بين اداء تلك المقدرات وقد اثبتت النتائج تفوق طريقة Local Linear estimator وخاصة في النقاط عند نقاط الحد وتميزها عن طريقة Nadaraya–Watson على الرغم من الاداء ا

This study is the first investigation in Iraq dealing with genotyping of IL-4 −590 (C>T) gene, especially in Iraqi patients with asthma. We studied forty-eight blood samples collected from patients with asthma and compared with age-matched 25 healthy individuals as controls. The polymorphism results of IL-4 −590 (C>T) gene by using amplification refractory mutation system (ARMS-PCR) showed the presence of C and T alleles and three genotypes (CC, CT, and TT). Interestingly the frequency of C allele and CC genotype was higher in patients with asthma in comparison with the same allele and geno

            The article describes a certain computation method of -arcs to construct the number of distinct -arcs in  for . In this method, a new approach employed to compute the number of -arcs and the number of distinct arcs respectively. This approach is based on choosing the number of inequivalent classes } of -secant distributions that is the number of 4-secant, 3-secant, 2-secant, 1-secant and 0-secant in each process. The maximum size of -arc that has been constructed by this method is . The new method is a new tool to deal with the programming difficulties that sometimes may lead to programming problems represented by the increasing number of arcs. It is essential to reduce the established number of -arcs in each cons

Catalytic reduction is considered an effective approach for the reduction of toxic organic pollutants from the environment, but finding an active catalyst is still a big challenge. Herein, Ag decorated CeO2 catalyst was synthesized through polyol reduction method and applied for catalytic reduction (conversion) of 4-nitrophenol (4-NP) to 4-aminophenol (4-AP). The Ag decorated CeO2 catalyst displayed an outstanding reduction activity with 99% conversion of 4-NP in 5 min with a 0.61 min−1 reaction rate (k). A number of structural characterization techniques were executed to investigate the influence of Ag on CeO2 and its effect on the catalytic conversion of 4-NP. The outstanding catalytic performances of the Ag-CeO2 catalyst can be assigne

The polymer was used to inhibit the corrosion of copper metal in salt media in different concentrations at room temperature using potentiometric polarization measurement. The polymer was prepared by mixing (0.1 M) 4-Hydroxy aniline (C6H7NO) with (0.25M) of ammonium persulfate as the initiator using the electro-deposition technique. The polymer’s results showed that copper in (3.5%) NaCl had good corrosion resistance. The findings demonstrate that the %IE for polymer-induced copper corrosion is 89.32% at 10 ppm concentration as a result of the 4-hydroxy aniline polymer’s adsorption from salt solution on the surface of copper metal. The numbers from the polarization method and the acquired standard data agree well. The coated copper by po

The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.

The cost-effective carbon cross-linked Y zeolite nanocrystals composite (NYC) was prepared using an eco-friendly substrate prepared from bio-waste and organic adhesive at intermediate conditions. The green synthesis method dependent in this study assures using chemically harmless compounds to ensure homogeneous distribution of zeolite over porous carbon. The greenly prepared cross-linked composite was extensively characterized using Fourier transform infrared, nitrogen adsorption/desorption, Field emission scanning electron microscope, Dispersive analysis by X-ray, Thermogravimetric analysis, and X-ray diffraction. NYC had a surface area of 176.44 m2/g, and a pore volume of 0.0573 cm3/g. NYC had a multi-function nature, sustained at a long-

A fracture is a damage to bone tissue that causes damage to the tissue surrounding the bone and may penetrate the skin. Subjects and methods: the present study included (80) fractured Iraqi patients (and 40) patients with DM2 and (40) without DM2 and compared them with (40) healthy control. Patients and control are matched in age. This study showed a significant increase in retinol-binding protein 4 (RBP4) and a considerable decrease in Vit .A GPT and GOT in fracture patients with and without DM2. In addition, there was a significant negative correlation between RBP4 with (GPT and GOT) in fracture patients with DM2 and a significant positive correlation between RBP4 with (GPT and GOT) in fracture patients without DM2.