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

The first chapter the importance of research and need for education scientists see that the roots of the use of a specimen Wheatley in learning and teaching back to Grayson Wheatley, one of the largest supporters of a modern construction, which lay the groundwork for the specimen stage and the form in which it is. That was attributed to him, often called his name called while some educators based learning strategy on the issue. He sees the learner in this model make him a meaningful understanding of problems during his progress, thereby acting with his colleagues to find solutions to them in small groups. He

        Borders Search: Search by students is determined by th

The grammar structure transforms from its fundamental field to another field that takes new dimensions, and is used in another way in speech that differs from the first one, because the formula basis of the name(Faael) in speech is a (distorted characteristic), and the distorted characteristic indicates the stability and the necessity of the characterized. as this characteristic has changed from its use as a distorted characteristic which was established by the elders. to a use that differs from the first and cannot be overlooked to achieve a new purpose, to be used as plural

The research aims to shed light on the role of E-Audit in raising Independence and professional competence of the external auditor, the study has been applied on a sample of the branches of the Rafidain Bank n have been addressed research topic beside the theoretical, as put forward by the literature of accounting, audit and that the contents of the section first, either the practical side was required to test the hypotheses use form questionnaire, which was distributed to a sample of the external auditors and bankers research sample. He has applied for his part in the search for a standard of independence and professionalism of the external auditor and the factors influencing these standards, and the most import

High‐quality factor Q  and elliptical cross‐section microcavity of small size are described. We present a numerical investigation of the performance of the elliptical microcavity. We design elliptical microcavities to control the emission rate of dipolar emitters and investigate how the ellipticity factor influences the Purcell and Q ‐factors. We demonstrate an enhancement of up to 16 × 10 ³ in the Purcell factor for TiO ₂ ‐based mirrors and 8 × 10

Objective: The aim of this study was to evaluate the effect of pumice, burning investment material
and black sand on the surface roughness of heat cure acrylic resin.
Methodology: Sixty specimens were prepared from pink heat cure acrylic resin, the specimens
where grouped into; 20 specimens which polished with pumice and water (control group); 20
specimens which polished with investment material (after burning it) and water; and 20 specimens
which polished with black sand and water. The average surface roughness of specimens after
polishing procedure had been determined by profilometer (surface roughness tester).
Results: Through the application of ANOVA and LSD tests, the result of this study showed that there
wa

Premature failure in asphalt concrete pavement has been the main concern for pavement construction companies and engineers in recent years because of the large rise in traffic volume and loads and the temperature extremes in the summer and winter. The use of modifiers in asphalt concrete mixtures has attracted much attention to increase the performance and lifespan of pavements. As nanotechnology developed, several researchers concentrated on how these materials can help increase pavement serviceability by minimizing rutting and moisture damage. This study evaluates the Hydrated Lime (HL) effect by two methods (wet and dry hydrated lime) on the durability of the warm mix asphalt. The first method, HL, has been supplemented to the as

Increasing material prices coupled with the emission of hazardous gases through the production and construction of Hot Mix Asphalt (HMA) has driven a strong movement toward the adoption of sustainable construction technology. Warm Mix Asphalt (WMA) is considered relatively a new technology, which enables the production and compaction of asphalt concrete mixtures at temperatures 15-40 °C lower than that of traditional hot mix asphalt. The Resilient modulus (Mr) which can be defined as the ratio of axial pulsating stress to the corresponding recoverable strain, is used to evaluate the relative quality of materials as well as to generate input for pavement design or pavement evaluation and analysis. Based on the aforementioned preface, it is

Recently, some of Iraq's newly constructed asphalt concrete pavements showed premature failures with significant negative impacts on roadway safety and the economy. Using Nano hydrated lime (NHL) in pavement construction could be one of the possible steps to improve pavement durability. This article discusses how NHL affects the durability of hot mix asphalt. NHL was added in two methods to the asphalt concrete mixture for the wearing course. The first is the dry method, i.e., on the aggregate, whereas the second is the wet addition method, i.e., to the bitumen. The percentages were tried for each additional method; 1, 2, and 3% by weight of aggregate for the dry method and 0.5, 1, and 1.5% by weight of asphalt concrete for the wet

Iraq suffers from lack of water resources supply because the headwaters of the rivers located outside its borders and the influence of upstream countries on the quantities of flowing water, in addition to the increase of pressure on available water as a result of population increase and not adopting the principle of rationalization where misuse and wastage and lack of strategic vision to treat and manage water use in accordance with the economic implications fall.  This is reflected fallout on water security and subsequently on national and food security, while the issue of using water resources is development top priority in different countries in the world because of the importance of water effect on the security of indivi