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

he concept of small monoform module was introduced by Hadi and Marhun, where a module U is called small monoform if for each non-zero submodule V of U and for every non-zero homomorphism f ∈ Hom R (V, U), implies that ker f is small submodule of V. In this paper the author dualizes this concept; she calls it co-small monoform module. Many fundamental properties of co-small monoform module are given. Partial characterization of co-small monoform module is established. Also, the author dualizes the concept of small quasi-Dedekind modules which given by Hadi and Ghawi. She show that co-small monoform is contained properly in the class of the dual of small quasi-Dedekind modules. Furthermore, some subclasses of co-small monoform are investiga

This paper aims to deal with the understanding of the properties of the molecular gas hydrogen in the extragalactic spirals sample. It is critical to make observations of CO (J = 1-0) line emission for spiral galaxies, particularly those with an energetic nucleus.  In the sample of spiral galaxies compiled, a carbon monoxide CO (1-0) emission line can be observed. This sample of galaxies' gas kinematics and star-forming should be analyzed statistically utilizing appropriate atomic gas HI, molecular gas H2, infrared (1μm-1000μm), visual (at λblue-optical=4400A0), and radio spectrum (at νradio=1.4 GHz and 5GHz) databases. STATISTICA is software that allows us to perform this statistical analysis. The presence of a high scale of s

The ability of insurance companies to achieve goals depends on their ability to meet customers' requirements, and this requires them to identify target markets and respond to needs and wishes of the markets, the skill is to convince the company to operate what is in the interest of the customer if he is convinced the customer service provided to him, he would repeat to deal with, and where the cost of maintaining existing customers is less than the cost of attracting new customers, the insurance companies that is working hard to maintain their customers, the more customer satisfaction with the services provided has increased loyalty and weakened the ability of competitors lured.

       &nbs

This search include the synthesis of some new 1,3-oxazepine derivatives have been prepared, starting from reaction of L-ascorbic acid with dry acetone in presence of dry hydrogen chloride afforded the acetal (I). Treatment of the latter with p-nitrobenzoyl chloride in dry pyridine yielded the ester (II) which was dissolved in (65%) acetic acid in absolute ethanol yielded the glycol (III). The reaction of the glycol (III) with sodium periodate in distilled water at room temperature produced the aldehyde (IV). The compound (V) [2-amino-5-mercapato-1,3,4-thiadiazole] was prepared through the reaction of thiosemicarbazide with carbon disulphide (CS2) in entity of anhydrous (Na2CO3) in (abs. ethanol ). Compound (VI) [2-(5-mercapto-1,3,4-thiadiaz

 A new series of Sulfamethoxazole derivatives was prepared and examined for antifibrinolytic and antimicrobial activities. Sulfamethoxazole derivatives bear heterocyclic moieties such as 1,3,4-thiadiazine {3},  pyrazolidine-3,5-diol {4} 6-hydroxy-1,3,4-thiadiazinane-2-thione {5} and [(3-methyl-5-oxo-4,5-dihydro-1H-pyrazol-4-yl)diazenyl] {8}. Their structures were elucidated by spectral methods (FT-IR, H¹-NMR). Physical properties are also determined for all compound derivatives.  Recently prepared compounds were tested for their antimicrobial activity in the laboratory. Each screened compound showed good tendency to moderate antimicrobial activity.

The subject of the act and its transformations in the presentation is of great importance at the level of study, analysis and interpretation, and through that the researcher adopted the following title (The Dramatic Act and Its Transformations in the Iraqi Theatrical Show). The play of Black Astronomy was chosen as a sample for analysis, and the aim of the research came in order to achieve a special knowledge of the extent of the transformation that occurred between the dramatic structure of the act and theatrical embodiment and its multiple elements of operation in the Iraqi theatrical shows. It was limited to the show of the Iraqi theater in the year (2020) and included the theoretical framework that accommodated three sections. As for

The importance of the Arabic language and its deep vocabulary in the live translation of the work of science and interior design can't be hidden from the whole world. The previous studies have dealt with the role of the linguistic vocabulary and Arabic calligraphy in interior spaces in terms of decoration and design. However, this research sheds light on the importance of linguistic vocabulary in the construction of design thought and how it has become the a basic motivation in the process of scientific and practical construction and not just aesthetic formations that took their place in the interior spaces, as linguistic vocabulary emerged recently and echoed within the specialization of interior design and formed a key motive to explor

In this manuscript, the effect of substituting strontium with barium on the structural properties of Tl_0.8Ni_0.2Sr_2-xBr_xCa₂Cu₃O_9-δcompound with x= 0, 0.2, 0.4, have been studied. Samples were prepared using solid state reaction technique, suitable oxides alternatives of Pb₂O₃, CaO, BaO and CuO with 99.99% purity as raw materials and then mixed. They were prepared in the form of discs with a diameter of 1.5 cm and a thickness of (0.2-0.3) cm under pressures 7 tons / cm², and the samples were sintered at a constant temperature o

Was appointed acid steady disintegration of organic EkandThe results proved that organic Allicand acting and Konnh solid baseBy Tgrav Pearson has possible account Maamat hardness and softness of organic Ekand