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

Introduction: We aimed to assess the impact of adhesive and wires types on the tensile bond strength of fixed lingual retainers. Methods: A total of 160 intact bovine teeth were collected, cleaned, stored in 25% sodium hypochlorite, and randomly assigned to two groups based on the adhesive type: a two-step adhesive and a one-step adhesive. Each group was further divided into four subgroups based on the type of lingual retainer wire, which included (A) 8-strand braided stainless steel wire, (B) three-strand titanium retainer wire, (C) stainless steel chain, and (D) fiber-reinforced retainer. A tensile bond strength test was conducted using a universal testing machine at a controlled speed of 10 mm/min. Result: The 8-strand braided stainles

The crystal structures of a new polymorph and seven new derivatives of 2-(1-phenyl-1H-1,2,3-triazol-4-yl)pyridine have been characterized and examined along with three structures from the literature to identify trends in their intermolecular contact patterns and packing arrangements in order to develop an insight into the crystallization behaviour of this class of compound. Seven unique C-H...X contacts were identified in the structures and three of these are present in four or more structures, indicating that these are reliable supramolecular synthons. Analysis of the packing arrangements of the molecules using XPac identified two closely related supramolecular constructs that are present in eight of the 11 structures; in all cases, the st

The research aims to identify the most important variables affecting shooting from jumping high and compare them for the two foot the weak and strong, where the researchers adopted the descriptive method, and the sample was chosen by the intentional method, which consists of (4) players from the Iraqi Sports Army Club, where these variables were studied and their impact on The accuracy of aiming at the two men, and the researchers concluded that most of the players have more accuracy in aiming at the strong leg than at the weak leg, which leads to the loss of many real opportunities during the match because of the players changing the situation or wasting the available opportunity when the position of correction is an opportunity for the w

The article approaches the characteristics of Russian literature in the time of Khrushchev or the "thaw" period a very short period of Soviet history, characterized by the easing of the dictatorship of power and relaxation in various areas of people's lives. The interest in the research is focused on the importance of interpreting the family portrait in a short but distinct period in the development of Russian/Soviet literature. The research material is the story of Sholokhov's “The Fate of Man” 1956, the story of Panova “Serioga” 1955, and Abramov’s story “Fatherless” 1961. В статье рассматриваются особенности художественной литературы периода хруще

The financial crises that occurred in South East Asia and America, and the discovery of the financial and administrative corruption that affected these companies, which led to the crisis. Since then, organizations and institutions interested in accounting have begun new ways to further rationalize the management of these companies. Hence the concept of governance, which means good governance. Al-Susiya confirmed its adoption of the financial reporting standards and adopted internal and external auditing for the purpose of increasing the reliability and credibility of the financial and reports that increase the confidence of investors in making their investment decisions in the financial markets The study dealt with the contributi

Two Schiff bases, namely, 3-(benzylidene amino) -2-thioxo-6-methyl 2,5-dihydropyrimidine-4(3H)-one (LS])and 3-(benzylidene amino)-6-methyl pyrimidine 4(3H, 5H)-dione(LA)as chelating ligands), were used to prepare some complexes of Cr(III), La(III), and Ce(III)] ions. Standard physico-chemical procedures including metal analysis M%, element microanalysis (C.H.N.S) , magnetic susceptibility, conductometric measurements, FT-IR and UV-visible Spectra were used to identify Metal (III) complexes and  Schiff bases (LS) and (LA). According to findings, a [Cr(III) complex] showed six coordinated octahedral geometry, while [La(III), and Ce(III) complexes]were structured with coordination number seven.  Schiff's bases a

            Density Functional Theory (DFT) method of the type (B3LYP) and a Gaussian basis set (6-311G) were applied for calculating the vibration frequencies and absorption intensities for normal coordinates (3N-6) at the equilibrium geometry of the Di and Tetra-rings layer (6, 0) zigzag single wall carbon nanotubes (SWCNTs) by using Gaussian-09 program. Both were found to have the same symmetry of D_6d point group with C--C bond alternation in all tube rings (for axial bonds, which are the vertical C--Ca bonds in rings layer and for circumferential bonds C—Cc in the outer and mid rings bonds). Assignments of the modes of vibration IR active and inactive vibration frequ

      The article examines the definition of the verb in the form of the imperative mood (imperative) _ general information about the verb in Russian .

       A verb in Russian is one of the parts of speech that unify all parts of speech, expressing the meaning of action, movement, process in grammatical forms of time, type, mood, face and voice. The imperative mood is a grammatical feature of the verb expressed through several forms of the verb that urges someone to do things. In other words, imperative mood or (imperative) : -  one of the single meaning of the form . The form of the imperative expresses a supplicatio