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 main idea that led me to write such research paper within the framework of Germanic linguistics is that I have not found any topic dealing with the term correlate in the German language, except in several articles in linguistic journals as well as one topic in a book describing the use of such a linguistic phenomenon in the language system. The research initially deals with the definition of the correlate at the level of the German language system. Correlate is unity describes specific relation of two sentences and identifies denoted constructs. Correlate is called a placeholder at the syntactic level because it does not occupy its original topological fields in the syntactic structure. The correlate (es) or the prepositiona

The aim of the research is to identify the economic and cultural role of contemporary interactive artworks from the public's point of view, with knowledge of the most important obstacles and proposals to improve the level of design and spread of interactive artworks. The descriptive approach was used, and the researcher used a questionnaire tool that was distributed to the audience for the events of Noor Al Riyadh (2021) and the size of the participating sample was (194) individuals from all spectrums of society. It was found through the results of the existence of public approval of the economic role of contemporary interactive artworks, as they contribute to supporting the national economy. It attracts the public to attend various paid

The goal of this work is demonstrating, through the gradient observation of a   of type linear ( -systems), the possibility for reducing the effect of any disturbances (pollution, radiation, infection, etc.) asymptotically, by a suitable choice of related actuators of these systems. Thus, a class of  ( -system) was developed based on finite time  ( -system). Furthermore, definitions and some properties of this concept -system and asymptotically gradient controllable system ( -controllable) were stated and studied. More precisely, asymptotically gradient efficient actuators ensuring the weak asymptotically gradient compensation system ( -system) of known or unknown disturbances are examined. Consequently, under convenient hypo

In this research velocity of moving airplane from its recorded digital sound is introduced. The data of sound file is sliced into several frames using overlapping partitions. Then the array of each frame is transformed from time domain to frequency domain using Fourier Transform (FT). To determine the characteristic frequency of the sound, a moving window mechanics is used, the size of that window is made linearly proportional with the value of the tracked frequency. This proportionality is due to the existing linear relationship between the frequency and its Doppler shift. An algorithm was introduced to select the characteristic frequencies, this algorithm allocates the frequencies which satisfy the Doppler relation, beside that the tra

Software cost management is a significant feature of project management. As such, it needs to be employed in a project or line of work. Software cost management is integral to software development failures, which, in turn, cause software failure. Thus, it is imperative that software development professionals develop their cost management skills to deliver successful software projects. The aim of this study is to examine the impact of cost management success factors with project management factors and three agile methodologies – Extreme Programming (XP), Scrum and Kanban methodologies which are used in the Pakistani software industry. To determine the results, the researchers applied quantitative approach through an extensive survey on

The factors influencing the financial market are rapidly becoming more complex. The impact of non-financial factors on the performance of a company’s common stock can increase in ways that were not previously expected. This study investigated how brand capital affects the risk of stock prices in Iraqi private banks listed on the Iraq Stock Exchange failing by identifying the likelihood of a crash caused by a negative deviation in the distribution of returns on ordinary shares. As a result, the current study’s concept is to review an analytical knowledge framework of the nature of that relationship, its changes, and its impact on the pricing of ordinary shares of the banks of the researched sector for the years 2009 to 2017, as w