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

الزكاة فريضة من فرائض الإسلام وعبادة من العبادات التي اقرها الشرع الإسلامي هذه الفريضة المالية التعبدية بالإضافة الى دورها المعنوي الذي يهدف الى إرساء قواعد العدالة الاجتماعية والقضاء على مشكلة الفقر في المجتمع الاسلامي وكما ينص عليها الدين الإسلامي فان لها ابعادها ووظائفها الكثيرة التي تخدم اليات العمل الاقتصادي في مجتمع يعمل وفق نظام اقتصادي أسلامي .

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Abstract
The study was conducted in Baghdad and aimed to:
The impact of moving the educational activities in the conservation of literary
texts and the development of literary taste in the fifth grade students moral "by
verifying the validity of hypotheses Elsafreeten following forms:
The first hypothesis:
- There are no differences in women with statistical significance between means
of scores of students three experimental groups, the experimental group first
used upstream activities in the teaching material of literature and texts, the
second experimental group used the activities of building in the teaching
material itself and the experimental group the third use activities concluding
taught the same

We found that 4,5- diphenyl- 3(2- propynyl) thio- 1??-triazole [1? forms a complex with Pd (11) ion of ratio 1:1 which absorbs light in CH2CI2 at 400 nm, and 4,5- diphenyl- 3(2- propenyl) thio- 1,2,4- triazole [II] forms complexes with Pd (II) ion of ratio 1:1 which absorbs light at 390 nm, and of ratio 2:1 which absorbs light at 435 nm. On the other hand, we found that the new derivative 4- phenyl- 5( p- amino phenyl) -3- mercapto- 1,2,4- triazole ?111? forms complexes with Cu (II) ion of the ratio 1:1 which absorbs light at 380 nm, with Ni (II) ion of the ratio 3:1 which absorbs light at 358 nm; and with Co (11) ion of the ratio 3.2:1 which absorbs light at 588 nm. The ratio of the complexes were determined by measuring the electronic spe

The research aims to identify: 1-Designing a test to measure the movement compatibility of the eye and the leg for the students of the Faculty of Physical Education and Sports Sciences, Samarra University. 2-Codification (setting scores and standard levels) for the results of the motor compatibility test for the eye and the leg for students of the Faculty of Physical Education and Sports Sciences, Samarra University. The researchers reached the some following conclusions: 1-A test to measure the movement compatibility of the eye and the leg for the students of the Faculty of Physical Education and Sports Sciences. 2-There is a discrepancy in the standard levels of the research sample.

 The financial markets are one of the sectors whose data is characterized by continuous movement in most of the times and it is constantly changing, so it is difficult to predict its trends , and this leads to the need of methods , means and techniques for making decisions, and that pushes investors and analysts in the financial markets to use various and different methods in order to reach at predicting the movement of the direction of the financial markets. In order to reach the goal of making decisions in different investments, where the algorithm of the support vector machine and the CART regression tree algorithm are used to classify the stock data in order to determine

Information security in data storage and transmission is increasingly important. On the other hand, images are used in many procedures. Therefore, preventing unauthorized access to image data is crucial by encrypting images to protect sensitive data or privacy. The methods and algorithms for masking or encoding images vary from simple spatial-domain methods to frequency-domain methods, which are the most complex and reliable. In this paper, a new cryptographic system based on the random key generator hybridization methodology by taking advantage of the properties of Discrete Cosine Transform (DCT) to generate an indefinite set of random keys and taking advantage of the low-frequency region coefficients after the DCT stage to pass them to

The current research deals with the dialectical relationship resulting from the conflict in the violent combination and construction of the living ( the actor)and the dead (the item) in the structure of the Sinography construction and the emergence of the theatrical play space , which can be summed up by the following question: what is the nature of the dialectical relationship between the living (the actor) and the dead( the item) in the Sinography creation, which limited the research in a central objective : to identify the controversy of the living (actor) and the dead (item) in the performance unit of the theatrical scene . The research, in its objective limits set forth in its methodological framework, analyzes this controversy in o

Abstract:

   Witness the current business environment changes rapidly reflected on the performance of the facility wishing to stay , which is no longer style reaction enough to handle installations with their environment , and quickly began to lose its luster with the emergence of a message and the vision of contemporary business environment from a set of parts interacting with each other and the concept of behavioral includes all dimensions of performance, it is imperative to adopt a system installations influence variables and positive interaction through the development of strategic plans and the use of implementation and follow-up strategies to ensure the effectiveness of the method for meas

Every researcher must say that the world in continually progress toward the best and that
the Arab and Islamic civilization had produced much of systems and virtuous educational
practices which raised from Islamic heritage. This nation was not isolated from external
world, but it was made a clear active for promote the banner of other nations which entered
under her influence to promote Islamic banner and Muslims. Consequently also Muslims are
affected and influenced, this resulted a clear impact in the civilization and educational
ideology especially in the contemporary teaching methods.