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

المقدمة

 الحمد لله رب العالمين، وأفضل السلام وأتم التسليم على سيدنا محمد، وعلى آله وصحبه، أجمعين، وعلى من تبعهم بإحسان إلى يوم الدين، أما بعد.

 فإن مسألة التعارض بين الرواية، والفتوى، من المسائل المشهورة عند الأصوليين والفقهاء،وهي من مباحث السنة عند الأصوليين، والتي تبنى عليها مسائل متعددة، وهي من أسباب اختلاف الفقهاء، فإذا ما روى أحد الرواة حديثاً معيناً، ثم عمل بخلاف ما روى، فللعل

Background: Aluminium (Al) intoxication was recognised as a causal agent in p a t i ent s undergoing haemodialysis and then was linked to Alzheimer's disease. Nevertheless, environmental pollution with Al is mainly v i a drinking water, particularly when acidic rain falls on Al containing soil and bedrock. In addition, aluminium utens i l s are widely used for cooking. Therefore, an increasing concern is emerging for the role of pH in the absorption of aluminium from ingested food.
Materials and methods: The objective of this study was to establish the effect of acidification with1 ml/dL of concentrated acetic acid on the absorption of aluminium from a 5 mM a l u mi n i u m sulphate\ solution taken orally

      The study was conducted for the detection of Aflatoxin B1(AFB1) in the serum and urine of 42 early and middle childhood patients (26 male and  16 female ) with renal function disease, liver function disease, in additional to atrophy in the growth and other symptoms depending on the information within consent obtained from each patient, in addition to 8 children, apparently healthy, as  the control. The technique of HPLC was used for the detection of AFB1 from all samples. The results showed that out of 42 patient children, 19 (45.2%) gave positive detection of AFB1 in the serum among all age groups patients with a mean of 0.88 ng/ml and a range of (0.12-3.04) ng/ml. This was compared with the cont

      This study deals with the challenges and risks faced by mobile banking services and their plagiarism and reduction, the issue of risk management and review, as it acquires financial importance for banks that provide electronic mobile banking services, as included by the Basel Committee, financial accounting via mobile phone, and in line with treason works Traditional commercial banks invest in modern ones, including mobile phones.

This research addresses the relevance of men and women and the consequent provisions
such as dowry and alimony ... Of the like, marriage is to organize links masculinity and
femininity any sexual meeting between men and women a special system that must be
produces reproduction him and alone, which gets its reproduction in human kind, and has no
family and on the basis of private life is being organized.
The importance of the topic see Islam has urged marriage and forbade celibacy, and ensure
that the Lord of Glory Almighty married subsidy nor the origin of the differences between
men and women in money or workmanship or blue-chip Every Muslim inept any Muslim and
every Muslim efficient for any Muslim.
The impor

Modern asphalt technology has adopted nanomaterials as an alternative option to assert that asphalt pavement can survive harsh climates and repeated heavy axle loading during service life and prolong pavement life. This work aims to elucidate the behavior of the modified asphalt mixture fracture model and assess the fatigue and Rutting performance of Hot Mix Asphalt (HMA) mixes using the outcomes of indirect Tensile Strength (IDT), Semicircular bend (SCB) and rutting resistance; for this, a single PG (64−16) nanomodified asphalt binder with 5 % SiO2 and TiO2 have been investigated through a series of laboratory tests, including: Resilient modulus, Creep compliance, and tensile strength, SCB, and Flow Number (FN) to study their potential

The paper is highlighting the athletics and heroic sports which encouraged and played at Greek and Islamic period. The paper is identifying the Islamic athletics and heroic sport and compare them with Greek sports, as it is the model of sports while the sport during the Islamic period was not undertaken by scientific researches or articles even in Wikipedia. Although, this period was encouraged and practice many sports such as archery, sword grappling and wrestling, equestrianism, jogging and running whereas there are many Arabic references revealed during the Islamic 610 A.D. while the Greek and Olympic was known at 732 A.D. The paper is followed the literature review and historical to shied a light scientifically about traditional sports

Background Mitral valve (MV) is one of the most complex structures in human heart with a challenging exposure. Traditionally, MV is approached via left atriotomy (LAA) while superior septal approach (SSA) is an alternative.
Objective:  is to highlight the merits and demerits of these two approaches in providing access to the MV in term of the aortic cross clamp time (ACCT), quality of exposure, and potential complications in view of the published literature.

Patients and Method: Over an 18-month period ending at June 30^th, 2019, 56 patients with MV disease ± other cardiac diseases were enrolled in this study. Twenty patients had surgery via LAA (one surgeon) w