Momentum Ranking Function of Z-Numbers and its Application to Game Theory

بعد أن قدم زاده مفهوم ارقام - z أبدى العلماء في مختلف المجالات اهتماما كبيرا بتطبيق هذا المفهوم على مختلف التطبيقات. في تطبيقات أرقام - z ، لمقارنة رقمين z ، يعد إجراء الترتيب ضروريا. في حين تم بالفعل اقتراح عدد قليل من وظائف الترتيب في الأدبيات ، هناك حاجة لتطوير بعض وظائف الترتيب الجيدة. في هذه الورقة ، تم اقتراح دالة ترتيب جديدة لأرقام - z  "وظيفة ترتيب الزخم" (MRF). أيضا ، تم النظر في المشكلات النظرية للعبة حيث تكون عناصر مصفوفة العائد هي أرقام - z وتم توضيح تطبيق وظيفة ترتيب الزخم في مثل هذه المشكلات.After Zadeh introduced the concept of z-number scientists in various fields have shown keen interest in applying this concept in various applications. In applications of z-numbers, to compare two z-numbers, a ranking procedure is essential.  While a few ranking functions have been already proposed in the literature there is a need to evolve some more good ranking functions.  In this paper, a novel ranking function for z-numbers is proposed- "the Momentum Ranking Function"(MRF). Also, game theoretic problems where the payoff matrix elements are z-numbers are considered and the application of the momentum ranking function in such problems is demonstrated

Is the binomial coefficient (2nn)2n \choose n square free?

In this paper, we prove the Erd\"os conjecture that the binomial coefficient ${2n \choose n}$ is never square free, for all $n>4$

The Role of Herbal Medicine in Oxidative Stress: Prevention of Diabetes

The pathophysiology of diabetes mellitus is heavily influenced by oxidative stress, which is defined by an imbalance between reactive oxygen species (ROS) and antioxidant defenses. Innovative methods for managing and preventing diabetes are required given that it is a growing worldwide health concern. Herbal medicine, which has a long history of use in traditional therapeutic methods, has drawn interest for its ability to reduce the incidence of diabetes and combat oxidative stress. The processes underpinning the damage caused by ROS to cellular components and signaling pathways are revealed in this chapter as it delves into the complex interactions between oxidative stress and diabetes. The essential function of antioxidant substances in reducing oxidative stress is investigated, emphasizing the change from traditional herbal knowledge to contemporary scientific validation. The botanical substances that provide a source of inorganic antioxidants are at the center of this discussion. Fenugreek (Trigonella foenum-graecum) and Bitter Melon (Momordica charantia), two important medicinal herbs, are investigated for their strong antioxidant capacities and their capacity to modify glucose homeostasis and insulin sensitivity.Scientific studies, including in vitro experiments and clinical trials, shed light on how well herbal treatments for diabetes prevention actually work. Additionally, the beneficial effects of herbal combinations are clarified, as well as the importance of combining these interventions with lifestyle changes. The fusion of herbal medicine and conventional therapies appears as a promising route for diabetes prevention as the movement toward holistic health gains popularity. In conclusion, this chapter underscores the multifaceted potential of herbal medicine in addressing oxidative stress as a crucial factor in diabetes prevention. By embracing the wisdom of ancient traditions and leveraging contemporary scientific insights, herbal interventions offer a holistic and integrative strategy to safeguard against the escalating global burden of diabetes