Евразийский журнал математической теории и компьютерных наук

Matematik fizika va kompleks tahlilda o‘zaro bog‘liq ko‘plab nazariyalar mavjud bo‘lib, ular orasida Li-Yang teoremasi alohida o‘rin tutadi. Bu teorema statistik fizika va fazaviy o‘tishlar nazariyasida muhim rol o‘ynaydi. Polinomlarning kompleks tekislikdagi ildizlarini tahlil qilish orqali fizik tizimlarning xatti-harakatini o‘rganish imkonini beradi. Shuningdek, bu teorema fizikada termodinamik limit va holat o‘tishlarining nazariy asosi sifatida ko‘riladi. Li-Yang teoremasining asosiy ahamiyati, u kompleks o‘zgaruvchilar polinomining ildizlarini geometrik jihatdan chegaralaydi va statistik tizimlarning xususiyatlarini aniqlashga yordam beradi. Ushbu tadqiqotning asosiy maqsadi Li-Yang teoremasining  n=2 va n=3 hollar uchun matematik isbotini batafsil keltirish va uning statistik fizika bilan bog‘liq ahamiyatini o‘rganishdan iboratdir.

The increasing prevalence of vascular diseases poses significant challenges to global healthcare systems. Effective prediction and monitoring are essential for early diagnosis, personalized treatment, and improved patient outcomes. This study explores the application of prediction and monitoring techniques using correlation and regression models to analyze and manage vascular diseases. Correlation analysis identifies the relationships between key risk factors—such as age, obesity, hypertension, and lifestyle habits—and the onset of vascular conditions. Regression models, including linear, logistic, and multivariate approaches, predict disease progression, treatment efficacy, and mortality rates.