Eurasian Journal of Mathematical Theory and Computer Sciences

There are many interrelated theories in mathematical physics and complex analysis, among which the Lee-Yang theorem has a special place. This theorem plays an important role in statistical physics and the theory of phase transitions. By analyzing the roots of polynomials in the complex plane, it allows to study the behavior of physical systems. Also, this theorem is considered as a theoretical basis of thermodynamic limit and state transitions in physics. The main importance of the Lee-Yang theorem is that it geometrically limits the roots of polynomials of complex variables and helps to determine the properties of statistical systems. The main goal of this study is to provide a detailed mathematical proof of the Lee-Yang theorem for the cases n=2 and n=3 and to study its significance in relation to statistical physics.

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.