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.

Stochastic programming has emerged lately as an advanced mathematical method to develop a decision-making process under uncertainty. This work investigates its use in enhancing Multi-Factor Authentication systems by establishing a probability- maximized framework for dynamic authentication processes in real time. Tra- ditional MFA methods, though effective in reducing the risks of compromised credentials, usually have problems with user friction, lack of adaptability, and are vulnerable against advanced threats, including phishing and social engineer- ing. We propose a dynamic approach where stochastic models are integrated into MFA to adjust the authentication requirements based on real-time risk eval- uations and user behavior for better security and user experience.

This article is written about cloud technologies and capabilities of gamma.app, creation of presentation material, import and editing of files in gamma.app.

Ushbu maqolada “Temurbeklar maktab” harbiy akademik litseylarida Davlat va huquq asoslari fanlarida jinoyat huquqi sohasini o`qitishda qonun hujjatlarining ahamiyati tahlil qilingan.

The article examines the role of academic mobility in the formation of competitive specialists in the context of reforming the higher educational system of Uzbekistan. The main mechanisms of academic mobility, its impact on the professional development of students and adaptation to the requirements of the global labor market, are considered.

This article provides the methodology for compiling, content and goals of the educational and methodological complex in the academic subject of engineering and computer graphics, the basics of fundamental knowledge.

This article is dedicated to the analysis of the concept of logarithmic residues in the theory of several complex variables. Logarithmic residues serve as a powerful tool for studying the behavior of multivariable holomorphic and plurisubharmonic functions in complex domains. The article provides a mathematical definition of logarithmic residues, their key properties, and methods for calculating them using integrals.

This article explores the application of blockchain technology for digital identification in smart cities, focusing on its potential implementation in Tashkent. It analyzes the fundamental principles of digital identification, its current challenges, and the advantages of decentralized solutions. Special attention is given to the potential of blockchain in creating a Self-Sovereign Identity (SSI) system, allowing citizens to have full control over their personal data. The article provides examples of successful implementations in various countries and discusses possible risks and challenges for integrating blockchain into Tashkent's urban infrastructure. Key aspects necessary for the effective adoption of this technology in city management are identified.