This scientific study provides an in-depth analysis of the factors influencing the management efficiency of free economic zones (FEZs) in the Republic of Uzbekistan, assessing their contribution to socio-economic development using mathematical modeling. Using the Jizzakh Free Economic Zone as a case study, the research identifies key factors affecting production volume from 2015 to 2024 — namely, foreign investment and employment levels. The study employs the Cobb-Douglas production function to construct a classical linear regression model, along with an autoregressive (AR) model, correlation-regression analysis, and evaluation through Fisher’s criterion, Student’s t-test, and the Durbin-Watson statistic.

This article explores the theoretical and practical aspects of economic-mathematical modeling of the electronic commerce system based on interval data. The study analyzes the advantages of using interval data in evaluating e-commerce indicators, the possibilities of modeling economic processes under uncertainty, and mechanisms for forecasting the efficiency of electronic commerce in the digital economy. In addition, the economic significance of decrees and resolutions adopted in the Republic of Uzbekistan for the development of electronic commerce is highlighted. According to the research results, it is substantiated that interval modeling methods can serve to reduce risks in the electronic commerce system, increase the accuracy of forecasts, and optimize management decisions

This paper provides an in-depth analysis of the practical applications of the definite integral. It begins by explaining the application of the definite integral to calculating the surface area of geometric figures in a plane. Examples of economic problems are also given, including output, labor productivity, and income inequality through the Gini coefficient. Based on the supply and demand functions, consumer and producer surpluses are expressed using the definite integral. Each topic is illustrated with mathematical formulas, graphs, and real-life examples, demonstrating the importance of integral calculus not only in theory but also in economic and social practice. This work is a useful resource for students of definite integrals, as well as for those who wish to apply mathematical methods to economic problems.

This article analyzes the problem of optimizing investment flows in a self-organizing trading system. From a mathematical perspective, the apparatus of stochastic calculus, particularly Itô stochastic differential equations, is employed. The trading system is modeled as a self-organizing structure capable of adapting to external economic processes. Based on the Gronwall–Bellman equation, a mathematical model is proposed that enables the determination of the optimal trajectory for the allocation of investment resources. The obtained results are of significant importance for forecasting economic systems, optimizing resource allocation, and developing market strategies

This paper presents a methodology for mathematical and numerical modeling of nonstationary transverse wave processes in porous-elastic media containing a spherical obstacle. Simply and doubly connected domains are considered, allowing for the influence of the domain's internal structure on wave propagation and scattering. The study is based on Biot's linear theory of porous-elasticity. Boundary-value and initial-boundary-value problems for the equations of motion are constructed, conjugation conditions at the boundary of the spherical obstacle are formulated, and effective methods for their numerical solution are proposed. The obtained results have practical implications for problems in geophysics, porous media acoustics, and engineering mechanics.

This article highlights in detail the theoretical and practical foundations of assessment based on the rating system in strengthening the sustainability of commercial banks. The article analyzes the international experience of banking supervision, methods of rating assessment, as well as approaches to assessment based on the Camels system. The evaluation criteria, scales and methodological approaches used in rating systems, in particular numerical and alphabetical rating expressions, are considered in detail. The advantages, limitations, and conditions of using complex and expert assessment methods are also substantiated, as well as essential aspects of the assessment model when choosing a criterion. The article highlights the need to collect high-quality information, apply mathematical and statistical models, and choose the right assessment parameters to improve the effectiveness of the rating system. The rating system is recognized as an important tool in improving the reliability and stability of banks through an objective assessment of their financial condition.