Structural sums on the complex plane and their application to composite materials

Vladimir Mityushev — Mon, 30 Dec 2024 00:00:00 +0000

Consider a two-dimensional, two-component composite consisting of non-overlapping, identical circular disks embedded in a uniform host. The conductivity of the considered composites is modeled by the R -linear conjugation problem for functions analytic in the domains occupied by the components of composites and H¨older continuous in their closures. The effective conductivity of these dispersed random composites can be determined using constructive homogenization theory, which assumes strictly stationary fields. The Eisenstein summation method is applied to analyze conditionally convergent sums that arise during the homogenization process. Additionally, the Clausius-Mossotti approximation, which is valid for macroscopically isotropic two-dimensional composites up to $O(f3)$, is justified for random composites. A new analytical formula for the effective conductivity tensor of macroscopically anisotropic composites is derived up to $O(f3)$. This formula contains a conditionally convergent sum $S'_2$ coinciding with the Rayleigh lattice sum for the square array of disks calculated by the Eisenstein summation method. Moreover, $S'_2$ depends on a curve connecting a finite point with infinity. This approach provides a robust framework for understanding the behavior of such materials and offers insights into their effective conductivity properties.

Development of a penetration testing methodology for wireless networks to enhance smart city security in Kazakhstan

Mon, 30 Dec 2024 00:00:00 +0000

Modern cities are increasingly adopting information technologies and becoming “smart”. It is important to note that with the development of technology, the potential for cyber attacks also increases. This paper examines the significant problem of wireless network cybersecurity in smart cities of Kazakhstan. The study proposes a comprehensive penetration testing approach to identify and mitigate vulnerabilities in wireless networks. This approach includes a strategy that promotes security in the smart city ecosystem and supports Kazakhstan's overall efforts to protect urban infrastructure. Particular attention is paid to the vulnerabilities of wireless networks, which are a key element of the infrastructure of smart cities. This paper proposes a comprehensive approach to penetration testing aimed at identifying vulnerabilities in the wireless networks of smart cities. This approach includes various stages, starting with collecting information about the target system and ending with a detailed report on the identified vulnerabilities. The research results can contribute to enhancing cybersecurity in smart cities in Kazakhstan and the development of effective strategies for protection against cyberattacks.

Bulletin of L.N. Gumilyov Eurasian National University. Mathematics, computer science, mechanics series

Structural sums on the complex plane and their application to composite materials

Development of a penetration testing methodology for wireless networks to enhance smart city security in Kazakhstan