List of publications on a keyword: «continuity»

In this publication, the author proposes to find an elementary proof of Fermat's Last Theorem from the point of view of an engineering approach. As a model, a construction of three concentrically nested n-cubes or spheres with a common centre and integer edges or radii, a, b, c, is studied, provided that each point/unit cube of a small sphere corresponds to another point/unit cube of this subset of layers between the middle and the large sphere enclosed spheres. An insoluble conflict between the symmetric form and the content of the construction is studied for the case when n is greater than two. The proposed proof forces us to make broader generalisations concerning the necessity of the asymmetry of the universe as a condition for the emergence of matter and the origin of life. The proof of Fermat's Last Theorem, known as the "mathematical pearl", has an important symbolic, historical and educational significance.

This article discusses the impact of demographic aging of the population in developed countries on their economies. The coefficients for assessing the financial condition of the pension system are given. The level of participation of the population in pension provision is considered to assess the effectiveness and sustainability of the pension system. The contributions to pension insurance in the system of compulsory state insurance are analyzed.

Adaptation in secondary schools acts as an indispensable stage in the life of every student. The present article examines, above all, the definition of continuity and its functions. It also describes the system of requirements for the work to ensure continuity.

The article provides a comprehensive analysis of the transformation of auditing activities in the context of geo-economic instability in 2024-2025. The study is based on data from a representative sample of audit companies and respondents from the real sector of the economy. Key trends in the digitalization of audit procedures have been identified, and changes in the regulatory framework for auditing activities have been analyzed. Practical recommendations have been developed for the implementation of hybrid audit models combining traditional methods with artificial intelligence and big data analysis technologies. Methods for assessing the risks of business continuity in the context of sanctions pressure and turbulence in global markets are proposed.