This paper explores the potential of large language models (LLMs) to enhance interactions between students and educators within digital educational platforms. It analyzes modern state-of-the-art solutions – such as YandexGPT, Mistral, Qwen, LLaMA, and their variants – along with their architectural features, performance, and adaptability for educational tasks. The study demonstrates that proper model parameter tuning enables their effective use in automating routine tasks, personalizing learning, and expanding instructors' toolsets.

This article describes the experience of implementing adaptive programming educational systems in teaching elementary school students. Developed under a state assignment from the Russian Academy of Sciences, the textless "childish" PictoMir programming environment and its hybrid successor PictoMir-K are designed to develop basic algorithmic competencies in elementary school students, as mandated by the Federal State Educational Standard (FGOS), even before they begin learning and using full-featured programming languages and environments. The key pedagogical technique in PictoMir is the use of program templates, i.e. algorithmic structures like linear sequences, loops, subroutines predefined in a two-dimensional table, into which students inserts operators. This approach has proven effective, minimizing syntax errors and focusing on the semantics of the algorithm. This article describes a methodological experiment and demonstrates how the gradual relaxation of rigid templates in PictoMir prepares students for a more comfortable and successful transition to the PictoMir-K hybrid programming environment, fostering not only algorithmic thinking but also structural flexibility.

This article is devoted to some questions about the number of polynomials with coefficients in an algebraic number field k such that deg f = 9, for which the corresponding hyperelliptic field k(x)(√ƒ) has a fundamental S-unit of degree 13 and for which the continued fraction expansion of √ƒ is periodic. It is proved that for any algebraic number field k, there are only finitely many such polynomials, and we obtain a universal estimate for this number, independent of the field k. Moreover, we prove that for , the set of such polynomials is nonempty for some field k that is the definition field of the coefficient set of polynomial f. Symbolic computations with Gröbner bases play a significant role in the proof of the main results.

This paper examines possible approaches to implementing functional blocks for a control library for electrical power drives that is being developed as a replacement for foreign software in automated process control systems.

This paper examines possible approaches to implementing functional blocks for a control library for electrical power drives that is being developed as a replacement for foreign software in automated process control systems

 An information card is provided for monitoring patients with natural and surgical postmenopause. The card is the result of a structured organization of data for analyzing the climacteric period and the possibilities of hormone replacement therapy (HRT) in the postmenopausal period. The use of such card for the purpose of designing a computer data bank system is discussed. 

The article analyzes the evolution of digital educational platforms in the context of education transformation. A new classification is proposed, distinguishing three system types: traditional LMS, management paradigm-rejecting NoLMS, and intelligent virtual Smart LMS. The possibility of converging these approaches within a unified educational ecosystem is demonstrated. The key result is the concept of a virtual platform infrastructure that combines management functionality with the flexibility of pedagogical solutions