Abstract: The research subject is the methods of building the user interface of university websites based on the intended purpose, the needs of the audience, and user limitations, including sensory-motor and cognitive-psychological limitations.
As a starting point for studying the target audience and compliance with accessibility standards, eight university websites are analyzed based on open-source data.
The main violations that prevent users from using a university's website to varying degrees are considered, as well as the most well-known and often-used approaches to interface design and design that make interfaces more convenient without overloading the user's short-term memory and causing premature fatigue.
As a result of the research, the basic requirements for designing the interface of the university's website are formed. According to the main conclusion of this study, to adapt the University's website to the limitations of users' capabilities, it is necessary to follow the main standards of usability and accessibility considered, such as GOST R 52872-2019, WCAG 2.1 and GOST R ISO 9241-20-2014, and also take into account the peculiarities of legislation that affect the formation of sections of the site and its accessibility for people with disabilities. It is necessary to adhere to such principles of interface organization and information presentation as Hick's Law, Gestalt Principles, Miller's Law, Jacob's Law, and Heuristics.
The author's special contribution to the topic is the analysis of the verification of eight sites of Russian universities for compliance with accessibility standards. This analysis showed that even the visually impaired versions of the sites reviewed do not meet accessibility standards, which makes it difficult for people with disabilities to access information and emphasizes the importance of the study.
The novelty of the research lies in the formation of the basic requirements for the user interface of university websites. The study's results can be further used in constructing such information systems.

Abstract: The research subject is the methods of building the user interface of university websites based on the intended purpose, the needs of the audience, and user limitations, including sensory-motor and cognitive-psychological limitations.

As a starting point for studying the target audience and compliance with accessibility standards, eight university websites are analyzed based on open-source data.

The main violations that prevent users from using a university's website to varying degrees are considered, as well as the most well-known and often-used approaches to interface design and design that make interfaces more convenient without overloading the user's short-term memory and causing premature fatigue.

As a result of the research, the basic requirements for designing the interface of the university's website are formed. According to the main conclusion of this study, to adapt the University's website to the limitations of users' capabilities, it is necessary to follow the main standards of usability and accessibility considered, such as GOST R 52872-2019, WCAG 2.1 and GOST R ISO 9241-20-2014, and also take into account the peculiarities of legislation that affect the formation of sections of the site and its accessibility for people with disabilities. It is necessary to adhere to such principles of interface organization and information presentation as Hick's Law, Gestalt Principles, Miller's Law, Jacob's Law, and Heuristics.

The author's special contribution to the topic is the analysis of the verification of eight sites of Russian universities for compliance with accessibility standards. This analysis showed that even the visually impaired versions of the sites reviewed do not meet accessibility standards, which makes it difficult for people with disabilities to access information and emphasizes the importance of the study.

The novelty of the research lies in the formation of the basic requirements for the user interface of university websites. The study's results can be further used in constructing such information systems.

Abstract: The subject of the study is the architecture of the RSS feed aggregation system. The author considers in detail such aspects of the topic as choosing the right data aggregation strategy, an approach to scaling a distributed system, designing and implementing the main modules of the system, such as an aggregation strategy definition module, a content aggregation module, a data processing module, a search module. Particular attention in this study is given to a detailed description of the libraries and frameworks chosen for the implementation of the system under consideration, as well as databases. The main part of the system under consideration is implemented in the C# programming language (.Net Core) and is cross-platform. The study describes the interaction with the main data stores used in the development of the aggregation system, which are PostgreSQL and Elasticsearch. The main conclusion of the study is that before developing an aggregation system, it is necessary to analyze the publication activity of data sources, on the basis of which it is possible to form an acceptable strategy for updating the search index, saving a significant amount of resources. computing power. Content aggregation systems, such as the one considered in this study, should be distributed, built on the basis of event-driven and microservice architectures. This approach will make the system resistant to high loads and failures, as well as easily expandable. The author's special contribution to the study of the topic is a detailed description of the high-level architecture of the RSS aggregator, designed to process 50,000 channels.

Abstract: The subject of the study is the features of the organization of virtual reality interfaces.
The author examines in detail such aspects of the topic as user involvement in the virtual environment,
various ways and scenarios of user interaction with virtual reality, user security in the virtual environment, as well as such a phenomenon as cyberbullying and ways to prevent it. The study also considers the use of voice control as an alternative to manual.
Particular attention in this study is paid to the classification of virtual reality interfaces, among which sensory interfaces, interfaces based on user motor skills, sensorimotor interfaces, interfaces for modeling and developing virtual reality are distinguished and considered in detail.    The main conclusion of the study is that the virtual reality interface should be designed taking into account the ergonomics of users to prevent muscle fatigue and cyber-pain.
In addition, it is very important to ensure the user's safety when designing virtual environment interfaces: using the virtual reality interface should not lead to injury to the user.
To create an ergonomic and secure virtual reality interface, a combination of different types of interfaces is often required, through which the user can access an alternative control method or improved navigation.
A special contribution of the author to the study of the topic is the description of the classification of virtual reality interfaces.

Abstract: The subject of this research is the key methods for creating the architecture of information aggregators, methods for increasing scalability and effectiveness of such systems, methods for reducing the delay between the publication of new content by the source and emergence of its copy in the information aggregator. In this research, the content aggregator implies the distributed high-load information system that automatically collects information from various sources, process and displays it on a special website or mobile application. Particular attention is given to the basic principles of content aggregation: key stages of aggregation and criteria for data sampling, automation of aggregation processes, content copy strategies, and content aggregation approaches. The author's contribution consists in providing detailed description of web crawling and fuzzy duplicate detection systems. The main research result lies in the development of high-level architecture of the content aggregation system. Recommendations are given on the selection of the architecture of styles and special software regime that allows creating the systems for managing distributed databases and message brokers. The presented architecture aims to provide high availability, scalability for high query volumes, and big data performance. To increase the performance of the proposed system, various caching methods, load balancers, and message queues should be actively used. For storage of the content aggregation system, replication and partitioning must be used to improve availability, latency, and scalability. In terms of architectural styles, microservice architecture, event-driven architecture, and service-based architecture are the most preferred architectural approaches for such system.

Abstract: The subject of this research is the problem of incommensurability and the crisis of foundations of the Ancient Greek mathematics. The article describes that the crisis of foundations was caused by the discovery of irrationality by the Pythagorean Hippasus of Metapontum, which resulted in the theoretical instability of mathematics of the Pythagoreans, who believed that everything could be expressed through numbers. The discovery of incommensurable line segments demonstrated that the relations between rational numbers cannot express any variable, for example the diagonal of a square with one side equal to one. Analysis is conducted on the achievements of the Pythagorean School in the field of mathematics. Special attention is given to the role of a number in the philosophy of this school. The article explores the main ways for overcoming this crisis, philosophical explanation of the unfolded situation, based on which the Pythagoreans formulate the methodological ways out of the discovered problem of incommensurability. It is noted that the Pythagoreans were actively elaborating on their philosophy and mathematical apparatus intending to find the answer to the discovery of incommensurability. The author’s special contribution lies in the statement that the discovery of irrationality was not critical for the Pythagoreans: they continued working towards the answer to the problem of incommensurability, as well as refined the mathematical theory of proportions, reconsidered the representation of infiniteness as a certain numerical characteristic of the things and processes. This article is first to advance a hypothesis on the possibility of dividing the object into an infinitely large number of infinitely small parts, which is now understood as the limit of function, which contributes to the development and application of dialectics. The problem of incommensurability led to the creation of new, complex theories in the history of science, culture, architecture, and art.