In this study we provide a descriptive framework of an Eigenplace function that maps from the relational space between objects to the numerical coordinate space that is a part of external reality.Our approach assumes that the Eigenplace function maps cognitively valid space (the relational structure linked with temporal intervals) to a mathematical set of coordinates.After a description of a detailed spatial ontology, some generalizations are discussed.

In this paper we design a quantum algorithm for the NP-complete problem of finding the domatic number.The DOMATIC NUMBER problem asks to determine the largest integer k, such that a given undirected graph with n vertices can be partitioned into k pairwise disjoint dominating sets.This problem finds significant applications, such as in wireless sensor networks, where the selection of multiple dominating sets balances energy consumption and extends network lifetime.Each node communicates exclusively with designated nodes, and dominant sets ensure network resilience by enabling seamless replacement in case of node cluster failure.The importance of this problem lies in its implications for network optimization, highlighting the advantages of quantum computing in addressing complex combinatorial challenges.We present a quantum algorithm that solves this problem in time O(2.4143 n ), which we further improve to O(2.3845 n ).

Web-based services occupy an increasingly large place in the lives of people around the world.Users with disabilities may find it difficult to use many websites and platforms due to technical barriers.To improve access to websites, international organisations like International Organization for Standardization (ISO), European Telecommunications Standards Institute (ETSI), or World Wide Web Consortium (W3C) develop web accessibility standards and guidelines, which provide an introduction to accessibility issues.By following some basic recommendations, any website and platform can become a good environment for exchanging information to digitally include people with disabilities.Due to the rapid development of artificial intelligence (AI) recent 5 years and its application in various sectors (e.g., game industry, e-commerce, facial recognition systems, agriculture, financial and economic sectors, cyber security, education, etc.), this also implies its application to help people with special needs to ensure digital accessibility.In this regard, the aim of this paper is related to proposing a method for heuristic evaluation of AIpowered web accessibility assistants.The method was tested using AI-powered accessibility assistants.The paper's objectives that meet its purpose and research questions are: (1) review of artificial intelligence application in web accessibility practices; (2) evaluation of selected tools based on the proposed method to prove its applicability.The method has been tested by heuristic evaluation of AI-powered accessibility assistants for websites.Web accessibility, measured in number of errors and alerts by applying WAVE tool, was compared before and after accessibility assistants were enabled.

Most air purification systems are formed on the basis of the "modular principle" using a waste-free production scheme, standardized dust collection equipment and ventilation systems.The disadvantages of such a complex, which is assembled from heterogeneous purification equipment, are the large overall dimensions of the devices, low individual performance and low gas flow rates in the devices, which limit the ability to purify large volumes of air, and therefore the task of preliminary verification of their capabilities arises.Modern computer simulation software makes it possible to study the movement of microscopic particles and determine the stable patterns of this process.This study focuses on the mathematical and computer simulation of the process of movement of respirable dust particles in the working area, based on the principles of designing efficient modular devices that maximize the use of centrifugal force to improve the performance of dust and gas cleaning equipment.The object of study is the proposed air purification device as a separate part of the overall purification complex.The subject of the study is computer simulation of the movement of dust particles in the air flow.The scientific and practical value of the research results is that for the first time the regularities of aerodynamic processes occurring in the cylindrical body of the "centrifugation module" were determined, which were obtained by mathematical and computer simulation methods, which confirms the effectiveness of air purification by the proposed device and makes it possible to introduce it into mass production.

Large data sets of state registers of judicial decisions are publicly available in almost all European countries, while the analysis of these data, often reaching millions of decisions, is not automated.We are developing a labeled dataset for automated data processing of Ukrainian court decisions, which will allow us to identify patterns and discrepancies in judicial practice in Ukraine using statistical analysis and machine learning methods.

The services for information communication technology (ICT) infrastructure management (i.e., ICT strategy creation, ICT configuration, ICT incidence management, reengineering) have become an increasingly important and complex processes in nowadays works and as well as in recent educational institutions.The pursuit of the effectiveness of ICT infrastructure management services and the ability to convey information of various profiles in the work of educational institutions requires a wide range of non-homogeneous ICT infrastructure management changes.The article examines the development possibilities of ICT management methodology and service provision tools, which become significant in the work of administration of ICT infrastructure of the educational institution.The application of the proposed methodology ITIL v4 forms a new understanding of value acquired through ICT infrastructure development.An approach of creation of ICT infrastructure and ITIL library was developed and helps in service management processes by having an impact on the training of ICT infrastructure management specialists and the maintaining of the entire ICT infrastructure.An approach includes the inter-operability of using of appropriate computerized, cloud-based systems like National Registers, LITNET online IS, "FreshDesk", etc., which are used for ICT administration processes.The case study under consideration covers the management of the infrastructure of the ICT sector of the secondary education institution, starting with the improvement of the communication network infrastructure, and enabling the specialized development and management of incident management and content delivery tools.The results of ITIL v4 methodology implementation were illustrated by providing the detection and elimination of ICT incidents.The usage of some software packages for automatization of ICT management services as "FreshDesk", LITNET online IS are demonstrated on real working ICT infrastructure of the typical educational institution.

Most socioeconomic processes (Processes) develop by performing various processdriving actions.A large amount of data is usually generated at the same time; they form specific indicators that are more or less distinctive for the Process.No Process management can really perform all the relevant actions to achieve progress of the whole set of indicators.Hence, prioritization of the action lines and determination of the key performance indicators (KPIs) has become an essential factor.Unfortunately, KPIs and their weighting are still largely subjectively defined and there is a lack of qualitative and quantitative justifications for choices.The article describes the universal methodology developed for objective mathematical computation of KPIs of the Processes and their weighting.By means of the regression analysis algorithms for statistically significant KPIs are computed and mathematical expression has been obtained showing the impact of each selected KPI on the Process development.The methodology has been tested in several Processes, achieving convincing results; applying it to variety of Processes requires mediocre programming skills only.Process management can put the methodology into practice to monitor the achieved development level of the Process in statics and dynamics, to observe progress and deficiencies in separate aspects, to take these into account when making the sustainable planning and strategic decisions.

Software tool extension is a long-standing problem.The simplest kind of extension is to add, to an existing tool, new custom tabs that invoke extension programs for viewing the data in a novel way.However even this task is not simple and roughly speaking every advanced tool does this in its own way.The goal of this paper is to develop a unified method of adding new custom tabs for tools whose back-end is deployed on a data server, but the front-end is browser-based (HTML web pages).More precisely, adding custom tabs is considered, to define new views of data stored on the Data server.The instrument used in this paper will be the Interaction Flow Modeling Language (IFML) designed for building precise Platform Independent Models (PIMs) for the described systems.The proposed extension method will be explained on a Deep Learning Lifecycle Data Management (DL LDM) task: first build a simple DL LDM base tool which is already practically usable, then add a PLUS component which permits the end-user to define new views of back-end data in a relatively simple way (without using the internal implementation of the base tool).