Generalized integration of three information systems’s algebraic models

As a mathematically consistent and algebraically potent formal system, soft set theory is well-suited for capturing the inherent uncertainty, vagueness, and parameter-based variability in complex decision-making and information systems. Within this theoretical framework, the present study introduces the soft symmetric difference complement–gamma product, a novel binary operation defined on soft sets whose parameter spaces are intrinsically structured by group-theoretic properties. Formulated through a rigorous axiomatic foundation, the operation is shown to maintain full compatibility with generalized soft subsethood and soft equality, thereby ensuring its structural integration within the broader algebraic fabric of soft set theory. A comprehensive algebraic examination is conducted to identify and verify the operation’s key structural properties, including closure, associativity, commutativity, and idempotency. The operation’s interactions with identity and absorbing elements, as well as with the null and absolute soft sets, are rigorously analyzed within the constraints imposed by group-parameterized domains. The findings confirm that the soft symmetric difference complement–gamma product satisfies all required algebraic conditions dictated by group-theoretic parameter structures, resulting in a coherent and robust algebraic framework over the universe of soft sets. In addition to its foundational value, the operation substantially enriches the structural landscape of soft set theory and offers a formal pathway toward the construction of a generalized soft group theory, where soft sets indexed by group-based parameters emulate classical algebraic operations. Its consistency with generalized notions of soft equality and its seamless integration into layered soft inclusion hierarchies further emphasize its algebraic depth and applicability. Accordingly, this work not only delivers a significant algebraic innovation but also provides a principled platform for extending soft set theory to fields that demand formal mechanisms for handling uncertainty, abstract algebraic modeling, and multi-criteria decision-making frameworks.

The object of consideration is design automation and prototyping of complex signals and their generation and processing devices. The subject of the analysis is the substantiation of the structure, composition and implementation method of a modeling system aimed at modeling and prototyping promising devices for the generation and processing of complex signals based on fast transformations in Galois fields. The purpose of the analysis is a reasonable choice of methods and tools for computational, simulation and prototyping that achieve high display accuracy, performance, flexibility and ease of modeling. The solutions are based on the principles and mathematical models developed by the authors: methods and algorithms for fast transformations in Galois fields, an algebraic representation model and the structure of fast delay acquisition devices for a subclass of sequences. The article is devoted to the development of a software and hardware modeling systems that allows the most accurate mapping of fast algebraic transformations in Galois fields to algorithmic models of various levels of representation to ensure high performance, flexibility and ease of modeling, as well as prototyping of promising devices for the generation and processing of complex signals. The results of the work will be useful in the design of promising devices of various information and communication systems, scientific research, as well as in the educational process.

Railroad Transportation Planning Models and Their Success

Rapid global urbanization and the growth of the urban population lead to the emergence of serious, systemic problems that critically and negatively affect the ecological, economic, and social sustainability of cities. In this context, the search and implementation of effective models of spatial development, which ensure the resilience of the territorial system and increase its competitiveness and adaptability in a changing external environment, is a relevant and strategic task of urban management. The aim of the work is to increase the overall efficiency of urban environment management through in-depth systematization and critical analysis of modern experience in implementing the Smart Cities concept, focused on effective intellectual decision-making. The object of the study is the concept of a "smart city" and the technologies for its implementation within a unified, integrated intellectual management of the urban environment. It is determined that the lack of a single universal definition of a "smart city" and unified approaches to its implementation necessitates the systematic comprehension of this concept and the study of evolutionary smartization models. The systemic representation of the Smart City concept is formulated for the first time using three complementary methods – verbal, graphical, and algebraic modeling. This approach focuses attention on its unique functional aspects, in particular, on data sets, the architecture of software solutions, and functional indicators. Special attention is paid to the effective use of open geospatial data (specifically, OpenStreetMap) in combination with 3D modeling tools. Such an integrated approach ensures the rapid and cost-effective creation of a reliable digital environment (digital twin), which significantly simplifies the implementation of Smart City, guaranteeing the flexibility, scalability, and adaptability of these projects. A formalized component approach to Smart City design is proposed. It regulates the design of functional modules of a smart city using components of existing software solutions, which increases the overall efficiency of their modernization and scaling, and also provides the necessary flexibility in the integration of absolutely new technologies. The obtained results can be successfully implemented in high-level automated urban management systems, where they will ensure comprehensive modeling, monitoring, and intelligent decision-making regarding the long-term development of urban infrastructure.

This paper builds on top of a collaborative ATFM framework previously published, which demonstrated a potential in significant pre-tactical system delay reduction over the current European ATFM practices. In this paper, we aim to raise the technology readiness level (TRL) of the original works, focusing on improving the tractability of its DCB optimizer. To this end, we apply a Dantzig-Wolfe (DW) decomposition approach and use high performance computing (HPC) techniques to attempt the solution in a short time. The main contribution of this paper is to mitigate the computational burden faced by previous approaches, which will make all the contributions demonstrated therein more operationally feasible.