A method for processing data from tests of building materials is proposed in order to identify the optimal functional relationships between the physicomechanical characteristics and the technological parameters of building materials. The least squares method (MLS) was used and to improve the accuracy of calculations, a three-level optimization of calculations was introduced using groups of transforming functions (180 items). Taking into account the increased volume of statistical computations, computer subroutines have been developed, which, together with standard MLS computational programs, make it possible to realize the choice of the indicated optimal functional connections.

A mathematical model has been proposed for processing data from tests of building materials and obtaining optimal links between the characteristics of the bearing capacity and technological parameters of building materials for the use of these connections in refined design and construction procedures for building structures. To improve the accuracy of the results obtained, a three-level optimization principle was applied using the least squares method and a computational algorithm was compiled that allows us to develop an additional computational subroutine expanding the capabilities of the corresponding standard computer programs.

Cellular glass by its composition, structure and technical parameters is a high-performance multifunctional material, and its use in construction and engineering is extremely important. The problem of developing cellular glass power consumption technology on the base of natural amorphous aluminosilicates and silica rocks in a single technological process, combining the synthesis of a given glass composition and the formation of its cellular structure is solved by introduction of a nanodispersed modifier into the rock and by the mechanical activation of the charge, creating an impact possibility in the system at the atomic-molecular level. With the involvement of a complex modern theoretical and experimental methods, the processes of glass wool rock modifyed sintering and expanding were investigated, which served as a base for creating the cellular glass technology in the form of products and granules. The study of the secondary glass synthesis dynamics during sintering of volcanic glasses with sodium hydroxide solution showed that the hydrated amorphous neoplasms of sodium silicates synthesized at low temperatures and silica aluminosilicates with temperature rise gradually enriched with silica and formed hydrated secondary glasses, the dehydration of which expanded the mass upon reaching the pyroplastic state. Power consumption technologies of the new type cellular glasses based on the volcanic glass-wool and other amorphous silicate rocks, which allow to combine the processes of synthesis of low-melting glass and its expansion by sintering are challenging for the production and for application in construction and engineering.

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The article analyzes the backbone concepts of the spatial theory of sustainable development of modern countries – information space. The aim of the study is to substantiate the author's interpretation of the conceptual apparatus of spatial analysis, taking into account the principles of methodological institutionalism (comparative studies). In accordance with the purpose of the research, the following tasks are set and solved in the article: the essence of the information space in the system of sustainable development as a set of interactions of economic agents affecting the environment is disclosed; the attributive properties of the information space are formulated; the directions of its transformation under the influence of sustainable development processes are determined; the hypothesis about the transformation of the information space into information and communication under the influence of digitalization processes is formulated. It is concluded that the enrichment of the conceptual apparatus of the theory of spatial economics is a necessary prerequisite for the development of tools for implementing the sustainable development strategy in the digital and spatial dimensions.