CO₂ emission limits introduced by the European Union are encouraging works on new-generation materials with reduced clinker content. Currently, fumed silica from hard coal combustion is used in cement and concrete technology in Europe and Poland. Its wide application depends mainly on its chemical and phase composition, especially the reactivity of pozzolanic acids and its high fineness similar to cement Many authors studied the influence of fly ashes from hard coal combustion, in accordance with PN-EN 450-1 and 450-2, on the properties of concrete, including the course of the carbonation process. There are no studies in the literature involving ashes from sewage sludge. The objective of the research is to assess the course of carbonation of concrete produced on the basis of fly ash from the thermal transformation of sewage sludge over time and to describe this phenomenon in a mathematical form. An additional objective was to analyze the physicochemical composition of sludge ash in accordance with the requirements of EN 450-1, ASTM-C618-03. In addition, this study also demonstrated the possibility of producing fly ash-modified standard concrete through the thermal treatment of sewage sludge. The average compressive strengths of Krakow gray concrete after curing for 28, 56, 90, and 365 days were 50.1 MPa, 50.6 MPa, 50.8 MPa, and 61.9 MPa, respectively. On the one hand, the additives introduced in the concrete mixture accelerate the carbonation process by shifting the carbonation front deep into the concrete and, on the other hand, create a denser microstructure In all cases, the largest increase in carbonation depth was observed up to the 56th day of the study, while the smallest increase was observed between 90 and 180 days. The diffusivity decreases and the rate of carbonation is reduced. The determined regression coefficients of hyperbolic models indicate the proper adjustment of the adopted hyperbolic model to the results of laboratory tests under accelerated carbonation conditions (R = 0.85–0.99), regardless of the content of fly ash from sewage sludge in ordinary concrete samples.

A two-dimensional physical and mathematical model is proposed for determining the components of the stress tensor and stress intensity in an electroconductive plate of rectangular cross-section under the action of an unsteady electromagnetic field. The two-dimensional thermomechanics problem for such a plate is formulated. The determining functions are the component of the magnetic field intensity vector tangent to the plate bases, temperature, and components of the stress tensor. The methodology for solving the formulated thermomechanics problem by approximating all the determining functions by the thickness variable with cubic polynomials is developed. As a result, the original two-dimensional problems related to the determining functions are reduced to one-dimensional problems on the integral characteristics of these functions. To solve the obtained systems of equations for the integral characteristics of the determining functions, a finite integral transformation in the transverse variable is used. During induction heating of a copper plate by a homogeneous quasi-steady-state electromagnetic field, the change in the stress intensity depending on the Fourier time, as well as its distribution across the plate cross-section depending on the parameters of induction heating and the Biot criterion, is numerically analyzed.

Structural properties of the currency market were examined with the use of topological networks. Relationships between currencies were analyzed by constructing minimal spanning trees (MSTs). The dissimilarities between time series of currency returns were measured in various ways: by applying Euclidean distance, Pearson’s linear correlation coefficient, Spearman’s rank correlation coefficient, Kendall’s coefficient, partial correlation, dynamic time warping measure, and Kullback–Leibler relative entropy. For the constructed MSTs, their topological characteristics were analyzed and conclusions were drawn regarding the influence of the dissimilarity measure used. It turned out that the strength of most types of correlations was highly dependent on the choice of the numeraire currency, while partial correlations were invariant in this respect. It can be stated that a network built on the basis of partial correlations provides a more adequate illustration of pairwise relationships in the foreign exchange market. The data for quotations of 37 of the most important world currencies and four precious metals in the period from 1 January 2019 to 31 December 2022 were used. The outbreak of the COVID-19 pandemic in 2020 and Russia’s invasion of Ukraine in 2022 triggered changes in the topology of the currency network. As a result of these crises, the average distances between tree nodes decreased and the centralization of graphs increased. Our results confirm that currencies are often pegged to other currencies due to countries’ geographic locations and economic ties. The detected structures can be useful in descriptions of the currency market, can help in constructing a stable portfolio of the foreign exchange rates, and can be a valuable tool in searching for economic factors influencing specific groups of countries.

Purpose – The aim of this article was to assess the changes in the topological structure of the currency market caused by two crises: the COVID-19 pandemic in 2020 and Russia’s aggression against Ukraine in 2022. A network of major world currencies was analysed over three six-month sub-periods: the pandemic period 1.02–31.07.2020, the war period 1.02–31.07.2022 and the reference period 1.02–31.07.2021. Research method – We have used the dynamic time warping (DTW) method for comparing time series. DTW distances between pairs of individual currencies were calculated, and, based on them, minimum spanning trees (MST) were constructed, whose topological characteristics were analysed. Results – It turned out that the topological structure of the foreign exchange market varies in the sub-periods studied, and the analysed crises affected the currency network. In addition, the networks generated by the MST depend on the choice of base currency used to measure the value of all other currencies. Originality / value / implications / recommendations – The significance of the results obtained lies in providing a description of the topological structure of the market during the observed crises. The detected hierarchical structures can be useful in theoretical descriptions of currencies and in the search for economic factors affecting specific groups of countries.