Indoor air quality (IAQ) in nursery schools is an emerging public health challenge. Particular attention should be paid to younger children, because they are more vulnerable to air pollution than older children. Among air pollutants, fine particulate matter (PM_2.5) is of the greatest interest mainly due to its strong association with acute and chronic effects on children’s health. In this paper, we present concentrations of PM_2.5 and the composition of its trace elements at naturally ventilated nursery schools located in the area of Gliwice, Poland. The nursery schools were selected to characterize areas with different degrees of urbanization and traffic densities during the winter and spring seasons. The results indicate there is a problem with elevated concentrations of PM_2.5 inside the examined classrooms. The children’s exposure to trace elements was different based on localization and season. PM_2.5 concentration and its trace element composition have been studied using correlation coefficients between the different trace elements, the enrichment factor (EF) and principal component analysis (PCA). PCA allowed the identification of the three components: anthropogenic and geogenic sources (37.2%), soil dust contaminated by sewage sludge dumping (18.6%) and vehicular emissions (19.5%).

This study reports the concentrations of PM1 trace elements (As, Cd, Co, Cr, Hg, Mn, Ni, Pb, Sb and Se) content in highly mobile (F1), mobile (F2), less mobile (F3) and not mobile (F4) fractions in samples that were collected in the surroundings of power plants in southern Poland. It also reports source identification by enrichment factors (EF) and a principal component analysis (PCA). There is limited availability of scientific data concerning the chemical composition of dust, including fractionation analyses of trace elements, in the surroundings of power plants. The present study offers important results in order to fill this data gap. The data collected in this study can be utilized to validate air quality models in this rapidly developing area. They are also crucial for comparisons with datasets from similar areas all over the world. Moreover, the identification of the bioavailability of selected carcinogenic and toxic elements in the future might be used as output data for potential biological and population research on risk assessment. This is important in the context of air pollution being hazardous to human health.

Dendrogram (DE), heat map (HM) and principal component analysis (PCA) methods were used in order to identify possible emission sources of As, Cd, Co, Cr, Hg, Mn, Ni, Pb, Sb and Se in ambient PM10 collected in the surroundings of working power plants. Each statistical tool resulted in slightly different clusters. The best approximation of possible emission sources was received by the use of statistical analysis of trace-element concentrations combined with characterization of the sampling sites. In the study, PCA was indicated as the most useful statistical tool for source apportionment of trace elements in PM10. Major sources identified by PCA included: (1) coal combustion, (2) soil and road-dust resuspension, (3) the use of pesticides and (4) waste incineration.

The analysis reported in this study was performed to characterize the concentrations and water-soluble content of trace elements (As, Cd, Co, Cr, Hg, Mn, Ni, Pb, Sb and Se) in PM2.5, PM10 and PM2.5-10 samples collected in the surroundings of power plants in southern Poland. The solubility of trace elements bound to PM2.5 and PM10 was higher than for PM2.5-10, and in most cases, significant differences were revealed in the relative percentage concentrations of the water-soluble fractions. The occurrence of Cd, Cr, Mn, Ni, Pb and Se in first PCA (Principal Component Analysis) factor (PC1) – indicate coal combustion processes as the potential source of these elements. Other factors indicate two further anthropogenic sources: the resuspension of road dust due to vehicular activities and waste burning in domestic sources – factor (PC2), and, soil dust sources affected by fugitive dust from the mining processes and unpaved roads, as well as transportation and deposition of coal –factor (PC3).

The Troesch problem is a well-known and important problem; the ability to solve it is important due to the practical applications of this problem. In this paper, we propose a method to solve this problem using a combination of two useful algorithms: Different Transform Method (DTM) and Adomian Decomposition Method (ADM). The combination of these two methods resulted in a continuous approximate solution to this problem and eliminated the problems that occur when trying to use each of these methods separately. The great advantages of the DTM method are the continuous form of the solution and the fact that it easy to implement error control. However, in too-complex tasks, this method becomes difficult to use. By using a hybrid of ADM and DTM, we obtain a relatively simple-to-implement method that retains the advantages of the DTM approach.