This paper shows how GeoGebra can be helpful in teaching mathematics. GeoGebra is an interactive geometry, algebra, statistics and calculus application, intended for learning and teaching mathematics and science from primary school to university level. It can be used for active and problem oriented teaching and fosters mathematical experiments and discoveries both in classroom and at home. In this work we show the sketch of using the above-mentioned software to build, solve and illustrate mathematical problems.

Trace elements play an important role in the pathogenesis of several serious ophthalmological disorders, such as glaucoma, age-related macular degeneration (AMD), diabetic retinopathy, cataract, etc. This study aimed to measure alterations of chemical elements’ (67) levels in the aqueous humor of patients undergoing cataract surgery. The pilot study included 115 patients, (age 74 ± 7.27, female 64.35%, male 35.65%). The aqueous levels of elements were measured by the use of the inductively coupled plasma optical emission spectrometry (ICP-OES), quality controlled with certified standards. The classification of elements based on their concentration was achieved by hierarchical cluster analysis. This is the first screening study that quantifies over 60 elements which are present in the fluid from the anterior chamber of the eye of cataract patients. The obtained results can be suitable for understanding and identifying the causes that may play a role in the initiation and progression of lens opacity.

The article presents the potential application of the time domain reflectometry (TDR) technique to measure moisture transport in unsaturated porous materials. The research of the capillary uptake phenomenon in a sample of autoclaved aerated concrete (AAC) was conducted using a TDR sensor with the modified construction for non-invasive testing. In the paper the basic principles of the TDR method as a technique applied in metrology, and its potential for measurement of moisture in porous materials, including soils and porous building materials are presented. The second part of the article presents the experiment of capillary rise process in the AAC sample. Application of the custom sensor required its individual calibration, thus a unique model of regression between the readouts of apparent permittivity of the tested material and its moisture was developed. During the experiment moisture content was monitored in the sample exposed to water influence. Monitoring was conducted using the modified TDR sensor. The process was additionally measured using the standard frequency domain (FD) capacitive sensor in order to compare the readouts with traditional techniques of moisture detection. The uncertainty for testing AAC moisture, was expressed as RMSE (0.013 cm3/cm3) and expanded uncertainty (0.01–0.02 cm3/cm3 depending on moisture) was established along with calibration of the applied sensor. The obtained values are comparable to, or even better than, the features of the traditional invasive sensors utilizing universal calibration models. Both, the TDR and capacitive (FD) sensor enabled monitoring of capillary uptake phenomenon progress. It was noticed that at the end of the experiment the TDR readouts were 4.4% underestimated and the FD readouts were overestimated for 12.6% comparing to the reference gravimetric evaluation.

This paper presents the results of studies aiming at the assessment and classification of wastewater using an electronic nose. During the experiment, an attempt was made to classify the medium based on an analysis of signals from a gas sensor array, the intensity of which depended on the levels of volatile compounds in the headspace gas mixture above the wastewater table. The research involved samples collected from the mechanical and biological treatment devices of a full-scale wastewater treatment plant (WWTP), as well as wastewater analysis. The measurements were carried out with a metal-oxide-semiconductor (MOS) gas sensor array, when coupled with a computing unit (e.g., a computer with suitable software for the analysis of signals and their interpretation), it formed an e-nose—that is, an imitation of the mammalian olfactory sense. While conducting the research it was observed that the intensity of signals sent by sensors changed with drops in the level of wastewater pollution; thus, the samples could be classified in terms of their similarity and the analyzed gas-fingerprint could be related to the pollution level expressed by physical and biochemical indicators. Principal component analysis was employed for dimensionality reduction, and cluster analysis for grouping observation purposes. Supervised learning techniques confirmed that the obtained data were applicable for the classification of wastewater at different stages of the purification process.

The paper presented the methodology for the construction of a soft sensor used for activated sludge bulking identification. Devising such solutions fits within the current trends and development of a smart system and infrastructure within smart cities. In order to optimize the selection of the data-mining method depending on the data collected within a wastewater treatment plant (WWTP), a number of methods were considered, including: artificial neural networks, support vector machines, random forests, boosted trees, and logistic regression. The analysis conducted sought the combinations of independent variables for which the devised soft sensor is characterized with high accuracy and at a relatively low cost of determination. With the measurement results pertaining to the quantity and quality of wastewater as well as the temperature in the activated sludge chambers, a good fit can be achieved with the boosted trees method. In order to simplify the selection of an optimal method for the identification of activated sludge bulking depending on the model requirements and the data collected within the WWTP, an original system of weight estimation was proposed, enabling a reduction in the number of independent variables in a model—quantity and quality of wastewater, operational parameters, and the cost of conducting measurements.

This article analyses the connection of the two types of floors on the ground (floors on joists and self-supporting floors), with the external wall made of a hemp–lime composite for the occurrence of thermal bridges. Several factors that may affect the heat transfer in the junction were taken into account: the level of the floor on the ground, the wall thickness, the thermal conductivity of the composite, and the location of the timber frame construction. The technology of using hemp and lime is relatively new, and there is a lack of such analyses in the literature. The two-dimensional (2D) heat-transfer in the described construction joints was analyzed based on the finite-element method with the use of the THERM 7.4 software. The results were presented as averaged and linear thermal transmittance coefficients dependent on the above mentioned factors. The possibility of surface condensation was also checked. The differences in the values of the thermal transmittance of the junction between the two variants of ground floors reached around 0.13%–1.67% and the values of linear thermal transmittance factor reached approximately 2.43%–10.13%. The junctions with the highest floor level showed a decrease in the thermal transmittance value by about 3.00%–5.77% and in the linear thermal transmittance, by about 21.98%–53.83%, compared to the junctions with the lowest floor level. Calculations showed that almost all analyzed junctions are free from surface condensation causing mould growth, because the minimum temperature factors f0.25 were higher than 0.78 (except for junctions with the lowered floor levels). The junction with a floor on the timber joists showed better thermal parameters than the junction with a self-supporting floor in each of the analyzed variants. By increasing the level of floor insulation, it is possible to limit the thermal bridges and improve the thermal properties of the junction.

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