Fully implicit time-discretization of hyperbolic systems can significantly reduce restrictions on the choice of time steps in numerical methods. The price to be paid may be the resolution of large fully coupled nonlinear algebraic systems to update the numerical solution. Therefore, several efforts have been done recently to reduce the complexity of such algebraic systems. In this work, we present a high-resolution well-balanced implicit scheme to solve numerically hyperbolic systems of balance laws. The scheme has a compact stencil which allows an efficient application of fast algebraic solvers like fast sweeping method. The scheme is formally second-order accurate in time and space, but space and time limiters are added to avoid unphysical oscillations in numerical solutions. The method produces nonlinear algebraic equations whose size is analogous to the first-order accurate fully implicit scheme. Moreover, the methods are well-balanced in the following sense: they preserve exactly all the continuous stationary solutions in the one-dimensional case whenever local equilibria can be obtained analytically and they are able to preserve a family of given stationary solutions in the two-dimensional case. The method is applied to Burgers’ equation with source term and the shallow water equations in 1D and 2D: several numerical experiments confirm these properties of the proposed scheme.
Nitro compounds (NCs) are a class of organic pollutants with significant environmental and health risks, including toxicity, carcinogenicity, and mutagenicity. Despite their limited solubility in water, their widespread use in explosives, dyes, agrochemicals, and pharmaceuticals has led to persistent contamination of aquatic systems. The detection of NCs in water is challenging due to their low concentrations and the complexity of environmental matrices. This review summarizes current advances in analytical methods for the determination of nitro-based explosives in water, with emphasis on recent developments in sample preparation and extraction techniques. Classical approaches such as solid-phase extraction (SPE) are compared with miniaturized and solvent-saving methods including solid-phase microextraction (SPME), dispersive liquid–liquid microextraction (DLLME), and single-drop microextraction (SDME). Innovative approaches employing deep eutectic solvents (DESs) and magnetic materials are also highlighted. These greener techniques not only reduce solvent consumption (e.g., SDME using as little as 3 μL of solvent) but also solidification of aqueous drop solid-phase extraction (SADSPE) demonstrate high analytical performance, achieving detection limits in the ng/L to μg/L range. Environmental sustainability has increasingly been quantified using green chemistry metrics such as AGREE, AGREEprep, and AESA, with several techniques scoring above 70
Buildings represent fundamental elements of urban systems, and the management and updating of their representations in spatial information systems are therefore essential. Despite long-term research efforts, the automatic detection and extraction of building footprints from available data sources remain challenging. Difficulties arise from factors such as vegetation cover, close proximity of buildings in dense urban areas, varying levels of detail, inconsistent building definitions across datasets, and irregular geometry of detected footprints. LiDAR data, due to their increasing availability and geometric accuracy, offer significant potential for building footprint detection and updating. This paper aims to automatically or semi-automatically extract, vectorize, and regularize building footprints from classified point clouds, considering the accessibility of commonly used software tools. First, tools available in widely used GIS software environments (ArcGIS and QGIS) are applied, followed by the development of a custom Python-based program incorporating cluster analysis, polygonization, data cleaning, and regularization using available libraries and functions. All three approaches are applied in a case study (Bratislava, Slovakia) and evaluated by the aggregated shape similarity index using manually vectorized building footprints and cadastral data as an external data source. The results demonstrate that the proposed Python-based approach provides reliable and customizable outputs, particularly in contexts where only LiDAR data are available, while also supporting the integration of heterogeneous spatial data sources.
In this paper we count all the subpaths of a given graph G; including the subpaths of length zero, and we call this quantity the subpath number of G. The subpath number is related to the extensively studied number of subtrees, as it can be considered as counting subtrees with the additional requirement of maximum degree being two. We first give the explicit formula for the subpath number of trees and unicyclic graphs. We show that among connected graphs on the same number of vertices, the minimum of the subpath number is attained for any tree and the maximum for the complete graph. Further, we show that the complete bipartite graph with partite sets of almost equal size maximizes the subpath number among all bipartite graphs. The explicit formula for cycle chains, i.e. graphs in which two consecutive cycles share a single edge, is also given. This family of graphs includes the unbranched catacondensed benzenoids which implies a possible application of the result in chemistry. The paper is concluded with several directions for possible further research where several conjectures are provided.
The study presents an application of classification-based machine learning techniques to a dataset comprising the radiation dose measurements with solid-state nuclear track detectors of poly(allyl diglycol carbonate) type. The detectors were irradiated with alpha particles and fast neutrons in various experimental configurations making the final dataset complex and suitable for machine learning methods. The most suitable experiment is chosen as a stepping stone, and the proposed evaluation method is tested. The detectors are analysed with the commercially available TASLImage system and the final performance in dose determination is compared to the machine learning efforts. Moreover, the uncertainty quantification algorithm is applied to better judge the future applicability of the new evaluation method.
