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- ItemExploring the Influence of Soil Types on the Mineral Profile of Honey: Implications for Geographical Origin Prediction(MDPI, 2024-07-26) Schmidlová, Simona; Javůrková, Zdeňka; Tremlová, Bohuslava; Hernik, Józef; Prus, Barbara; Marcinčák, Slavomír; Marcinčáková, Dana; Štarha, Pavel; Čížková, Helena; Kružík, Vojtěch; Bodor, Zsanett; Benedek, Csilla; Titěra, Dalibor; Boržíková, Jana; Pospiech, MatejHoney contains a wide range of inorganic substances. Their content can be influenced, i.e., by the type of soil on which the bee pasture is located. As part of this study, the mineral profile of 32 samples of honey from hobby beekeepers from the Czech Republic wasevaluated and then compared with soil types in the vicinity of the beehive location. Pearson's correlation coefficient was used to express the relationship between mineral substances and soil type. There was a high correlation between antroposol and Zn (R = 0.98), Pb (R = 0.96), then between ranker and Mn (0.95), then regosol and Al (R = 0.97) (p < 0.05). A high negative correlation was found between regosol and Mg (R = -0.97), Cr (R = -0.98) and between redzinas and Al (R = -0.97) (p < 0.05). Both positive and negative high correlations were confirmed for phaeozem. The CART method subsequently proved that the characteristic elements for individual soil types are B, Ca, Mg, Ni, and Mn. The soil types of cambisol, fluvisol, gleysol, anthrosol, and kastanozem had the closest relationship with the elements mentioned, and it can therefore be assumed that their occurrence indicates the presence of these soil types within the range of beehive location.
- ItemA digital 3D Jordan-Brouwer separation theorem(Ovidius University Constanta, 2024-10-25) Šlapal, JosefWe introduce a connectedness in the digital space Z^3 induced by a quaternary relation. Using this connectedness, we prove a digital 3D Jordan-Brouwer separation theorem for boundary surfaces of the digital polyhedra that may be face-to-face tiled with certain digital tetrahedra in Z^3. An advantage of the digital Jordan surfaces obtained over those given by the Khalimsky
- ItemPeriodic solutions in a linear delay difference system(Bolyai Institute, University of Szeged, 2025-04-05) Čermák, Jan; Fedorková, Lucie; Nechvátal, LuděkThe paper investigates periodicity properties of a linear autonomous difference system with two delayed terms. Assuming that the system matrices are simultaneously triangularizable, we formulate necessary and sufficient conditions guaranteeing the existence of a nonzero periodic solution (with an a priori given period) of the studied system. The analytical form of such conditions is shown to generalize the existing results on this topic. Moreover, it is supported by a geometric reformulation, offering a better understanding of the derived periodicity conditions. Information on the form of the searched periodic solution (including its prime period) is also provided.
- ItemDamage behaviour of quasi-brittle composites: mathematical and computational aspects(MDPI, 2025-04-11) Vala, Jiří; Tomáš, JiříIn the present paper, an evaluation of the damage behaviour of quasi-brittle composites exposed to mechanical, thermal, and other loads is studied by means of viscoelastic and/or viscoplastic material models, applying some non-local regularisation techniques to the initiation and development of damages. The methods above are presented as a strong tool for a deeper understanding of material structures in miscellaneous engineering disciplines like civil, mechanical, and many others. Nevertheless, all of the software packages reflect certain compromises between the need for effective computational tools, with parameters obtained from inexpensive experiments, within the possibilities and the complexity of both physical and geometrical descriptions of structure deformation within processes. The article is devoted to the mathematical aspects regarding a considerably wide class of computational modelling problems, emphasising the following ones: (i) the existence and the uniqueness of solutions of engineering problems formulated in terms of the deterministic initial and boundary value problems of partial differential equations theory; (ii) the problems of convergence of computational algorithms applied to (i). Both aspects have numerous references to possible generalisations and investigations connected with open problems.
- ItemON NON-OSCILLATION FOR TWO DIMENSIONAL SYSTEMS OF NON-LINEAR ORDINARY DIFFERENTIAL EQUATIONS(UNIV MISKOLC INST MATH, 2024-11-28) Opluštil, ZdeněkThe paper studies the non-oscillatory properties of two-dimensional systems of non-linear differential equations u ' = g(t)|v|1/alpha sgn v, v ' = -p(t)|u|(alpha)sgn u, where the functions g: [0, +infinity[-> [0, +infinity[, p: [0, +infinity[-> & Ropf; are locally integrable and alpha > 0. We are especially interested in the case of integral(+infinity)g(s) ds < +infinity. In the paper, new non-oscillation criteria are established. Among others, they generalize well-known results for linear systems as well as second order linear and also half-linear differential equations. The criteria presented complement the results of Hartman-Wintner's type for the system in question.