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Monoidne algebre in grafovski produkti
No full textIn this note, we extend results about unique n^th roots and cancellation of finite disconnected graphs with respect to the Cartesian, the strong and the direct product, to the rooted hierarchical products, and to a modified lexicographic product. We show that these results also hold for graphs with countably many finite connected components, as long as every connected component appears only finitely often (up to isomorphism). The proofs are via monoid algebras and generalized power series rings
Can nuisance species profit from new materials for marine artificial structures
No full textGrowing ocean-based human activities are causing the expansion of concrete structures in the marine envi- ronment, stressing the need for new solutions to minimize their ecological impact and carbon footprint. A promising approach in this perspective involves the use of biochar, a carbon-rich byproduct from thermo- chemical treatment of waste biomass, as an additive to concrete. However, the introduction of novel substrata could pose unintended threats to marine ecosystems, including the potential diffusion of nuisance species. Here, through a set of laboratory experiments, we provided preliminary evidence on the effects of biochar addition to concrete on settlement and survival of the bloom-forming jellyfish Chrysaora hysoscella. The acute 24/48-h mortality test demonstrated a very low sensitivity of planulae to biochar. At both 7 and 14 days since the exposure to colonization of planula larvae, the number of settled polyps did not differ between concrete con- taining biochar (5–10 % wt.) and conventional concrete. Once settled, polyps exhibited comparable survival regardless of the substratum. Our findings support the hypothesis that biochar-based concrete does not favor the invasiveness of this nuisance species with respect to conventional concrete, paving the way for future research on a wider range of (bio)char types and potentially harmful species, enabling broader implementations of these materials. The inherent advantages of biochar addition to concrete for marine uses, such as waste recycling and carbon storage potential, combined with its neutral effect on the spread of nuisance species, could represent a practicable and biocompatible solution to enhance the sustainability of marine artificial structures
Ločno disjunktne hamiltonske poti v kartezičnih produktih usmerjenih ciklov
No full textWe show that if C1 and C2 are directed cycles (of length at least two), then the Cartesian product C1 □ C2 has two arc-disjoint hamiltonian paths. (This answers a question asked by J. A. Gallian in 1985.) The same conclusion also holds for the Cartesian product of any four or more directed cycles (of length at least two), but some cases remain open for the Cartesian product of three directed cycles. We also discuss the existence of arc-disjoint hamiltonian paths in 2-generated Cayley digraphs on (finite or infinite) abelian groups
