Utilizing the theory of fixed point index for compact maps, we establish new results on the existence of positive solutions for a certain third order boundary value problem. The boundary conditions that we study are of nonlocal type, involve Stieltjes integrals and are allowed to be nonlinear.
Water-filled tree holes are abundant microhabitats in forests worldwide and are inhabited by specialized communities of invertebrates. Despite their importance, the temporal dynamics of communities within and between years are largely unknown. Here, I present a case study on the phenology of insect larvae in two holes in a beech tree (lower and upper canopy) located in southern Germany over a period of three years. I asked whether water temperature and the characteristics of insect larvae at the community and population levels are similar in periodicity every year and whether they differ in the lower and upper canopy. The water temperature in tree holes differed greatly from air temperature, and this effect was more pronounced in the lower than in the upper canopy, which resulted in a lower probability of drying out occurring in the lower canopy. This was associated with a higher species richness in the lower canopy and greater abundance of drought tolerant species in the upper canopy. There was a significant periodicity in larval abundance, biomass, species richness and body size distribution of abundant species in both tree holes, but it was not seasonal. This result indicates that unpredictable drying out of tree holes are more important drivers of tree hole community dynamics than changes in water temperature. The community of larvae in the tree hole in the upper canopy lagged behind that in the lower canopy, which indicates that most species mainly colonize the more stable microhabitats in the lower canopy. Hopefully this case study will encourage future larger-scale phenological studies to test (1) whether the patterns observed in this study can be generalized over larger spatial scales and (2) the relative importance of abiotic and biotic drivers of the dynamics of communities in tree holes., Martin M. Gossner., and Obsahuje bibliografii
In this paper we present a topological duality for a certain subclass of the Fω-structures defined by M. M. Fidel, which conform to a non-standard semantics for the paraconsistent N. C. A. da Costa logic Cω. Actually, the duality introduced here is focused on Fω-structures whose supports are chains. For our purposes, we characterize every Fω-chain by means of a new structure that we will call down-covered chain (DCC) here. This characterization will allow us to prove the dual equivalence between the category of Fω-chains and a new category, whose objects are certain special topological spaces (together with a distinguished family of open sets) and whose morphisms are particular continuous functions.