The great capricorn beetle or Cerambyx longicorn (Cerambyx cerdo, Linnaeus, 1758) is an internationally protected umbrella species representing the highly diverse and endangered fauna associated with senescent oaks. For the conservation and monitoring of populations of C. cerdo it is important to have a good knowledge of its microhabitat requirements. We investigated determinants and patterns of C. cerdo distribution within individual old, open-grown oaks. Trees inhabited by this species were climbed, and the number of exit holes and environmental variables recorded at two sites in the Czech Republic. Distribution of exit holes in relation to height above the ground, trunk shading by branches, orientation in terms of the four cardinal directions, diameter, surface and volume of inhabited tree parts were investigated. This study revealed that the number of exit holes in the trunks of large open-grown oaks was positively associated with the diameter of the trunk and openness and negatively with height above the ground, and the effects of diameter and openness changed with height. The number of exit holes in the surface of a trunk was also associated with the cardinal orientation of the surface. Approximately half of both C. cerdo populations studied developed less than 4 m and approximately a third less than 2 m above the ground. This indicates that most C. cerdo develop near the ground. Active management that prevents canopy closure is thus crucial for the survival of C. cerdo and searching for exit holes is an effective method of detecting sites inhabited by this species., Jan Albert, Michal Platek, Lukas Cizek., and Obsahuje seznam literatury
A set $S$ of vertices in a graph $G$ is called a paired-dominating set if it dominates $V$ and $\langle S\rangle $ contains at least one perfect matching. We characterize the set of vertices of a tree that are contained in all minimum paired-dominating sets of the tree.
We consider the theory of very weak solutions of the stationary Stokes system with nonhomogeneous boundary data and divergence in domains of half space type, such as $\mathbb R^n_+$, bent half spaces whose boundary can be written as the graph of a Lipschitz function, perturbed half spaces as local but possibly large perturbations of $\mathbb R^n_+$, and in aperture domains. The proofs are based on duality arguments and corresponding results for strong solutions in these domains, which have to be constructed in homogeneous Sobolev spaces. In addition to very weak solutions we also construct corresponding pressure functions in negative homogeneous Sobolev spaces.