Consider a stationary Boolean model X with convex grains in Rd and let any exposed lower tangent point of X be shifted towards the hyperplane N0={x∈Rd:x1=0} by the length of the part of the segment between the point and its projection onto the N0 covered by X. The resulting point process in the halfspace (the Laslett's transform of X) is known to be stationary Poisson and of the same intensity as the original Boolean model. This result was first formulated for the planar Boolean model (see N. Cressie \cite{Cressie}) although the proof based on discretization is partly heuristic and not complete. Starting from the same idea we present a rigorous proof in the d-dimensional case. As a technical tool equivalent characterization of vague convergence for locally finite integer valued measures is formulated. Another proof based on the martingale approach was presented by A. D. Barbour and V. Schmidt \cite{barb+schm}.
Průběh koryta a niva Lužnice zaznamenaly po povodních v roce 2002 a 2006 značné změny. Vznikla nová mrtvá ramena a tůně. Tyto změny ale neměly výrazný destruktivní vliv na ekosystém nivy. Autor popisuje různé typy tůní a procesy jejich vzniku a zániku i společenstva mokřadních rostlin v nivě Lužnice. and The watercourse and floodplain of the Lužnice river were greatly changed after flooding in 2002 and 2006. New river branches and pools were created, but these changes have not influenced negatively floodplain ecosystems. The author describes different types of pools and their development, as well as communities of wetland plants in the Lužnice river floodplain.