No abstract

The Turkey oak (Quercus cerris L.), the natural range of which embraces southern Europe and Asia Minor, belongs to trees rarely introduced into Polish forests. Tree stands where it appears, established before the Second World War, can be found in some 20 localities, mostly in the western part of the country. Because this species is capable of a natural renewal in a woodland environment, a research was made to find in what conditions and how far it undergoes spontaneous naturalisation. Three study sites were chosen in the forests of central Wielkopolska. An inventory was made of mature stands of the Turkey oak and its generative renewal. Plant communities in which the young generation of Q. cerris usually appears were characterised. It was found that self-sown seedlings of this species grew at a distance of up to 2,500 m from parent trees. The highest number and the greatest density of specimens of the secondary generation of the Turkey oak were found at 'Racot', which is a 100-hectare, mid-field woodland island where mesotrophic habitats predominate and where about 50% of the area is occupied by communities with manmade pine tree stands. At all sites, Q. cerris penetrates primarily this type of deformed phytocoenoses, developing mostly on former farmland. It has become a permanent component of the underbrush and undergrowth in them, and in some places, it also makes up the tree layer. It was observed that in the study area, it penetrated the woodland environment much more effectively than Quercus rubra, considered an invasive species. The expansion of the Turkey oak in several of the examined localities can be regarded as a basic manifestation of its naturalisation in places where there are phytocoenoses with pine stands in broad-leaf forest habitats in the neighbourhood of parent trees.

Abstract. It is shown that polarization formulas have explicit matrix representations. This enables us to prove that polarization formulas of n-positive maps between C * -algebras are coordinatewise positive.