Distribution and ecology of the lichen Fellhanera gyrophorica in the Pojezierze Olsztyńskie Lakeland and its status in Poland

The study presents recent data on the distribution of Fellhanera gyrophorica (Pilocarpaceae, Ascomycota) in Poland, a rare lichen with a crustose, usually sterile thallus. Both previous and new localities of the species are presented with data on its eco­logy and general distribution. Furthermore, this paper provides detailed results on floristic investigations of the species in the forest areas of the Pojezierze Olsztyńskie Lakeland (Northern Poland). Fertile specimens of F. gyrophorica have been observed in Poland for the second time and in the world – for the third time. Also, a new substrate for this species has been found: Acer platanoides. In addition, Carpinus betulus and Populus tremula were also found to be the species' substrates in Poland. Based on this study and previous reports, F. gyrophorica seems to be a relatively common species in north-eastern Poland

Lichens of red oak Quercus rubra in the forest environment in the Olsztyn Lake District (NE Poland)

A list of 63 species of lichens and 4 species of lichenicolous fungi recorded on the bark of red oak (Quercus rubra L.) in Poland is given. Literature data and the results of field studies conducted in the forest in the Olsztyn Lake District between 1999 and 2005 are used in the report. Fifty-five taxa, including lichens rare in Poland, for instance Lecanora albella, Lecidella subviridis, Ochrolechia turneri, were recorded

Structural Properties of an Open Problem in Preemptive Scheduling

Structural properties of optimal preemptive schedules have been studied in a number of recent papers with a primary focus on two structural parameters: the minimum number of preemptions necessary, and a tight lower bound on `shifts', i.e., the sizes of intervals bounded by the times created by preemptions, job starts, or completions. So far only rough bounds for these parameters have been derived for specific problems. This paper sharpens the bounds on these structural parameters for a well-known open problem in the theory of preemptive scheduling: Instances consist of in-trees of $n$ unit-execution-time jobs with release dates, and the objective is to minimize the total completion time on two processors. This is among the current, tantalizing `threshold' problems of scheduling theory: Our literature survey reveals that any significant generalization leads to an NP-hard problem, but that any significant simplification leads to tractable problem. For the above problem, we show that the number of preemptions necessary for optimality need not exceed $2n-1$; that the number must be of order $\Omega(\log n)$ for some instances; and that the minimum shift need not be less than $2^{-2n+1}$. These bounds are obtained by combinatorial analysis of optimal schedules rather than by the analysis of polytope corners for linear-program formulations, an approach to be found in earlier papers. The bounds immediately follow from a fundamental structural property called `normality', by which minimal shifts of a job are exponentially decreasing functions. In particular, the first interval between a preempted job's start and its preemption is a multiple of 1/2, the second such interval is a multiple of 1/4, and in general, the $i$-th preemption occurs at a multiple of $2^{-i}$. We expect the new structural properties to play a prominent role in finally settling a vexing, still-open question of complexity

Notes on Caloplaca lucifuga (Teloschistales, Ascomycota) in Poland

The current knowledge on the occurrence of Caloplaca lucifuga, a rare lichen with an inconspicuous crustose sorediate thallus, is discussed. Both previous and new localities are presented. The most important data on the ecology and general distribution of the species are given. Diagnostic characters related to the morphology, anatomy and chemistry of C. lucifuga that help to differentiate it from similar species are described

Specific vicariance of two primeval lowland forest lichen indicators

To date, the lichens Chrysothrix candelaris and Varicellaria hemisphaerica have been classified as accurate primeval lowland forest indicators. Both inhabit particularly valuable remnants of oak-hornbeam forests in Europe, but tend toward a specific kind of vicariance on a local scale. The present study was undertaken to determine habitat factors responsible for this phenomenon and verify the indicative and conservation value of these lichens. The main spatial and climatic parameters that, along with forest structure, potentially affect their distribution patterns and abundance were analysed in four complexes with typical oak-hornbeam stands in NE Poland. Fifty plots of 400 m^{2} each were chosen for detailed examination of stand structure and epiphytic lichens directly associated with the indicators. The study showed that the localities of the two species barely overlap within the same forest community in a relatively small geographical area. The occurrence of Chrysothrix candelaris depends basically only on microhabitat space provided by old oaks and its role as an indicator of the ecological continuity of habitat is limited. Varicellaria hemisphaerica is not tree specific but a sufficiently high moisture of habitat is essential for the species and it requires forests with high proportion of deciduous trees in a wide landscape scale. Local landscape-level habitat continuity is more important for this species than the current age of forest stand. Regardless of the indicative value, localities of both lichens within oak-hornbeam forests deserve the special protection status since they form unique assemblages of exclusive epiphytes, including those with high conservation value