We give a full characterization of the closed one-codimensional subspaces of $c_0$, in which every bounded set has a Chebyshev center. It turns out that one can consider equivalently only finite sets (even only three-point sets) in our case, but not in general. Such hyperplanes are exactly those which are either proximinal or norm-one complemented.
An alternative polynomial approximation for the activation sigmoid function is developed here. It can considerably simplify the input/output operations of a neural network. The recursive algorithm is found for Chebyshev expansion of all constituting polynomials.
The second version of the checklist and Red List of bryophytes of the Czech Republic is provided. Generally accepted infraspecific taxa have been incorporated into the checklist for the first time. With respect to the Red List, IUCN criteria version 3.1 has been adopted for evaluation of taxa, and the criteria used for listing in the respective categories are listed under each red-listed taxon. Taxa without recent localities and those where extinction has not been proven are listed as a subset of DD taxa. Little known and rare non-threatened taxa with incomplete knowledge of distribution which are worthy of further investigation are listed on the so-called attention list. In total, 849 species plus 5 subspecies and 19 varieties have been accepted. 23 other historically reported species and one variety were evaluated as doubtful with respect to unproven but possible occurrence in the territory, and 6 other species with proven occurrence require taxonomic clarification. 43 taxa have been excluded from our flora compared to the last checklist version. 48.6 % of evaluated taxa have been listed in either of the Red List categories (EX (RE), CR, EN, VU, LR or DD), which is comparable to other industrialized regions of Central Europe.
Transformation models for two samples of censored data are considered. Main examples are the proportional hazards and proportional odds model. The key assumption of these models is that the ratio of transformation rates (e. g., hazard rates or odds rates) is constant in time. A method of verification of this proportionality assumption is developed. The proposed procedure is based on the idea of Neyman's smooth test and its data-driven version. The method is suitable for detecting monotonic as well as nonmonotonic ratios of rates.
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This first version of the Red List of lichens of the Czech Republic uses IUCN criteria version 3.1 for evaluating the species (no infraspecific taxa are included). The Red List is at the same time a new version of the checklist of lichens of the Czech Republic. Differences from the previous checklist published in the Catalogue of lichens of the Czech Republic in 1999 are: 98 species are excluded (non-lichenized fungi, species not documented in the Czech Republic, misidentifications, doubtful/dubious records and other errors) and nomenclatural changes are listed in the chapter on synonyms. In total, 1497 species of lichenized fungi (without lichenicolous and lichen-allied fungi) are included. Of these, 120 (8%) suspicious records and taxonomically problematic or not well explored taxa were not evaluated against the IUCN criteria (NE category). In total, 560 species (37.4%) are threatened: 130 (8.7%) are critically endangered (CR), 184 (12.3%) are endangered (EN) and 246 (16.4%) are vulnerable (VU). In addition, 140 species (9.4%) are extinct in the Czech Republic (RE category), 174 species (11.6%) are listed in the category near threatened (NT) and 190 (12.7%) in least concern (LC). In total, 313 species (20.9%) are listed as data deficient (DD) because insufficient data are available for a categorization.