In this note, we prove that the countable compactness of {0, 1} R together with the Countable Axiom of Choice yields the existence of a nonmeasurable subset of . This is done by providing a family of nonmeasurable subsets of whose intersection with every non-negligible Lebesgue measurable set is still not Lebesgue measurable. We develop this note in three sections: the first presents the main result, the second recalls known results concerning non-Lebesgue measurability and its relations with the Axiom of Choice, the third is devoted to the proofs.
We tested the hypothesis that males of meadow pipits (Anthus pratensis) respond differentially to simulated territorial intrusions (song playback + bird model) by conspecific, related (tree pipit, Anthus trivialis), and unrelated individuals (willow warbler, Phylloscopus trochilus), and evaluated the effect of playback order. All tested males responded aggressively to the conspecific playback; reactions to heterospecific stimuli occurred only after previous excitation by the conspecific song and dummy, and were usually weaker. Apparently, although males were able to discriminate between playbacks, excitation by intrusion of a conspecific rival elicited an aggressive reaction to otherwise neutral stimuli. Reactions to heterospecific playbacks closely following the conspecific one did not differ significantly between congeneric and unrelated species. The response to a subsequent heterospecific stimulus, however, was taxon-dependent: congeneric species elicited a significantly stronger reaction than an unrelated one. We presume that this was due to the morphological similarity between pipits, and that the more intensive reaction could have been caused by stronger visual stimulus from the respective model. We discuss the potential benefits as well as limitations of using models (dummies) in playback experiments, and suggest that overexcitation by previous stimuli should be considered during experimental setup and data analysis in studies focusing both on interspecific aggressiveness and on neighbour-stranger interactions.
By a sign pattern (matrix) we mean an array whose entries are from the set $\lbrace +,-,0\rbrace $. The sign patterns $A$ for which every real matrix with sign pattern $A$ has the property that its inverse has sign pattern $A^T$ are characterized. Sign patterns $A$ for which some real matrix with sign pattern $A$ has that property are investigated. Some fundamental results as well as constructions concerning such sign pattern matrices are provided. The relation between these sign patterns and the sign patterns of orthogonal matrices is examined.
Large veteran trees are key structures sustaining biodiversity in wooded landscapes. Many organisms associated with
such trees are, however, also able to inhabit suitable trees with smaller diameters or other surrogate habitats. Understanding the
mechanisms behind the importance of veteran trees and the conditions enabling veteran tree specialists to exploit smaller trees
might help conservation efforts targeted at the diverse and highly endangered biota associated with veteran trees. To investigate
this, we studied local patterns in the exploitation of trees by a veteran tree specialist, the great capricorn beetle (Cerambyx cerdo),
at three sites with different soil characteristics, namely fl oodplain, dry-sandy and dry-rocky sites, where this beetle exploits oaks
of large (~1.5 m), medium (~0.75 m) and small (~0.25 m) diameters, respectively. We recorded the presence and number of exit
holes made by C. cerdo on each tree and related these to the characteristics of the trees: their diameters, openness of the canopy
around them and their state of health. The probability of occurrence and the number of exit holes increased with tree diameter,
canopy openness, and decreasing tree health, but these relationships differed considerably among the study sites. In dry conditions, trees of small diameters were more likely to be exploited by the beetle than in the fl oodplain. The number of exit holes, on
the other hand, was a function of tree diameter, with large trees sustaining more beetles and thus acting as larger habitat patches.
The species of oak affected the probability of exit hole presence as the sessile oak (Quercus petraea) and pedunculate oak (Q.
robur) were preferred over Turkey oak (Q. cerris). The slope orientation also affected the presence of exit holes as trees on slopes
with either an eastern or northern orientation were not exploited by the beetle. This study revealed a high level of between-site
variability in the tree characteristics relevant to predicting the occurrence of C. cerdo, mainly with respect to diameter. Therefore,
while the general patterns of habitat use and the fundamental niche of this beetle are well known, survival and protection of local
populations is dependent on site-specifi c characteristics. The realized niche of this beetle must therefore be carefully considered
when planning conservation management for a particular site. The results also signify that at some sites, small trees can, at least
temporarily, substitute for scarce large trees if the state of their health is managed using proper conservation measures.