We deal with a suitable weak solution (v, p) to the Navier-Stokes equations in a domain Ω ⊂ R 3 . We refine the criterion for the local regularity of this solution at the point (fx0, t0), which uses the L 3 -norm of v and the L 3/2 -norm of p in a shrinking backward parabolic neighbourhood of (x0, t0). The refinement consists in the fact that only the values of v, respectively p, in the exterior of a space-time paraboloid with vertex at (x0, t0), respectively in a ''small'' subset of this exterior, are considered. The consequence is that a singularity cannot appear at the point (x0, t0) if v and p are “smooth” outside the paraboloid.
We study axisymmetric solutions to the Navier-Stokes equations in the whole three-dimensional space. We find conditions on the radial and angular components of the velocity field which are sufficient for proving the regularity of weak solutions.
The changes in shape of the marginal coenobial cells in an experimentally cultured population of Pediastrum duplex Meyen var. duplex were investigated. The methods of landmark-based geometric morphometrics, including sliding landmarks registration, were used. The populations were cultured at 11 different pH levels and the changes in shape related to pH were studied using multivariate regression. The results of relative warps analysis revealed that morphological trends are related to both size and pH. The potential application of the results of this geometric morphometrical analysis of Pediastrum for biomonitoring and palaeoecological studies are discussed.
Článek přibližuje výsledky interdisciplinárního výzkumu spontánních procesů spojených se změnou biodiverzity v průběhu osidlování toxických substrátů (rudná/strusko-popílková odkaliště) různými skupinami organismů od mikroskopických hub, přes půdní řasy, lišejníky, mechy, až po byliny a porosty dřevin a na ně vázanými bezobratlými i obratlovci, jako jsou např. roztoči, mšice, mravenci, pískomilné druhy hmyzu, někteří ptáci a savci. Na základě praktických výsledků výzkumu byly formulovány návrhy, jak s nízkými náklady obnovit vegetaci těchto antropogenně vzniklých stanovišť. and This article emphasizes the interdisciplinary study of spontaneous processes related to biodiversity changes during colonization of toxic substrates (ore/ash slag deposits) by different groups of organisms, from microscopic fungi, soil algae, lichens, and mosses to herb and woody stands with their associated invertebrates and vertebrates, such as mites, aphids, ants, psammophilous insects, some birds and mammals. The practical results of these studies include suggestions on how to restore the vegetation on these non-natural bodies at a minimum cost.
The relationships of 14 Central European species of the genus Micrasterias were analysed using landmark-based geometric morphometrics. The analysis of relative warps was used to depict the principal components of the variation in shape and cluster analysis to reveal the groupings of individual species within the genus. All the analysed cells were correctly placed in their appropriate species clusters on the basis of geometric morphometric data. The width of the polar lobe associated with depth of the incisions between lateral lobules is the dominant morphological trend in the data investigated.
Geometric morphometric analyses were conducted on cultured populations of five Micrasterias species (M. crux-melitensis, M. papillifera, M. rotata, M. thomasiana, M. truncata). The patterns in the morphological variation measured using the morphospaces spanned by a PCA of morphometric data for individual populations were compared. In addition, the 18S rDNA sequences of these species are reported. The phenetic comparisons demonstrated the overall great similarity of morphometric indicators extracted from isolated polar lobe data and 18S rDNA genetic distances, and also indicated that the morphometric data of complete semicells were less well correlated with 18S rDNA distances. The phylogenetic analysis revealed clustering of the Micrasterias sequences into two clades, which correspond to qualitative patterns in the morphological variation of isolated polar lobe data. We propose that patterns of variation in the polar lobes of Micrasterias should be used in phenotype analyses of morphologically closely similar or cryptic species.