The topological centralizers of Toeplitz flows and their z2-extensions

The topological centralizers of Toeplitz flows satisfying a condition (Sh) and their Z2-extensions are described. Such Toeplitz flows are topologically coalescent. If {q0,q1,…} is a set of all except at least one prime numbers and I0,I1,… are positive integers then the direct sum [fórmula disponible al document original] can be the topological centralizer of a Toeplitz flow

The morphology and morphometry of the so-called "meningo-orbital foramen" in humans

The so-called meningo-orbital foramen creates an additional link between the orbit and the cranial cavity. This bony canal, not always present in the human skull, contains a branch from the middle meningeal artery, providing an accessory blood supply to the orbit. This vessel, like the foramen, is characterised by great variability. Although older textbooks of basic anatomy suggested that it was a rare occurrence, some current data indicate a more frequent incidence of this foramen. These discrepancies were verified in our research. 92 orbits were studied on 46 macerated human skulls (25 male and 21 female). Although the incidence of the meningo-orbital foramen in the material as a whole was 28%, the foramen in female skulls was observed to be 40.5%, compared to 18% in male skulls. This difference was statistically significant. A double foramen was encountered in three orbits, and in one orbit there was a triple foramen. This means that in the material as a whole multiple foramina were observed in 4% of cases. Two measurements were taken to determine the localisation of the meningo- orbital foramen. The minimal distance between the supraorbital notch (or foramen) and the meningo-orbital foramen was 35.0 (28–44) mm. The minimal distance from the cross-point of the entrance to the orbit and the fronto-zygomatic suture was (21.3-35.5) mm. This indicates that the meningo-orbital foramen can lie near an operating field in some surgical interventions through the lateral orbital wall

Body mass distributions along successional gradients in epigeic carabid beetle fauna (Coleoptera: Carabidae)

Background and purpose: Body mass distributions may be related to the stage of succession of a habitat and provide with information for assessing successional processes. Therefore, body mass distributions of carabid assemblages were studied in three research areas, which were post-industrial areas near the city of Bełchatów (Central Poland) planted with different tree and shrub species, moist and wet forest stands in the Puszcza Knyszyńska forest (Northeastern Poland), and beech stands in the Ruhr valley (Western Germany) in order to analyze the changes in body mass distributions within single assemblages along successional gradients.   Materials and Methods: For each carabid assemblage, the mean individual biomass (MIB) as well as MIB standard deviation (SD) and coefficient of variation (CV) were calculated. SD and CV were plotted against the age of study sites and MIB values, respectively. Analyses of Covariance (ANCOVA) were carried out with SD and CV as dependent variables and the age of study sites and MIB as covariates.   Results: SD was low at young stages of succession, but increased rapidly and plateaued at advanced stages in beech but not in wet forest stands. Accordingly, CV was low at very young stages of succession, showing a rapid increase and subsequent decrease in the beech stands, whereas in the wet stands it stayed on a constant level. ANCOVA revealed significant differences in SD and CV between the research areas and significant changes with age or MIB, but, with the exception of CV as dependent variable and MIB as covariate, interactions were also significant.   Conclusions: The results of the study suggest that data on body mass distributions within single carabid assemblages may be useful in the assessment and comparison of successional stages and processes between different habitat types.</p