In this paper, we deduce explicit formulas to evaluate the determinants of nonsymmetrical structure Toeplitz Bohemians by two determinants of specific Hessenberg Toeplitz matrices, which are linear combinations in terms of determinants of specific Hessenberg Toeplitz matrices. We get some new results very di¤erent from [Massimiliano Fasi, Gian Maria Negri Porzio, Determinants of normalized upper Hessenberg matrices, Electronic Journal of Linear Algebra, Volume 36, pp. 352-366, June 2020].

The population dynamics of Hazel Grouse was studied by presence/ absence recording at stationary sites along fixed routes (110 km) during 1972-2019 in the central part of the Bohemian Forest (Šumava, Czech Republic). The 100-km² study area covered altitudes between 600 m (Rejstejn) and 1,253 m a.s.l., (mount Sokol). Our data base contained indices of Hazel Grouse occupancy: positive sites/ controlled sites for a yearly increasing number of Hazel Grouse occurrence sites (N = 134) for 48 years. We used a loglinear Poisson-regression method to analyze the long-term population trend for Hazel Grouse in the study area. In the period 1972 to 2006 we found a stable Hazel Grouse population (p = 0.83). From 2006-2007 to 2019, the population index dropped (-3.8% per year, p < 0.05) for the last 13 years. This decline is assumed to be influenced by habitat loss due to succession resulting in older, more open forest stands, by strongly increasing forestry and windstorm “Kyrill” followed by clear cutting, bark-beetle damage, and removal of pioneer trees in spruce plantations, which diminished buds and catkins, the dominant winter food. The influence of disturbance by increasing touristic activities and/or predation is discussed. Our results could help to optimize conservation efforts for Hazel Grouse in the Bohemian Forest.

The Krudum granite body comprises highly fractionated granitic rocks ranging from medium-F biotite granites to high-F, high-P₂O₅ Li-mica granites. This unique assemblage is an ideal site to continue recent efforts in petrology to characterize the role of zircon, monazite and xenotime as hosts to REEs. The granitic rocks of the Krudum body analysed in this study were found to contain variable concentrations of monazite and zircon, while xenotime was only found in the high-F, high-P₂O₅ Li-mica granites and in the alkali-feldspar syenites of the Vysoký Kámen stock. For analysed monazites of all magmatic suites cheralite substitution was significant. The highest concentration of cheralite was found in monazites from the high-F, Li-mica granites and from the alkali-feldspar syenites. The proportion of YPO₄ in all analysed xenotimes ranges from 71 to 84 mol. %. Some xenotimes were found to be hydrated and the observed water content estimated from analytical data ranged from 5 to 11 wt. % H₂O. Analysed xenotimes were commonly enriched in HREEs (9.3– 19.5 wt. % HREE₂O₃) and thorite-coffinite and cheralite exchange was observed. Analysed zircons from granite suites of the Krudum granite body contained moderate Hf concentrations (1.0–4.7 wt. % HfO₂; 0.010–0.047 apfu Hf). The highest concentrations of HfO₂ were found in zircons from the high-F, high P₂O₅ Li-mica granites (1.2–4.7 wt. % HfO₂) and from the alkali-feldspar syenites (1.3–4.1 wt. % HfO₂). Zircons from the high-F, high-P₂O₅ Li-mica granites were often hydrated and fluorised. The concentrations of F in zircon from partly greisenised high-F, high-P₂O₅ Li-mica granites reached up to 1.2 wt. % (0.26 apfu F). In zircons from the alkali-feldspar syenites enrichment in P, which is not associated with a simultaneous enrichment in Y + REE, was also observed. Analysed zircons from the high-F, high P₂O₅ Li-mica granites were enriched in Y (up to 5.5 wt. % Y₂O₃; 0.10 apfu Y) and Sc (up to 1.17 wt. % Sc₂O₃; 0.03 apfu Sc).