Proalgebraic crossed modules of quasirational presentations

We introduce the concept of quasirational relation modules for discrete and pro-$p$ presentations of discrete and pro-$p$ groups and show that aspherical presentations and their subpresentations are quasirational. In the pro-$p$-case quasirationality of pro-$p$-groups with a single defining relation holds. For every quasirational (pro-$p$)relation module we construct the so called $p$-adic rationalization, which is a pro-fd-module $\overline{R}\widehat{\otimes}\mathbb{Q}_p= \varprojlim R/[R,R\mathcal{M}_n]\otimes\mathbb{Q}_p$. We provide the isomorphisms $\overline{R^{\wedge}_w}(\mathbb{Q}_p)=\overline{R}\widehat{\otimes}\mathbb{Q}_p$ and $\overline{R_u}(\mathbb{Q}_p)=\mathcal{O}(G_u)^*$, where $R^{\wedge}_w$ and $R^{\wedge}_u$ stands for continuous prounipotent completions and corresponding prounipotent presentations correspondingly. We show how $\overline{R^{\wedge}_{w}}$ embeds into a sequence of abelian prounipotent groups. This sequence arises naturally from a certain prounipotent crossed module, the latter bring concrete examples of proalgebraic homotopy types. The old-standing open problem of Serre, slightly corrected by Gildenhuys, in its modern form states that pro-$p$-groups with a single defining relation are aspherical. Our results give a positive feedback to the question of Serre.Comment: This is a corrected version of the paper which appeared in the Extended Abstracts Spring 2015, Interactions between Representation Theory, Algebraic Topology and Commutative Algebra, Research Perspectives CRM Barcelona, Vol.5, 201

Seed sowing quality and productivity of Bunias orientalis when grown in the middle taiga subzone of the Komi Republic

Hill mustard (Bunias orientalis L.) is a perennial herbaceous plant. In the last decades the interest of Russian scientists to the cultivation of this species as fodder plant has considerably increased. Scientific literature contains a significant amount of data about the prospects of its use, longevity, productivity and quality of above-ground mass. The cultivation of hill mustard in the nursery of the Botanical garden of the Institute of biology Komi SC UB RAS also indicates preconditions of its introduction. Before using this rare plant in culture in the North it is necessary to study the possibilities of its seeds. The article presents the research results of seed quality and seed yield of hill mustard conducted in 2008 - 2010 in the middle taiga subzone of the Komi Republic. It has been shown that individual plants of hill mustard annually form fertile seeds. Laboratory germination ability is low and amounts to 3.1%; in the field conditions it varies from 38 to 53% depending on the terms of sowing. Optimal time of seed sowing is autumn. To create sustainable long-lived plants for seeds spaced planting (60x60, 60x45 cm) should be used. The maximum seed productivity was obtained from plants of a third year of life, grown on an area of 60x30 cm (212.7 g/m2), when the average area for perennials is 120-130 g/m2. Potential and real seed productivity is high; the proportion of fruit reaches 42-71%, depending on a plant age and seasonal weather conditions. Thus, there is stable assurance of producing seeds and creation of reserve seeds with a storage life of up to three years of perennial species of hill mustard in the middle taiga subzone of the Komi Republic

PROSPECTS OF USING FODDER PLANTS UNDER THE CONDITIONS OF THE EUROPEAN NORTH-EAST OF RUSSIA

Summary. The article sum up the results of introductory study of some representatives of the Botanical Garden’s collection fund of fodder plants of the Institute of Biology of the Komi Scientific Center of the Ural’s Branch of the Russian Academy of Sciences. To perspective species of complex use, recommended for cultivation in the North, appertain: Helianthus tuberosus which is plant growing to 200–215 cm, with the mass of tubers about 1,5–4,0 kg/m2 and the aboveground mass up to 8 kg/m2; Silphium perfoliatum is a perennial plant with a shoot height of more than 200 cm and the aboveground mass about 6–9 kg/m2, the leaf coverage about 40–50 % and the protein content up to 23 % in absolutely dry matter; Rhaponticum carthamoides and Serratula coronata with an overhead crop yield of up to 4–5 kg/m2 and seed productivity of 30–60 g/m2. The content of ekdisteroids in absolutely dry substance is 0,44–1 % in the Rhaponticum carthamoides and 1,0–1,2 % in the Serratula coronata; Galega orientalis is a perennial, highly productive, stable, capable of self-renewing of agrocenosis and valuable, as a precursor, due to the foliar nitrogen fixation of plants; Bunias orientalis is characterized by winter hardiness up to 98 %, resistance to diseases and pests, longevity up to 6–8 years, biomass yield of 4–5 kg/m2, leaf coverage up to 40 %, protein content in wet weight the above-ground mass up to 21 % and annual formation of fertile seeds; Aconogonon weyrichii is characterized by longevity of plantation about 50 years and more, productivity of the above-ground mass up to 8 kg/m2 annually and seed efficiency of 50–100 g/m2.Работа проводилась на базе УНУ «Научная коллекция живых растений» Ботанического сада Института биологии Коми НЦ УрО РАН, регистрационный номер 507428. Исследования выполнены в рамках государственного задания по теме «Закономерности процессов репродукции ресурсных растений в культуре на европейском Северо-Востоке» № АААА-А17-117122090004-9