Semi-invariants of symmetric quivers of tame type

A symmetric quiver $(Q,\sigma)$ is a finite quiver without oriented cycles $Q=(Q_0,Q_1)$ equipped with a contravariant involution $\sigma$ on $Q_0\sqcup Q_1$. The involution allows us to define a nondegenerate bilinear form on a representation $V$ of $Q$. We shall say that $V$ is orthogonal if is symmetric and symplectic if $$ is skew-symmetric. Moreover, we define an action of products of classical groups on the space of orthogonal representations and on the space of symplectic representations. So we prove that if $(Q,\sigma)$ is a symmetric quiver of tame type then the rings of semi-invariants for this action are spanned by the semi-invariants of determinantal type $c^V$ and, when matrix defining $c^V$ is skew-symmetric, by the Pfaffians $pf^V$. To prove it, moreover, we describe the symplectic and orthogonal generic decomposition of a symmetric dimension vector

Crystal and magnetic structures of Ba4Mn3O10

A polycrystalline sample of Ba4Mn3O10 has been prepared and characterized by X-ray diffraction (290 K), neutron diffraction (290, 80, 5K) and magnetometry (5 ≤ T(K) ≤ 1000). At 290 K the compound is paramagnetic and isostructural with Ba4Ti2PtO10. Mn3O12 trimers, built up from MnO6 octahedra, are linked through common vertices to form corrugated sheets perpendicular to the y-axis of the orthorhombic unit cell (Space group Cmca, a = 5.6850(1), b = 13.1284(1), c = 12.7327(1) Å); Ba atoms occupy the space between the layers. On cooling, the magnetic susceptibility shows a broad maximum at ∼130 K, and a sharp transition at 40 K. Neutron diffraction has shown that long-range antiferromagnetic order is present at 5 K but not at 80 K, although magnetometry at 5K has revealed a remanent magnetization (0.002 μB per Mn) which is below the detection limit of the neutron experiment. © 2002 Elsevier Science (USA)

Meiobenthos of the Oxic/Anoxic Interface in the Southwestern Region of the Black Sea: Abundance and Taxonomic Composition

The Black Sea contains the World’s largest body of anoxic water. Based on new and published data, we describe trends among selected protozoan and metazoan meiofaunal taxa at water depths of 120–240 m in the northwestern part of the Black Sea near the submarine Dnieper Canyon. This transect spans the transition between increasingly hypoxic but non-sulfidic bottom water and the deeper anoxic/sulfidic zone, the boundary between these two domains being located at approximately 150–180 m depth. This transition zone supports a rich rose-Bengal-stained fauna. Among the protozoans, gromiids are common only at 120 and 130 m. All other groups exhibit more or less distinct abundance maxima near the base of the hypoxic zone. Foraminifera peak sharply at ?160 m while ciliates are most abundant at 120, 160–190, and 240 m, where they are possibly associated with concentrations of bacterial cells. The three most abundant metazoan taxa also exhibit maxima in the hypoxic zone, the nematodes and polychaetes at 160 m, and the harpacticoid copepods at 150 m. Most of the polychaetes belong to two species, Protodrilus sp. and Vigtorniella zaikai, the larvae of which are widely distributed in severely hypoxic water just above the anoxic/sulfidic zone of the Black Sea. Both protozoans and metazoans are usually concentrated in the 0–1 cm layer of the sediment, except at the shallowest (120–130 m) site where deeper layers may yield a substantial proportion of the assemblage. The concentration of nematodes in the 3–5 cm layer at 120 m is particularly notable. Our data suggest that some benthic species can tolerate anoxic/sulfidic conditions in the Black Sea. An important caveat is that anoxia or severe hypoxia may lead to the corpses of nonindigenous organisms being preserved in our samples. However, we argue that the morphological integrity of specimens, the high population densities (associated with high bacterial concentrations in the case of ciliates), the presence of taxa often found in hypoxic settings, and the presence of all life stages (including gravid females) among nematodes and harpacticoids, suggests that at least some of the organisms are indigenous. Further comparative studies of shallow- and deep-water meiobenthic communities in the Black Sea are necessary in order to establish which species are characteristic and indicative of hypoxic/anoxic conditions