Eine Topologie auf der Menge der endlichdimensionalen nichtassoziativen Algebren über einem lokalen Körper

Motivated by an investigation ofKuz'min [2], in this note we introduce a topology on the set of nonassociative algebras of a fixed dimensionr< over a local fieldF. We obtain a space, which is notT ₁. If the trivial algebra is removed, the remaining subspace is quasicompact. The space is homeomoprhic to the group of square classes ofF ^*; forr3 the space is notT ₁. The set of division algebras is open in.     

An investigation into causes and effects of high cyanide levels in the palladium-catalyzed cyanation reaction

[reaction: see text] The palladium-catalyzed cyanation reaction is known to be sensitive to dissolved cyanide. Investigation into some causes of high levels of dissolved cyanide is presented here, along with a robust solution to this problem.     

The Varietal Influence of Flavour Precursors from Grape Marc on Monoterpene and C13-Norisoprenoid Profiles in Wine as Determined by Membrane-Assisted Solvent Extraction (MASE) GC-MS

The winemaking by-product grape marc (syn. pomace) contains significant quantities of latent flavour in the form of flavour precursors which can be extracted and used to modulate the volatile composition of wine via chemical hydrolysis. Varietal differences in grapes are widely known with respect to their monoterpene content, and this work aimed to extend this knowledge into differences due to cultivar in volatiles derived from marc precursors following wine-like storage conditions. Marc extracts were produced from floral and non-floral grape lots on a laboratory-scale and from Muscat Gordo Blanco marc on a winery -scale, added to a base white wine for storage over five to six months, before being assessed using a newly developed membrane-assisted solvent extraction gas chromatography-mass spectrometry (GC-MS) method. The geraniol glucoside content of the marc extracts was higher than that of juices produced from each grape lot. In all wines with added marc extract from a floral variety, geraniol glucoside concentration increased by around 150–200%, with increases also observed for non-floral varieties. The relative volatile profile from extracts of the floral varieties was similar but had varied absolute concentrations. In summary, while varietally pure extracts would provide the greatest control over flavour outcomes when used in winemaking, aggregated marc parcels from floral cultivars may provide a mechanism to simplify the production logistics of latent flavour extracts for use in the wine sector.     

Enynones in organic synthesis. I. Spiroannulation by tandem oxy-cope rearrangement-electrocyclic ring closure

Bis-acetylenic alcohols of proper design undergo a facile oxy-Cope rearrangement to afford mixtures of E- and Z-enynones. These latter compounds afford methylenecyclopentenones upon enolization and electrocyclic ring closure.     

Anthropogenic changes of nitrogen loads in a small river: external nutrient sources vs. internal turnover processes

Anthropogenic nutrient inputs increase the N-load in many aquatic systems, leading to eutrophication and potential changes of biological N-retention capacity. In this study, nitrate inputs in a small river were investigated along a gradient of anthropogenic influence. We aimed to determine changes in nitrate load and isotope signatures in the water column and to identify the anthropogenic influence on biological nitrogen assimilation and nitrification or denitrification in sediments. In seasonal sampling campaigns, we analysed dissolved inorganic nitrogen concentrations, and stable isotopes of nitrate. To differentiate rates of nitrate production and consumption in the pristine vs. agricultural river section, intact sediment cores were incubated with ¹⁵N-labelled nitrate. δ¹⁵N values of nitrate in the pristine river section were low, reflecting natural sources, but, as expected, increased with nitrate concentration in all seasons along the gradient. In general, nitrate retention and consumption were higher in the anthropogenically impacted than in the pristine river section, and nitrate consumption exceeded production. In addition to our measurements, modelled results also show that even in a small river, the anthropogenically enhanced consumption capacity is overwhelmed by surplus N-inputs, and nitrate consumption cannot increase in turn with external loads.     

Real loci of based loop groups

Let (G, K) be a Riemannian symmetric pair of maximal rank, where G is a compact simply connected Lie group and K is the fixed point set of an involutive automorphism σ. This induces an involutive automorphism τ of the based loop space Ω(G). There exists a maximal torus T ⊂ G such that the canonical action of T × S ¹ on Ω(G) is compatible with τ (in the sense of Duistermaat). This allows us to formulate and prove a version of Duistermaat’s convexity theorem. Namely, the images of Ω(G) and Ω(G) ^τ (fixed point set of τ) under the T × S ¹ moment map on Ω(G) are equal. The space Ω(G) ^τ is homotopy equivalent to the loop space Ω(G/K) of the Riemannian symmetric space G/K. We prove a stronger form of a result of Bott and Samelson which relates the cohomology rings with coefficients in \mathbbZ₂ {\mathbb{Z}_2} of Ω(G) and Ω(G/K). Namely, the two cohomology rings are isomorphic, by a degree-halving isomorphism (Bott and Samelson [BS] had proved that the Betti numbers are equal). A version of this theorem involving equivariant cohomology is also proved. The proof uses the notion of conjugation space in the sense of Hausmann, Holm, and Puppe [HHP].     

Vierdimensionale quadratische Divisionsalgebren über Hilbert-Körpern

Zusammenfassung Inhalt der vorliegenden Untersuchung ist eine Klassifizierung der vierdimensionalen quadratischen Divsionsalgebren über einem Hilbert-Körper. Die Anregung dazu entstammt einer Arbeit von Kuz'min [6], in der endlichdimensionale reelle Divisionsalgebren durch Aussagen über ihre Multiplikationskonstanten charakterisiert werden. Der Schwerpunkt liegt dort auf den quadratischen Divisionsalgebren. Deren Struktur wird wesentlich durch quadratische Formen bestimmt. Deshalb ist es naheliegend, diese Algebren für eine allgemeinere Klasse von Körpern mit einer überschaubaren Theorie der quadratischen Formen zu betrachten. A Fröhlich [5] hat eine axiomatische Beschreibung für eine Klasse von Körpern, die sogenannten Hilbert-Körper, gegeben, die eine Theorie der quadratischen Formen wie die -adischen Zahlen oder die reellen Zahlen haben. Diese Körper legen wir in der Untersuchung zugrunde. Eine genauere Motivation für das Vorgehen und einen Ausblick auf die Ergebnisse gibt die folgende Einleitung.Die Verfasserin dankt Herrn Prof. Dr. K. Strambach, Erlangen, für die Anregung und Begleitung dieser Arbeit und Herrn Prof. Dr. L. Bröcker, Münster, für die konstruktiven Vorschläge zur Überarbeitung des ursprünglichen Manuskiptes.