The second cohomology of current algebras of general Lie algebras

Let $A$ be a unital commutative associative algebra over a field of characteristic zero, \k be a Lie algebra, and \z a vector space, considered as a trivial module of the Lie algebra \g := A \otimes \k. In this paper we give a description of the cohomology space H^2(\g,\z) in terms of well accessible data associated to $A$ and \k. We also discuss the topological situation, where $A$ and \k are locally convex algebras.Comment: Some minor corrections have been made in this versio

Lie group structures on groups of smooth and holomorphic maps on non-compact manifolds

We study Lie group structures on groups of the form C^\infty(M,K)}, where M is a non-compact smooth manifold and K is a, possibly infinite-dimensional, Lie group. First we prove that there is at most one Lie group structure with Lie algebra C^\infty(M,k) for which the evaluation map is smooth. We then prove the existence of such a structure if the universal cover of K is diffeomorphic to a locally convex space and if the image of the left logarithmic derivative in \Omega^1(M,k) is a smooth submanifold, the latter being the case in particular if M is one-dimensional. We also obtain analogs of these results for the group O(M,K) of holomorphic maps on a complex manifold with values in a complex Lie group. We show that there exists a natural Lie group structure on O(M,K) if K is Banach and M is a non-compact complex curve with finitely generated fundamental group.Comment: 39 page

Preserving neural function under extreme scaling

Important brain functions need to be conserved throughout organisms of extremely varying sizes. Here we study the scaling properties of an essential component of computation in the brain: the single neuron. We compare morphology and signal propagation of a uniquely identifiable interneuron, the HS cell, in the blowfly (Calliphora) with its exact counterpart in the fruit fly (Drosophila) which is about four times smaller in each dimension. Anatomical features of the HS cell scale isometrically and minimise wiring costs but, by themselves, do not scale to preserve the electrotonic behaviour. However, the membrane properties are set to conserve dendritic as well as axonal delays and attenuation as well as dendritic integration of visual information. In conclusion, the electrotonic structure of a neuron, the HS cell in this case, is surprisingly stable over a wide range of morphological scales

Cold flow modelling of char concentration in the recirculated bed material stream of a dual fluidized bed steam gasification system

The dual fluidized bed (DFB) steam gasification technology of biomass was developed at Vienna University of Technology and is well-established for transforming biomass into a product gas which can be used for further applications. The DFB steam gasification reactor consists of a gasification chamber (bubbling bed, fluidized with steam) and a combustion chamber (turbulent bed, fluidized with air). Biomass is fed into the gasification chamber and gets in contact with the bed material, typically Olivine, at about 840°C. The released volatiles leave the gasification reactor as product gas. A part of the solid residue, called char, flows with the bed material via a chute to the combustion chamber where it is burnt with air. The bed material is heated up, separated from the flue gas stream in a cyclone and flows back to the gasification reactor via a loop seal where it provides the heat for devolatilization and drying of the biomass. The movement of the char is crucial since a sufficient amount has to flow to the combustion chamber and burn to provide enough energy for bed material heat-up. Up to now little is known about the char concentration in the bed material recirculation stream (or short recirculation stream) and its influencing variables. Therefore, a cold flow model, operated with ambient air, was constructed to study the influence of various parameters on the char concentration in the recirculation stream. Bronze is used as bed material since is matches closest to the scaling criteria. The char is also scaled; polyethylene is used as model char. The cold flow model, see Figure 1 for the flowsheet, consists of a “gasification chamber” which corresponds to the gasification chamber in the hot plant and is as well operated as a bubbling bed. Via a chute the recirculation stream moves to a rotary valve which enables to set a fixed recirculation rate and make it independent from the following pneumatic conveying. Then, gas and solids are separated in a cyclone and the recirculation stream finally flows back to the gasification chamber. After the loop seal samples are taken for investigation of the model char concentration in the recirculation stream. In the present study the influence of fluidization rate in the gasification chamber, bed material recirculation rate and model char mass in the system on the char concentration in the recirculation stream are investigated. It was found that the model char particles show a flotsam behavior. Higher fluidization rates increase the model char concentration in the recirculation stream because of better mixing, whereas the bed material recirculation rate has only little influence. Doubling and tripling the overall char mass in the system did not lead to a doubling or tripling model char concentration in the recirculation stream. The present observations are helping to better understand the ongoing phenomena inside of the dual fluidized bed gasification reactor and provide knowledge to further optimize it. Please click Additional Files below to see the full abstract

Einführung des outputorientierten Haushalts bei kirchlichen Körperschaften: Konzeptionelle Grundsätze und erste Überlegungen zur Implementierung eines entscheidungsorientiertes Rechnungswesen

Auch auf dem Hintergrund der bereits vorliegenden Ergebnisse der Rats-AG ist es richtig, wenn die Kirchen die vorwiegend in den Kommunen entwickelten Modelle der neuen Steuerungsinstrumente nicht 1 zu 1 übernehmen, sondern auf ihre Belange und ihre Anforderungsprofile ausrichten. Nicht zuletzt deshalb ist es inzwischen kein Thema mehr, dass die Umstellung auch ein neues Buchhaltungssystem (z.B. kaufmännisches Rechnungswesen) erfordern würde. Die Instrumente der erweiterten Betriebskameralistik sowie die von der KIGST angebotenen Finanzwesenprogramme mit den Verbundrechnung als Grundphilosophie reichen für die kirchlichen Belange und der damit verbundenen Anforderungen vollkommen aus. Dies erleichtert den Verwaltungen wesentlich den technischen Paradigmenwechsel zu vollziehen. Auch ist mit einer solchen Entscheidung keineswegs ausgeschlossen, mittel- bis langfristig den sanften und gleitenden Übergang in ein kaufmännisch orientiertes Rechnungswesen vorzunehmen. --