On the 6-exo-trig ring closure of substituted 5-hexen-1-oxyl radicals

Substituted 5-hexen-1-oxyl radicals have been generated from N-(5-hexen-1-oxy)-5-(p-methoxyphenyl)-4-methylthiazole-2(3H)-thiones under tin-free conditions and have been successfully applied as reactive intermediates in a mechanistic study on the formation of bromomethyl-substituted tetrahydropyrans via 6-exo-trig selective cyclizations.     

A chip-based platform for the in vitro generation of tissues in three-dimensional organization

We describe a multi-purpose platform for the three-dimensional cultivation of tissues. The device is composed of polymer chips featuring a microstructured area of 1-2 cm(2). The chip is constructed either as a grid of micro-containers measuring 120-300 x 300 x 300 microm (h x l x w), or as an array of round recesses (300 microm diameter, 300 microm deep). The micro-containers may be separately equipped with addressable 3D-micro-electrodes, which allow for electrical stimulation of excitable cells and on-site measurements of electrochemically accessible parameters. The system is applicable for the cultivation of high cell densities of up to 8 x 10(6) cells and, because of the rectangular grid layout, allows the automated microscopical analysis of cultivated cells. More than 1000 micro-containers enable the parallel analysis of different parameters under superfusion/perfusion conditions. Using different polymer chips in combination with various types of bioreactors we demonstrated the principal suitability of the chip-based bioreactor for tissue culture applications. Primary and established cell lines have been successfully cultivated and analysed for functional properties. When cells were cultured in non-perfused chips, over time a considerable degree of apoptosis could be observed indicating the need for an active perfusion. The system presented here has also been applied for the differentiation analysis of pluripotent embryonic stem cells and may be suitable for the analysis of the stem cell niche.     

Microwave-assisted generation of alkoxyl radicals and their use in additions, beta-fragmentations, and remote functionalizations

Microwave irradiation (2.45 GHz, 300-500 W) of N-(alkoxy)thiazole-2(3H)-thiones in low-absorbing solvents affords alkoxyl radicals, which were identified by (i) spin adduct formation (EPR-spectroscopy) and (ii) fingerprint-type selectivities in intramolecular additions (stereoselective synthesis of disubstituted tetrahydrofurans), beta-fragmentations (formation of carbonyl compounds), and C,H-activation of aliphatic subunits, by delta-selective hydrogen atom transfer. C-Radicals formed from oxygen-centered intermediates were trapped either by Bu(3)SnH, L-cysteine ethyl ester, the reduced form of glutathione (reductive trapping), or by bromine atom donor BrCCl(3) (heteroatom functionalization) The results suggest that microwave activation is superior to UV/Vis-photolysis and conductive heating for alkoxyl radical generation from N-(alkoxy)thiazolethiones. It offers by far the shortest reaction times along with the option to reduce the amount of trapping reagent significantly.     

Discrete Morse theory for totally non-negative flag varieties

In a seminal 1994 paper Lusztig (1994) [26], Lusztig extended the theory of total positivity by introducing the totally non-negative part (G/P)_?0 of an arbitrary (generalized, partial) flag variety G/P. He referred to this space as a “remarkable polyhedral subspace”, and conjectured a decomposition into cells, which was subsequently proven by the first author Rietsch (1998) [33]. In Williams (2007) [40] the second author made the concrete conjecture that this cell decomposed space is the next best thing to a polyhedron, by conjecturing it to be a regular CW complex that is homeomorphic to a closed ball. In this article we use discrete Morse theory to prove this conjecture up to homotopy-equivalence. Explicitly, we prove that the boundaries of the cells are homotopic to spheres, and the closures of cells are contractible. The latter part generalizes a result of Lusztig's (1998) [28], that (G/P)_?0 - the closure of the top-dimensional cell - is contractible. Concerning our result on the boundaries of cells, even the special case that the boundary of the top-dimensional cell (G/P)_>0 is homotopic to a sphere, is new for all G/P other than projective space.     

Kobalt

Ohne Zusammenfassung     

Unifying scaling theory for vortex dynamics in two-dimensional turbulence

We present a scaling theory for unforced inviscid two-dimensional turbulence. Our model unifies existing spatial and temporal scaling theories. The theory is based on a self-similar distribution of vortices of different sizes A. Our model uniquely determines the spatial and temporal scaling of the associated vortex number density which allows the determination of the energy spectra and the vortex distributions. We find that the vortex number density scales as n(A,t)-t(-2/3)/A, which implies an energy spectrum E-k(-5), significantly steeper than the classical Batchelor-Kraichnan scaling. High-resolution numerical simulations corroborate the model.