Linear extension sums as valuations on cones

The geometric and algebraic theory of valuations on cones is applied to understand identities involving summing certain rational functions over the set of linear extensions of a poset.     

Cohomological uniqueness of the Cauchy problem solutions for the Einstein equation

In this paper we analyze the Cauchy problem for the Einstein equation in the case of a non-characteristic initial hypersurface. To find the correct notions for the characteristic and Cauchy data we introduce a complex, which we call the Einstein complex. Then the Cauchy problem acquires correctness in terms of the associated spectral sequence. We define the Cauchy data in such way that they allow us to reconstruct a cohomologously unique formal solution.     

Chemoenzymatic synthesis of both enantiomers of 3-hydroxy- and 3-amino-3-phenylpropanoic acid

Ethyl (S)-3-hydroxy-3-phenylpropionate (S)-2 was obtained by the asymmetric reduction of ethyl 3-phenyl-3-oxopropionate 1 with the yeast Saccharomyces cerevisiae (ATCC 9080). The kinetic resolution of racemic ethyl 2-acetoxy-3-phenyl-propionate rac-3 with the same microorganism, gave after hydrolysis ethyl (R)- and (S)-3-hydroxy-3-phenylpropionates (R)-2 and (S)-2 which were converted by a straightforward series of reactions to the enantiomers of 3-amino-3-phenyl-propionic acids (S)-6 and (R)-6. The asymmetric reduction and hydrolytic kinetic resolution were also tested with several other whole cell systems under a variety of conditions.     

Larger locally compact monothetic semigroups

Semigroup Forum - We show that for every $$k\in {\mathbb {N}}$$, there is a locally compact noncompact monothetic semigroup S with identity such that S is homeomorphic to a closed nowhere dense...     

Geometries and NMR properties of cisplatin and transplatin revisited at the four-component relativistic level

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A Tunable,Fullerene-Based Molecular Amplifier for Vibrational Circular Dichroism

Vibrational circular dichroism (VCD) studies are reported on a chiral compound in which a fullerene C₆₀ moiety is used as an electron acceptor and local VCD amplifier for an alanine-based peptide chain. Four redox states are investigated in this study, of which three are reduced species that possess low-lying electronic states as confirmed by UV/Vis spectroelectrochemistry. VCD measurements in combination with (TD)DFT calculations are used to investigate (i) how the low-lying electronic states of the reduced species modulate the amplification of VCD signals, (ii) how this amplification depends on the distance between oscillator and amplifier, and (iii) how the spatial extent of the amplifier influences amplification. These results pave the way for further development of tailored molecular VCD amplifiers.     

Optimization of the cathode porosity via mechanochemical synthesis with carbon black

Journal of Solid State Electrochemistry - Nanostructured carbon–coated composite cathode materials LiFe0.5Mn0.5PO4/C (LFMP/C) are prepared by the mechanochemically assisted solid-state...