Half-flat structures on S^3\times S^3

We describe left-invariant half-flat $ \mathrm{SU }(3) $ -structures on $ S^3\times S^3$ using the representation theory of $ \mathrm SO (4) $ and matrix algebra. This leads to a systematic study of the associated cohomogeneity one Ricci-flat metrics with holonomy $ \mathrm G _2$ obtained on $ 7 $ -manifolds with equidistant $ S^3\times S^3$ hypersurfaces. The generic case is analysed numerically.     

Luminescence Spectroscopy of Rhodamine Homodimer Dications in Vacuo Reveals Strong Dye-Dye Interactions

Being alone or together makes a difference for the photophysics of dyes but for ionic dyes it is difficult to quantify the interactions due to solvent screening and nearby counter ions. Gas-phase luminescence experiments are desirable and now possible based on recent developments in mass spectrometry. Here we present results on tailor-made rhodamine homodimers where two dye cations are separated by methylene linkers, (CH₂)_n. In solution the fluorescence is almost identical to that from the monomer whereas the emission from bare cation dimers redshifts with decreasing n. In the absence of screening, the electric field from the charge on one dye is strong enough to polarize the other dye, both in the ground state and in the excited state. An electrostatic model based on symmetric dye responses (equal induced-dipole moments in ground state) captures the underlying physics and demonstrates interaction even at large distances. Our results have possible implications for gas-phase Förster Resonance Energy Transfer.     

A note on dual modules and the transpose

Archiv der Mathematik - It is a classical result in matrix algebra that any square matrix over a field can be conjugated to its transpose by a symmetric matrix. For F a non-Archimedean local field,...     

The retro Grignard addition reaction revisited: the reversible addition of benzyl reagents to ketones

The Grignard addition reaction is known to be a reversible process with allylic reagents, but so far the reversibility has not been demonstrated with other alkylmagnesium halides. By using crossover experiments it has been established that the benzyl addition reaction is also a reversible transformation. The retro benzyl reaction was shown by the addition of benzylmagnesium chloride to di-tert-butyl ketone followed by exchange of both the benzyl and the ketone moiety with another substrate. Similar experiments were performed with phenylmagnesium bromide and tert-butylmagnesium chloride, but in these two cases the Grignard addition reaction did not show any sign of a reverse transformation.     

Terrestrial and space-grown HAP and OCP crystals: effect of growth conditions on perfection and morphology

This paper reports comparative characterizations of calcium phosphate crystals grown on earth and in space. At the CaCl2 and KH2PO4 + K2HPO4 solution concentrations and the pH used, only hydroxyapatite (HAP) crystals grow under terrestrial condition while both HAP and octacalcium phosphate (OCP) crystals grew during the space experiment. The space-grown OCP crystals reach 3 mm in size, the space-grown HAP crystals reach sizes up to 100 times larger than the earth-grown crystallites. It was found also that the space-grown crystallites are more perfect than the terrestrial ones, being more stable under electron beam during HRTEM examination. Spherolites of hydroxyapatite consist of small and thin HAP crystals with different orientations. Space-grown OCP crystals containing almost pure OCP phase show strong striations along the c direction due to thickness variations. Terrestrial OCP crystals grown at lowest supersaturation on earth may be almost as large as the space-grown ones, possess a regular habit and are homogeneous in thickness. However, they always contain substantial regions of HAP structure. Also, in these crystals electron irradiation induces phase transformation from crystalline to amorphous (disordered) state during transmission electron microscopy observations. In the space-grown crystals, such transformation needs longer radiation time. We believe that the differences described above come from much lower supersaturation and different pH for crystals nucleating and growing in space compared to those formed on earth.     

Nucleic acid secondary structures containing the double-headed nucleoside 5'(S)-C-(2-(thymin-1-yl)ethyl)thymidine

Oligodeoxynucleotides containing the double-headed nucleoside 5'(S)-C-(2-(thymin-1-yl)ethyl)thymidine were prepared by standard solid phase synthesis. The synthetic building block for incorporating the double-headed moiety was prepared from thymidine, which was stereoselectively converted to a protected 5'(S)-C-hydroxyethyl derivative and used to alkylate the additional thymine by a Mitsunobu reaction. The oligodeoxynucleotides were studied in different nucleic acid secondary structures: duplexes, bulged duplexes, three-way junctions and artificial DNA zipper motifs. The thermal stability of these complexes was studied, demonstrating an almost uniform thermal penalty of incorporating one double-headed nucleoside moiety into a duplex or a bulged duplex, comparable to the effects of the previously reported double-headed nucleoside 5'(S)-C-(thymin-1-yl)methylthymidine. The additional base showed only very small effects when incorporated into DNA or RNA three-way junctions. The various DNA zipper arrangements indicated that extending the linker from methylene to ethylene almost completely removed the selective minor groove base-base stacking interactions observed for the methylene linker in a (-3)-zipper, whereas interactions, although somewhat smaller, were observed for the ethylene linker in a (-4)-zipper motif.     

The Koszul dual of a weakly Koszul module

We study the so-called weakly Koszul modules and characterise their Koszul duals. We show that the (adjusted) associated graded module of a weakly Koszul module exactly determines the homology modules of the Koszul dual. We give an example of a quasi-Koszul module which is not weakly Koszul.     

Iridium catalysed synthesis of piperazines from diols

A green and atom-economical method has been developed for the synthesis of piperazines by cyclocondensation of diols and amines in aqueous media in the presence of a catalytic amount of [Cp*IrCl2]2.