Categorification of Wedderburn’s basis for {\mathbb{C}}[S_{n}]

M. Neunh?ffer studies in [21] a certain basis of with the origins in [14] and shows that this basis is in fact Wedderburn’s basis, hence decomposes the right regular representation of S _n into a direct sum of irreducible representations (i.e. Specht or cell modules). In the present paper we rediscover essentially the same basis with a categorical origin coming from projective-injective modules in certain subcategories of the BGG-category . Inside each of these categories, there is a dominant projective module which plays a crucial role in our arguments and will additionally be used to show that Kostant’s problem ([10]) has a negative answer for some simple highest weight module over the Lie algebra . This disproves the general belief that Kostant’s problem should have a positive answer for all simple highest weight modules in type A. The first author was partially supported by STINT, the Royal Swedish Academy of Sciences, and the Swedish Research Council, the second author by EPSRC.     

Translation and shuffling of projectively presentable modules and a categorification of a parabolic Hecke module

We investigate certain singular categories of Harish-Chandra bimodules realized as the category of -presentable modules in the principal block of the Bernstein-Gelfand-Gelfand category . This category is equivalent to the module category of a properly stratified algebra. We describe the socles and endomorphism rings of standard objects in this category. Further, we consider translation and shuffling functors and their action on the standard modules. Finally, we study a graded version of this category; in particular, we give a graded version of the properly stratified structure, and use graded versions of translation functors to categorify a parabolic Hecke module.

     

Pressure dependence of the electrical resistivity of Ag(Mn), both in the dilute limit and in the spin glass regime

The electrical resistivity of the dilute spin glass alloys Ag(1,540 ppm Mn) and Ag(1,015 ppm Mn) has been measured from 1.3–30 K at pressures up to 70 kbars. The temperature of the resistance maximum,T _m , is found to shift to higher temperatures, this shift being stronger for the more concentrated alloys.Additionally an Ag(20 ppm Mn) Kondo-alloy has been investigated. Application of pressure causes an increase of the Kondo temperatureT _K from which the volume dependence of the effective exchange constantJ is derived.With this information theT _m -shift in the spin glass alloys can be understood in a qualitative and quantitative manner within Larsen's model.     

Sensitive determination of prohibited drugs in dried blood spots (DBS) for doping controls by means of a benchtop quadrupole/Orbitrap mass spectrometer

In the present study, a new type of mass spectrometer combining a quadrupole mass filter, a higher collision dissociation (HCD) cell and an Orbitrap detector, was evaluated for the analysis of dried blood spots (DBS) in doping controls. DBS analysis is characterized by the necessity to detect prohibited compounds in sub-nanogram-per-milliliter levels with high identification capacity. After extraction of DBS with an organic solvent and liquid chromatographic separation (using a regular C18-RP-analytical UHPLC-column) of target analytes, mass spectrometry is performed with a high-resolution full scan in positive and negative mode by means of electrospray ionisation. Single-product ion mass spectra are acquired using the data-dependent analysis mode (employing an inclusion list) for previously selected precursors of known prohibited compounds with fixed retention time ranges. Besides, a sensitive screening in a targeted approach, non-targeted analysis for retrospective data evaluation is thus possible. The chosen experimental design enables the determination of various drugs from different classes with one generic sample preparation which is shown for 26 selected model compounds (Δ⁹-tetrahydrocannabinol (THC), tetrahydrocannabinol-9-carboxylic acid (THC-COOH), methylhexaneamine, methylphenidate, cocaine, nikethamide, 3,4-methylenedioxyamphetamine, N-methyl-3,4-methylenedioxyamphetamine, strychnine, mesocarb, salbutamol, formoterol, clenbuterol, metandienone, stanozolol, bisoprolol, propranolol, metoprolol, anastrazole, clomiphene, exemestane, dexamethasone, budesonide, selective androgen receptor modulator (SARM) S4 (andarine), SARM S1, hydrochlorothiazide). Generally, only qualitative result interpretation was focussed upon, but for target analytes with deuterium-labelled internal standards (salbutamol, clenbuterol, cocaine, dexamethasone, THC-COOH and THC) quantitative analysis was also possible. Especially the most challenging analytes, THC and its carboxy metabolite, were detected in DBS at relevant concentrations (<0.5 ng/mL) using targeted HCD experiments. The method was validated for the parameters: specificity, linearity (0–20 ng/mL), precision (<25%), recovery (mean 60%), limit of detection/quantification, ion suppression, stability and accuracy (80–120%). Six isotope-labelled analogues used as internal standards facilitate a quantitative result interpretation which is of utmost importance especially for in-competition drug sports testing.     

Single molecule studies of calix[4]arene-linked perylene bisimide dimers: relationship between blinking, lifetime and/or spectral fluctuations

We recorded fluorescence time traces, and simultaneously either the fluorescence lifetime or the emission spectra from single perylene bisimide (PBI) dimers embedded in a polystyrene matrix. In these traces three distinct intensity levels can be distinguished, which reflect the photo-induced radicalisation of one of the perylene subunits. Differences in the energy transfer rate between the neutral PBI and the reversibly formed radical anion give rise to variations in the chronological order of the appearance of the intensity levels, which allowed us to categorise the time traces into three distinct groups: Type 1 blinking corresponds to a high energy transfer rate, type 2 blinking to fluctuations between large and small transfer rates (dynamic quenching), and type 3 blinking results from small energy transfer rates together with Coulomb blockade. The information that we obtain from the distributions of the fluorescence lifetimes at the various signal levels allows us to relate these differences to properties of the local polymer environment of the dimers.     

Energy transfer in calixarene-based cofacial-positioned perylene bisimide arrays

The synthesis of multichromophoric perylene bisimide-calix[4]arene arrays with up to five perylene units (containing orange, violet, and green perylene bisimide chromophores) and of monochromophoric model compounds was achieved by subsequent imidization of mono-Boc functionalized calix[4]arene linkers with three different types of perylene bisimide dye units. The optical properties of all compounds were studied with UV/vis absorption and steady state and time-resolved fluorescence spectroscopy. Upon excitation of the inner orange dye at 490 nm of array 3, strong fluorescence emission of the outer green perylene bisimide (PBI) chromophore at 744 nm is observed. The fluorescence excitation spectra of compounds 3 and 4 (lambdadet = 850 nm) show all absorption bands of the parent chromophores (e.g., all perylene units contribute to the emission from S1 state of the green PBI). Thus, the fluorescence emission and excitation spectra as well as time-resolved data of fluorescence lifetimes in the absence (tauD = 5.1 ns) and in the presence of an acceptor (tauDA = 0.8 ns) suggest efficient energy transfer processes between the perylene bisimide dye units. For the bichromophoric array 4, the energy transfer rate is calculated to a value of 1.05 x 109 s-1. These results demonstrate highly efficient energy transfer in cofacially assembled dye arrays.