A “maximum principle for semicontinuous functions” applicable to integro-partial differential equations

We formulate and prove a non-local “maximum principle for semicontinuous functions” in the setting of fully nonlinear and degenerate elliptic integro-partial differential equations with integro operators of second order. Similar results have been used implicitly by several researchers to obtain compare/uniqueness results for integro-partial differential equations, but proofs have so far been lacking.     

Broadband single-polarization photonic crystal fiber

We demonstrate a single-mode photonic crystal fiber that supports only one polarization state in a 220-nm-broad spectral region centered at 727 nm. The fiber has a mode-field diameter of 15.5 microm and background losses of < 15 dB/km in the single-polarization region. To our knowledge, these are the broadest bandwidth and the largest mode size yet reported for a single-polarization fiber.     

Unusual observation of nitrogen chemical shift anisotropies in tetraalkylammonium halides by 14N MAS NMR spectroscopy

¹⁴N Magic-angle spinning (MAS) NMR spectra for a number of polycrystalline, symmetrical tetraalkylammonium halides with short alkyl chains (C₂H₅– to n-C₄H₉–) have been recorded following a careful setup of the experimental conditions. Analysis of the spectra demonstrates the presence of ¹⁴N chemical shift anisotropies (CSAs) on the order of |δ_σ|=10–30 ppm along with ¹⁴N quadrupole coupling constants in the range of 10–70 kHz. The magnitude and sign of the CSAs determined from ¹⁴N MAS NMR are confirmed by recording and analysis of the corresponding slow-speed spinning (500–650 Hz) ¹⁵N CP/MAS NMR spectra. Most interestingly, it is observed experimentally and demonstrated theoretically and by simulations, that these CSAs are reflected in the spinning sideband (ssb) intensities of the ¹⁴N MAS spectra at much higher spinning speeds than can be applied to retrieve the corresponding ¹⁵N CSAs from the ssb pattern in the ¹⁵N CP/MAS spectra.     

2H chemical shift anisotropies from high-field 2H MAS NMR spectroscopy

2H chemical shift anisotropies (CSAs) have been determined for the first time for polycrystalline samples employing 2H MAS NMR spectroscopy at high magnetic field strength (14.1 T). The 2H CSA is reflected as distinct asymmetries in the manifold of spinning sidebands (ssbs) observed for the two overlapping single-quantum transitions. Least-squares fitting to the manifold of ssbs allows determination of the 2H CSA parameters along with the quadrupole coupling parameters. This is demonstrated for KD2PO4, ND4D2PO4, KDSO4, KDCO3, alpha-(COOD)2, alpha-(COOD)2.2D2O, and boehmite (AlOOD) which exhibit 2H shift anisotropies in the range 13< or =deltasigma< or =27 ppm. For fixed values of the shift anisotropy and the 2H quadrupole coupling it is shown that the precision of the CSA parameters depends strongly on the asymmetry parameter (etaQ) for the quadrupole coupling tensor, giving the highest precision for etaQ approximately 0. The 2H CSA parameters (deltasigma and etasigma) are in good agreement with 1H CSA data reported in the literature for the corresponding protonated samples from 1H NMR spectra employing various homonuclear decoupling techniques. The determination of 2H quadrupole coupling parameters and 2H (1H) CSAs from the same 2H MAS NMR experiment may be particularly useful in studies of hydrogen bonding since the 2H quadrupole coupling constant and the CSA appear to characterize bond lengths in a hydrogen bond in a different manner.     

Rapidity dependence of antiproton-to-proton ratios in Au+Au collisions at square root of (sNN) = 130 GeV

Measurements, with the BRAHMS detector, of the antiproton-to-proton ratio at midrapidities and forward rapidities, are presented for Au+Au reactions at square root of [s(NN)] = 130 GeV, and for three different collision centralities. For collisions in the 0%-40% centrality range, we find N(&pmacr;)/N(p) = 0.64+/-0.04((stat))+/-0.06((syst)) at y approximately 0, 0.66+/-0.03+/-0.06 at y approximately 0.7, and 0.41+/-0.04+/-0.06 at y approximately 2. The ratios are found to be nearly independent of collision centrality and transverse momentum. The antiproton and proton rapidity densities vary differently with rapidity, and indicate a significant degree of collision transparency, although a net-baryon free midrapidity plateau (Bjorken limit) is not yet reached.     

Wave and Dirac operators,and representations of the conformal group

Let M be the flat Minkowski space. The solutions of the wave equation, the Dirac equations, the Maxwell equations, or more generally the mass 0, spin s equations are invariant under a multiplier representation U_s, of the conformal group. We provide the space of distributions solutions of the mass 0, spin s equations with a Hilbert space structure H_s, such that the representation U_s, will act unitarily on H_s. We prove that the mass 0 equations give intertwining operators between representations of principal series. We relate these representations to the Segal-Shale-Weil (or “ladder”) representation of U(2, 2).     

Enantiospecific synthesis of 1-azafagomine

For the first time the two enantiomeric forms of the glycosidase inhibitor 1-azafagomine have been synthesised starting from D- and L-xylose. D-Xylose was converted to the 2,3,5-tribenzylfuranose, which upon reductive amination with tert-butyl carbazate gave the protected 1-hydrazino-1-deoxypentitol in high yield. N-acetylation, mesylation of the 4-OH, removal of the Boc group, cyclisation and deprotection gave (+)-1-azafagomine ((+)-1). By a similar sequence of reactions, L-xylose was converted to (-)-1-azafagomine ((-)-1). Enzymatic and other routes to optically pure 1-azafagomine were also studied. Compound (-)-1 is a potent competitive glycosidase inhibitor, while (+)-1 has no biological activity. The inhibition of almond beta-glucosidase by (-)-1 was found to be slow owing to a slow binding step of inhibitor to enzyme, with no subsequent conformational rearrangement. The rate constants for binding and release were found to be 3.3 x 10(4)M(-1)s(-1) and 0.011 s(-1), respectively, yielding Ki = 0.33 microM.     

Two-dimensional LC-MS fractioning and cross-matching of mass spectrometric data for rational identification of bioactive compounds in crude extracts

Bioprospecting aims at the identification of biological compounds with novel properties. Identification of such compounds in crude complex biological extracts is a comprehensive challenge. As a large number of extracts must be screened for successful identification of one potential promising lead, rational screening strategies must be developed. Here we report on a novel two stage rational LC-MS strategy of extracts already pre-screened and proven to contain bioactive compound(s). All extracts are initially fractionated using one and the same LC condition with parallel mass spectrometric detection. Fractions containing bioactive compound(s) are then subjected to a second fractional stage using two different chromatographic conditions. Mass detection is also included at this stage, and a cross-matching algorithm for comparison of processed mass chromatograms from the two dimensions was developed. The algorithm reports only masses present in bioactive fractions in both dimensions and enable therefore an efficient identification of potential masses that causes the bioactivity. This mass list can be used to search in natural compound database(s) for a rapid evaluation if the mass belongs to an already identified compound or if it is a potentially new one. This strategy enables thorough screening of several hundred crude extracts in one week on one single instrument.