Normal Subgroups of B u Aut(Ω)

Aut(Ω) denotes the group of all order preserving permutations of the totally ordered set Ω, and if e ≤ u ∈ Aut(Ω), then B _u Aut(Ω) denotes the subgroup of all those permutations bounded pointwise by a power of u. It is known that if Aut(Ω) is highly transitive, then Aut(Ω) has just five normal subgroups. We show that if Aut(Ω) is highly transitive and u has just one interval of support, then B _u Aut(Ω) has normal subgroups, and there is a certain ideal of the lattice of subsets of (), the power set of the integers, such that the lattice of normal subgroups of every such Aut(Ω) is isomorphic to . To Bernhard Banaschewski on the occasion of his 80th birthday.     

Time-of-flight variant to image mixing of granular media in a 3D fluidized bed

This paper describes a variant of time-of-flight magnetic resonance (MR) imaging that provides a method of measuring the inherent mixing in a fluidized bed without the introduction of tracer particles. The modifications to conventional time-of-flight imaging enable the measurement of the axial mixing of a precisely controlled initial particle distribution, thereby providing measurements suitable for a direct comparison with models of solids mixing in granular systems. The imaging sequence is applied to characterize mixing, over time scales of 25-1000 ms, in a gas-fluidized bed of Myosotis seed particles; mixing over short timescales, inaccessible using conventional tracer techniques, is studied using this technique. The mixing pattern determined by this pulse sequence is used in conjunction with MR velocity images of the motion of the particles to provide new insight into the mechanism of solids mixing in granular systems.     

Full wave-field reflection coefficient inversion

This paper develops a Bayesian inversion for recovering multilayer geoacoustic (velocity, density, attenuation) profiles from a full wave-field (spherical-wave) seabed reflection response. The reflection data originate from acoustic time series windowed for a single bottom interaction, which are processed to yield reflection coefficient data as a function of frequency and angle. Replica data for inversion are computed using a wave number-integration model to calculate the full complex acoustic pressure field, which is processed to produce a commensurate seabed response function. To address the high computational cost of calculating short range acoustic fields, the inversion algorithms are parallelized and frequency averaging is replaced by range averaging in the forward model. The posterior probability density is interpreted in terms of optimal parameter estimates, marginal distributions, and credibility intervals. Inversion results for the full wave-field seabed response are compared to those obtained using plane-wave reflection coefficients. A realistic synthetic study indicates that the plane-wave assumption can fail, producing erroneous results with misleading uncertainty bounds, whereas excellent results are obtained with the full-wave reflection inversion.     

Uncertainty estimation in seismo-acoustic reflection travel time inversion

This paper develops a nonlinear Bayesian inversion for high-resolution seabed reflection travel time data including rigorous uncertainty estimation and examination of statistical assumptions. Travel time data are picked on seismo-acoustic traces and inverted for a layered sediment sound-velocity model. Particular attention is paid to picking errors which are often biased, correlated, and nonstationary. Non-Toeplitz data covariance matrices are estimated and included in the inversion along with unknown travel time offset (bias) parameters to account for these errors. Simulated experiments show that neglecting error covariances and biases can cause misleading inversion results with unrealistically high confidence. The inversion samples the posterior probability density and provides a solution in terms of one- and two-dimensional marginal probability densities, correlations, and credibility intervals. Statistical assumptions are examined through the data residuals with rigorous statistical tests. The method is applied to shallow-water data collected on the Malta Plateau during the SCARAB98 experiment.     

Dipolar Cycloaddition Reactions of Azomethine Ylides Generated by endocyclic‐exocyclic 1,3‐dipole Rearrangement

Dipolar cycloaddition of polycyclic azomethine ylides, in which the central nitrogen atom is part of a pyrrolidine ring and bears a methoxycarbonyl group with norbornenes has been shown to produce two main types of products featuring pyrrolizidine rings. In conjuction with results of quantum chemical calculations (B3LYP), mechanistic rationale was postulated. The key reaction step is unprecedented endocyclic to exocyclic azomethine ylide rearrangement by an intermolecular prototropic migration (formal [1,3] H‐shift).     

Identification of a single light atom within a multinuclear metal cluster using valence-to-core X-ray emission spectroscopy

Iron valence-to-core Fe Kβ X-ray emission spectroscopy (V2C XES) is established as a means to identify light atoms (C, N, O) within complex multimetallic frameworks. The ability to distinguish light atoms, particularly in the presence of heavier atoms, is a well-known limitation of both crystallography and EXAFS. Using the sensitivity of V2C XES to the ionization potential of the bound ligand, energetic shifts of ~10 eV in the ligand 2s ionization energies of bound C, N, and O may be observed. As V2C XES is a high-energy X-ray method, it is readily applicable to samples in any physical form. This method thus has great potential for application to multimetallic inorganic frameworks involved in both small molecule storage and activation.     

Online enzymatic sequencing of glycans from Trastuzumab by phospholipid-assisted capillary electrophoresis

CE separations of glycans taken from the cancer drug, Trastuzumab (Herceptin(?)), were accomplished using phospholipid additives. Glycans were labeled with 1-aminopyrene-3,6,8-trisulfonic acid and were separated with efficiencies as high as 510000 theoretical plates in a 60.2 cm 25 μm id fused-silica capillary. The thermally tunable phospholipid was loaded into the capillary when it possessed a viscosity similar to that of water. The temperature was increased, and the separations were performed when the material exhibited higher viscosity. Enzymes were integrated into the separation with the phospholipid additive. Neuraminidase, β1-4 galactosidase, and β-N-acetylglucosaminidase were injected into the capillary without covalent modification and used for enzyme hydrolysis. Exoglycosidase enzymes cleaved the terminal glycan residues. The glycan sequence could be verified based on enzyme specificity. Neuraminidase was used to determine total glycan content of the low-abundance glycans containing sialic acid. β1-4 Galactosidase and β-N-acetylglucosaminidase were used sequentially in-capillary, to determine the structure of the high-abundance glycans.     

Towards homonuclear J solid-state NMR correlation experiments for half-integer quadrupolar nuclei: experimental and simulated 11B MAS spin-echo dephasing and calculated 2J(BB) coupling constants for lithium diborate

Magic-angle spinning (MAS) NMR spin-echo dephasing is systematically investigated for the spin I = 3/2 (11)B nucleus in lithium diborate, Li(2)O·2B(2)O(3). A clear dependence on the quadrupolar frequency (ω(Q)(PAS)/2π = 3C(Q)/[4I(2I- 1)]) is observed: the B3 (larger C(Q)) site dephases more slowly than the B4 site at all investigated MAS frequencies (5 to 20 kHz) at 14.1 T. Increasing the MAS frequency leads to markedly slower dephasing for the B3 site, while there is a much less evident effect for the B4 site. Considering samples at 5, 25, 80 (natural abundance) and 100% (11)B isotopic abundance, dephasing becomes faster for both sites as the (11)B isotopic abundance increases. The experimental behaviour is rationalised using density matrix simulations for two and three dipolar-coupled (11)B nuclei. The experimentally observed slower dephasing for the larger C(Q) (B3) site is reproduced in all simulations and is explained by the reintroduction of the dipolar coupling by the so-called "spontaneous quadrupolar-driven recoupling mechanism" having a different dependence on the MAS frequency for different quadrupolar frequencies. Specifically, isolated spin-pair simulations show that the spontaneous quadrupolar-driven recoupling mechanism is most efficient when the quadrupolar frequency is equal to twice the MAS frequency. While for isolated spin-pair simulations, increasing the MAS frequency leads to faster dephasing, agreement with experiment is observed for three-spin simulations which additionally include the homogeneous nature of the homonuclear dipolar coupling network. First-principles calculations, using the GIPAW approach, of the (2)J(11B-11B) couplings in lithium diborate, metaborate and triborate are presented: a clear trend is revealed whereby the (2)J(11B-11B) couplings increase with increasing B-O-B bond angle and B-B distance. However, the calculated (2)J(11B-11B) couplings are small (0.95, 1.20 and 2.65 Hz in lithium diborate), thus explaining why no zero crossing due to J modulation is observed experimentally, even for the sample at 25% (11)B where significant spin-echo intensity remains out to durations of ～200 ms.     

Boron environments in Pyrex® glass--a high resolution, Double-Rotation NMR and thermodynamic modelling study

It is shown, using the important technological glass Pyrex? as an example, that 1D and 2D (11)B Double-Rotation (DOR) NMR experiments, in combination with thermodynamic modelling, are able to provide unique structural information about complex glasses. (11)B DOR NMR has been applied to Pyrex? glass in order to remove both dipolar and quadrupolar broadening of the NMR lines, leading to high resolution spectra that allow unambiguous, accurate peak fitting to be carried out, of particular importance in the case of the 3-coordinated [BO(3)] (B3) trigonal planar environments. The data obtained are of sufficient quality that they can be used to test the distributions of borate and borosilicate superstructural units predicted by the thermodynamics-based Model of Associated Solutions. The model predicts the dominant boron-containing chemical groupings in Pyrex? glass to be those associated with B(2)O(3) and sodium tetraborate (with smaller amounts of sodium triborate, sodium diborate, sodium pentaborate, danburite and reedmergnerite). Excellent agreement is found between model and experiment provided the (11)B peaks with isotropic chemical shifts of -1.4 ppm and 0.5 ppm are assigned to B4 species from borosilicate units ([B(OSi)(4)] and [B(OSi)(3)(OB)]) and borate superstructural units (mainly triborate rings with some pentaborate and diborate) respectively. The peaks with isotropic shifts of 14 ppm and 18.1 ppm are then assigned to B3 in borate superstructural units (mainly triborate and pentaborate along with connecting B3) and boroxol rings respectively. The assignments of the DOR NMR peaks, are supported by the presence of cross-peaks in (11)B spin-diffusion DOR NMR spectra which can be used to develop a structural model in which B(2)O(3)-like regions are linked, via borate and borosilicate superstructural units, to the majority silica network. Pyrex? is thus shown to have a heterogeneous structure, with distinct molecular groupings that are far removed from a random distribution of network polyhedra with only short-range order.