Efficient symmetry-based homonuclear dipolar recoupling of quadrupolar spins: double-quantum NMR correlations in amorphous solids

We report novel symmetry-based pulse sequences for exciting double-quantum (2Q) coherences between the central transitions of half-integer spin quadrupolar nuclei in the NMR of rotating solids. Compared to previous 2Q-recoupling techniques, numerical simulations and 23Na and 27Al NMR experiments on Na2SO4 and the open-framework aluminophosphate AlPO-CJ19 verify that the new dipolar recoupling schemes display higher robustness to both radio-frequency field inhomogeneity and to spreads in resonance frequencies. These advances allowed for the first demonstration of 2Q-recoupling in an amorphous solid for revealing its intermediate-range structural features, in the context of mapping 27Al-27Al connectivities between the aluminium polyhedra (AlO4, AlO5 and AlO6) of a lanthanum aluminate glass (La0.18Al0.82O1.5).     

Long-Term-Average Spectrum Characteristics of Country Singers During Speaking and Singing

Five premier male country singers involved in our previous studies spoke and sang the words of both the national anthem and a country song of their choice. Long-term-average spectra were made of the spoken and sung material of each singer. The spectral characteristics of county singers' speech and singing were similar. A prominent peak in the upper part of the spectrum, previously described as the "speaker's formant," was found in the county singers' speech and singing. The singer's formant, a strong spectral peak near 2.8 kHz, an important part of the spectrum of classically trained singers, was not found in the spectra of the country singers. The results support the conclusion that the resonance characteristics in speech and singing are similar in country singing and that county singing is not characterized by a singer's formant.     

Efficient orientational averaging by the extension of Lebedev grids via regularized octahedral symmetry expansion

Gaussian spherical quadrature methods in the guise of the Lebedev sampling grids are highly efficient for some orientational ("powder") averaging problems in solid state NMR. However, their applicability is currently restricted, as the sets of orientations are derived analytically and because they are not well adapted to simulate the broad peakshapes encountered, for example, in the NMR on static powders or on half-integer quadrupolar spins subject to second order quadrupolar interactions under magic-angle spinning conditions. We remedy these problems by (i) introducing the recursive procedure regularized octahedral symmetry expansion (ROSE), to which any existing Lebedev set may be subjected. Each recursive step gives a 9-fold enlarged set of orientations. (ii) We demonstrate that ROSE-expanded grids, in conjunction with spectral interpolation, is well suited for calculating broad peakshapes. These advances combine into the apparently most efficient general-purpose two-angle orientational averaging technique proposed to date for solid state NMR applications.     

In vitro enzymatic oxidation of a fluorine-tagged sulfido substrate analogue: a 19F NMR investigation

1H-decoupled 19F NMR has been used to monitor the highly regioselective oxidation of a fluorine-tagged thia-fatty acid derivative by castor stearoyl-ACP delta9 desaturase. The major enzymatic product, after reductive work-up, was identified as 9-fluoro-1-nonanol. This compound could be easily distinguished from substrate and a 9-sulfoxy by-product on the basis of its 19F NMR chemical shift and spiking experiments using authentic standards. Structural assignment of the cleavage product was confirmed by GC-MS analysis of the enzymatic products.     

In-source CID of guanosine: Gas phase ion-molecule reactions

In-source collision induced dissociation was applied to access second generation ions of protonated guanosine. The in-source gas-phase behavior of [BH2]+-NH3 (m/z 135, C5H3N4O+) was investigated. Adduct formation and reactions with available solvent molecules (H2O and CH3OH) were demonstrated. Several addition/elimination sequences were observed for this particular ion and solvent molecules. Dissociation pathways for the newly formed ions were developed using a QqTOF mass spectrometer, permitting the assignment of elemental compositions of all product ions produced. Reaction schemes were suggested arising from the ring-opened intermediate of the protonated base moiety [BH2]+, obtained from fragmentation of guanosine. The mass spectral data revealed that the in-source CH3OH-reaction product underwent more complex fragmentations than the comparable ion following reaction with H2O. A rearrangement and a parallel radical dissociation pathway were discerned. Apart from the mass spectrometric evidence, the fragmentation schemes are supported by density functional theory calculations, in which the reaction of the ring-opened protonated guanine intermediate with CH3OH and a number of subsequent fragmentations were elaborated. Additionally, an in-source transition from the ring-opened intermediate of protonated guanine to the ring-opened intermediate of protonated xanthine was suggested. For comparison, a low-energy collision induced dissociation study of xanthosine was performed. Its dissociation pathways agreed with our assumption.     

Socles of Buchsbaum modules, complexes and posets

The socle of a graded Buchsbaum module is studied and is related to its local cohomology modules. This algebraic result is then applied to face enumeration of Buchsbaum simplicial complexes and posets. In particular, new necessary conditions on face numbers and Betti numbers of such complexes and posets are established. These conditions are used to settle in the affirmative Kühnel's conjecture for the maximum value of the Euler characteristic of a 2k-dimensional simplicial manifold on n vertices as well as Kalai's conjecture providing a lower bound on the number of edges of a simplicial manifold in terms of its dimension, number of vertices, and the first Betti number.     

Mathematical Literacy and Abstraction in the 21st Century

Ed Dubinsky received his Ph.D. in mathematics from the University of Michigan in 1962 and for the next 25 years engaged in research in theoretical mathematics. In the mid‐80′s he became interested in mathematics education and has worked exclusively in the area since then. In his research, he tries to understand how a person's mind might be working when he or she tries to understand mathematical concepts at the postsecondary level. Based on this research, he has conducted large‐scale curriculum development projects in calculus, discrete mathematics, abstract algebra and cooperative learning. He has been editor or co‐editor of UME Trends, Research in Collegiate Mathematics Education, and the Journal of Computers in Mathematics and Science Teaching. He has held faculty positions at 8 universities in 5 countries on 3 continents: Fourah Bey College (Sierra Leone), University of Ghana, Tulane University, McMaster University, Polish Academy of Sciences, Clarkson University, Purdue University, and Georgia State University. Dr. Dubinsky is presently retired and consults with several universities on education matters.     

Investigations of quark fragmentation universality

We propose event cuts in deep inelastic scattering, suitable for an examination of quark fragmentation universality. We compare the current hemisphere of the Breit frame with the hemispheres in annihilation events, using Monte Carlo simulations. The agreement between the two processes is improved after the suggested event cuts are introduced. A method to study the scale evolution in the quark hemispheres using data from fixed-energy experiments is presented. This makes it possible to use the high statistics from LEP1 also at scales below the mass. We also discuss observables which are sensitive to the dynamics of regions closer to the remnant. The observables probe the relatively clean region on the current side of the hardest emission in the event, and can be used to distinguish between different assumptions about remnant effects and mechanisms for the parton evolution. Received: 3 November 1998 / Revised version: 25 January 1999 / Published online: 30 June 1999     

Meaning and Formalism in Mathematics

This essay is an exploration of possible sources (psychological, not mathematical) of mathematical ideas. After a short discussion of plationism and constructivism, there is a brief review of some suggestions for these sources that have been put forward by various researcher (including this author). These include: mental representations, deductive reasoning, metaphors, natural language, and writing computer programs.The problem is then recast in terms of the relation between meaning and formalism. On one hand, formalism can be seen as a tool for expressing meaning that is already present in an individual's mind. On the other hand, and the discussion of this point is the main contribution of this paper, it is not only possible, but a standard activity of mathematicians, to use formalism to construct meaning and this can also be a source of mathematical ideas.Although using formalism to construct meaning is a very difficult method for students to learn, it may be that this is the only route to learning large portions of mathematics at the upper high school and tertiary levels. The essay ends with an outline of a pedagogical strategy for helping students travel this route.This revised version was published online in September 2005 with corrections to the Cover Date.     

Multidisciplinary characterization of novel emulsion polymers

A series of novel emulsion styrene‐butadiene copolymer blends were characterized using a multidisciplinary approach involving both analytical and rheological measurements. The blends were composed of 50/50 w/w high molecular weight (ca. 800,000 Da) ESBR and low molecular weight (ca. 200,000 Da) ESBR, each component having a different bound styrene level. When the difference in bound styrene between the two components was greater than 18%, a two phase co‐continuous morphology was observed by scanning probe microscopy, consistent with two glass transitions measured by temperature modulated DSC. Molecular weight and molecular weight distributions were characterized by both size exclusion chromatography and thermal field flow fractionation with multiangle light scattering detection. ThFFF was unique in its ability to detect ultra‐high molecular weight (> 10⁷ Da) fractions suggesting that traditional SEC often under‐estimates polymer molecular weight. Blending polymers of different molecular weights and styrene levels resulted in reduced molecular weight between entanglements which, based on rheological measurements, would be expected to improve processability.