Moduli of twisted spin curves

In this note we give a new, natural construction of a compactification of the stack of smooth -spin curves, which we call the stack of stable twisted -spin curves. This stack is identified with a special case of a stack of twisted stable maps of Abramovich and Vistoli. Realizations in terms of admissible -spaces and -line bundles are given as well. The infinitesimal structure of this stack is described in a relatively straightforward manner, similar to that of usual stable curves.

We construct representable morphisms from the stacks of stable twisted -spin curves to the stacks of stable -spin curves and show that they are isomorphisms. Many delicate features of -spin curves, including torsion free sheaves with power maps, arise as simple by-products of twisted spin curves. Various constructions, such as the -operator of Seeley and Singer and Witten's cohomology class go through without complications in the setting of twisted spin curves.

     

Applying the silver‐tube introduction method for thermal conversion elemental analyses and a new δ2H value for NBS 22 oil

The δ²H_VSMOW–SLAP value of total hydrogen of the international measurement standard NBS 22 oil was determined by a new method of sealing water in silver tubes for use in a thermal conversion elemental analysis (TC/EA) reduction unit. The isotopic fractionation of water due to evaporation is virtually non‐existent in this silver‐tube method. A new value for the δ²H_VSMOW–SLAP of NBS 22 oil, calibrated with isotopic reference waters, was determined to be ?116.9 ± 0.8‰ (1σ and n = 31). Published in 2010 by John Wiley & Sons, Ltd.     

Synthesis and crystal structures of Ni(II), Cu(II) and μ-oxo-Fe(III) complexes of a salen type ligand: Mononuclear versus multinuclear complex formation

The nickel, copper and iron complexes of bis(salicylidene)-meso-1,2-diphenylethylendiaminato (mdpSal^2?) and their propensity to form multinuclear complexes similar to those observed for Co(mdpSal) are reported. The syntheses of the primary compounds were carried out with M(OAc)₂·xH₂O (M = Fe, Ni or Cu) and mdpSalH₂ in methanol. The Ni and Cu reactions resulted in the isolation of mononuclear Ni(mdpSal) (1) and Cu(mdpSal) (2) complexes. Both species 1 and 2 adopt approximate square planar geometries in the monoclinic space group P2₁/n and are iso-structural to the previously reported Co(mdpSal). Although structurally similar, neither 1 nor 2 exhibit comparable reactivity as reported for the cobalt analogue of mdpSal^?2 in forming multinuclear complexes. The iron reaction yielded a μ-oxo species [Fe(mdpSal)]₂O (3) in which each iron center is oxidized to +3 and ligated to one mdpSal^2? ligand frame with each iron center adopting distorted square pyramid geometry. In addition, Co(Salophen) (4) (SalophenH₂ = N,N′-bis(salicylidene)-1,2-phenylenediamine) has been synthesized and its reactivity assessed and compared to Co(mdpSal). Complexes 1–3 have been characterized by X-ray crystallography as well as UV–Vis and IR spectroscopy. A detailed comparison of the structural and spectral characteristics of the iso-structural complexes 1 and 2 with Co(mdpSal) are presented along with a discussion of factors that contributed to the unique reactivity observed for [Co(mdpSal)].     

A synchrotron radiation study of the one‐dimensional complex of sodium with (1S)‐N‐carboxylato‐1‐(9‐deazaadenin‐9‐yl)‐1,4‐dideoxy‐1,4‐imino‐d‐ribitol,a member of the 'immucillin' family

The sodium salt of [immucillin‐A–CO₂H]⁻ (Imm‐A), namely catena‐poly[[[triaquadisodium(I)](μ‐aqua)[μ‐(1S)‐N‐carboxylato‐1‐(9‐deazaadenin‐9‐yl)‐1,4‐dideoxy‐1,4‐imino‐d ‐ribitol][triaquadisodium(I)][μ‐(1S)‐N‐carboxylato‐1‐(9‐deazaadenin‐9‐yl)‐1,4‐dideoxy‐1,4‐imino‐d ‐ribitol]] tetrahydrate], {[Na₂(C₁₂H₁₃N₄O₆)₂(H₂O)₇]·4H₂O}_n, (I), forms a polymeric chain via Na⁺—O interactions involving the carboxylate and keto O atoms of two independent Imm‐A molecules. Extensive N,O—H...O hydrogen bonding utilizing all water H atoms, including four waters of crystallization, provides crystal packing. The structural definition of this novel compound was made possible through the use of synchrotron radiation utilizing a minute fragment (volume ∼2.4 × 10⁻⁵ mm⁻³) on a beamline optimized for protein data collection. A summary of intra‐ring conformations for immucillin structures indicates considerable flexibility while retaining similar intra‐ring orientations.     

Learning a novel phonological contrast depends on interactions between individual differences and training paradigm design

Studies evaluating phonological contrast learning typically investigate either the predictiveness of specific pretraining aptitude measures or the efficacy of different instructional paradigms. However, little research considers how these factors interact--whether different students learn better from different types of instruction--and what the psychological basis for any interaction might be. The present study demonstrates that successfully learning a foreign-language phonological contrast for pitch depends on an interaction between individual differences in perceptual abilities and the design of the training paradigm. Training from stimuli with high acoustic-phonetic variability is generally thought to improve learning; however, we found high-variability training enhanced learning only for individuals with strong perceptual abilities. Learners with weaker perceptual abilities were actually impaired by high-variability training relative to a low-variability condition. A second experiment assessing variations on the high-variability training design determined that the property of this learning environment most detrimental to perceptually weak learners is the amount of trial-by-trial variability. Learners' perceptual limitations can thus override the benefits of high-variability training where trial-by-trial variability in other irrelevant acoustic-phonetic features obfuscates access to the target feature. These results demonstrate the importance of considering individual differences in pretraining aptitudes when evaluating the efficacy of any speech training paradigm.     

High-power broadband laser source tunable from 3.0 μm to 4.4 μm based on a femtosecond Yb:fiber oscillator

We describe a tunable broadband mid-IR laser source based on difference-frequency mixing of a 100?MHz femtosecond Yb:fiber laser oscillator and a Raman-shifted soliton generated with the same laser. The resulting light is tunable over 3.0?μm to 4.4?μm, with a FWHM bandwidth of 170?nm and maximum average output power up to 125?mW. The noise and coherence properties of this source are also investigated and described.     

Novel silver‐tubing method for quantitative introduction of water into high‐temperature conversion systems for stable hydrogen and oxygen isotopic measurements

A new method to seal water in silver tubes for use in a TC/EA (thermal conversion/elemental analyzer) reduction unit using a semi‐automated sealing apparatus can yield reproducibilities (1 standard deviation) of δ²H and δ¹⁸O measurements of 1.0‰ and 0.06‰, respectively. These silver tubes containing reference waters may be preferred for the calibration of H‐ and O‐bearing materials analyzed with a TC/EA reduction unit. The new sealing apparatus employs a computer‐controlled stepping motor to produce silver tubes identical in length. The reproducibility of the mass of water sealed in tubes (in a range of 200–400 µg) can be as good as 1%. Approximately 99% of the sealed silver tubes are satisfactory (leak free). Although silver tubes sealed with reference waters are robust and can be shaken or heated to 110°C with no loss of integrity, they should not be frozen because the expansion during the phase transition of water to ice will break the cold seals and all the water will be lost. The tubes should be shipped in insulated containers. This new method eliminates air inclusions and isotopic fractionation of water associated with the loading of water into capsules using a syringe. The method is also more than an order of magnitude faster than preparing water samples in ordinary Ag capsules. Nevertheless, some laboratories may prefer loading water into silver capsules because expensive equipment is not needed, but users of this method are cautioned to apply the necessary corrections for evaporation, back exchange with laboratory atmospheric moisture, and blanks. Copyright © 2010 John Wiley & Sons, Ltd.     

Evaluating the accuracy of theoretical one‐bond 13C─13C scalar couplings and their ability to predict structure in a natural product

This study explores the feasibility of using a combination of experimental and theoretical 1‐bond ¹³C─¹³C scalar couplings (¹J_CC) to establish structure in organic compounds, including unknowns. Historically, ⁿJ_CC and ⁿJ_CH studies have emphasized 2 and 3‐bond couplings, yet ¹J_CC couplings exhibit significantly larger variations. Moreover, recent improvements in experimental measurement and data processing methods have made ¹J_CC data more available. Herein, an approach is evaluated in which a collection of theoretical structures is created from a partial nuclear magnetic resonance structural characterization. Computed ¹J_CC values are compared to experimental data to identify candidates giving the best agreement. This process requires knowledge of the error in theoretical methods, thus the B3LYP, B3PW91, and PBE0 functionals are evaluated by comparing to 27 experimental values from INADEQUATE. Respective errors of ±1.2, ±3.8, and ±2.3 Hz are observed. An initial test of this methodology involves the natural product 5‐methylmellein. In this case, only a single candidate matches experimental data with high statistical confidence. This analysis establishes the intramolecular hydrogen‐bonding arrangement, ring heteroatom identity, and conformation at one position. This approach is then extended to hydroheptelidic acid, a natural product not fully characterized in prior studies. The experimental/theoretical approach proposed herein identifies a single best‐fit structure from among 26 candidates and establishes, for the first time, 1 configuration and 3 conformations to complete the characterization. These results suggest that accurate and complete structural characterizations of many moderately sized organic structures (<800 Da) may be possible using only ¹J_CC data.