Commutative quantum operator algebras

A key notion bridging the gap between quantum operator algebras [26] and vertex operator algebras [4, 9] is the definition of the commutativity of a pair of quantum operators (see Section 2). This is not commutativity in any ordinary sense, but it is clearly the correct generalization to the quantum context. In [26] we give a definition of a commutative quantum operator algebra. We show in [26] that a vertex operator algebra gives rise to a special case of a CQOA. The main purpose of the current paper is to further develop the foundations for a complete mathematical theory of CQOAs. We give proofs of most of the relevant results announced in [26], and we carry out some calculations with sufficient detail to enable the interested reader to become proficient with the algebra of commuting quantum operators.     

The cages, dynamics, and structuring of incipient methane clathrate hydrates

Interest in describing clathrate hydrate formation mechanisms spans multiple fields of science and technical applications. Here, we report findings from multiple molecular dynamics simulations of spontaneous methane clathrate hydrate nucleation and growth from fully demixed and disordered two-phase fluid systems of methane and water. Across a range of thermodynamic conditions and simulation geometries and sizes, a set of seven cage types comprises approximately 95% of all cages formed in the nucleated solids. This set includes the ubiquitous 5(12) cage, the 5(12)6(n) subset (where n ranges from 2-4), and the 4(1)5(10)6(n) subset (where n also ranges from 2-4). Transformations among these cages occur via water pair insertions/removals and rotations, and may elucidate the mechanisms of solid-solid structural rearrangements observed experimentally. Some consistency is observed in the relative abundance of cages among all nucleation trajectories. 5(12) cages are always among the two most abundant cage types in the nucleated solids and are usually the most abundant cage type. In all simulations, the 5(12)6(n) cages outnumber their 4(1)5(10)6(n) counterparts with the same number of water molecules. Within these consistent features, some stochasticity is observed in certain cage ratios and in the long-range ordering of the nucleated solids. Even when comparing simulations performed at the same conditions, some trajectories yield swaths of multiple adjacent sI unit cells and long-range order over 5 nm, while others yield only isolated sI unit cells and little long-range order. The nucleated solids containing long-range order have higher 5(12)6(2)/5(12) and 5(12)6(3)/4(1)5(10)6(2) cage ratios when compared to systems that nucleate with little long-range order. The formation of multiple adjacent unit cells of sI hydrate at high driving forces suggests an alternative or addition to the prevailing hydrate nucleation hypotheses which involve formation through amorphous intermediates.     

A Construction of Generalized Harish-Chandra Modules for Locally Reductive Lie Algebras

We study cohomological induction for a pair $ {\left( {\mathfrak{g},\mathfrak{k}} \right)} $ , $ \mathfrak{g} $ being an infinitedimensional locally reductive Lie algebra and $ \mathfrak{k} \subset \mathfrak{g} $ being of the form $ \mathfrak{k}_{0} \subset C_{\mathfrak{g}} {\left( {\mathfrak{k}_{0} } \right)} $ , where $ \mathfrak{k}_{0} \subset \mathfrak{g} $ is a finite-dimensional reductive in $ \mathfrak{g} $ subalgebra and $ C_{\mathfrak{g}} {\left( {\mathfrak{k}_{0} } \right)} $ is the centralizer of $ \mathfrak{k}_{0} $ in $ \mathfrak{g} $ . We prove a general nonvanishing and $ \mathfrak{k} $ -finiteness theorem for the output. This yields, in particular, simple $ {\left( {\mathfrak{g},\mathfrak{k}} \right)} $ -modules of finite type over k which are analogs of the fundamental series of generalized Harish-Chandra modules constructed in [PZ1] and [PZ2]. We study explicit versions of the construction when $ \mathfrak{g} $ is a root-reductive or diagonal locally simple Lie algebra.     

Effect of environmental weathering on flexural creep behavior of long fiber-reinforced thermoplastic composites

Flexural creep behavior of nylon 6/6 (NY66)- and polypropylene (PP)- based long fiber (l/d = 2000−10 000) thermoplastic (LFT) composites was investigated as a function of ultraviolet irradiation and moisture absorption. Extrusion/compression-molded panels were prepared according to ASTM D-2990 and conditioned according to ASTM D-618. NY66 and PP LFTs were characterized using scanning electron microscopy (SEM), differential scanning calorimetry (DSC), and Fourier-transform infrared (FTIR) spectroscopy in the unexposed condition, and as-exposed to 253.7 nm UV radiation. The creep compliance of PP LFT increased with increasing UV exposure, whereas the creep compliance of NY66 LFT showed a moderate decrease with increasing UV exposure. Moisture absorption experiments were performed in boiling water until saturation on NY66 and its LFT composites. Characterization of desorbed moisture absorption specimens suggested slight variation in the structure, and an analysis of creep compliances showed minimal changes as compared to the dry/unexposed specimens.     

A review of analytical methods for the identification and quantification of hydrocarbons found in jet propellant 8 and related petroleum based fuels

Jet propellant 8 (JP-8) is a complex mixture of compounds that varies from batch to batch. Quantification of various compound classes of JP-8, including BTEX, PAHs and VOCs, has been accomplished. Very few papers have tackled total JP-8 quantification because of its complexity. The components in JP-8 tend to co-elute and present at low concentrations, often nondetectable. JP-8 is the major source of chemical exposure for Department of Defense personnel and a potential hazard for civilians and marine animals. Some components of JP-8 have been identified as possible human carcinogens and have been studied extensively. Development of analytical methods to analyze the components of this fuel are essential to measure the extent of exposure, as well as the short-term and long-term exposure in rodents, humans and marine life. To date, JP-8 has been examined in urine, blood, contaminated water and fish tissue. This paper reviews methods currently utilized in the literature for the analysis of JP-8 and its components. This paper also discusses extraction methods and detectors commonly used in JP-8 and hydrocarbon analysis in general. Finally, the effects of exposure and the future of JP-8 and petroleum analysis with respect to human health are discussed.     

Spin polarized La0.7Sr0.3MnO3 thin films on silicon

La_0.7Sr_0.3MnO₃ polycrystalline manganite thin films were grown on silicon (Si) substrates covered by SiO_x amorphous native oxide. Curie temperatures of about 325 K were achieved for 70-nm-thick films. Strong room temperature XMCD signal was detected indicating high spin polarization at the surface. Cross-sectional TEM images show sharp interface between SiO_x and manganite without signature of chemical reaction at the interface. Unusual sharp splitting of the manganite film was observed: on the top of a transition layer characterized by low crystalline order, a magnetically robust layer is formed.     

Comparison of the adsorption of N2 on Ru(1 0 9) and Ru(0 0 1) - A detailed look at the role of atomic step and terrace sites

We present a direct side-by-side comparison of the adsorption and desorption of nitrogen on the atomically-stepped Ru(1 0 9) surface and the atomically-flat Ru(0 0 1) surface. Both infrared reflection absorption spectroscopy (IRAS) and temperature programmed desorption (TPD) are employed in this study, along with density functional theory (DFT). We find that the chemisorptive terminal binding of N₂ is stronger on the atomic step sites than on the terrace sites of Ru(1 0 9) as indicated by TPD and by a reduction of the singleton vibrational frequency, ν(N₂), by ∼9 cm⁻¹, comparing steps to terraces. In addition, we find that metal-metal compression effects on the terrace sites of Ru(1 0 9) cause stronger binding of N₂ than found on the Ru(0 0 1) surface, as indicated by a reduction of the terrace-N₂ singleton vibrational frequency by ∼11 cm⁻¹ when compared to the singleton N₂ mode on Ru(0 0 1). These spectroscopic results, comparing compressed terrace sites to Ru(0 0 1) sites and confirmed by TPD and DFT, indicate that N₂ bonds primarily as a σ-donor to Ru. Using equimolar ¹⁵N₂ and ¹⁴N₂, it is found that dynamic dipole coupling effects present at higher N₂ coverages may be partially eliminated by isotopically detuning neighbor oscillators. These experiments, considered together, indicate that the order of the bonding strength for terminal-N₂ on Ru is: atomic steps > atomic terraces > Ru(0 0 1). DFT calculations also show that 4-fold coordinated N₂ may be stabilized in several structures on the double-atom wide steps of Ru(1 0 9) and that this form of bonding produces substantial decreases in the N₂ vibrational frequency and increases in the binding energy, compared to terminally-bound N₂. These highly coordinated N₂ species are not observed by IRAS.     

Investigation of microphones as near-ground sensors for seismic detection of buried landmines

Commercially available microphones were investigated as near-ground sensors to measure the acoustic pressure and the vertical pressure gradient of evanescent air-acoustic waves associated with audio-frequency seismic waves. Measurements in close proximity to the surface and the use of waveguides were found to improve the microphone signal's quality, the comparison of its seismic sensitivity to its sensitivity to propagating sound (ambient acoustic noise and nonseismic reverberation). Landmine images formed using microphone data collected in a laboratory experimental model clearly locate buried inert landmines but exhibit more clutter than images of the same objects formed with seismic displacement data collected using other techniques.     

Synthesis and solid-phase application of suitably protected gamma-hydroxyvaline building blocks

Recently, an unexpected modified residue, gamma-hydroxy-D-valine (D-Hyv), was identified within ribosomally expressed polypeptide chains of four conopeptides from the venoms of Conus gladiator and Conus mus. To assemble Hyv-containing peptides, we have explored several routes for the synthesis of appropriately functionalized Hyv building blocks. D-Hyv was produced from D-Val by using a variation of the previously published K2PtCl4/CuCl2 oxidative method. Direct synthesis of Boc- or Cbz-D-Hyv lactone proceeded in low yield; additionally, the lactones are too unreactive for solid-phase applications. 9-Borabicyclononane or copper-complexed D-Hyv was prepared and treated with tert-butyldimethylsilyl trifluoromethanesulfonate (TBDMSOTf) to produce D-Hyv(O-TBDMS). The most efficient complex disruption was achieved by Chelex 110 resin (Na+ form) treatment of copper-complexed D-Hyv(O-TBDMS). Reaction of D-Hyv(O-TBDMS) with Fmoc-OSu produced Fmoc-D-Hyv(O-TBDMS) in 26% yield from D-Val. The Fmoc-D-Hyv(O-TBDMS) diastereomers were separated by preparative RP-HPLC in 13% yield from D-Val. Fmoc-D-Hyv(O-TBDMS) was used for the synthesis of the conopeptide gld-V* from Conus gladiator. The isolated synthetic and natural products had coincidental mass and NMR spectra. The methodology presented herein will greatly facilitate biological studies of Hyv-containing sequences, such as receptor responses to hydroxylated versus nonhydroxylated conopeptides and the relative susceptibility of proteins to modification by oxidative stress.