Boundaries of weak peak points in noncommutative algebras of Lipschitz functions

It has been shown that any Banach algebra satisfying ‖f ²‖ = ‖f‖² has a representation as an algebra of quaternion-valued continuous functions. Whereas some of the classical theory of algebras of continuous complex-valued functions extends immediately to algebras of quaternion-valued functions, similar work has not been done to analyze how the theory of algebras of complex-valued Lipschitz functions extends to algebras of quaternion-valued Lipschitz functions. Denote by Lip(X, \mathbbF\mathbb{F}) the algebra over R of F-valued Lipschitz functions on a compact metric space (X, d), where \mathbbF\mathbb{F} = ℝ, ℂ, or ℍ, the non-commutative division ring of quaternions. In this work, we analyze a class of subalgebras of Lip(X, \mathbbF\mathbb{F}) in which the closure of the weak peak points is the Shilov boundary, and we show that algebras of functions taking values in the quaternions are the most general objects to which the theory of weak peak points extends naturally. This is done by generalizing a classical result for uniform algebras, due to Bishop, which ensures the existence of the Shilov boundary. While the result of Bishop need not hold in general algebras of quaternion-valued Lipschitz functions, we give sufficient conditions on such an algebra for it to hold and to guarantee the existence of the Shilov boundary.     

Structural stability and optical properties of nanomaterials with reconstructed surfaces

We present density functional and quantum Monte Carlo calculations of the stability and optical properties of semiconductor nanomaterials with reconstructed surfaces. We predict the relative stability of silicon nanostructures with reconstructed and unreconstructed surfaces, and we show that surface step geometries unique to highly curved surfaces dramatically reduce the optical gaps and decrease excitonic lifetimes. These predictions provide an explanation of both the variations in the photoluminescence spectra of colloidally synthesized nanoparticles and observed deep gap levels in porous silicon.     

Beliefs,Practical Knowledge,and Context: A Longitudinal Study of a Beginning Biology Teacher's 5E Unit

The purpose of this three‐year case study was to understand how a beginning biology teacher (Alice) designed and taught a 5E unit on natural selection, how the unit changed when she took a position in a different school district, and why the changes occurred. We examined Alice's developing beliefs about science teaching and learning, practical knowledge, and perceptions of school context in relation to the 5E unit. Data sources consisted of interviews, classroom observations, and lesson materials. We found that Alice placed more emphasis on the explore phase, less emphasis on the engage and explain phases, and removed the elaborate phase over time. Alice's beliefs about science teaching and learning acted as a filter for making sense of practical knowledge and perceptions of context. Although her beliefs were student centered, they aligned with discovery learning in which little intervention from the teacher is required. We discuss how her beliefs, practical knowledge, and perceptions of context explained the changes in her practice. This study sheds insight into the nature of beliefs and how they relate to the 5E lesson phases, as well as the different lenses for viewing the 5E instructional model. Implications for science teacher preparation and induction programs are discussed.     

Not All Fluorescent Nanodiamonds Are Created Equal: A Comparative Study

Fluorescent nanodiamonds (FNDs) are vital to many emerging nanotechnological applications, from bioimaging and sensing to quantum nanophotonics. Yet, understanding and engineering the properties of fluorescent defects in nanodiamonds remain challenging. The most comprehensive study to date is presented, of the optical and physical properties of five different nanodiamond samples, in which fluorescent nitrogen‐vacancy (NV) centers are created using different fabrication techniques. The FNDs' fluorescence spectra, lifetime, and spin relaxation time (T₁) are investigated via single‐particle confocal fluorescence microscopy and in ensemble measurements in solution (T₁ excepted). Particle sizes and shapes are determined using scanning electron microscopy and correlated with the optical results. Statistical tests are used to explore correlations between the properties of individual particles and also analyze average results to directly compare different fabrication techniques. Spectral unmixing is used to quantify the relative NV charge‐state (NV^? and NV⁰) contributions to the overall fluorescence. A strong variation is found and quantified in the properties of individual particles within all analyzed samples and significant differences between the different particle types. This study is an important contribution toward understanding the properties of NV centers in nanodiamonds. It motivates new approaches to the improved engineering of NV‐containing nanodiamonds for future applications.     

Long-term trend in CHF2Cl (HCFC-22) from high spectral resolution infrared solar absorption measurements and comparison with in situ measurements

The average tropospheric volume mixing ratio of CHF₂Cl (HCFC-22) has been retrieved from a time series of high spectral resolution ground-based infrared solar absorption spectra recorded with the McMath Fourier transform spectrometer located at the U.S. National Solar Observatory facility on Kitt Peak in southern Arizona (31.9°N, 111.6°W, 2.09 km altitude) for the time period October 1987–November 2002. The retrievals are based on fits to the well-isolated, unresolved 2ν₆ Q branch at 829.05 cm⁻¹ and the SFIT2 retrieval algorithm. The measured daily averages show a near linear rise per year in the mean tropospheric volume mixing ratio as a function of time with a best fit yielding an average increase rate of (5.66±0.15) parts per trillion (10⁻¹²) by volume per year, corresponding to (6.47±0.17)%yr⁻¹, 1 sigma, at the beginning of the time series. The tropospheric mixing ratios retrieved from the solar spectra have been compared with monthly average surface flask sampling measurements from the Climate Monitoring and Diagnostic Laboratory (CMDL) station at Niwot Ridge, Colorado (40.0°N, 105.5°W, 3013 m altitude), archived measurement from the same location, and early CMDL northern hemisphere Pacific cruise measurements. The average ratio of the retrieved tropospheric mixing ratio relative to the CMDL surface mixing ratio is 1.053 for the overlapping 1987 to 2002 time period. The retrieved mean tropospheric mixing ratio is consistent with the surface measurements within the errors estimated for the remote sensing observations.     

Interconverting Lanthanum Hydride and Borohydride Catalysts for C=O Reduction and C−O Bond Cleavage

The high catalytic reactivity of homoleptic tris(alkyl) lanthanum La{C(SiHMe₂)₃}₃ is highlighted by C?O bond cleavage in the hydroboration of esters and epoxides at room temperature. The catalytic hydroboration tolerates functionality typically susceptible to insertion, reduction, or cleavage reactions. Turnover numbers (TON) up to 10 000 are observed for aliphatic esters. Lanthanum hydrides, generated by reactions with pinacolborane, are competent for reduction of ketones but are inert toward esters. Instead, catalytic reduction of esters requires activation of the lanthanum hydride by pinacolborane.     

Heterogeneous Solution NMR Signal Amplification by Reversible Exchange

A novel variant of an iridium‐based organometallic catalyst was synthesized and used to enhance the NMR signals of pyridine in a heterogeneous phase by immobilization on polymer microbead solid supports. Upon administration of parahydrogen (pH₂) gas to a methanol mixture containing the HET‐SABRE catalyst particles and the pyridine, up to fivefold enhancements were observed in the ¹H NMR spectra after sample transfer to high field (9.4 T). Importantly, enhancements were not due to any residual catalyst molecules in solution, thus supporting the true heterogeneity of the SABRE process. Further significant improvements may be expected by systematic optimization of experimental parameters. Moreover, the heterogeneous catalyst is easy to separate and recycle, thus opening a door to future potential applications varying from spectroscopic studies of catalysis, to imaging metabolites in the body without concern of contamination from expensive and potentially toxic metal catalysts or accompanying organic molecules.     

A Plausible Simultaneous Synthesis of Amino Acids and Simple Peptides on the Primordial Earth

Following his seminal work in 1953, Stanley Miller conducted an experiment in 1958 to study the polymerization of amino acids under simulated early Earth conditions. In the experiment, Miller sparked a gas mixture of CH₄, NH₃, and H₂O, while intermittently adding the plausible prebiotic condensing reagent cyanamide. For unknown reasons, an analysis of the samples was not reported. We analyzed the archived samples for amino acids, dipeptides, and diketopiperazines by liquid chromatography, ion mobility spectrometry, and mass spectrometry. A dozen amino acids, 10 glycine‐containing dipeptides, and 3 glycine‐containing diketopiperazines were detected. Miller’s experiment was repeated and similar polymerization products were observed. Aqueous heating experiments indicate that Strecker synthesis intermediates play a key role in facilitating polymerization. These results highlight the potential importance of condensing reagents in generating diversity within the prebiotic chemical inventory.     

An LX-10 kinetic model calibrated using simulations of multiple small-scale thermal safety tests

A new chemical kinetic model for the beta-delta transition and decomposition of LX-10 (95% octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine, 5% Viton A binder) is presented here. This model implements aspects of previous kinetic models but calibrates the model parameters to data sets of three experiments: differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), and one-dimensional time to explosion (ODTX). The calibration procedure contains three stages: one stage uses open-pan DSC and TGA to develop a base reaction for formation of heavy gases, a second stage features closed-pan DSC to ascertain the autocatalytic behavior of reactant gases attacking the solid explosive, and a final stage adjusts the rate for the breakdown of heavy reactant gases using ODTX experimental data. The resultant model presents a large improvement in the agreement between simulated DSC and TGA results and their respective experiments while maintaining the same level of agreement with ODTX, scaled thermal explosion, and laser heating explosion times when compared to previous models.     

Yb(OTf)3-catalyzed reactions of 5-alkylidene Meldrum's acids with phenols: one-pot assembly of 3,4-dihydrocoumarins, 4-chromanones, coumarins, and chromones

[reaction: see text] The Yb(OTf)3-catalyzed annulation reactions of phenols with 5-alkylidene Meldrum's acids enabled the synthesis of structurally diverse heterocycles in high isolated yields. A series of 4-substituted 3,4-dihydrocoumarins, 2,2-disubstituted 4-chromanones, coumarins, and 2-substituted chromones were readily and efficiently assembled, including the naturally occurring coumarins citropten, scoparone, and ayapin. Addition of phenols to biselectrophilic 5-alkylidene Meldrum's acids proceeded through two distinct multibond-forming modes: Friedel-Crafts C-alkylation/O-acylation and Friedel-Crafts C-acylation/O-alkylation. The regioselectivity of the catalytic annulation reaction was controlled by the degree of substitution on the alkylidene moiety.