Correlation of nonexponentiality with dynamic heterogeneity from four-point dynamic susceptibility χ4(t) and its approximation χT(t)

Various properties of vitrifying liquids are correlated with the dispersity of the dynamics, the latter reflected in the magnitude of the nonexponentiality parameter, β(K), describing the distribution of relaxation times. These properties include the mean relaxation time, τ(α), the fragility, and the dynamic crossover. The correlations with β(K) are observed in both experimental data and the results from molecular dynamics simulations on Lennard-Jones (LJ) type systems. Another, rather obvious property to correlate with β(K) is the dynamic heterogeneity, which can be quantified from the number of molecules, N(c), dynamically correlated over a time span τ(α). For a given LJ system, N(c) can be rigorously calculated and we find that it does indeed correlate with β(K) over a range of thermodynamic conditions. However, the analysis of experimental data for a broad range of real materials, wherein an approximation is required to obtain N(c), reveals the absence of any relationship between N(c) and β(K) among different materials.     

Rapid and sensitive trace gas detection with continuous wave Optical Parametric Oscillator-based Wavelength Modulation Spectroscopy

A fiber-amplified Distributed Bragg Reflector diode laser is used to pump a continuous wave, singly resonant Optical Parametric Oscillator (OPO). The output radiation covers the 3–4 μm with ability of rapid (100 THz/s) and broad mode-hop-free tuning (5 cm⁻¹). Wavelength Modulation Spectroscopy is combined with the OPO to take optimal advantage of the spectral scan speed. The sensitivity of the system was determined as 0.8 ppbv (parts-per-billion by volume) for ethane (C₂H₆) for the absorption peak at 2996.9 cm⁻¹ recorded in 1.3 seconds, corresponding to a noise equivalent absorption sensitivity (NEAS) of 1.2×10⁻⁹ cm⁻¹/Hz^1/2. A comparison between results using the 1^st, 2^nd and 4^th harmonic derivative signal from wavelength modulation was performed. The broad continuous tunability was demonstrated by covering 35 cm⁻¹ while recording absorption features of ethane, methane and water.     

Addition of Me3SiCN to trifluoromethyl derivates of N‐(pyridylmethylidene) anilines catalyzed by Lewis acids

A series of novel Shiff bases (1a–h) was synthesized by condensation of pyridinecarboxaldehydes (1–4) with 3‐ and 4‐trifluoromethylanilines (5, 6) in the presence of molecular sieves (4 Å). It was found that AlCl₃ and AlBr₃ catalyzed the addition of Me₃SiCN to the C?N bond of the imines obtained, whereas the other Lewis acids studied (YCl₃, LaCl₃, ZnI₂) were not active. The reactivity of the imines in the title reaction, on the whole, correlated with their basicity. Besides the addition giving the expected α‐amino nitriles (2a,b,d–f,h), an unusual reaction leading to unsaturated nitriles (3a–h) was observed. The structures of saturated and unsaturated products 2d and 3c were determined by X‐ray diffraction. Copyright © 2001 John Wiley & Sons, Ltd.     

Metric Inequality, Subdifferential Calculus and Applications

In this paper we establish characterizations of Asplund spaces in terms of conditions ensuring the metric inequality and intersection formulae. Then we establish chain rules for the limiting Fréchet subdifferentials. Necessary conditions for constrained optimization problems with non-Lipschitz data are derived.     

Structural Revision and Elucidation of the Biosynthesis of Hypodoratoxide by 13C,13C COSY NMR Spectroscopy

Feeding of (2,3,4,5,6‐¹³C₅)mevalonolactone to the fungus Hypomyces odoratus resulted in a completely labeled sesquiterpene ether. The connectivity of the carbon atoms was easily deduced from a ¹³C,¹³C COSY spectrum, revealing a structure that was different from the previously reported structure of hypodoratoxide, even though the reported ¹³C NMR data matched. A structural revision of hypodoratoxide is thus presented. Its absolute configuration was tentatively assigned from its co‐metabolite cis‐dihydroagarofuran. Its biosynthesis was investigated by feeding of (3‐¹³C)‐ and (4,6‐¹³C₂)mevalonolactone, which gave insights into the complex rearrangement of the carbon skeleton during terpene cyclization by analysis of the ¹³C,¹³C couplings.     

Diverse Visible-Light-Promoted Functionalizations of Benzotriazoles Inspired by Mechanism-Based Luminescence Screening

Three new visible-light-promoted functionalizations of benzotriazole substrates were discovered using a mechanism-based screening method. ortho-Thiolated, borylated, and alkylated N-arylbenzamide products were obtained under mild reaction conditions in a new denitrogenative synthetic approach to functionalized aniline derivatives. The functional group tolerance of the borylation reaction was further analyzed in the first application of an additive-based robustness screen in a photocatalytic transformation. All the functionalizations proceed via photocatalytically initiated chain mechanisms as indicated by determination of the reaction quantum yields and Stern–Volmer analyses.