Fundamental solutions for a class of non-elliptic homogeneous differential operators

We compute temperate fundamental solutions of homogeneous differential operators with real-principal type symbols. Via analytic continuation of meromorphic distributions, fundamental solutions for these non-elliptic operators can be constructed in terms of radial averages and invariant distributions on the unit sphere.     

Spectroscopic and crystallographic characterization of "alternative resting" and "resting oxidized" enzyme forms of bilirubin oxidase: implications for activity and electrochemical behavior of multicopper oxidases

While there is broad agreement on the catalytic mechanism of multicopper oxidases (MCOs), the geometric and electronic structures of the resting trinuclear Cu cluster have been variable, and their relevance to catalysis has been debated. Here, we present a spectroscopic characterization, complemented by crystallographic data, of two resting forms occurring in the same enzyme and define their interconversion. The resting oxidized form shows similar features to the resting form in Rhus vernicifera and Trametes versicolor laccase, characterized by "normal" type 2 Cu electron paramagnetic resonance (EPR) features, 330 nm absorption shoulder, and a short type 3 (T3) Cu-Cu distance, while the alternative resting form shows unusually small A(||) and high g(||) EPR features, lack of 330 nm absorption intensity, and a long T3 Cu-Cu distance. These different forms are evaluated with respect to activation for catalysis, and it is shown that the alternative resting form can only be activated by low-potential reduction, in contrast to the resting oxidized form which is activated via type 1 Cu at high potential. This difference in activity is correlated to differences in redox states of the two forms and highlights the requirement for efficient sequential reduction of resting MCOs for their involvement in catalysis.     

The effect of annealing on the surface morphology of strained and unstrained InxAl1−xN thin films

In_xAl_1−xN is a particularly useful group-III nitride alloy because by adjusting its composition it can be lattice matched to GaN. Such lattice-matched layers may find application in distributed Bragg reflectors (DBRs) and high electron mobility transistors (HEMTs). However, compared with other semiconducting nitride alloys, In_xAl_1-xN has not been researched extensively. In this study, thin In_xAl_1−xN epilayers were grown by metal-organic vapour phase epitaxy (MOVPE) on GaN and Al_yGa_1−yN layers. Samples were subjected to annealing at their growth temperature of 790 °C for varying lengths of time, or alternatively to a temperature ramp to 1000 °C. Their subsequent surface morphologies were analysed by atomic force microscopy (AFM). For both unstrained In_xAl_1−xN epilayers grown on GaN and compressively strained epilayers grown on Al_yGa_1−yN, surface features and fissures were seen to develop as a consequence of thermal treatment, resulting in surface roughening. It is possible that these features are caused by the loss of In-rich material formed on spinodal decomposition. Additionally, trends seen in the strained In_xAl_1−xN layers may suggest that the presence of biaxial strain stabilises the alloy by suppressing the spinode and shifting it to higher indium compositions.     

Rapid nanoscale quantitative analysis of plant sphingolipid long-chain bases by GC-MS

In eukaryotic organisms, sphingolipids are major structural lipids of biological membranes and perform additional essential functions as signalling molecules. While long-chain bases (LCB), the common precursor to all sphingolipid classes, is represented by only one major molecular species in animals and fungi, up to nine LCB have been found in plants. In the absence of genuine plant sphingolipid references required for proper quantification, we have reinvestigated and optimized a protocol destined to the quantification of total plant LCB that relies on the use of gas chromatography-mass spectrometry (GC-MS). This rapid three-step protocol sequentially involves (1) the release of LCB from biological samples using barium hydroxide solution, (2) their oxidation into aldehydes by metaperiodate, and (3) the subsequent identification/quantification of these aldehydes by GC-MS. It is simple and reliable and enables separation of aldehydes upon their stero-specificity. It further enables the quantification of total LCB from a wide variety of samples including yeast and animal cell cultures.     

Copper catalyst activation driven by photoinduced electron transfer: a prototype photolatent click catalyst

PET cat. While the copper(II) tren ketoprofenate precatalyst 1 (see picture) is inactive at room temperature in methanol, it is quantitatively and rapidly reduced to its cuprous state upon light irradiation to provide a highly reactive click catalyst. By simply introducing air into the reaction medium the catalysis can be switched off and then switched on again by bubbling argon followed by irradiation.     

A novel stereoselective one-pot conversion of alcohols into alkyl halides mediated by N,N'-diisopropylcarbodiimide

Alcohols can be converted in high yields to the corresponding alkyl halides in a one-pot procedure via the corresponding O-alkylisourea; very short reaction times are possible when microwave irradiation is used.     

Synthesis of pulvinones via tandem Dieckmann condensation-alkoxide β-elimination

A series of pulvinones were prepared in three steps from a common precursor, methyl 3-phenylglycidate. This compound was readily converted to several diesters containing an ether function. Then, treatment of these compounds with lithium hexamethyldisilazide afforded the corresponding pulvinones, via tandem Dieckmann condensation-alkoxide β-elimination. The use of a 2,2,2-trifluoroethyl ether instead of a methyl ether facilitated the β-elimination and led to better yields of product.     

Semiclassical spectral estimates for Schrödinger operators at a critical energy level. Case of a degenerate minimum of the potential

We study the semi-classical trace formula at a critical energy level for a Schrödinger operator on Rn. We assume here that the potential has a totally degenerate critical point associated to a local minimum. The main result, which computes the contribution of this equilibrium, is valid for all time in a compact and establishes the existence of a total asymptotic expansion whose top order coefficient depends only on the germ of the potential at the critical point.     

Convolutions of semi-classical spectral distributions and periodic-orbit theory

We study the convolution of semi-classical spectral distributions associated to h-pseudodifferential operators on Rn. Under standard assumptions the micro-support of this object can be characterized via families of periodic orbits correlated simultaneously by energy and periods. When all the orbits are non-degenerate the convolution admits, as h tends to 0, an explicit asymptotic expansion in term of the respective dynamical systems. In this setting, this result validates the theory of orbits pairs used by physicists in quantum chaos. Some new contributions, related to the crossing of the period functions, are also analyzed.