Consistency of general bootstrap methods for degenerate -type and -type statistics

We provide general results on the consistency of certain bootstrap methods applied to degree-2 degenerate statistics of U-type and V-type. While it follows from well known results that the original statistic converges in distribution to a weighted sum of centred chi-squared random variables, we use a coupling idea of Dehling and Mikosch to show that the bootstrap counterpart converges to the same distribution. The result is applied to a goodness-of-fit test based on the empirical characteristic function.     

Hecke group algebras as quotients of affine Hecke algebras at level 0

The Hecke group algebra of a finite Coxeter group , as introduced by the first and last authors, is obtained from by gluing appropriately its 0-Hecke algebra and its group algebra. In this paper, we give an equivalent alternative construction in the case when is the finite Weyl group associated to an affine Weyl group W. Namely, we prove that, for q not a root of unity of small order, is the natural quotient of the affine Hecke algebra H(W)(q) through its level 0 representation.The proof relies on the following core combinatorial result: at level 0 the 0-Hecke algebra H(W)(0) acts transitively on . Equivalently, in type A, a word written on a circle can be both sorted and antisorted by elementary bubble sort operators. We further show that the level 0 representation is a calibrated principal series representation M(t) for a suitable choice of character t, so that the quotient factors (non-trivially) through the principal central specialization. This explains in particular the similarities between the representation theory of the 0-Hecke algebra and that of the affine Hecke algebra H(W)(q) at this specialization.     

Isothermal desorption measurements of self-diffusion in supercooled o-terphenyl

Isothermal desorption of o-terphenyl thin-film bilayers was used to measure self-diffusion coefficients of supercooled o-terphenyl near the glass transition temperature (Tg=243 K). Diffusion coefficients from 10(-15.5) to 10(-12) cm2 s(-1) were obtained between 246 and 265 K. Protio and deuterio o-terphenyl were sequentially vapor deposited, then annealed to simultaneously diffuse and desorb the sample in a vacuum chamber. During the desorption of the bilayer, the concentration of each isotope was detected by a mass spectrometer, which revealed the extent of interfacial broadening. In these experiments, isotopic interdiffusion is indistinguishable from self-diffusion and the measured interfacial broadening is consistent with Fickian diffusion. The samples prepared under several different deposition conditions yielded the same self-diffusion coefficients, indicating that the experiments were conducted in the equilibrium supercooled liquid state.     

Effect of noise on the classical and quantum mechanical nonlinear response of resonantly coupled anharmonic oscillators

Multidimensional infrared spectroscopy probes coupled molecular vibrations in complex, condensed phase systems. Recent theoretical studies have focused on the analytic structure of the nonlinear response functions required to calculate experimental observables in a perturbative treatment of the radiation-matter interaction. Classical mechanical nonlinear response functions have been shown to exhibit unbounded growth for anharmonic, integrable systems, as a consequence of the nonlinearity of classical mechanics, a feature that is absent in a quantum mechanical treatment. We explore the analytic structure of the third-order vibrational response function for an exactly solvable quantum mechanical model that includes some of the important and theoretically challenging aspects of realistic models of condensed phase systems: anharmonicity, resonant coupling, fluctuations, and a well-defined classical mechanical limit.     

Mechanistic implications in the Morita-Baylis-Hillman alkylation: isolation and characterization of an intermediate

An intermediate phosphonium salt has never been isolated from the Morita-Baylis-Hillman (MBH) reaction. Due to the weakly basic counterion produced in the MBH alkylation and allylation reactions, the reaction can be stopped after electrophilic attack on the zwitterionic enolate and an intermediate isolated. Upon analysis of the crystal structure, a trans geometry is observed, suggesting that there is no electrostatic interaction between phosphorus and oxygen in the zwitterionic enolate that undergoes alkylation, thus giving new mechanistic insight into the MBH reaction.     

A dynamic tricopper double helicate

The reaction between 8-aminoquinoline, 1,10-phenantholine-2,9-dicarbaldehyde, and copper(I) tetrafluoroborate gave a quantitative yield of a tricopper double helicate. The presence of dynamic covalent imine (C=N) bonds allowed this assembly to participate in two reactions not previously known in helicate chemistry: 1) It could be prepared through subcomponent substitution from a dicopper double helicate that contained aniline residues. An electron-poor aniline was quantitatively displaced; a more electron-rich aniline competed effectively with the aminoquinoline, setting up an equilibrium between dicopper and tricopper helicates that could be displaced towards the tricopper through the addition of further copper(I). 2) Both dicopper and tricopper helicates could be prepared simultaneously from a mixture of phenanthroline dialdehyde, aniline, and aminoquinoline, which contained all possible imine condensation products in equilibrium. Following the addition of copper(I), thermodynamic equilibration on both covalent and coordinative levels eliminated all partially-formed and mixed imine ligands from the mixture, leaving the helicates as exclusive products.     

Synthesis of zirconia monoliths for chromatographic separations

The aim of this work is to join the advantages of two different kinds of stationary phases: monolithic columns and zirconia-based supports. On the one hand, silica monolithic columns allow a higher efficiency with a lower back-pressure than traditional packed columns. On the other hand, chromatographic stationary phases based on zirconia have a higher thermal and chemical stability and specific surface properties. Combining these advantages, a zirconia monolith with a macroporous framework could be a real improvement in separation sciences. Two main strategies can be used in order to obtain a zirconia surface on a monolithic skeleton: coating or direct synthesis. The coverage by a zirconia layer of the surface of a silica-based monolith can be performed using the chemical properties of the silanol surface groups. We realized this coverage using zirconium alkoxide and we further grafted n-dodecyl groups using phosphate derivatives. Any loss of efficiency was observed and fast separations have been achieved. The main advance reported in this paper is related to the preparation of zirconia monoliths by a sol-gel process starting from zirconium alkoxide. The synthesis parameters (hydrolysis ratio, porogen type, precursor concentration, drying step, etc.) were defined in order to produce a macroporous zirconia monoliths usable in separation techniques. We produced various homogeneous structures: zirconia rod 2 cm long with a diameter of 2.3 mm, and zirconia monolith inside fused silica capillaries with a 75 microm I.D. These monoliths have a skeleton size of 2 microm and have an average through pore size of 6 microm. Several separations have been reported.     

High resolution 1H detected 1H,13C correlation spectra in MAS solid-state NMR using deuterated proteins with selective 1H,2H isotopic labeling of methyl groups

MAS solid-state NMR experiments applied to biological solids are still hampered by low sensitivity and resolution. In this work, we employ a deuteration scheme in which individual methyl groups are selectively protonated. This labeling scheme allows the acquisition of proton carbon correlation spectra with a resolution comparable to that in solution-state NMR experiments. We observe an increase in resolution by a factor of 10-15 compared to standard heteronuclear correlation experiments using PMLG for 1H,1H dipolar decoupling in the indirect dimension. At the same time, the full sensitivity of the proton-based experiment is retained. In comparison to the heteronuclear detected version of the experiment, a gain in sensitivity of a factor of approximately 4.7 is achieved.     

Better characterization of surface organometallic catalysts through resolution enhancement in proton solid state NMR spectra

Delayed-acquisition methods, namely, echo and constant-time-acquisition approaches, allow a significant improvement in resolution in the proton solid state NMR spectra of surface organometallic catalysts such as [syn-(SiO)Mo(=NAr)(=CH(t)Bu)(CH2(t)Bu)] and [(SiO)Re(C(t)Bu)(=CH(t)Bu)(CH2(t)Bu)] (syn/anti ratio = 1:1). This enables the observation of all of the proton resonances, which is not possible with the simple proton single-pulse technique under magic-angle spinning. For example, the methylene protons of the neopentyl ligands, buried in the large peak associated with all of the methyls in the 1H MAS spectrum, can easily be identified by recording a delayed-acquisition spectrum (resolution enhancement of a factor of 3 is obtained). Moreover, combining constant-time acquisition with heteronuclear carbon-proton correlation spectroscopy also improves the resolution of the 2D HETCOR spectra.     

Use of molybdate as novel complex-forming selector in the analysis of polyhydric phenols by capillary zone electrophoresis

Molybdate was examined as a complex-forming additive to the CE background electrolytes (BGE) to affect the selectivity of separation of polyhydric phenols such as flavonoids (apigenin, hyperoside, luteolin, quercetin and rutin) and hydroxyphenylcarboxylic acids (ferulic, caffeic, p-coumaric and chlorogenic acid). Effects of the buffer concentrations and pH and the influence of molybdate concentration on the migration times of the analytes were investigated. In contrast to borate (which is a buffering and complex-forming agent generally used in CE at pH ≥9) molybdate forms more stable complexes with aromatic o-dihydroxy compounds and hence the complex-formation effect is observed at considerably lower pH. Model mixtures of cinnamic acid, ferulic acid, caffeic acid and 3-hydroxycinnamic acid were separated with 25 mM morpholinoethanesulfonic acid of pH 5.4 (adjusted with Tris) containing 0.15 mM sodium molybdate as the BGE (25 kV, silica capillary effective length 45 cm × 0.1 mm I.D., UV-vis detection at 280 nm). With 25 mM 2-hydroxy-3-[4-(2-hydroxyethyl)-1-piperazinyl]propanesulphonic acid/Tris of pH^* 7.4 containing 2 mM sodium molybdate in aqueous 25% (v/v) methanol as the BGE mixtures of all the above mentioned flavonoids, p-coumaric acid and chlorogenic acid could be separated (the same capillary as above, UV-vis detection at 263 nm). The calibration curves (analyte peak area versus concentration) were rectilinear (r > 0.998) for ≈8-35 μg/ml of an analyte (with 1-nitroso-2-naphthol as internal standard). The limit of quantification values ranged between 1.1 mg l⁻¹ for p-coumaric acid and 2.8 mg l⁻¹ for quercetin. The CE method was employed for the assay of flavonoids in medicinal plant extracts. The R.S.D. values ranged between 0.9 and 4.7% (n = 3) when determining luteolin (0.08%) and apigenin (0.92%) in dry Matricaria recutita flowers and rutin (1.03%) and hyperoside (0.82%) in dry Hypericum perforatum haulm. The recoveries were >96%.