Change point estimation for a stochastic heat equation

We study a change point model based on a stochastic partial differential equation (SPDE) corresponding to the heat equation governed by the weighted Laplacian $\Delta_\vartheta = \nabla\vartheta\nabla$, where $\vartheta=\vartheta(x)$ is a space-dependent diffusivity. As a basic problem the domain $(0,1)$ is considered with a piecewise constant diffusivity with a jump at an unknown point $\tau$. Based on local measurements of the solution in space with resolution $\delta$ over a finite time horizon, we construct a simultaneous M-estimator for the diffusivity values and the change point. The change point estimator converges at rate $\delta$, while the diffusivity constants can be recovered with convergence rate $\delta^{3/2}$. Moreover, when the diffusivity parameters are known and the jump height vanishes with the spatial resolution tending to zero, we derive a limit theorem for the change point estimator and identify the limiting distribution. For the mathematical analysis, a precise understanding of the SPDE with discontinuous $\vartheta$, tight concentration bounds for quadratic functionals in the solution, and a generalisation of classical M-estimators are developed

HPLC–HR-ESI–MS/MS identification of fluorescent dyes and optical brighteners and their degradation products in daylight fluorescent paints

Abstract Daylight fluorescent paints are luminous colors that are increasingly used in contemporary art. The pigments consist of a synthetic resin in which fluorescent dyes and optical brighteners are embedded. In the recent years, several research articles have been published on the composition of daylight fluorescent pigments. Despite the growing research on the aging behavior of daylight fluorescent paints, little is known to date about the chemical processes involved in aging. In the research presented here, we used dialysis to separate the colorants from the resin. HPLC–HR-ESI–MS/MS was used to extend the elucidation of the dye composition. A variety of rhodamines and coumarins, an aminonaphthalimide dye and another optical brightener were determined. NMR was used to elucidate the structure of an additional hemicyanine dye not listed in the Colour Index. Furthermore, reference substances were artificially aged under visible light and UV radiation and the degradation products were analyzed accordingly. N-deethylation, hydroxylation and higher oxidation processes were found to be the main degradation pathways for all colorants. For most dyes and optical brighteners, there was no difference between aging under visible light and aging under UV radiation. When the results were checked on samples of aged paint mock-ups, it was found that only a few of the degradation products can still be detected in the case of very advanced aging even with the smallest sample quantities

Solid-state NMR spectroscopic studies of 13C,15N,29Si-enriched biosilica from the marine diatom Cyclotella cryptica

Diatoms are algae producing micro- and nano-structured cell walls mainly containing amorphous silica. The shape and patterning of these cell walls is species-specific. Herein, the biosilica of Cyclotella cryptica , a centric marine diatom with a massive organic matrix, is studied. Solid-state NMR spectroscopy is applied to gain deeper insight into the interactions at the organic–inorganic interface of the cell walls. The various organic compounds like polysaccharides as well as proteins and long-chain polyamines (LCPAs) are detected by observation of heteronuclei like 13 C and 15 N whereas the silica phase is studied using 29 Si NMR spectroscopy. The sensitivity of the NMR experiments is strongly enhanced by isotope-labeling of the diatoms during cultivation with 13 C, 15 N and 29 Si. The presence of two different chitin species in the biosilica is demonstrated. This observation is supported by a monosaccharide analysis of the silica-associated organic matrix where a high amount of glucosamine is found. Moreover, the Rotational Echo Double Resonance (REDOR) experiment provides distance information for heteronuclear spins. 13 C{ 29 Si} REDOR experiments reveal proximities between different organic compounds and the silica phase. The closest contacts between silica and organic compounds appear for different signals in the 13 C-chemical shift range of 40–60 ppm, the typical range for LCPAs

Solid-state NMR spectroscopic studies of 13C,15N,29Si-enriched biosilica from the marine diatom Cyclotella cryptica

Diatoms are algae producing micro- and nano-structured cell walls mainly containing amorphous silica. The shape and patterning of these cell walls is species-specific. Herein, the biosilica of Cyclotella cryptica , a centric marine diatom with a massive organic matrix, is studied. Solid-state NMR spectroscopy is applied to gain deeper insight into the interactions at the organic–inorganic interface of the cell walls. The various organic compounds like polysaccharides as well as proteins and long-chain polyamines (LCPAs) are detected by observation of heteronuclei like 13 C and 15 N whereas the silica phase is studied using 29 Si NMR spectroscopy. The sensitivity of the NMR experiments is strongly enhanced by isotope-labeling of the diatoms during cultivation with 13 C, 15 N and 29 Si. The presence of two different chitin species in the biosilica is demonstrated. This observation is supported by a monosaccharide analysis of the silica-associated organic matrix where a high amount of glucosamine is found. Moreover, the Rotational Echo Double Resonance (REDOR) experiment provides distance information for heteronuclear spins. 13 C{ 29 Si} REDOR experiments reveal proximities between different organic compounds and the silica phase. The closest contacts between silica and organic compounds appear for different signals in the 13 C-chemical shift range of 40–60 ppm, the typical range for LCPAs