On Solutions to Riemann's Functional Equation

In 1921 Hamburger proved that Riemann's functional equation characterizes the Riemann zeta function in the space of functions representable by ordinary Dirichlet series satisfying certain regularity conditions. We consider solutions to a more general functional equation with real weight k. In the case of Hamburger's theorem, k = . We show that, under suitable conditions, the generalized functional equation admits no nontrivial solutions for k > 0 unless k = . Our proof generalizes an elegant proof of Hamburger's theorem given by Siegel, and employs a generalized integral transform.1997 Sunrise Way     

Evidence for Degradation of the Chrome Yellows in Van Gogh’s Sunflowers: A Study Using Noninvasive In Situ Methods and Synchrotron‐Radiation‐Based X‐ray Techniques

This paper presents firm evidence for the chemical alteration of chrome yellow pigments in Van Gogh’s Sunflowers (Van Gogh Museum, Amsterdam). Noninvasive in situ spectroscopic analysis at several spots on the painting, combined with synchrotron‐radiation‐based X‐ray investigations of two microsamples, revealed the presence of different types of chrome yellow used by Van Gogh, including the lightfast PbCrO₄ and the sulfur‐rich PbCr_1?xS_xO₄ (x≈0.5) variety that is known for its high propensity to undergo photoinduced reduction. The products of this degradation process, i.e., Cr^III compounds, were found at the interface between the paint and the varnish. Selected locations of the painting with the highest risk of color modification by chemical deterioration of chrome yellow are identified, thus calling for careful monitoring in the future.     

Elucidating the Color of Rosé Wines Using Polyphenol-Targeted Metabolomics

The color of rosé wines is extremely diverse and a key element in their marketing. It is due to the presence of anthocyanins and of additional pigments derived from them and from other wine constituents. To explore the pigment composition and determine its links with color, 268 commercial rosé wines were analysed. The concentration of 125 polyphenolic compounds was determined by a targeted metabolomics approach using ultra high-performance liquid chromatography coupled to triple quadrupole mass spectrometry (UHPLC-QqQ-MS) analysis in the Multiple Reaction Monitoring (MRM) mode and the color characterised by spectrophotometry and CieLab parameters. Chemometrics analysis of the composition and color data showed that although color intensity is primarily determined by polyphenol extraction (especially anthocyanins and flavanols) from the grapes, different color styles correspond to different pigment compositions. The salmon shade of light rosé wines is mostly due to pyranoanthocyanin pigments, resulting from reactions of anthocyanins with phenolic acids and pyruvic acid, a yeast metabolite. Redness of intermediate color wines is related to anthocyanins and carboxypoyranoanthocyanins and that of dark rosé wines to products of anthocyanin reactions with flavanols while yellowness of these wines is associated to oxidation.