Oxidation and Cross-Linking in the Curing of Air-Drying Artists' Oil Paints

In this study, the chemistry of air-drying artist's oil paint curing and aging up to 24 months was studied. The objective is to improve our molecular understating of the processes that lead to the conversion of the fluid binder into a dry film and how this evolves with time, which is at the base of a better comprehension of degradation phenomena of oil paintings and relevant to the artists' paint manufacturing industry. To this aim, a methodological approach based on thermogravimetric (TG) analysis, differential scanning calorimetry (DSC), gas chromatography-mass spectrometry (GC-MS), and analytical pyrolysis coupled with gas chromatography and mass spectrometry (Py-GC-MS) was implemented. Model paintings based on linseed oil and safflower oil (a drying and a semidrying oil, respectively) mixed with two historically relevant pigments - lead white (a through drier) and synthetic ultramarine blue (a pigment often encountered in degraded painting layers) - were investigated. The oil curing under accelerated conditions (80 °C under air flow) was followed by isothermal TG analysis. The oxygen uptake profiles were fit by a semiempiric equation that allowed to study the kinetics of the oil oxidation and estimate oxidative degradation. The DSC signal due to hydroperoxide decomposition and radical recombination was used to monitor the radical activity over time and to evaluate the stability of peroxides formed in the paint layers. GC-MS was performed at 7 and 24 months of natural aging to investigate the noncovalently cross-linked fractions and Py-GC-MS to characterize the whole organic fraction of the model paintings, including the cross-linked network. We show that the oil-pigment combination may have a strong influence on the relative degree of oxidation of the films formed with respect to its degree of cross-linking, which may be correlated with the literature on the stability of painting layers. Undocumented pathways of oxidation are also highlighted

de Branges-Rovnyak spaces: basics and theory

For $S$ a contractive analytic operator-valued function on the unit disk ${\mathbb D}$, de Branges and Rovnyak associate a Hilbert space of analytic functions ${\mathcal H}(S)$ and related extension space ${\mathcal D(S)}$ consisting of pairs of analytic functions on the unit disk ${\mathbb D}$. This survey describes three equivalent formulations (the original geometric de Branges-Rovnyak definition, the Toeplitz operator characterization, and the characterization as a reproducing kernel Hilbert space) of the de Branges-Rovnyak space ${\mathcal H}(S)$, as well as its role as the underlying Hilbert space for the modeling of completely non-isometric Hilbert-space contraction operators. Also examined is the extension of these ideas to handle the modeling of the more general class of completely nonunitary contraction operators, where the more general two-component de Branges-Rovnyak model space ${\mathcal D}(S)$ and associated overlapping spaces play key roles. Connections with other function theory problems and applications are also discussed. More recent applications to a variety of subsequent applications are given in a companion survey article

Operator theory and function theory in Drury-Arveson space and its quotients

The Drury-Arveson space $H^2_d$, also known as symmetric Fock space or the $d$-shift space, is a Hilbert function space that has a natural $d$-tuple of operators acting on it, which gives it the structure of a Hilbert module. This survey aims to introduce the Drury-Arveson space, to give a panoramic view of the main operator theoretic and function theoretic aspects of this space, and to describe the universal role that it plays in multivariable operator theory and in Pick interpolation theory.Comment: Final version (to appear in Handbook of Operator Theory); 42 page

3D cephalometry and artificial intelligence

Orthodontists today work more and more in a three-dimensional (3D) universe with cone-beam examinations occurring more frequently, now supplemented by digital prints and 3D portraits. So far these documents are used primarily as esthetic imagery; superimposition techniques, issued from geometric morphometrics, allow a pseudoquantified approach. The implementation of true cephalic biometrics requires consideration of the complete craniofacial set at different anatomical levels (alveolodental/basic bone/frame or overall architecture) and in three dimensions. It must lead to a quantified description of the anatomy, dysmorphism, and the necessary therapy to correct it. A parametric approach is needed to choose the landmarking, the definition of the orthogonal reference, the definition, and selection of parameters. Given the number of parameters required for a description without fault, the use of a simple tool with artificial intelligence is inevitable