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

An explicit state-space approach to the one-block super-optimal distance problem

An explicit state-space approach is presented for solving the super-optimal Nehari-extension problem. The approach is based on the all-pass dilation technique developed in (Jaimoukha and Limebeer in SIAM J Control Optim 31(5):1115–1134, 1993) which offers considerable advantages compared to traditional methods relying on a diagonalisation procedure via a Schmidt pair of the Hankel operator associated with the problem. As a result, all derivations presented in this work rely only on simple linear-algebraic arguments. Further, when the simple structure of the one-block problem is taken into account, this approach leads to a detailed and complete state-space analysis which clearly illustrates the structure of the optimal solution and allows for the removal of all technical assumptions (minimality, multiplicity of largest Hankel singular value, positive-definiteness of the solutions of certain Riccati equations) made in previous work (Halikias et al. in SIAM J Control Optim 31(4):960–982, 1993; Limebeer et al. in Int J Control 50(6):2431–2466, 1989). The advantages of the approach are illustrated with a numerical example. Finally, the paper presents a short survey of super-optimization, the various techniques developed for its solution and some of its applications in the area of modern robust control

An Inverse Spectral Problem for Hankel Operators

We prove that given any compact subset of the complex plane containing zero, there exists a Hankel operator having this set as its spectrum. 1