In-situ fluorimetry: A powerful non-invasive diagnostic technique for natural dyes used in artefacts: Part II. Identification of orcein and indigo in Renaissance tapestries

In this paper, three Renaissance tapestries depicting scenes painted by Raffaello Sanzio, conserved at the Vatican Museum, were investigated using in-situ UV–Visible fluorimetric measurements. The results show that this technique is suitable for the detection of natural organic colorants used for dyeing the threads woven in these tapestries. The emission signals detected on red–purple colours were assigned to the colorant orcein and those on different nuances of blue and green colours to indigo by comparison with data from reference laboratory samples. The assignments were supported by chromatographic experiments carried out on threads taken from the back side of the tapestry in the same points analysed by spectrofluorimentry.     

Dual Sufficient Optimality Conditions for the Generalized Problem of Bolza

We develop sufficient conditions for optimality in the generalized problem of Bolza. The basis of our approach is the dual Hamilton–Jacobi inequality leading to a new sufficient criterion for optimality in which we assume the existence of a function satisfying, together with the Hamiltonian, a certain inequality. Consequently, using this criterion, we derive new sufficient conditions for optimality of first and second order for a relative minimum.