Tortoiseshell or Polymer? Spectroscopic Analysis to Redefine a Purported Tortoiseshell Box with Gold Decorations as a Plastic Box with Brass

The study and preservation of museum collections requires complete knowledge and understanding of constituent materials that can be natural, synthetic, or semi-synthetic polymers. In former times, objects were incorporated in museum collections and classified solely by their appearance. New studies, prompted by severe degradation processes or conservation-restoration actions, help shed light on the materiality of objects that can contradict the original information or assumptions. The selected case study presented here is of a box dating from the beginning of the 20th century that belongs to the Portuguese National Ancient Art Museum. Museum curators classified it as a tortoiseshell box decorated with gold applications solely on the basis of visual inspection and the information provided by the donor. This box has visible signs of degradation with white veils, initially assumed to be the result of biological degradation of a proteinaceous matrix. This paper presents the methodological rationale behind this study and proposes a totally non-invasive methodology for the identification of polymeric materials in museum artifacts. The analysis of surface leachates using 1H and 13C nuclear magnetic resonance (NMR) complemented by in situ attenuated total reflection infrared spectroscopy (ATR FT-IR) allowed for full characterization of the object s substratum. The NMR technique unequivocally identified a great number of additives and ATR FT-IR provided information about the polymer structure and while also confirming the presence of additives. The pressure applied during ATR FT-IR spectroscopy did not cause any physical change in the structure of the material at the level of the surface (e.g., color, texture, brightness, etc.). In this study, variable pressure scanning electron microscopy (VP-SEM-EDS) was also used to obtain the elemental composition of the metallic decorations. Additionally, microbiologic and enzymatic assays were performed in order to identify the possible biofilm composition and understand the role of microorganisms in the biodeterioration process. Using these methodologies, the box was correctly identified as being made of cellulose acetate plastic with brass decorations and the white film was identified as being composed mainly of polymer exudates, namely sulphonamides and triphenyl phosphate.

A pointwise constrained version of the Liapunov convexity theorem for vectorial linear first-order control systems

We generalize the Liapunov convexity theorem's version for vectorial control systems driven by linear ODEs of first-order p = 1 , in any dimension d ∈ N , by including a pointwise state-constraint. More precisely, given a x ‾ ( ⋅ ) ∈ W p , 1 ( [ a , b ] , R d ) solving the convexified p-th order differential inclusion L p x ‾ ( t ) ∈ co { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e., consider the general problem consisting in finding bang-bang solutions (i.e. L p x ˆ ( t ) ∈ { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e.) under the same boundary-data, x ˆ ( k ) ( a ) = x ‾ ( k ) ( a ) & x ˆ ( k ) ( b ) = x ‾ ( k ) ( b ) ( k = 0 , 1 , … , p − 1 ); but restricted, moreover, by a pointwise state constraint of the type 〈 x ˆ ( t ) , ω 〉 ≤ 〈 x ‾ ( t ) , ω 〉 ∀ t ∈ [ a , b ] (e.g. ω = ( 1 , 0 , … , 0 ) yielding x ˆ 1 ( t ) ≤ x ‾ 1 ( t ) ). Previous results in the scalar d = 1 case were the pioneering Amar & Cellina paper (dealing with L p x ( ⋅ ) = x ′ ( ⋅ ) ), followed by Cerf & Mariconda results, who solved the general case of linear differential operators L p of order p ≥ 2 with C 0 ( [ a , b ] ) -coefficients. This paper is dedicated to: focus on the missing case p = 1 , i.e. using L p x ( ⋅ ) = x ′ ( ⋅ ) + A ( ⋅ ) x ( ⋅ ) ; generalize the dimension of x ( ⋅ ) , from the scalar case d = 1 to the vectorial d ∈ N case; weaken the coefficients, from continuous to integrable, so that A ( ⋅ ) now becomes a d × d -integrable matrix; and allow the directional vector ω to become a moving AC function ω ( ⋅ ) . Previous vectorial results had constant ω, no matrix (i.e. A ( ⋅ ) ≡ 0 ) and considered: constant control-vertices (Amar & Mariconda) and, more recently, integrable control-vertices (ourselves).