On oxidative degradation of parchment and its non-destructive characterisation and dating

Historic parchment is an extremely complex material, not only due to the various methods of production used and various past environmental histories of objects, but also due to its inhomogeneous structure. Many traditional methods of characterisation are empirical, but useful since they have gained recognition by the end-users. In this paper, we investigated the shrinkage temperature of collagen and the influence of lipids contained in parchment on the measurements. While the content of lipids does not seem to significantly affect shrinkage temperature measurements themselves, it strongly affects the decrease of shrinkage temperature of collagen during degradation, and thus its thermomechanical properties. This confirms the high importance of lipid peroxidation during degradation of parchment.     

Quantitative characterisation of historic paper using THz spectroscopy and multivariate data analysis

THz spectroscopy in the time domain was explored in combination with multivariate data analysis, for quantitative determination of chemical and mechanical properties of historic paper, such as lignin content, tensile strength, and ash content. Using partial least squares (PLS) regression, it was shown that quantitative prediction of the material properties is possible, which indicates the potential of THz spectroscopy for chemical characterisation of complex organic materials of natural origin. In addition, the results demonstrate that THz spectra and PLS loading weights for lignin content differ significantly, which leads to the conclusion that THz spectra of composite macromolecular materials do not represent sums of spectra of the individual components. This supports the premise that THz spectra reflect intermolecular interactions. The study was carried out using 250 historical paper samples from the sixteenth century to present. Although the measurements were performed in vacuum to improve the quality of spectra, THz spectroscopy is in principle non-destructive. This research therefore reinforces the role of THz spectroscopy in characterisation of valuable historic materials, where invasive analysis is often not possible.     

Modular forms,hypergeometric functions and congruences

Let $$A_k(n)=\sum_{\substack{i_1,i_2,\ldots, i_k \ge0\\ i_1+i_2+\cdots+ i_k=n}}\binom{2i_1}{i_1}^2 \binom{2i_2}{i_2}^2\cdots \binom{2i_k}{i_k}^2, \quad \textrm{for } k,n\in\mathbb{N}. $$ Using the theory of Stienstra and Beukers (Math. Ann., 271:269–304, 1985), we prove that the numbers A ₃(n) and A ₃(n?1)?16A ₃(n?2) satisfy three term congruence relations similar to those satisfied by Apery numbers. Moreover, for k≥3 and p prime, we prove divisibility by p of some simple linear combinations of the numbers A _k (n), for $n\in \mathbb{N}$ . To obtain this, we study the arithmetic properties of the Fourier coefficients of certain holomorphic and weakly holomorphic modular forms.     

On Embeddings of Tori in Euclidean Spaces

Using the relation between the set of embeddings of tori into Euclidean spaces modulo ambient isotopies and the homotopy groups of Stiefel manifolds, we prove new results on embeddings of tori into Euclidean spaces.     

Real-time optodynamic monitoring of pulsed laser decoating rate

This paper deals with a laser-cleaning process for removing a layer of paint. The effects of each individual laser pulse were monitored by a three-probe system. Ultrasonic signals from the rear surface of the substrate were obtained using an arm compensated Michelson interferometer, the optoacoustic waves in the surrounding air were detected using a laser beam deflection probe and the shape of the growing crater was measured using a laser anamorph profilometer. Two different cleaning lasers were used: an Excimer and a Nd:YAG laser. Typical parameters of the optodynamic signals versus the laser-pulse number are presented. A linear correlation between the quantity of ablated material and the integral of the ultrasonic signals was found together with an exponential relationship between the time-of-flight of the optoacoustic signals and the decoating rate.