Influence of composition and roughness on the pigment mapping of paintings using mid-infrared fiberoptics reflectance spectroscopy (mid-IR FORS) and multivariate calibration

Mid-infrared fiberoptics reflectance spectroscopy (mid-IR FORS) is a very interesting technique for artwork characterization purposes. However, the fact that the spectra obtained are a mixture of surface (specular) and volume (diffuse) reflection is a significant drawback. The physical and chemical features of the artwork surface may produce distortions in the spectra that hinder comparison with reference databases acquired in transmission mode. Several studies attempted to understand the influence of the different variables and propose procedures to improve the interpretation of the spectra. This article is focused on the application of mid-IR FORS and multivariate calibration to the analysis of easel paintings. The objectives are the evaluation of the influence of the surface roughness on the spectra, the influence of the matrix composition for the classification of unknown spectra, and the capability of obtaining pigment composition mappings. A first evaluation of a fast procedure for spectra management and pigment discrimination is discussed. The results demonstrate the capability of multivariate methods, principal component analysis (PCA), and partial least squares discrimination analysis (PLS-DA), to model the distortions of the reflectance spectra and to delimitate and discriminate areas of uniform composition. The roughness of the painting surface is found to be an important factor affecting the shape and relative intensity of the spectra. A mapping of the major pigments of a painting is possible using mid-IR FORS and PLS-DA when the calibration set is a palette that includes the potential pigments present in the artwork mixed with the appropriate binder and that shows the different paint textures. Graphical Abstract

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On fuzzy subgroups and fuzzy ideals under triangular norms

In this communication, we explicitly point out that the principal results of Liu 1982 basically deduced from the definition of binary operation ° on the set F(X) of all fuzzy subsets of X, also hold if one uses the weaker definition of product under triangular norm °_t. Fuzzy ideals with respect to the triangular norms are also defined.     

Investigation of the possible origins of sulfur in 19th century salted paper photographs by x‐ray fluorescence spectroscopy

An X‐ray fluorescence method to determine whether sulfur is present in 19th century photographs due to intentional toning or to environmental deterioration is proposed. In the 19th century salted paper print photographic process, AgCl formed on the surface of a sheet of paper was exposed to sunlight in contact with a negative, leading to the printing out of a Ag image that was fixed by immersing it in a sodium thiosulfate solution or hypo. The improper execution of the fixing in these photographs may result in the presence of sulfur, mostly manifested in image fading, irregular staining, and discoloration. Also, 19th century artists produced salted paper prints with a variety of image tonalities, for example, by using an artificially aged thiosulfate bath. The presence of sulfur in photographs may also be due to sulfur‐containing environmental pollutants. Therefore, knowledge about the location and amounts of sulfur is important to understand the artistic technique and/or the deterioration processes. In this study, the amounts of sulfur and the silver to sulfur signal ratios were determined for a salted paper print made in the laboratory following a 19th century procedure and for two artistic salted paper photographs using X‐ray fluorescence and standards prepared with different amounts of retained hypo and quantified by inductively coupled plasma atomic emission spectroscopy. The amounts of sulfur and the normalized silver to sulfur ratios for the artistic photographs were evaluated based on the results obtained in the samples prepared in the laboratory and in the context of the 19th century practices. Copyright © 2016 John Wiley & Sons, Ltd.     

On the numerical solution of the quadratic eigenvalue complementarity problem

The Quadratic Eigenvalue Complementarity Problem (QEiCP) is an extension of the Eigenvalue Complementarity Problem (EiCP) that has been introduced recently. Similar to the EiCP, the QEiCP always has a solution under reasonable hypotheses on the matrices included in its definition. This has been established in a previous paper by reducing a QEiCP of dimension n to a special 2n-order EiCP. In this paper we propose an enumerative algorithm for solving the QEiCP by exploiting this equivalence with an EiCP. The algorithm seeks a global minimum of a special Nonlinear Programming Problem (NLP) with a known global optimal value. The algorithm is shown to perform very well in practice but in some cases terminates with only an approximate optimal solution to NLP. Hence, we propose a hybrid method that combines the enumerative method with a fast and local semi-smooth method to overcome the latter drawback. This algorithm is also shown to be useful for computing a positive eigenvalue for an EiCP under similar assumptions. Computational experience is reported to demonstrate the efficacy and efficiency of the hybrid enumerative method for solving the QEiCP.     

On measures of fuzziness of solutions of fuzzy relation equations with generalized connectives

By using a general class of fuzzy connectives of Yager [Fuzzy Sets and Systems4 (1980), 235–242], Pedrycz [Fuzzy relational equations with generalized convectives and their applications, Fuzzy Sets and Systems10 (1983), 185–201] has shown that the classical fuzzy relation equations of Sanchez [in “Fuzzy Automata and Decision Processes” (M. M. Gupta, G. N. Saridis, and B. R. Gaines, Eds.), pp. 221–234, North-Holland, Amsterdam, 1977] can be considered as a particular case of a more extensive class of fuzzy equations. For such types of equations, in this paper the solutions having the greatest energy measure and the smallest possible entropy measure of fuzziness are characterized.     

Copolymerization of styrene with (Z)-1,3-pentadiene in the presence of a syndiotactic-specific catalyst

Copolymerization of styrene with (Z)-1,3-pentadiene affords copolymers mostly containing 1,2 pentadiene units. Both the styrene and the pentadiene units are in syndiotactic arrangement but the comonomer sequence distribution is far from bernoullian. Interestingly, the behavior of (Z)-1,3-pentadiene does not change much when polymerization temperature raises from −20 to +20°C, notwithstanding that (Z)-1,3-pentadiene affords a 1,2-syndiotactic homopolymer at −20°C but a prevailingly 1,4 cis homopolymer at +20°C. © 1997 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 35 : 2697–2702, 1997     

The Prime Spectrum of an MV-Algebra

In this paper we show that the prime ideal space of an MV-algebra is the disjoint union of prime ideal spaces of suitable local MV-algebras. Some special classes of algebras are defined and their spaces are investigated. The space of minimal prime ideals is studied as well. Mathematics Subject Classification : 03B50, 06D99.     

Differential cross sections for K+n elastic scattering between 0.64 and 1.51 GeV/c

We present experimental results on the K⁺n → K⁺n differential cross sections measured in deuterium at 13 momenta between 0.64 and 1.51 GeV/c.