Lead(II) Formate in Rembrandt's Night Watch: Detection and Distribution from the Macro- to the Micro-scale

The Night Watch, painted in 1642 and on view in the Rijksmuseum in Amsterdam, is considered Rembrandt's most famous work. X-ray powder diffraction (XRPD) mapping at multiple length scales revealed the unusual presence of lead(II) formate, Pb(HCOO)₂, in several areas of the painting. Until now, this compound was never reported in historical oil paints. In order to get insights into this phenomenon, one possible chemical pathway was explored thanks to the preparation and micro-analysis of model oil paint media prepared by heating linseed oil and lead(II) oxide (PbO) drier as described in 17^th century recipes. Synchrotron radiation based micro-XRPD (SR-μ-XRPD) and infrared microscopy were combined to identify and map at the micro-scale various neo-formed lead-based compounds in these model samples. Both lead(II) formate and lead(II) formate hydroxide Pb(HCOO)(OH) were detected and mapped, providing new clues regarding the reactivity of lead driers in oil matrices in historical paintings.     

Preparation of refractive index matching polymer film alternative to oil for use in a portable surface-plasmon resonance phenomenon-based chemical sensor method

In order to simplify the procedure for assembling a surface-plasmon resonance (SPR) sensor, a refractive index matching polymer film was prepared as an alternative to the conventionally used matching oil. The refractive index matching polymer film, the refractive index of which was nearly equal to the prism and sensor chip material (a cover glass) of the SPR sensor, was prepared by casting a tetrahydrofuran solution of poly (vinyl chloride) (PVC) containing equal weights of dioctyl phthalate and tricresyl phosphate. The refractive index matching polymer film was found to have a refractive index of 1.516, which is identical to that of the prism and the cover glass used for the present SPR sensor. The utility of the matching polymer film for the SPR sensor was confirmed by the detection of anti-human albumin, based on an antigen-antibody reaction.     

A mathematical approach to HIV infection dynamics

In order to obtain a comprehensive form of mathematical models describing nonlinear phenomena such as HIV infection process and AIDS disease progression, it is efficient to introduce a general class of time-dependent evolution equations in such a way that the associated nonlinear operator is decomposed into the sum of a differential operator and a perturbation which is nonlinear in general and also satisfies no global continuity condition. An attempt is then made to combine the implicit approach (usually adapted for convective diffusion operators) and explicit approach (more suited to treat continuous-type operators representing various physiological interactions), resulting in a semi-implicit product formula. Decomposing the operators in this way and considering their individual properties, it is seen that approximation–solvability of the original model is verified under suitable conditions. Once appropriate terms are formulated to describe treatment by antiretroviral therapy, the time-dependence of the reaction terms appears, and such product formula is useful for generating approximate numerical solutions to the governing equations. With this knowledge, a continuous model for HIV disease progression is formulated and physiological interpretations are provided. The abstract theory is then applied to show existence of unique solutions to the continuous model describing the behavior of the HIV virus in the human body and its reaction to treatment by antiretroviral therapy. The product formula suggests appropriate discrete models describing the dynamics of host pathogen interactions with HIV1 and is applied to perform numerical simulations based on the model of the HIV infection process and disease progression. Finally, the results of our numerical simulations are visualized and it is observed that our results agree with medical and physiological aspects.     

On scrambled sets and a theorem of Kuratowski on independent sets

The measure of scrambled sets of interval self-maps was studied by many authors, including Smítal, Misiurewicz, Bruckner and Hu, and Xiong and Yang. In this note, first we introduce the notion of ``-chaos" which is related to chaos in the sense of Li-Yorke, and we prove a general theorem which is an improvement of a theorem of Kuratowski on independent sets. Second, we apply the result to scrambled sets of higher dimensional cases. In particular, we show that if a map of the unit -cube is -chaotic on , then for any there is a map such that and are topologically conjugate, and has a scrambled set which has Lebesgue measure 1, and hence if , then there is a homeomorphism with a scrambled set satisfying that is an -set in and has Lebesgue measure 1.

     

On the distributions of some test criteria for a covariance matrix under local alternatives and bootstrap approximations

The asymptotic distribution of some test criteria for a covariance matrix are derived under local alternatives. Except for the existence of some higher moments, no assumption as to the form of the distribution function is made. As an illustration, a case of t distribution included normal model is considered and the power of the likelihood ratio test and Nagao's test for sphericity, as described in Srivastava and Khatri and Anderson, is computed. Also, the power is computed using the bootstrap method. In the case of t distribution, the bootstrap approximation does not appear to be as good as the one obtained by the asymptotic expansion method.     

Monte Carlo simulations of the exchange kinetics of polymers adsorbed on a solid surface

The exchange kinetics of polymers adsorbing on a solid surface is extensively studied by dynamic Monte Carlo simulations. A model employed simulates a semidilute polymer solution placed in contact with a solid surface that attracts polymer segments by the adsorption interaction (χ_s). The exchange process of polymer chains, between the solution and the adsorbed polymer layer, is examined under various conditions. The exchange kinetics shows two characteristic regimes with increasing chain length. One is the diffusion‐controlled regime found with a small χ_s , and the other the detachment‐controlled regime with a large χ_s . These two regimes are well described by a kinetic theory. Various dynamic quantities show that the diffusion‐controlled regime is not due to sluggish dynamics near the surface, but rather to bulk diffusion of chains. The diffusion‐controlled regime found in this study is considered to appear at the high temperature limit.     

Oxidation state and proton doping level in copolymers of 2-aminobenzoic acid and 2-methoxyaniline

UV-vis spectra of homopolymers and copolymers of 2-aminobenzoic acid (OAB) and 2-methoxyaniline (OMA) were analyzed in order to obtain information about the oxidation state and proton doping level of these polymers. Dimethyl sulfoxide (DMSO) was used as a solvent in which protonated forms of polyanilines are preserved and a mixture of N-methyl-2-pyrrolidone and triethylamine (0.5 %) as a solvent (NMP/TEA) in which polyanilines are assumed to be non-protonated. Polymers were prepared in the emeraldine salt form, externally doped with HCl. It was found that only external doping is eliminated in NMP/TEA while internal doping by carboxylate groups bound in OAB units remains operative. Since doped quinoid units do not contribute to the quinoid band (Q-band at 630 nm), the intensity ratio of the Q-band and benzenoid band (B-band at 320 nm) cannot be simply correlated with the oxidation state of poly(OMA-co-OAB) copolymers in contrast to poly(OMA) and polyaniline. Spectra of copolymers with less than 60 % of OMA units as well as those of poly(OAB) in DMSO and NMP/TEA are almost identical due to internal doping, which is proposed to lead to structures in which main-chain protons are coulombically bound with immobile carboxylate anions. In the spectra of copolymers with less than 60 % of OMA units, a well-resolved band occurs at 500 nm, which can be ascribed to alternating or close-to-alternating sequences of OMA and OAB units.