Analysis of the Chemical Composition of Red Pigments and Inks for the Characterization and Differentiation of Contemporary Prints

Prints are one of the most popular artistic forms. They consist of an original matrix that is printed on a paper support. The stamps are part of a series, and each series is composed of a particular number of prints. Many contemporary prints are made using oil inks and synthetic pigments (reds and yellows). Inks are mainly composed of pigments (organic or inorganic) and a binding medium. The analysis of inks has the potential to facilitate and complement the identification of stamps of different origins.

Fourier transform infrared spectroscopy (FTIR) and Scanning Electron Microscopy-Energy Dispersive X-ray (SEM-EDX) are techniques that are typically available in museums and centers related to the study of works of art. Both can be classified as micro-destructive and provide complementary information about the organic and some inorganic compounds (FTIR), and the elemental composition (SEM-EDX). In this article, the two techniques were used to analyze the composition of red ink in prints. As a result of these analyses, it was possible to distinguish among nearly all of the pigments and inks, indicating that the composition of the red ink can be reliably used to differentiate between stamps of different origins in a series of prints.     

New method to solve electromagnetic parabolic equation

This paper puts forward a new method to solve the electromagnetic parabolic equation （EMPE） by taking the vertically-layered inhomogeneous characteristics of the atmospheric refractive index into account. First, the Fourier transform and the convo- lution theorem are employed, and the second-order partial differential equation, i.e., the EMPE, in the height space is transformed into first-order constant coefficient differential equations in the frequency space. Then, by use of the lower triangular characteristics of the coefficient matrix, the numerical solutions are designed. Through constructing ana- lytical solutions to the EMPE, the feasibility of the new method is validated. Finally, the numerical solutions to the new method are compared with those of the commonly used split-step Fourier algorithm.     

Higher-order time integration with a local Lax–Wendroff procedure for a central scheme on an overlapping grid

We have implemented a high-order Lax–Wendroff type time integration for a central scheme on an overlapping grid for conservation law problems. Using a local iterative approach presented by Dumbser et al. (JCP, 2008) [12], we extend a local high-order spatial reconstruction on each cell to a local higher-order space–time polynomial on the cell. We rewrite the central scheme in a fully discrete form to avoid volume integration in the space–time domain. The fluxes at cell interfaces are calculated directly via integrating a higher-order space–time reconstruction of the flux. We compare this approach with the corresponding multi-stage Runge–Kutta time integration (RK). Numerical results show that the new time integration is more cost-effective.     

Liquid crystal mixtures for potential infrared applications

Liquid crystals (LCs) with diazo linkages have high dielectric and optical anisotropy. Two newly synthesized liquid crystalline compounds were dissolved in room temperature LC hosts, E7 and PTTP-24/36, to assess their properties. It was found that these mixtures have higher birefringence, larger dielectric anisotropy, and better elastic properties than the hosts. Satisfactory viscoelastic coefficients were also obtained for these mixtures, showing that they are promising LC materials for applications in the near IR region.     

On the moments of the time to ruin in dependent Sparre Andersen models with emphasis on Coxian interclaim times

The structural properties of the moments of the time to ruin are studied in dependent Sparre Andersen models. The moments of the time to ruin may be viewed as generalized versions of the Gerber–Shiu function. It is shown that structural properties of the Gerber–Shiu function hold also for the moments of the time to ruin. In particular, the moments continue to satisfy defective renewal equations. These properties are discussed in detail in the model of Willmot and Woo (2012), which has Coxian interclaim times and arbitrary time-dependent claim sizes. Structural quantities needed to determine the moments of the time to ruin are specified under this model. Numerical examples illustrating the methodology are presented.     

Some extensions of the operator entropy type inequalities

In this paper, we define the generalised relative operator entropy and investigate some of its properties such as subadditivity and homogeneity. As application of our result, we obtain the information inequality. In continuation, we establish some reverses of the operator entropy inequalities under certain conditions by using the Mond–Pe?ari? method.     

Generating Excess Protons in Microsolvated Acid Clusters under Ambient Conditions: An Issue of Configurational Entropy versus Internal Energy

Acid dissociation, and thus liberation of excess protons in small water droplets, impacts on diverse fields such as interstellar, atmospheric or environmental chemistry. At cryogenic temperatures below 1 K, it is now well established that as few as four water molecules suffice to dissociate the generic strong acid HCl, yet temperature-driven recombination sets in simply upon heating that cluster. Here, the fundamental question is posed of how many more water molecules are required to stabilize a hydrated excess proton at room temperature. Ab initio path integral simulations disclose that not five, but six water molecules are needed at 300 K to allow for HCl dissociation independently from nuclear quantum effects. In order to provide the molecular underpinnings of these observations, the classical and quantum free energy profiles were decomposed along the dissociation coordinate in terms of the corresponding internal energy and entropy profiles. What decides in the end about acid dissociation, and thus ion pair formation, in a specific microsolvated water cluster at room temperature is found to be a fierce competition between classical configurational entropy and internal energy, where the former stabilizes the undissociated state whereas the latter favors dissociation. It is expected that these are generic findings with broad implications on acid–base chemistry depending on temperature in small water assemblies.     

Two weight commutators in the Dirichlet and Neumann Laplacian settings

In this paper we establish the characterization of the weighted BMO via two weight commutators in the settings of the Neumann Laplacian ${\mathrm{\Delta }}_{N_{+}}$ on the upper half space ${\mathbb{R}}_{+}^n$ and the reflection Neumann Laplacian ${\mathrm{\Delta }}_N$ on ${\mathbb{R}}^n$ with respect to the weights associated to ${\mathrm{\Delta }}_{N_{+}}$ and ${\mathrm{\Delta }}_N$ respectively. This in turn yields a weak factorization for the corresponding weighted Hardy spaces, where in particular, the weighted class associated to ${\mathrm{\Delta }}_N$ is strictly larger than the Muckenhoupt weighted class and contains non-doubling weights. In our study, we also make contributions to the classical Muckenhoupt–Wheeden weighted Hardy space (BMO space respectively) by showing that it can be characterized via the area function (Carleson measure respectively) involving the semigroup generated by the Laplacian on ${\mathbb{R}}^n$ and that the duality of these weighted Hardy and BMO spaces holds for Muckenhoupt $A^p$ weights with $p\in (1,2]$ while the previously known related results cover only $p\in (1,\frac{n+1}{n}]$. We also point out that this two weight commutator theorem might not be true in the setting of general operators L, and in particular we show that it is not true when L is the Dirichlet Laplacian ${\mathrm{\Delta }}_{D_{+}}$ on ${\mathbb{R}}_{+}^n$.