The use of Raman microscopy and laser desorption ionization mass spectrometry in the examination of synthetic organic pigments in modern works of art

Synthetic organic pigments are widely used in modern and contemporary works of art. They have been examined by a variety of techniques including spectroscopic methods such as Fourier transform infrared spectroscopy, Raman, and X‐ray powder diffraction as well as chromatographic or mass spectrometric techniques such as pyrolysis‐gas chromatography/mass spectrometry and laser desorption ionization mass spectrometry (LDI–MS). Often, a combination of techniques has been used to examine these pigments. This paper describes use of Raman spectroscopy to create a database of colorants including two pigments not previously reported, PO1 and PO2. Then, using Raman spectroscopy in combination with LDI–MS, samples from modern works of art by artists including Mark Rothko, Barnett Newman, and José de Rivera were examined in order to identify the pigments present. One finding was that Rothko used a variety of red pigments over the course of his career including PR11 which has not been previously reported in artwork, and PO2 found with its positional isomer PR1. Knowledge of the colorants serves to inform conservators about display and treatment decisions. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.     

Objective bayesian analysis of the Yule–Simon distribution with applications

The Yule–Simon distribution is usually employed in the analysis of frequency data. As the Bayesian literature, so far, has ignored this distribution, here we show the derivation of two objective priors for the parameter of the Yule–Simon distribution. In particular, we discuss the Jeffreys prior and a loss-based prior, which has recently appeared in the literature. We illustrate the performance of the derived priors through a simulation study and the analysis of real datasets.     

Diophantine equations with products of consecutive members of binary recurrences

We prove a finiteness result for the number of solutions of a Diophantine equation of the form \(u_n u_{n+1}\cdots u_{n+k}\pm 1 =\pm u_m^2\), where \(\{ u_n\}_{n\ge 1}\) is a binary recurrent sequence whose characteristic equation has roots which are real quadratic units.     

Existence and multiplicity of positive solutions for a system of difference equations with coupled boundary conditions

We study the existence and multiplicity of positive solutions for a system of nonlinear second-order difference equations subject to coupled multi-point boundary conditions.     

Density lower bound estimate for local minimizer of free interface problem with volume constraint

We prove a density lower bound for some functionals involving bulk and interfacial energies. The bulk energies are convex functions with p-power growth not subjected to any further structure conditions. The interface \(\partial E\) is the boundary of a set \(E\subset \Omega \) such that \(|E|=d\) is prescribed. Then we get \(\mathcal {H}^{n-1}((\partial E{\setminus }\partial E^*)\cup \Omega )=0\).

     

Finite mixtures of unimodal beta and gamma densities and the k-bumps algorithm

This paper addresses the problem of estimating a density, with either a compact support or a support bounded at only one end, exploiting a general and natural form of a finite mixture of distributions. Due to the importance of the concept of multimodality in the mixture framework, unimodal beta and gamma densities are used as mixture components, leading to a flexible modeling approach. Accordingly, a mode-based parameterization of the components is provided. A partitional clustering method, named $k$ -bumps, is also proposed; it is used as an ad hoc initialization strategy in the EM algorithm to obtain the maximum likelihood estimation of the mixture parameters. The performance of the $k$ -bumps algorithm as an initialization tool, in comparison to other common initialization strategies, is evaluated through some simulation experiments. Finally, two real applications are presented.     

An inventory-transportation system with stochastic demand

We study a logistic system in which a supplier has to deliver a set of products to a set of retailers to face a stochastic demand over a given time horizon. The transportation from the supplier to each retailer can be performed either directly, by expensive and fast vehicles, or through an intermediate depot, by less expensive but slower vehicles. At most one time period is required in the former case, while two time periods are needed in the latter case. A variable transportation cost is charged in the former case, while a fixed transportation cost per journey is charged in the latter case. An inventory cost is charged at the intermediate depot. The problem is to determine, for each time period and for each product, the quantity to send from the supplier to the depot, from the depot to each retailer and from the supplier to each retailer, in order to minimize the total expected cost. We first show that the classical benchmark policy, in which the demand of each product at each retailer is set equal to the average demand, can give a solution which is infinitely worse with respect to the optimal solution. Then, we propose two classes of policies to solve this problem. The first class, referred to as Horizon Policies, is composed of policies which require the solution of the overall problem over the time horizon. The second class, referred to as Reoptimization Policies, is composed of a myopic policy and several rolling-horizon policies in which the problem is reoptimized at each time period, once the demand of the time period is revealed. We evaluate the performance of each policy dynamically, by using Monte Carlo Simulation.     

Stability properties of an inverse parabolic problem with unknown boundaries

We treat the stability issue for an inverse problem arising from non-destructive evaluation by thermal imaging. We consider the determination of an unknown portion of the boundary of a thermic conducting body by overdetermined boundary data for a parabolic initial-boundary value problem. We obtain that when the unknown part of the boundary is a priori known to be smooth, the data are as regular as possible and all possible measurements are taken into account, the problem is exponentially ill-posed. Then, we prove that a single measurement with some a priori information on the unknown part of the boundary and minimal assumptions on the data, in particular on the thermal conductivity, is enough to have stable determination of the unknown boundary. Given the exponential ill-posedness, the stability estimate obtained is optimal. AMS 2000 Mathematics Subject Classification. Primary 35R30, Secondary 35B60, 33C90     

Online weighted flow time and deadline scheduling

In this paper we study some aspects of weighted flow time. We first show that the online algorithm Highest Density First is an O(1)-speed O(1)-approximation algorithm for P|r_i,pmtn|∑w_iF_i. We then consider a related Deadline Scheduling Problem that involves minimizing the weight of the jobs unfinished by some unknown deadline D on a uniprocessor. We show that any c-competitive online algorithm for weighted flow time must also be c-competitive for deadline scheduling. We then give an O(1)-competitive algorithm for deadline scheduling.     

Immobilized TiO<Subscript>2</Subscript> nanoparticles produced by flame spray for photocatalytic water remediation

Anatase/rutile mixed-phase titanium dioxide (TiO₂) photocatalysts in the form of nanostructured powders with different primary particle size, specific surface area, and rutile content were produced from the gas-phase by flame spray pyrolysis (FSP) starting from an organic solution containing titanium (IV) isopropoxide as Ti precursor. Flame spray-produced TiO₂ powders were characterized by means of X-ray diffraction, Raman spectroscopy, and BET measurements. As-prepared powders were mainly composed of anatase crystallites with size ranging from 7 to 15 nm according to the synthesis conditions. TiO₂ powders were embedded in a multilayered fluoropolymeric matrix to immobilize the nanoparticles into freestanding photocatalytic membranes. The photocatalytic activity of the TiO₂-embedded membranes toward the abatement of hydrosoluble organic pollutants was evaluated employing the photodegradation of rhodamine B in aqueous solution as test reaction. The photoabatement rate of best performing membranes significantly overcomes that of membranes produced by the same method and incorporating commercial P25-TiO₂.