Fundamental solution of the time‐fractional telegraph Dirac operator

In this work, we obtain the fundamental solution (FS) of the multidimensional time‐fractional telegraph Dirac operator where the 2 time‐fractional derivatives of orders α∈]0,1] and β∈]1,2] are in the Caputo sense. Explicit integral and series representation of the FS are obtained for any dimension. We present and discuss some plots of the FS for some particular values of the dimension and of the fractional parameters α and β. Finally, using the FS, we study some Poisson and Cauchy problems.     

A combined analytical approach applied to Medieval wall paintings from Puglia (Italy): The study of painting techniques and its conservation state

A combined analytical approach has been applied to the wall paintings, dated from 10th to 14th centuries, of the Santi Stefani crypt at Vaste (Lecce, Southern Italy). These paintings are a precious testimony of Medieval art in Southern Italy. However, the church shows problems of damp as well as clear evidences of flora, fungi and mold presence, and there is little knowledge of the pictorial methodologies used. Raman spectroscopy allowed to determine the palette and to reconstruct the worksite and the chronological sequence of the various paint layers. Kaolinite, calcite, carbon black, hematite, massicot, goethite, indigo and azurite were identified as pigments along with synthetic pigments, like phthalocyanine blue and chrome yellow. Attenuated total reflectance‐Fourier transform infrared spectroscopy suggested the presence of egg as a binder in some pictorial layers. The conservation state of the crypt is poor, and detachments of pigmented layers are frequent because of the presence of subflorescence and efflorescence: nitrate, sulfate and chloride salts have been identified spectroscopically and quantified by ion chromatography. The extensive use of kaolinite in Santi Stefani, actually not uncommon in Medieval art, is observed for the first time in a crypt of Puglia: its use to stabilize some pigments and to improve their adhesion on substrate is proposed. Copyright © 2015 John Wiley & Sons, Ltd.     

Influence of the vertical profile of Saharan dust on the visible direct radiative forcing

The vertical profile of Saharan dust in the atmosphere is generally characterized by a large aerosol concentration in the mid troposphere, differently from the climatological distribution of other types of particles, that show a peak at the surface and a rapid decrease with height. Saharan dust is also characterized by particles of relatively large size of irregular shape, and variable values of the single scattering albedo (the ratio between radiation scattering and extinction). The dust's peculiar vertical distribution is expected to produce an effect on the calculation of the direct aerosol radiative forcing at the surface and at the top of the atmosphere. This effect is investigated by comparing estimates of aerosol direct visible radiative forcing at the surface and at the top of the atmosphere for dust vertical profiles measured in the Mediterranean, and for the climatological profile. The radiative forcing is estimated by means of an accurate radiative transfer model, and for the ocean surface. The sensitivity of the results on the solar zenith angle, aerosol optical depth, and aerosol absorption is also investigated. The aerosol radiative forcing at the surface shows a very small dependency on the aerosol vertical profile. At the top of the atmosphere, the radiative forcing is weakly dependent on the vertical profile (up to 10% variation on the daily average forcing) for low absorbing particles; conversely, it shows a strong dependency (the daily radiative forcing may vary up to 100%) for absorbing particles. The top of the atmosphere visible radiative forcing efficiency produced by dust having single scattering albedo <0.7 is higher by 4 W m⁻² when the observed vertical profile instead of the standard profile is used in the calculations (i.e. it produces a lower cooling). For values of the single scattering albedo around 0.67, the sign of the forcing depends on the vertical profile. The influence of the vertical distribution on the radiative forcing is largest at small values of the solar zenith angle, and at short wavelengths.     

An improved two-stage optimization-based framework for unequal-areas facility layout

The unequal-areas facility layout problem is concerned with finding the optimal arrangement of a given number of non-overlapping indivisible departments with unequal area requirements within a facility. We present an improved optimization-based framework for efficiently finding competitive solutions for this problem. The framework is based on the combination of two mathematical optimization models. The first model is a nonlinear approximation of the problem that establishes the relative position of the departments within the facility, and the second model is an exact convex optimization formulation of the problem that determines the final layout. Aspect ratio constraints on the departments are taken into account by both models. Our computational results show that the proposed framework is computationally efficient and consistently produces competitive, and often improved, layouts for well-known instances from the literature as well as for new large-scale instances with up to 100 departments.     

Gravitational entropy of Kerr black holes

Classical invariants of General Relativity can be used to approximate the entropy of the gravitational field. In this work, we study two proposed estimators based on scalars constructed out from the Weyl tensor, in Kerr spacetime. In order to evaluate Clifton, Ellis and Tavakol’s proposal, we calculate the gravitational energy density, gravitational temperature, and gravitational entropy of the Kerr spacetime. We find that in the frame we consider, Clifton et al.’s estimator does not reproduce the Bekenstein–Hawking entropy of a Kerr black hole. The results are compared with previous estimates obtained by the authors using the Rudjord–Gr \(\varnothing \) n–Hervik approach. We conclude that the latter represents better the expected behaviour of the gravitational entropy of black holes.     

An Area Preserving Projection from the Regular Octahedron to the Sphere

In this paper, we propose an area preserving bijective map from the regular octahedron to the unit sphere ${\mathbb{S}^2}$ , both centered at the origin. The construction scheme consists of two steps. First, each face F _i of the octahedron is mapped to a curved planar triangle ${\mathcal{T}_i}$ of the same area. Afterwards, each ${\mathcal{T}_i}$ is mapped onto the sphere using the inverse Lambert azimuthal equal area projection with respect to a certain point of ${\mathbb{S}^2}$ . The proposed map is then used to construct uniform and refinable grids on a sphere, starting from any triangular uniform and refinable grid on the triangular faces of the octahedron.     

Fluorescent Flavin/PVP-Coated Silver Nanoparticles: Design and Biological Performance

A red-emitting fluorescent Riboflavin (RF)/Polyvinylpyrrolidone (PVP)-coated silver nanoparticles system, λ_em?=?527 nm, Φ?=?0.242, with a diameter of the metallic core of 27.33 nm and a zeta potential of ? 25.05 mV was prepared and investigated regarding its biological activity. We found that PVP has a key role in RF adsorption around the SNPs surface leading to an enhancement of antioxidant properties (～70%), low cytotoxicity (> 90% cell viability, at 50 µL/mL, after 48 h of incubation) as well as to an efficient process of its cellular uptake (～ 60%, after 24 h of incubation) in L929 cells. The results are relevant concerning the involvement of RF and its coenzymes forms in SNPs - based systems, in cellular respiration as well as for future studies as antioxidant marker system on tumoral cells for viewing and monitoring them, by cellular imaging.

     

Analysis of mural paintings using in situ non‐invasive XRF,FTIR spectroscopy and optical microscopy

An analytical protocol consisting of X‐ray fluorescence spectroscopy, optical microscopy and Fourier transform infrared spectroscopy was used to study the origin and the nature of the materials (pigments, binders and coating preparation) of the Fundenii Doamnei church mural paint from Bucharest. The main interest of the present study consisted in the original votive paint from narthex, painted in 1757 in a secco technique. During analysis, an unexpected pigment in the votive paint could be detected by the combined analytical techniques: ultramarine blue. Along with this pigment, the presence of gypsum binder based on egg and flax seed oil could also be evidenced. These results demonstrated a secco execution technique of the votive paint and also the presence of a restoration treatment. Moreover, during the present study, the components of the preparation layer and the constitutive pigments from both 1699 and 1757 years mural paints have been analyzed. Hence, the following pigments could be identified: vermilion, azurite, cinnabar, lead white, ochre, natural umber and gold, by using the combination of the analytical techniques. The novelty of our results consists in detecting the composition of the materials used in this church painting (fresco and a secco) during these 254 years since its first restoration. The results of these investigations pointed to the suitability of the non‐destructive and semi‐destructive analytical techniques in the complex characterization of the paints realized in different techniques, at different periods. Copyright © 2013 John Wiley & Sons, Ltd.     

Wavelet-based dynamic time warping

Dynamic Time Warping (DTW), a pattern matching technique traditionally used for restricted vocabulary speech recognition, is based on a temporal alignment of the input signal with the template models. The principal drawback of DTW is its high computational cost as the lengths of the signals increase. This paper shows extended results over our previously published conference paper, which introduces an optimized version of the DTW that is based on the Discrete Wavelet Transform (DWT).