Polynomial stability of a coupled system of wave equations weakly dissipative

In this work, we consider a coupled system of wave equation. We show that the solution of this system has a polynomial rate of decay as time tends to infinity, but does not have exponential decay. We presented a class of examples of application of the main result.     

Geochemical study of black crusts as a diagnostic tool in cultural heritage

This contribution focuses on spectrometric analyses carried out on crust samples covering the stone surface of the boundary walls of the Tower of London. The main goal of this research is to investigate the degradation processes related to the environmental impact on cultural heritage. Specifically, the chemical contamination of stone substrate in the Tower of London due to the crust formation was examined through laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS). This technique allowed us to achieve a complete characterization of the damage layers in terms of trace elements. In addition, optical microscopy (OM), scanning electron microscopy coupled with energy-dispersive X-ray spectrometry (SEM-EDS) and infrared spectroscopic techniques (FT-IR) were also used for an exhaustive characterization of the examined samples. Results obtained demonstrated that such a geochemical approach represents a powerful diagnostic tool in the study of black crusts, since it represents a reliable indicator of the environmental pollution. The higher concentrations of most heavy metals in black crusts with respect to the underlying stone suggest that crusts were greatly influenced by atmospheric inputs in their formation, mainly represented by mobile combustion sources. In addition, the possibility of analyzing in some samples the portion of altered substrate allowed us to hypothesize that some specific heavy metals tend to migrate from the crust to the unaltered substrate over time, becoming catalysts for the formation of new crust. Therefore, this research focuses on the role of diagnostics in order to plan suitable cleaning and consolidation intervention aimed at a better protection of the monument.     

Apparent diffusion coefficient of intervertebral discs related to matrix composition and integrity

While tremendous work has been performed to characterize degenerative disc disease through gross morphologic, biochemical, and histologic grading schemes, the development of an accurate and noninvasive diagnostic tool is required to objectively detect changes in the matrix with aging and disc degeneration. In the present study, quantitative magnetic resonance was used to determine if the quality of the nutritional supply to the intervertebral disc at various ages and levels of degeneration could be assessed through measurement of the apparent diffusion coefficients (ADCs). Modifications of the nucleus pulposus matrix content, specifically of water and glycosaminoglycan contents, with age and disc degeneration, were reflected in correlating changes in the ADCs. From unforced stepwise linear regression analyses, relations were established showing that decreases in glycosaminoglycan or water contents in the nucleus pulposus resulted in direct decreases in the ADCs. Relations obtained for the ADCs of the nucleus pulposus were direction dependent, in conformity with the anisotropic diffusion in the intervertebral discs. Changes in matrix integrity, as evidenced by the percentage of denatured collagen, were also detected in the nucleus pulposus with a low positive correlation to the ADC along the height of the disc and an inverse statistically significant regression to the ADC along the anterior to posterior axis of the disc. Correlations between the matrix content and integrity of the annulus fibrosus and its ADCs were not as evident, with only the ADC in the lateral direction of the disc of the anterior annulus fibrosus able to reflect changes in matrix content. The information obtained by the ADCs, particularly of the nucleus pulposus, can potentially be used in combination with quantitative T1, T2, and MT parameters to noninvasively obtain a quantitative assessment of the disc matrix composition and structural integrity.     

An integrated Raman and petrographic characterization of Italian mediaeval artifacts in pietra ollare (soapstone)

Ten fragments of pots made by pietra ollare (basic and ultrabasic metamorphic rocks belonging to greenschist facies) found in the archaeological site of Crocetta di Sant'Agata Bolognese (Bologna, Italy) have been studied to characterize them and to define their provenance. The fragments, dated between the 9^th and 10^th century AD, show traces of blackening from fire, indicating the use of these findings as pots by fire. The extensive use of a non‐destructive technique, Raman spectroscopy, in both laboratory and portable forms, for the provenance analysis of pietra ollare artifacts has been evaluated. Micro‐Raman spectroscopy was used for a detailed study of the main components, to identify the secondary minerals and to study the distribution of the mineral phases in the samples. The samples show schistose texture, are fine grained and consist mainly of talc and chlorite, and subordinate carbonates, oxides and serpentine. Olivine is rare. Based on the mineralogical composition, the material can be defined as chlorite and carbonate talc‐schist. Our samples of pietra ollare may be assigned to chlorite and magnesite‐bearing talc‐schists. The alpine areas of origin of this lithotype are Valtellina, Valchiavenna and Val Bregaglia. In particular, we can hypothesize that the origin of these findings is Valchiavenna, which had great commercial importance in the Middle Ages. Further measurements, obtained with a portable Raman spectrometer, directly on a quarry near Chiavenna, support our hypothesis. Copyright © 2013 John Wiley & Sons, Ltd.     

Merit functions: a bridge between optimization and equilibria

In the last decades, many problems involving equilibria, arising from engineering, physics and economics, have been formulated as variational mathematical models. In turn, these models can be reformulated as optimization problems through merit functions. This paper aims at reviewing the literature about merit functions for variational inequalities, quasi-variational inequalities and abstract equilibrium problems. Smoothness and convexity properties of merit functions and solution methods based on them will be presented.     

Thermal analysis of the RFX-mod2 operating conditions for the design of the temperature measurement system

Journal of Thermal Analysis and Calorimetry - The laminar two-dimensional mixed convection in a trapezoidal enclosure with a rotating inner circular cylinder and a sinusoidal bottom wall is studied...     

Multiconfiguration Dirac–Fock calculations of Zn K-shell radiative and nonradiative transitions

Zinc K-shell radiative and radiationless transition rates are calculated using the multiconfiguration Dirac–Fock method. Correlation up to the 4p orbital is included in almost all transition rate calculations. Calculated radiative transition rates and transition probabilities are compared with Scofield's Dirac–Hartree–Slater and Dirac–Hartree–Fock calculations, presenting good agreement with the later. Radiative transition intensity ratios involving the strongest lines are compared with theoretical, experimental, and empirical-fit values. Most ratios are in close agreement with the empirical-fit values from NIST's Fundamental Parameters database. Calculated radiationless transition rates and ratios are compared with Chen et al.'s Dirac–Fock values and Safronova et al.'s Dirac–Fock values. The K-LL transition rates are overall lower than Chen et al.'s values, whereas the K-LX and K-XY transition rates are overall higher. Calculated K-LX/K-LL and K-XY/K-LL ratios are relatively close to the experimental values compared. Some calculated intensities relative to K-L are in good agreement with the experimental values, whereas others present worse agreement. The calculated fluorescence yield is higher than all theoretical, experimental, and empirical-fitted values compared, probably because the total radiationless transition rate value calculated in the present work is relatively low.     

DFT characterization of the mechanism for Staudinger/aza-Wittig tandem organocatalysis

A computational simulation with DFT calculations and microkinetic modeling is carried out on a complete catalytic cycle, involving Staudinger ligation, aza-Wittig condensation and phosphine oxide recycle, for non-truncated substrates and catalyst. The Staudinger reaction produces phosphazenes (R₃P?=?NR), also known as iminophosphoranes, from phosphines and organic azides. Electrophilic carbonyl groups react with phospazenes to produce imines and phosphine oxides. Recently the Staudinger reaction and the aza-Wittig condensation have been combined to spawn intramolecular tandems producing cyclic molecules of great pharmaceutical interest (e.g. benzoxazoles). The release of diatomic nitrogen combined with the formation of phosphine oxide represents the driving force of the reaction. The implementation of in situ recycling of the exhausted phosphine oxide into the Staudinger/aza-Wittig tandem improves the scopes and the applicability of the reaction, transforming it into a powerful and versatile synthetic tool.     

Elastic indentation of a rough surface by a conical punch

In the contact of a cone with a rough plane the mean pressure in the contact area is constant. In particular, above a critical ratio of the opening angle of the cone with respect to the rms gradient of surface roughness, the mean pressure is the same of that for nominally flat contact, no matter how large is the normal load. We introduce a new variable, namely, the local density of contact area, whose integral over the smooth nominal contact domain gives the real contact area. The results given by the theoretical model agree with the numerical simulations of the same problem presented in the paper.     

Optimal Space Trajectories with Multiple Coast Arcs Using Modified Equinoctial Elements

Journal of Optimization Theory and Applications - The detection of optimal trajectories with multiple coast arcs represents a significant and challenging problem of practical relevance in space...