The representability number of a chain

For each pair of linear orderings (L,M), the representability number repr_M(L) of L in M is the least ordinal α such that L can be order-embedded into the lexicographic power . The case is relevant to utility theory. The main results in this paper are as follows. (i) If κ is a regular cardinal that is not order-embeddable in M, then repr_M(κ)=κ; as a consequence, for each κω₁. (ii) If M is an uncountable linear ordering with the property that A×_lex2 is not order-embeddable in M for each uncountable AM, then for any ordinal α; in particular, . (iii) If L is either an Aronszajn line or a Souslin line, then .     

A class of risk processes with reserve-dependent premium rate: sample path large deviations and importance sampling

Let (X(t)) be a risk process with reserve-dependent premium rate, delayed claims and initial capital u. Consider a class of risk processes {(X ^ε (t)): ε > 0} derived from (X(t)) via scaling in a slow Markov walk sense, and let Ψ_ε(u) be the corresponding ruin probability. In this paper we prove sample path large deviations for (X ε (t)) as ε → 0. As a consequence, we give exact asymptotics for log Ψ_ε(u) and we determine a most likely path leading to ruin. Finally, using importance sampling, we find an asymptotically efficient law for the simulation of Ψ_ε(u). AMS Subject Classifications 60F10, 91B30 This work has been partially supported by Murst Project “Metodi Stocastici in Finanza Matematica”     

Energy analysis of protons emitted from Nd:YAg laser-generated plasmas

Hydrogenated targets have been irradiated in vacuum with the pulsed Nd:YAg laser at intensities of the order of 10¹⁰ W/cm². The laser-generated plasma, produced by the interaction with the solid, emits protons and other ions along the normal to the target surface. Ion collectors and ion energy analyzer were used to measure the current, the angular emission and the energy distributions of the emitted protons. Time-of-flight measurements, Coulomb–Boltzmann-distributions and the fits of experimental data were also used in order to evaluate the equivalent ion plasma temperature and the ion acceleration developed in the non-equilibrium-pulsed plasma.     

Radiation effects and pulsed laser deposition of titanium by Nd:Yag laser

A study of Ti laser irradiation and thin film deposition produced by an Nd:Yag pulsed laser is presented. The laser pulse, 9?ns width, has a power density of the order of 10¹⁰?W/cm². The titanium etching rate is of the order of 1?µg/pulse, it increases with the laser fluence and shows a threshold value at about 30?J/cm² laser fluence. The angular distribution of ejected atoms (neutrals and ions) is peaked along the normal of the target surface. At high fluence, the fractional ionization of the plasma produced by the laser is of the order of 10%. Time-of-flight measurements demonstrate that the titanium ions, at high laser fluence, may reach kinetic energies of about 1?keV. Obtained results can be employed to produce energetic titanium ions, to produce coverage of thin films of titanium and to realize high adherent titanium-substrate interfaces. The obtained results can be employed to produce energetic titanium ions, to produce a coverage of thin titanium films on polymers, and to realize highly adherent titanium–substrate interfaces.     

Temperature and density spectroscopic measurements in different laser-generated plasmas

A pulsed Nd:Yag laser, at intensities of the order of 10¹⁰ W/cm², is employed to irradiate different thick metallic targets (Ti, Fe, Ag, and Ni) placed in vacuum. The obtained non-equilibrium plasmas are investigated with various analytical techniques. An electrostatic ion energy analyzer and different ion collectors are employed to monitor in situ the ions ejected from the plasma and to determine the core plasma temperature, the ion energy distributions and the ion angular emission. An optical spectrometer is employed to analyze the plasma corona emitted light vs. wavelength and to identify the emitted characteristic lines. The optical spectroscopy permitted to evaluate the electron temperatures and densities. Results show strong temperature and density gradients occurring in the laser-generated plasma plume.     

Investigation of the effect of plasma waves excitation on target normal sheath ion acceleration using fs laser‐irradiating hydrogenated structures

Measurements of ion acceleration in polymethylmethacrylate foils covered by a thin copper film irradiated by fs laser in target normal sheath acceleration regime are presented. The ion acceleration depends on the laser parameters, such as the pulse energy; depends on the irradiation conditions, such as the focal point position of the laser with respect to the target surface; and depends on the target properties, such as the metallic film thickness. The proton acceleration increases in the presence of the metallic film enhancing the plasma electron density, reaching about 1.6 MeV energy for a focal position on the target surface. The plasma diagnostics uses SiC detectors, absorber foils, Faraday cups, and gafchromic films. Employing p‐polarized laser light and a suitable oblique incidence, it is possible to increase the proton acceleration up to about 2.0 MeV thanks to the effects of laser absorption resonance due to plasma waves excitation.     

Tantalum ion acceleration in laser‐generated plasma and dependence on the pulse duration

The laser irradiation of tantalum targets is presented for different pulsed laser intensities ranging from 10¹⁰ up to about 10¹⁸ W/cm² and pulse durations from 9 ns up to 40 fs. The results show that the produced non‐equilibrium plasma accelerates Ta ions in the backward direction from values of the order of keV up to values of about 5 MeV. In thin foils, the forward plasma, developed behind the target along the direction of incoming laser, at intensities of about 10¹⁶ W/cm² and 300 ps pulse duration, accelerates Ta ions at energies of the order of 4.6 MeV and produces charge states up to about 40+. For fs lasers at intensities of the order of 10¹⁸ W/cm², only proton acceleration occurs up to 2.1 MeV while no Ta ions are accelerated, due to the reduced duration of the electric field and to the too high inertial mass of the Ta ions.     

Multielemental,Nutritional, and Proteomic Characterization of Different Lupinus spp. Genotypes: A Source of Nutrients for Dietary Use

Among grain pulses, lupins have recently gained considerable interest for a number of attractive nutritional attributes relating to their high protein and dietary fiber and negligible starch contents. The seeds of Lupinus albus (cv. Multitalia and Luxor, and the Modica ecotype); L. luteus (cv. Dukat, Mister, and Taper); and L. angustifolius (cv. Sonet) analyzed in this study were deposited within the germplasm collection of the Research Centre for Cereal and Industrial Crops of Acireale and were sowed in East Sicily in 2013/14. The collected seeds were analyzed for their multielemental micro- and macronutrient profiles, resulting in a wide variability between genotypes. Lupin seed flour samples were subjected to a defatting process using supercritical CO₂, with oil yields dependent on the species and genotype. We determined the fatty acid profile and tocopherol content of the lupin oil samples, finding that the total saturated fatty acid quantities of different samples were very close, and the total tocopherol content was about 1500.00 µg/g FW. The proteomic analysis of the defatted lupin seed flours showed substantial equivalence between the cultivars of the same species of Lupinus albus and L. luteus. Moreover, the L. angustifolius proteome map showed the presence of additional spots in comparison to L. albus, corresponding to α-conglutins. Lupin, in addition to being a good source of mineral elements, also contributes vitamin E and, thanks to the very high content of gamma-tocopherols, demonstrates powerful antioxidant activity.     

Numerical analysis of the Navier–Stokes/Darcy coupling

We consider a differential system based on the coupling of the Navier–Stokes and Darcy equations for modeling the interaction between surface and porous-media flows. We formulate the problem as an interface equation, we analyze the associated (nonlinear) Steklov–Poincaré operators, and we prove its well-posedness. We propose and analyze iterative methods to solve a conforming finite element approximation of the coupled problem.