Inflectional loci of scrolls

Let $X\subset \mathbb P^N$ be a scroll over a smooth curve $C$ and let \L=\mathcal O_{\mathbb P^N}(1)|_X denote the hyperplane bundle. The special geometry of $X$ implies that some sheaves related to the principal part bundles of \L are locally free. The inflectional loci of $X$ can be expressed in terms of these sheaves, leading to explicit formulas for the cohomology classes of the loci. The formulas imply that the only uninflected scrolls are the balanced rational normal scrolls.Comment: 9 pages, improved version. Accepted in Mathematische Zeitschrif

Stabilization in relation to wavenumber in HDG methods

Simulation of wave propagation through complex media relies on proper understanding of the properties of numerical methods when the wavenumber is real and complex. Numerical methods of the Hybrid Discontinuous Galerkin (HDG) type are considered for simulating waves that satisfy the Helmholtz and Maxwell equations. It is shown that these methods, when wrongly used, give rise to singular systems for complex wavenumbers. A sufficient condition on the HDG stabilization parameter for guaranteeing unique solvability of the numerical HDG system, both for Helmholtz and Maxwell systems, is obtained for complex wavenumbers. For real wavenumbers, results from a dispersion analysis are presented. An asymptotic expansion of the dispersion relation, as the number of mesh elements per wave increase, reveal that some choices of the stabilization parameter are better than others. To summarize the findings, there are values of the HDG stabilization parameter that will cause the HDG method to fail for complex wavenumbers. However, this failure is remedied if the real part of the stabilization parameter has the opposite sign of the imaginary part of the wavenumber. When the wavenumber is real, values of the stabilization parameter that asymptotically minimize the HDG wavenumber errors are found on the imaginary axis. Finally, a dispersion analysis of the mixed hybrid Raviart-Thomas method showed that its wavenumber errors are an order smaller than those of the HDG method

Transport Models for Backscattering and Transmission of Low Energy ( \u3c 3 Kilovolts) Electrons from Solids

This paper deals with the backscattering and the transmission of electrons with energy \u3c 3 keV through thin self supporting films, or on bulk metals. We present the main theoretical models used in such problems, and we analyse mainly the models based on the Boltzmann transport equation, similar to those developed in our laboratory. For any model shown here, we try to give the precise domain in which they give reliable results as well as the limitations connected to the simplifying assumptions. In the case of the most sophisticated model, we give original results for copper. The models are presented in a comparative form, and when it is possible we compare our results with the experimental ones. The theoretical models were applied to Al and Cu. We give, for bulk metals, the values of the backscattering yield, and the energy distributions of backscattered electrons. In the case of thin self supporting films, we studied mainly the backscattering and transmission coefficients, as well as the energy distributions of transmitted and backscattered electrons

Secondary Electron Emission Induced by Electron Bombardment of Polycrystalline Metallic Targets

The aim of the present paper is the analysis of the backward secondary electron emission phenomenon, under electron bombardment, on the basis of experimental and theoretical results. Among the theoretical models, we will mention the phenomenological models, those which use a Monte-Carlo type simulation method, and those based on the numerically solved Boltzmann transport equation. To correlate experimental and theoretical results on all the data characterizing this phenomenon, it is necessary to use an appropriate description for the excitation process of the internal secondary electrons; it also needs a complete description of the transport process for the excited electrons, which incorporates the elastic and inelastic interactions, as well as the energy and angular distribution of the incident primary beam. From this, it follows that it will be necessary, either to use a direct Monte-Carlo simulation method, or, in the case of the transport model, to carry out a preliminary treatment of the primary electron dispersion; this treatment is also based upon a Boltzmann equation resolution. The results of such an analysis will be useful in electron microscopy and in quantitative Auger spectroscopy

Circularly-Polarized Discrete Lens Antennas in the 60-GHz Band

This paper presents the design and demonstration of two circularly-polarized transmit-arrays operating in the 60-GHz band and generating a broadside beam and a 30°-tilted beam respectively. These arrays have a fairly simple structure with only three metal layers and are fabricated with a standard printed-circuit board technology. The simulated results show the performances of the unit-cells as well as the whole arrays, and detail their power budget. The experimental results in V-band are in very good agreement with the simulations and demonstrate very satisfactory characteristics. Power efficiencies up to 53.7% are reached with a 1-dB gain-bandwidth up to 9.1%, and low cross-polarization level

Recommendations for headache service organisation and delivery in Europe.

Headache disorders are a major public-health priority, and there is pressing need for effective solutions to them. Better health care for headache—and ready access to it—are central to these solutions; therefore, the organisation of headache-related services within the health systems of Europe becomes an important focus. These recommendations are the result of collaboration between the European Headache Federation and Lifting The Burden: the Global Campaign against Headache. The process of development included wide consultation. To meet the very high level of need for headache care both effectively and efficiently, the recommendations formulate a basic three-level model of health-care organisation rationally spread across primary and secondary health-care sectors, taking account of the different skills and expertise in these sectors. They recognise that health services are differently structured in countries throughout Europe, and not always adequately resourced. Therefore, they aim to be adaptable to suit these differences. They are set out in five sections: needs assessment, description of the model, adaptation, standards and educational implications

Bone and Energy Metabolism Parameters in Professional Cyclists during the Giro d’Italia 3-Weeks Stage Race

Cycling is a not weight-bearing activity and is known to induce bone resorption. Stage races are really strenuous endurance performances affecting the energy homeostasis. The recently highlighted link, in the co-regulation of bone and energy metabolism, demonstrates a central role for the equilibrium between carboxylated and undercarboxylated forms of osteocalcin. Aim of this study was to understand the acute physiological responses to a cycling stage race in terms of bone turnover and energy metabolism and the possible co-regulative mechanisms underlying their relationship. We studied nine professional cyclists engaged in 2011 Giro d'Italia stage race. Pre-analytical and analytical phases tightly followed academic and anti-doping authority's recommendations. Bone and energy metabolism markers (bone alkaline phosphatase, tartrate-resistant acid phosphatase 5b, total and undercarboxylated osteocalcin, leptin and adiponectin) and related hormones (cortisol and testosterone) were measured, by Sandwich Enzyme Immunoassays, at days -1 (pre-race), 12 and 22 during the race. The power output and the energy expenditure (mean and accumulated) were derived and correlated with the biochemical indexes. During the race, bone metabolism showed that an unbalance in behalf of resorption, which is enhanced, occurred along with a relative increase in the concentration of the undercarboxylated form of osteocalcin that was indirectly related to the enhanced energy expenditure, through adipokines modifications, with leptin decrease (high energy consumption) and adiponectin increase (optimization of energy expenditure). The exertion due to heavy effort induced a decrease of cortisol, while testosterone levels resulted unchanged. In conclusion, during a 3-weeks stage race, bone metabolism is pushed towards resorption. A possible relationship between the bone and the energy metabolisms is suggested by the relative correlations among absolute and relative concentrations trends of undercarboxylated OC, adipokines concentrations, BMI, fat mass (%), power output and the derived energy expenditure

Osculation for conic fibrations

Smooth projective surfaces fibered in conics over a smooth curve are investigated with respect to their k-th osculatory behavior. Due to the bound for the dimension of their osculating spaces they do not differ at all from a general surface for k=2, while their structure plays a significant role for k \geq 3. The dimension of the osculating space at any point is studied taking into account the possible existence of curves of low degree transverse to the fibers, and several examples are discussed to illustrate concretely the various situations arising in this analysis. As an application, a complete description of the osculatory behavior of Castelnuovo surfaces, i.e. rational surfaces whose hyperplane sections correspond to a linear system of nodal quartic plane curves. is given. The case k=3 for del Pezzo surfaces is also discussed, completing the analysis done for k=2$ i a previous paper of the authors (2001). Moreover, for conic fibrations X in P^N, whose k-th inflectional locus has the expected codimension a precise description of this locus is provided in terms of Chern classes. In particular, for N=8, it turns out that either X is hypo-osculating for k=3, or its third inflectional locus is 1-dimensional