Discontinuities Cause Essential Spectrum on Surfaces

Two-dimensional maps with discontinuities are considered. It is shown that, in the presence of discontinuities, the essential spectrum of the transfer operator is large whenever it acts on a Banach space with norm that is stronger than L infinity\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}L<^>\infty \end{document} or BV\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$BV$$\end{document}. Three classes of examples are introduced and studied, both expanding and partially expanding. In two dimensions, there is complication due to the geometry of the discontinuities, an issue not present in the one-dimensional case and which is explored in this work

Influence of mineral fillers on the rheological response of polymer-modified bitumens and mastics

AbstractThe rheological properties of the bituminous components (bitumen and bituminous mastic) within asphalt mixtures contribute significantly to the major distresses of flexible pavements (i.e. rutting, fatigue and low temperature cracking). Asphalt mixtures are usually composed of mastic-coated aggregates rather than pure bitumen-coated aggregates. The purpose of this study is to investigate the effects of mineral fillers on the rheological behaviour of several polymer-modified bitumens (PMBs) through laboratory mixing. A neat bitumen and two types of polymers (elastomeric and plastomeric) were used to produce PMBs, and two fillers with different minerals (limestone and basalt) were selected to obtain mastics. The dynamic shear rheometer (DSR) and bending beam rheometer (BBR) were used to characterize the rheological properties of PMBs and mastics. In particular, multiple stress creep recovery (MSCR) tests were performed to evaluate the rutting potential at high temperatures, whereas BBR tests were carried out to investigate the low temperature behaviour of these materials. BBR results for unmodified mastics show that the increase of stiffness is similar regardless of the filler type, whereas results for polymer-modified mastics indicate that the degree of stiffening depends on the combination of filler/polymer types. MSCR results show that adding filler leads to a reduced susceptibility of permanent deformation and an enhanced elastic response, depending on the combination of filler/polymer types. Overall results suggest that a physical–chemical interaction between the filler and bitumen occurs, and that the interaction level is highly dependent on the type of polymer modification

First optical validation of a Schwarzschild Couder telescope: the ASTRI SST-2M Cherenkov telescope

The Cherenkov Telescope Array (CTA) represents the most advanced facility designed for Cherenkov Astronomy. ASTRI SST-2M has been developed as a demonstrator for the Small Size Telescope in the context of the upcoming CTA. Its main innovation consists in the optical layout which implements the Schwarzschild-Couder configuration and is fully validated for the first time. The ASTRI SST-2M optical system represents the first qualified example for two mirrors telescope for Cherenkov Astronomy. This configuration permits to (i) maintain a high optical quality across a large FoV (ii) de-magnify the plate scale, (iii) exploit new technological solutions for focal plane sensors. The goal of the paper is to present the optical qualification of the ASTRI SST-2M telescope. The qualification has been obtained measuring the PSF sizes generated in the focal plane at various distance from the optical axis. These values have been compared with the performances expected by design. After an introduction on the Gamma Astronomy from the ground, the optical design and how it has been implemented for ASTRI SST-2M is discussed. Moreover the description of the setup used to qualify the telescope over the full field of view is shown. We report the results of the first--light optical qualification. The required specification of a flat PSF of $\sim 10$ arcmin in a large field of view ~10 deg has been demonstrated. These results validate the design specifications, opening a new scenario for Cherenkov Gamma ray Astronomy and, in particular, for the detection of high energy (5 - 300 TeV) gamma rays and wide-field observations with CTA.Comment: 6 pages, 5 figure

Characterization of multilayer stack parameters from X-ray reflectivity data using the PPM program: measurements and comparison with TEM results

Future hard (10 -100 keV) X-ray telescopes (SIMBOL-X, Con-X, HEXIT-SAT, XEUS) will implement focusing optics with multilayer coatings: in view of the production of these optics we are exploring several deposition techniques for the reflective coatings. In order to evaluate the achievable optical performance X-Ray Reflectivity (XRR) measurements are performed, which are powerful tools for the in-depth characterization of multilayer properties (roughness, thickness and density distribution). An exact extraction of the stack parameters is however difficult because the XRR scans depend on them in a complex way. The PPM code, developed at ERSF in the past years, is able to derive the layer-by-layer properties of multilayer structures from semi-automatic XRR scan fittings by means of a global minimization procedure in the parameters space. In this work we will present the PPM modeling of some multilayer stacks (Pt/C and Ni/C) deposited by simple e-beam evaporation. Moreover, in order to verify the predictions of PPM, the obtained results are compared with TEM profiles taken on the same set of samples. As we will show, PPM results are in good agreement with the TEM findings. In addition, we show that the accurate fitting returns a physically correct evaluation of the variation of layers thickness through the stack, whereas the thickness trend derived from TEM profiles can be altered by the superposition of roughness profiles in the sample image

Effect of feeding extruded flaxseed on milk quality of dairy cows

Aim of the present study was to evaluate the effect of feeding dairy cows with extruded flaxseed (EF) on milk quality. After a 7-d adaptation period, 40 Holstein dairy cows in midlactation were divided in two experimental groups, based on parity, milk yield and composition, and days in milk. Animals were fed for 28 d a standard total mixed ration containing or not (control) 1.8 kg/cow/d of a supplement based on extruded flaxseed (EF). Milk yield was recorded daily and individual milk samples were collected weekly for analysis. Milk yield was not affected by treatment and averaged 26.2 kg/d throughout the study. Feeding EF reduced milk fat (3.95 vs. 4.24%; P=0.053) and tended to reduce milk protein (3.32 vs. 3.50%; P=0.104). The milk from cows fed EF contained more (P<0.01) stearic (12.0 vs. 7.8 mg/100 mg of fat), oleic (21.2 vs. 18.0 mg/100 mg of fat), \u3b1-linolenic (0.85 vs. 0.41 mg/100 mg of fat) and vaccenic (1.43 vs. 0.62 mg/100 mg of fat) acids than control and also more c9,t11 CLA (0.91 vs. 0.59 mg/100 mg of fat). Conversely, compared with control, feeding EF reduced milk concentrations of palmitic acid (26.5 vs. 33.4 mg/100 mg of fat; P<0.01). The present results show that feeding EF to dairy cows is an efficient strategy to enrich milk in beneficial fatty acids such as vaccenic acid, CLA and omega-3 fatty acids. Nevertheless, the milk fat reducing effect of flaxseed as well as other sources of polyunsaturated fatty acids should be taken into account

Negotiating Narrative: Dialogic Dynamics of Known, Unknown and Believed in Harry Potter and Deathly Hallows

Abstract presentato al Convegno \u201cDialogue Analysis: Literature as Dialogue\u201d, 14th Conference of the International Association for Dialogue Analysis, 2nd - 4th April 2012, \uc5bo Akademi University, Turku, Finlan