The Implicit Function Theorem for continuous functions

In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on topological manifolds. As a consequence, some versions of these classic theorems are proved when we consider differenciable (not necessarily C^1) maps.Comment: 9 pages, no figure

Pump-and-probe optical transmission phase shift as a quantitative probe of the Bogoliubov dispersion relation in a nonlinear channel waveguide

We theoretically investigate the dispersion relation of small-amplitude optical waves superimposing upon a beam of polarized monochromatic light propagating along a single-mode channel waveguide characterized by an instantaneous and spatially local Kerr nonlinearity. These small luminous fluctuations propagate along the waveguide as Bogoliubov elementary excitations on top of a one-dimensional dilute Bose quantum fluid evolve in time. They consequently display a strongly renormalized dispersion law, of Bogoliubov type. Analytical and numerical results are found in both the absence and the presence of one- and two-photon losses. Silicon and silicon-nitride waveguides are used as examples. We finally propose an experiment to measure this Bogoliubov dispersion relation, based on a stimulated four-wave mixing and interference spectroscopy techniques.Comment: 17 pages, 7 figure

Worrying about 'vertical landscapes'. Terraced olive groves and ecosystem services in marginal land in central Italy

Terraced Mediterranean areas are distinctive man-made landscapes with historical and cultural relevance. Terraced land abandonment driven by physical and economic constraints had important ecological consequences. This study focuses on a marginal agricultural district in southern Latium, central Italy, where terracing dated back to the Roman period and olive groves are the main agricultural use. A diachronic assessment of land-use transformations was carried out to identify landscape dynamics and drivers of change around terraced land. Terraced landscape systems (TLS), derived from spatial aggregation of neighboring terraced patches, have been analyzed for landscape transformations considering slope as the main stratification variable. Structural and functional characteristics of TLS were analyzed using a landscape ecology approach. Soil bio-chemical indicators were finally assessed to study the impact of terraced olive agro-ecosystems on soil-related ecosystems services. The empirical findings outlined that TLS in central Italy are sensitive to urbanization and land abandonment. Cultivated terraces prevailed up to gentle-medium slope land, uncultivated and wooded areas dominated terraces on steep slopes. In this context, poly-cultural olive groves proved to be a cropping system particularly resilient to global change, irrespective of land slope. Terraced systems and extensive poly-cultural olive groves play a role in preserving ecosystem integrity, landscape quality, soil functionality and, therefore, environmental sustainability

Assessing impacts of climate change on phenology and quality traits of Vitis vinifera L. The contribution of local knowledge

Developing adaptation strategies in Vitis vinifera, a crop sensitive to climate change, is crucial for resilience of traditional viticultural systems, especially in climate-vulnerable areas like the Mediterranean basin. A progressive warming is demonstrated to alter the geographical distribution of grapevine, reducing land capability for typical grapes and vine productions in most Southern European districts traditionally specialized in tree crops. Grapevine growth and reproduction under climate change require a continuous monitoring to adapt agronomic practices and strategies to global change. The present study illustrates an empirical approach grounded on a set of bio-physical indicators assessing the genotype-related response to climate variation. This approach was tested in Umbria, central Italy, to verify the response of some major international and local grapevine varieties to climate variation during a relatively long time interval (1995-2015). Long-term data for ripening time and berry quality collected in the study area were correlated to representative bioclimatic indices including Winkler, Huglin, and Cool night indicators. Results of this study highlighted the increase of air temperature (reflecting the inherent growth in thermal availability for maturation) and the alteration of precipitation patterns toward more intense precipitation. Climate variability exerted distinctive impacts on grapevine phenology depending on the related genotype. Empirical findings underline the usefulness of a permanent field monitoring of the relationship between selected climate variables and grape ripening with the aim to develop adaptive viticultural practices at farm\u2019s scale

Evaluation of degree of conversion, rate of cure, microhardness, depth of cure and contraction stress of three nano hybrid composites containing pre-polymerized spherical filler

Aim: Manufacturers aim at improving filler technology to enhance the properties of the restorative materials, thus maximising the aesthetic and functional outcome of the restored tooth. The present study tested the degree of conversion (DC), rate of cure (RC), microhardness (VHN), depth of cure (VHR) and contraction stress (CS) of three new nano hybrid composites with pre-polymerized spherical filler. Methods: Three commercially available composite resin were characterised in the present study, namely the Ceram.X\uae universal shade A3 (CXUA3), Ceram.X\uae duo enamel shade E2, and Ceram.X\uae duo dentin shade D3 (CXDE2 and CXDD3). The materials were light-cured with a LED light (SmartLite Focus, measured output 1301 mW/cm2) following the protocol recommended by the manufacturer. DC was assessed by means of Fourier-transform infrared spectroscopy, calculating RC from a second-grade polynomial fitting of the kinetic curve. A microhardness testing machine equipped with a Vickers indenter served to measure the top and bottom VHN of 2 mm-high disc-shaped specimens, using the bottom/top surface values ratio (VHR) as indirect evaluation of the depth of cure. CS vs time was evaluated by a universal testing machine provided with an extensometer as feedback system, CS was normalized for the specimen bonding area. All data sets underwent statistical analysis with dedicated software and tested for the assumptions for the use of parametric tests. Multiple analyses of variance with Scheff\ue9 post hoc test were carried out to compare the dependent variables of interest among the tested materials. Results: All tested materials exhibited a DC lower than 50%, with CXUA3 reaching the lowest DC value after 10 s. RC of CXUA3 at 5 s was comparable to that of CXDE2, while after 10s RC of CXUA3 decreased to a value proportional to that of CXDD3. For all the tested materials, top-VHN was greater than bottom-VHN. Top-VHN of CXDE2 was lower than CXUA3 and CXDD3. CXDD3 was the only material achieving VHR>80%. The main differences in CS among the tested materials were found during the irradiation with curing-light: CXDE2 displaying the lowest CS after 10 s and CXDD3 the highest after 30 s. Conclusion: The present study proved that the light curing protocol suggested by the manufacturer for the three composites might be improved: 10 s of irradiation seemed insufficient to adequately cure CXUA3 and CXDE2. Longer curing times for these materials appear advisable

In vitro and in vivo evaluation of T and B lymphocyte functions in AKR mice.

To investigate whether AKR spontaneous leukaemogenesis is associated with a reduction in functional activity of T lymphocytes, the PHA response of AKR blood cells at different ages up to and including the preleukaemic period was studied. No significant differences were observed among young, adult and preleukaemic donors. In addition, the in vitro and in vivo AKR lymphocyte functions were compared with those of CBA lymphocytes by means of their response to stimulation with T and B lymphocyte selective mitogens (PHA, Con A and LSP respectively), and their response to immunization with thymus dependent (SRBC) or independent (LPS) antigens. We observed in vitro that while the B lymphocytes responded normally to mitogen, an intrinsic hyporeactivity to mitogens characterizes the T lymphocytes. Moreover, AKR mice exhibited a reduced in vivo response to both thymus dependent and independent antigens