On the location of two blow up points on an annulus for the mean field equation

We consider the mean field equation on two-dimensional annular domains, and prove that if $P$ and $Q$ are two blow up points of a blowing-up solution sequence of the equation, then we must have $P=-Q$.Comment: To appear in CRA

Quantum corrections to the stress-energy tensor in thermodynamic equilibrium with acceleration

We show that the stress-energy tensor has additional terms with respect to the ideal form in states of global thermodynamic equilibrium in flat spacetime with non-vanishing acceleration and vorticity. These corrections are of quantum origin and their leading terms are second order in the gradients of the thermodynamic fields. Their relevant coefficients can be expressed in terms of correlators of the stress-energy tensor operator and the generators of the Lorentz group. With respect to previous assessments, we find that there are more second order coefficients and that all thermodynamic functions including energy density receive acceleration and vorticity dependent corrections. Notably, also the relation between \rho and p, that is the equation of state, is affected by acceleration and vorticity. We have calculated the corrections for a free real scalar field -- both massive and massless -- and we have found that they increase, particularly for a massive field, at very high acceleration and vorticity and very low temperature. Finally, these non-ideal terms depend on the explicit form of the stress-energy operator, implying that different stress-energy tensor of the scalar field -- canonical or improved -- are thermodynamically inequivalent.Comment: 18 pages, 1 figure. Minor changes, to appear in PR

New insight into the Pleistocene deposits of Monte delle Piche, Rome, and remarks on the biochronology of Hippopotamus (Mammalia, Hippopotamidae) and Stephanorhinus etruscus (Mammalia, Rhinocerotidae) in Italy

Several large mammal assemblages have been collected in the Roman basin since the XIX century, but they usually lack any stratigraphic datum or details about the fossiliferous localities. In this work, the stratigraphic provenance of large mammal remains discovered at Monte delle Piche (Rome) is investigated. The systematic revision of these specimens allows the recording of the presence of Hippopotamus sp., Stephanorhinus sp. and Stephanorhinus etruscus. On the basis of micropalaeontological analysis performed on sediment sampled from the studied specimens and considering the stratigraphy of the area, two fossiliferous levels are recognised at Monte delle Piche. The remain of the hippopotamus was collected in fluvial gravels and sand deposits, in which the presence of Cyprideis is also recorded. This deposit is chronologically related to the latest Early-early Middle Pleistocene. Hippopotamus was present in Italy and Western Europe from the latest Villafranchian to MIS 4/3. The mandible of S. etruscus was collected in marine deposits along with abundant foraminifera and ostracods, which correlate with the late Early Pleistocene. Stephanorhinus etruscus occurred in Western Europe at the beginning of the Villafranchian, and it was documented until the end of the Villafranchian in Italy and until the Early-Middle Pleistocene transition in the Iberian Peninsula

L∞-norm and energy quantization for the planar Lane–Emden problem with large exponent

For any smooth bounded domain (Formula presented.), we consider positive solutions to (Formula presented.)which satisfy the uniform energy bound (Formula presented.)for (Formula presented.). We prove convergence to (Formula presented.) as (Formula presented.) of the (Formula presented.)-norm of any solution. We further deduce quantization of the energy to multiples of (Formula presented.), thus completing the analysis performed in De Marchis et al. (J Fixed Point Theory Appl 19:889–916, 2017)

The effect of primordial non-Gaussianity on the skeleton of cosmic shear maps

(abridged) We explore the imprints of deviations from Gaussian primordial density fluctuations on the skeleton of the large-scale matter distribution as mapped through cosmological weak lensing. We computed the skeleton length of simulated effective convergence maps covering $\sim 35$ sq. deg each, extracted from a suite of cosmological $n-$body runs with different levels of local primordial non-Gaussianity. The latter is expected to alter the structure formation process with respect to the fiducial Gaussian scenario, and thus to leave a signature on the cosmic web. We found that alterations of the initial conditions consistently modify both the cumulative and the differential skeleton length, although the effect is generically smaller than the cosmic variance and depends on the smoothing of the map prior to the skeleton computation. Nevertheless, the qualitative shape of these deviations is rather similar to their primordial counterparts, implying that skeleton statistics retain good memory of the initial conditions. We performed a statistical analysis in order to find out at what Confidence Level primordial non-Gaussianity could be constrained by the skeleton test on cosmic shear maps of the size we adopted. At 68.3% Confidence Level we found an error on the measured level of primordial non-Gaussianity of $\Delta f_\mathrm{NL}\sim 300$, while at 90% Confidence Level it is of $\Delta f_\mathrm{NL}\sim 500$. While these values by themselves are not competitive with the current constraints, weak lensing maps larger than those used here would have a smaller field-to-field variance, and thus would likely lead to tighter constraints. A rough estimate indicates $\Delta f_\mathrm{NL} \sim$ a few tens at 68.3% Confidence Level for an all-sky weak lensing survey.Comment: 11 pages, 9 figures. Accepted for publication on MNRA

Produção de mudas de espécies lenhosas.

Planejamento das instalações para produção de mudas; Técnicas de produção de mudas.bitstream/CNPF-2009-09/43217/1/doc130.pd