Functionals depending on curvatures with constraints

We deal with a family of functionals depending on curvatures and we prove for them compactness and semicontinuity properties in the class of closed and bounded sets which satisfy a uniform exterior and interior sphere condition. We apply the results to state an existence theorem for the Nitzberg and Mumford problem under this additional constraint.Comment: 20 pages. To appear on Rendiconti del Seminario Matematico dell'Universita' di Padov

Local calibrations for minimizers of the Mumford-Shah functional with a regular discontinuity set

Using a calibration method, we prove that, if w is a function which satisfies all Euler conditions for the Mumford-Shah functional on a two-dimensional domain, and the discontinuity set S of w is a regular curve connecting two boundary points, then there exists a uniform neighbourhood U of S such that w is a minimizer of the Mumford-Shah functional on U with respect to its own boundary conditions. We show that Euler conditions do not guarantee in general the minimality of w in the class of functions with the same boundary value of w and whose extended graph is contained in a neighbourhood of the extended graph of w, and we give a sufficient condition in terms of the geometrical properties of the domain and the discontinuity set under which this kind of minimality holds.Comment: 31 pages, 2 figure

Local calibrations for minimizers of the Mumford-Shah functional with rectilinear discontinuity sets

Using a calibration method, we prove that, if $w$ is a function which satisfies all Euler conditions for the Mumford-Shah functional on a two-dimensional open set $\Omega$, and the discontinuity set of $w$ is a segment connecting two boundary points, then for every point $(x_0, y_0)$ of $\Omega$ there exists a neighbourhood $U$ of $(x_0, y_0)$ such that $w$ is a minimizer of the Mumford-Shah functional on $U$ with respect to its own boundary values on $\partial U$.Comment: 22 pages, 4 figure

Diversity of Epigeal Ants (Hymenoptera: Formicidae) in Urban Areas of Alto Tietê

The objective of this study was to conduct an inventory of the ant fauna, evaluating indicators of diversity, litter community composition and similarity among seven areas located around the city of Mogi das Cruzes (SP). In each area 20 pitfalls were distributed, which remained in the field for seven days. Four samplings were performed, two in the rainy season and two during dry season. In total there were 92 recorded species, 36 genera, 19 tribes and seven subfamilies. The most frequent species belong to the genera Pheidole and Camponotus, both common in the Neotropics. Differences were observed in species composition with the formation of two groups, one under the influence of the Atlantic Forest and other in the urban region. Only one exotic species, Paratrechina longicornis, was recorded. The results indicate the importance of the forest surrounding the city to maintain the biological diversity of ant communities

Populists in power: from Municipalities to (European) Parliament, The case of the Italian Five star Movement

The article focuses on the strategic evolution of the Italian Five Star Movement (Movimento 5 Stelle\u2014M5S). The party was born in 2009 as a local and civic experience and it represents a new example of populism characterized by unprecedented traits. In 2010 the M5S obtained its first representatives during regional elections and in 2012 it achieved its first Major in a big town (Parma, in the heart of Italy)

Eccrine Syringofibroadenoma of the Eyelid

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Experimental investigation on CO2methanation process for solar energy storage compared to CO2-based methanol synthesis

The utilization of the captured CO2 as a carbon source for the production of energy storage media offers a technological solution for overcoming crucial issues in current energy systems. Solar energy production generally does not match with energy demand because of its intermittent and non-programmable nature, entailing the adoption of storage technologies. Hydrogen constitutes a chemical storage for renewable electricity if it is produced by water electrolysis and is also the key reactant for CO2 methanation (Sabatier reaction). The utilization of CO2 as a feedstock for producing methane contributes to alleviate global climate changes and sequestration related problems. The produced methane is a carbon neutral gas that fits into existing infrastructure and allows issues related to the aforementioned intermittency and non-programmability of solar energy to be overcome. In this paper, an experimental apparatus, composed of an electrolyzer and a tubular fixed bed reactor, is built and used to produce methane via Sabatier reaction. The objective of the experimental campaign is the evaluation of the process performance and a comparison with other CO2 valorization paths such as methanol production. The investigated pressure range was 2–20 bar, obtaining a methane volume fraction in outlet gaseous mixture of 64.75% at 8 bar and 97.24% at 20 bar, with conversion efficiencies of, respectively, 84.64% and 99.06%. The methanol and methane processes were compared on the basis of an energy parameter defined as the spent energy/stored energy. It is higher for the methanol process (0.45), with respect to the methane production process (0.41–0.43), which has a higher energy storage capability

Relationship between adipose tissue dysfunction, Vitamin D deficiency and the pathogenesis of non-alcoholic fatty liver disease

Non-alcoholic fatty liver disease ( NAFLD) is the most common chronic liver disease worldwide. Its pathogenesis is complex and not yet fully understood. Over the years many studies have proposed various pathophysiological hypotheses, among which the currently most widely accepted is the "multiple parallel hits" theory. According to this model, lipid accumulation in the hepatocytes and insulin resistance increase the vulnerability of the liver to many factors that act in a coordinated and cooperative manner to promote hepatic injury, inflammation and fibrosis. Among these factors, adipose tissue dysfunction and subsequent chronic low grade inflammation play a crucial role. Recent studies have shown that vitamin D exerts an immune-regulating action on adipose tissue, and the growing wealth of epidemiological data is demonstrating that hypovitaminosis D is associated with both obesity and NAFLD. Furthermore, given the strong association between these conditions, current findings suggest that vitamin D may be involved in the relationship between adipose tissue dysfunction and NAFLD. The purpose of this review is to provide an overview of recent advances in the pathogenesis of NAFLD in relation to adipose tissue dysfunction, and in the pathophysiology linking vitamin D deficiency with NAFLD and adiposity, together with an overview of the evidence available on the clinical utility of vitamin D supplementation in cases of NAFLD

Mutational Analysis of c-KIT and PDGFRA in Canine Gastrointestinal Stromal Tumors (GISTs)

Gastrointestinal stromal tumors (GISTs) are the most common mesenchymal tumors of the canine gastrointestinal tract and are diagnosed by the immunohistochemical expression of the receptor tyrosine kinase (RTK) KIT. Activating mutations of the proto-oncogenes c-KIT and PDGFRA drive GIST oncogenesis and are used to predict the response to RTK-inhibitors in human oncology. Currently, the frequency and significance of these mutations in canine GIST have not been adequately explored. Therefore, we investigated the mutational status of c-KIT (exons 9, 11 and 13) and PDGFRA (exons 12 and 18) genes by PCR followed by fragment analysis for c-KIT deletions and PCR followed by screening with DHPLC and direct sequencing confirmation for single nucleotide variations in 17 formalin-fixed paraffin-embedded canine GISTs confirmed by KIT immunopositivity. c-KIT mutations were detected in 47% of cases, with a mutation detection rate significantly higher (p = 0.0004, Fisher's exact test) and always involving exon 11. A PDGFRA gene mutation (exon 18) was identified in one case. Even if follow-up data were not available for all cases, four cases with documented abdominal metastases displayed c-KIT mutations. These data confirm that c-KIT exon 11 mutations occur frequently in canine GISTs, and identify the presence of a PDGFRA mutation similar to human GISTs. This study also suggests a potential association of c-KIT mutation with more aggressive biological behavior