Bilateral Riemann-Liouville Fractional Sobolev spaces

We establish some notation and properties of the bilateral Riemann-Liouville fractional derivative $D^s.$ We introduce the associated Sobolev spaces of fractional order $s$, denoted by $W^{s,1}(a,b)$, and the Bounded Variation spaces of fractional order $s$, denoted by $BV^{s}(a,b)$: these spaces are studied with the aim of providing a suitable functional framework for fractional variational models in image analysis

Riemann–Liouville Fractional Sobolev and Bounded Variation Spaces

none2noWe establish some properties of the bilateral Riemann–Liouville fractional derivative $D^s$. We set the notation, and study the associated Sobolev spaces of fractional order s, denoted by $W^{s,1}(a, b)$, and the fractional bounded variation spaces of fractional order s, denoted by $BV^s(a, b)$. Examples, embeddings and compactness properties related to these spaces are addressed, aiming to set a functional framework suitable for fractional variational models for image analysis.openAntonio Leaci; Franco TomarelliLeaci, Antonio; Tomarelli, Franc

Minimization of the buckling load of a clamped plate with perimeter constraint

We look for minimizers of the buckling load problem with perimeter constraint in any dimension. In dimension 2, we show that the minimizing plates are convex; in higher dimension, by passing through a weaker formulation of the problem, we show that any optimal set is open and connected. For higher eigenvalues, we prove that minimizers exist among convex sets with prescribed perimeter

Investigation of an outbreak of symptomatic SARS-CoV-2 VOC 202012/01-lineage B.1.1.7 infection in healthcare workers, Italy

Objectives: In December 2020, Italy began a national immunization campaign using the BNT162b2 coronavirus disease 2019 (COVID-19) mRNA vaccine, prioritizing healthcare workers (HCWs). Immune serum from vaccinated subjects seems (largely) to retain titres of neutralizing antibodies, even against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) VOC 202012/01-lineage B.1.1.7. Here, we describe an outbreak of SARS-CoV-2 lineage B.1.1.7 infection in three HCWs in a hospital setting; two of the HCWs were fully vaccinated (i.e. had received two doses). Methods: Two physicians and one nurse working on the same shift on 20th February 2021 were involved in the outbreak. Real-time PCR, antigen tests, and serological tests for the IgG anti-spike protein of SARS- CoV-2 were performed, along with whole-genome sequencing (WGS). Results: SARS-CoV-2 infection was confirmed in all three HCWs; all presented with mild symptoms of COVID-19. The two physicians were fully vaccinated with BNT162b2 vaccine, with the second dose administered 1 month before symptom onset. Both had high titres of IgG anti-spike antibodies at the time of diagnosis. WGS confirmed that all virus strains were VOC 202012/01-lineage B.1.1.7, suggesting a common source of exposure. Epidemiological investigation revealed that the suspected source was a SARS-CoV-2-positive patient who required endotracheal intubation due to severe COVID-19. All pro- cedures were carried out using a full suite of personal protective equipment (PPE). Conclusions: This mini-outbreak highlights some important issues about the efficacy of vaccines against transmission of SARS-CoV-2 variants, the high risk of exposure among HCWs, and the need for optimized implementation of PPE in hospitals. The wide circulation of VOC 202012/01 in Europe and Italy highlights the need to improve surveillance and genetic sequencing

Supplement: "Localization and broadband follow-up of the gravitational-wave transient GW150914" (2016, ApJL, 826, L13)

This Supplement provides supporting material for Abbott et al. (2016a). We briefly summarize past electromagnetic (EM) follow-up efforts as well as the organization and policy of the current EM follow-up program. We compare the four probability sky maps produced for the gravitational-wave transient GW150914, and provide additional details of the EM follow-up observations that were performed in the different bands

Constraints on cosmic strings using data from the first Advanced LIGO observing run

Cosmic strings are topological defects which can be formed in grand unified theory scale phase transitions in the early universe. They are also predicted to form in the context of string theory. The main mechanism for a network of Nambu-Goto cosmic strings to lose energy is through the production of loops and the subsequent emission of gravitational waves, thus offering an experimental signature for the existence of cosmic strings. Here we report on the analysis conducted to specifically search for gravitational-wave bursts from cosmic string loops in the data of Advanced LIGO 2015-2016 observing run (O1). No evidence of such signals was found in the data, and as a result we set upper limits on the cosmic string parameters for three recent loop distribution models. In this paper, we initially derive constraints on the string tension Gμ and the intercommutation probability, using not only the burst analysis performed on the O1 data set but also results from the previously published LIGO stochastic O1 analysis, pulsar timing arrays, cosmic microwave background and big-bang nucleosynthesis experiments. We show that these data sets are complementary in that they probe gravitational waves produced by cosmic string loops during very different epochs. Finally, we show that the data sets exclude large parts of the parameter space of the three loop distribution models we consider

Sulle soluzioni generalizzate di equazioni alle derivate parziali del primo ordine

In this paper we study two different boundary value problems for first order partial differential equations on sets of "finite perimeter".The second type of boundary value problems has been suggested by issues about the bounce problems

Relaxation Results for a Class of Variational Integrals

none2G.BUTTAZZO; A. LEACIG., Buttazzo; Leaci, Antoni