An isoperimetric inequality in the plane with a log-convex density

Given a positive lower semi-continuous density $f$ on $\mathbb{R}^2$ the weighted volume $V_f:=f\mathscr{L}^2$ is defined on the $\mathscr{L}^2$-measurable sets in $\mathbb{R}^2$. The $f$-weighted perimeter of a set of finite perimeter $E$ in $\mathbb{R}^2$ is written $P_f(E)$. We study minimisers for the weighted isoperimetric problem $$I_f(v):=\inf\Big\{ P_f(E):E\text{ is a set of finite perimeter in }\mathbb{R}^2\text{ and }V_f(E)=v\Big\}$$ for $v>0$. Suppose $f$ takes the form $f:\mathbb{R}^2\rightarrow(0,+\infty);x\mapsto e^{h(|x|)}$ where $h:[0,+\infty)\rightarrow\mathbb{R}$ is a non-decreasing convex function. Let $v>0$ and $B$ a centred ball in $\mathbb{R}^2$ with $V_f(B)=v$. We show that $B$ is a minimiser for the above variational problem and obtain a uniqueness result

Survey of neonatal respiratory care and surfactant administration in very preterm infants in the Italian Neonatal Network.

INTRODUCTION: Variation of respiratory care is described between centers around the world. The Italian Neonatal Network (INN), as a national group of the Vermont-Oxford Network (VON) allows to perform a wide analysis of respiratory care in very low birth weight infants. METHODS: We analyzed the dataset of infants enrolled in the INN in 2009 and 2010 and, for surfactant administration only, from 2006 to 2010 from 83 participating centers. All definitions are those of the (VON). A questionnaire analysis was also performed with a questionnaire on centers practices. RESULTS: We report data for 8297 infants. Data on ventilator practices and outcomes are outlined. Variation for both practices and outcome is found. Trend in surfactant administration is also analyzed. CONCLUSIONS. The great variation across hospitals in all the surveyed techniques points to the possibility of implementing potentially better practices with the aim of reducing unwanted variation. These data also show the power of large neonatal networks in identifying areas for potential improvement

Survey of neonatal respiratory care and surfactant administration in very preterm infants in the Italian neonatal network.

Introduction: Variation of respiratory care is described between centers around the world.The Italian Neonatal Network (INN), as a national group of the Vermont-Oxford Network (VON) allows to perform a wide analysis of respiratory care in very low birth weight infants. Methods:We analyzed the dataset of infants enrolled in the INN in 2009 and 2010 and, for surfactant administration only, from 2006 to 2010 from 83 participating centers. All definitions are those of the (VON). A questionnaire analysis was also performed with a questionnaire on centers practices. Results: We report data for 8297 infants. Data on ventilator practices and outcomes are outlined. Variation for both practices and outcome is found. Trend in surfactant administration is also analyzed. Conclusions. The great variation across hospitals in all the surveyed techniques points to the possibility of implementing potentially better practices with the aim of reducing unwanted variation. These data also show the power of large neonatal networks in identifying areas for potential improvement

Sensor response and radiation damage effects for 3D pixels in the ATLAS IBL Detector

Abstract Pixel sensors in 3D technology equip the outer ends of the staves of the Insertable B Layer (IBL), the innermost layer of the ATLAS Pixel Detector, which was installed before the start of LHC Run 2 in 2015. 3D pixel sensors are expected to exhibit more tolerance to radiation damage and are the technology of choice for the innermost layer in the ATLAS tracker upgrade for the HL-LHC programme. While the LHC has delivered an integrated luminosity of  ≃ 235 fb-1 since the start of Run 2, the 3D sensors have received a non-ionising energy deposition corresponding to a fluence of ≃ 8.5 × 1014 1 MeV neutron-equivalent cm-2 averaged over the sensor area. This paper presents results of measurements of the 3D pixel sensors' response during Run 2 and the first two years of Run 3, with predictions of its evolution until the end of Run 3 in 2025. Data are compared with radiation damage simulations, based on detailed maps of the electric field in the Si substrate, at various fluence levels and bias voltage values. These results illustrate the potential of 3D technology for pixel applications in high-radiation environments.</jats:p

Sensor response and radiation damage effects for 3D pixels in the ATLAS IBL Detector

Abstract Pixel sensors in 3D technology equip the outer ends of the staves of the Insertable B Layer (IBL), the innermost layer of the ATLAS Pixel Detector, which was installed before the start of LHC Run 2 in 2015. 3D pixel sensors are expected to exhibit more tolerance to radiation damage and are the technology of choice for the innermost layer in the ATLAS tracker upgrade for the HL-LHC programme. While the LHC has delivered an integrated luminosity of  ≃ 235 fb-1 since the start of Run 2, the 3D sensors have received a non-ionising energy deposition corresponding to a fluence of ≃ 8.5 × 1014 1 MeV neutron-equivalent cm-2 averaged over the sensor area. This paper presents results of measurements of the 3D pixel sensors' response during Run 2 and the first two years of Run 3, with predictions of its evolution until the end of Run 3 in 2025. Data are compared with radiation damage simulations, based on detailed maps of the electric field in the Si substrate, at various fluence levels and bias voltage values. These results illustrate the potential of 3D technology for pixel applications in high-radiation environments.</jats:p