Optimal Szeg\"o-Weinberger type inequalities

Denote with $\mu_{1}(\Omega;e^{h\left(|x|\right)})$ the first nontrivial eigenvalue of the Neumann problem \begin{equation*} \left\{\begin{array}{lll} -\text{div}\left(e^{h\left(|x|\right)}\nabla u\right) =\mu e^{h\left(|x|\right)}u & \text{in} & \Omega & & \frac{\partial u}{\partial \nu}=0 & \text{on} & \partial \Omega , \end{array} \right. \end{equation*} where $\Omega$ is a bounded and Lipschitz domain in $\mathbb{R}^{N}$. Under suitable assumption on $h$ we prove that the ball centered at the origin is the unique set maximizing $\mu_{1}(\Omega;e^{h\left(|x|\right)})$ among all Lipschitz bounded domains $\Omega$ of $\mathbb{R}^{N}$ of prescribed $e^{h\left(|x|\right)}dx$-measure and symmetric about the origin. Moreover, an example in the model case $h\left(|x|\right) =|x|^{2},$ shows that, in general, the assumption on the symmetry of the domain cannot be dropped. In the one-dimensional case, i.e. when $\Omega$ reduces to an interval $(a,b),$ we consider a wide class of weights (including both Gaussian and anti-Gaussian). We then describe the behavior of the eigenvalue as the interval $(a,b)$ slides along the $x$-axis keeping fixed its weighted length

Uniformly bounded representations and completely bounded multipliers of SL(2,R)

We estimate the norms of many matrix coefficients of irreducible uniformly bounded representations of SL(2, R) as completely bounded multipliers of the Fourier algebra. Our results suggest that the known inequality relating the uniformly bounded norm of a representation and the completely bounded norm of its coefficients may not be optimal

An eigenvalue problem for the anisotropic Φ\Phi-Laplacian

We study an eigenvalue problem involving a fully anisotropic elliptic differential operator in arbitrary Orlicz-Sobolev spaces. The relevant equations are associated with constrained minimization problems for integral functionals depending on the gradient of competing functions through general anisotropic $N$-functions. In particular, the latter need neither be radial, nor have a polynomial growth, and are not even assumed to satisfy the so called $\Delta_2$-condition. The resulting analysis requires the development of some new aspects of the theory of anisotropic Orlicz-Sobolev spaces

Experimental assessment on exploiting low carbon ethanol fuel in a light-duty dual-fuel compression ignition engine

Compression ignition (CI) engines are widely used in modern society, but they are also recognized as a significative source of harmful and human hazard emissions such as particulate matter (PM) and nitrogen oxides (NOx). Moreover, the combustion of fossil fuels is related to the growing amount of greenhouse gas (GHG) emissions, such as carbon dioxide (CO2). Stringent emission regulatory programs, the transition to cleaner and more advanced powertrains and the use of lower carbon fuels are driving forces for the improvement of diesel engines in terms of overall efficiency and engine-out emissions. Ethanol, a light alcohol and lower carbon fuel, is a promising alternative fuel applicable in the dual-fuel (DF) combustion mode to mitigate CO2 and also engine-out PM emissions. In this context, this work aims to assess the maximum fuel substitution ratio (FSR) and the impact on CO2 and PM emissions of different nozzle holes number injectors, 7 and 9, in the DF operating mode. The analysis was conducted within engine working constraints and considered the influence on maximum FSR of calibration parameters, such as combustion phasing, rail pressure, injection pattern and exhaust gas recirculation (EGR). The experimental tests were carried out on a single-cylinder light-duty CI engine with ethanol introduced via port fuel injection (PFI) and direct injection of diesel in two operating points, 1500 and 2000 rpm and at 5 and 8 bar of brake mean effective pressure (BMEP), respectively. Noise and the coefficient of variation in indicated mean effective pressure (COVIMEP) limits have been chosen as practical constraints. In particular, the experimental analysis assesses for each parameter or their combination the highest ethanol fraction that can be injected. To discriminate the effect on ethanol fraction and the combustion process of each parameter, a one-at-a-time-factor approach was used. The results show that, in both operating points, the EGR reduces the maximum ethanol fraction injectable; nevertheless, the ethanol addition leads to outstanding improvement in terms of engine-out PM. The adoption of a 9 hole diesel injector, for lower load, allows reaching a higher fraction of ethanol in all test conditions with an improvement in combustion noise, on average 3 dBA, while near-zero PM emissions and a reduction can be noticed, on the average of 1 g/kWh, and CO2 compared with the fewer nozzle holes case. Increasing the load insensitivity to different holes number was observed

Pilot Study of a New Mandibular Advancement Device

This study was conducted to determine the efficacy of a customized mandibular advancement device (MAD) in the treatment of obstructive sleep apnea (OSA). Eight patients (M = 3; F = 5; mean age = 56.3 ± 9.4) with a diagnosis of OSA confirmed by polysomnography (PSG) were re-cruited on the basis of the following inclusion criteria: apnea-hypopnea index (AHI) > 5, age between 18 and 75 years, body mass index (BMI) < 25, and PSG data available at baseline (T0). All were treated with the new NOA® MAD by OrthoApnea (NOA® ) for at least 3 months; PSG with NOA in situ was performed after 3 months of treatment (T1). The following parameters were calculated at T0 and T1: AHI, supine AHI, oxygen desaturation index (ODI), percentage of recording time spent with oxygen saturation <90% (SpO2 < 90%), and mean oxygen desaturation (MeanSpO2%). Data were submitted for statistical analysis. The baseline values were AHI = 21.33 ± 14.79, supine AHI = 35.64 ± 12.80, ODI = 17.51 ± 13.5, SpO2 < 90% = 7.82 ± 17.08, and MeanSpO2% = 93.45 ± 1.86. Four patients had mild OSA (5 > AHI < 15), one moderate OSA (15 > AHI < 30), and three severe OSA (AHI > 30). After treatment with NOA®, statistically significant improvements in AHI (8.6 ± 4.21) and supine AHI (11.21 ± 7.26) were recorded. OrthoApnea NOA® could be an effective alternative in the treatment of OSA: the device improved the PSG parameters assessed

Age-dependent skewing of X chromosome inactivation appears delayed in centenarians\u2019 offspring. Is there a role for allelic imbalance in Healthy Aging and Longevity?

Recently, it has been proposed that age-related X chromosome inactivation (XCI) skewing can clinically result in late-onset X-linked disorders. This observation leads to hypothesize that age-related skewed XCI might also influence lifespan in women. To investigate this issue, we employed a new experimental model of longevity and healthy aging including 55 female centenarians, 40 of their offspring, 33 age-matched offspring of both non-long-lived parents and 41 young women. Peripheral blood DNA from 169 females was screened for heterozygosity at the HUMARA locus. We confirmed that skewing of XCI is an age-dependent phenomenon. However, skewed XCI was significantly less severe and frequent in centenarians' offspring [degree of skewing (DS) = 0.16 \ub1 0.02] compared to age-matched offspring of both non-long-lived parents (DS = 0.24 \ub1 0.02) (P < 0.05). A second goal was to assess whether changes in XCI pattern could be a consequence of loss of methylation on X chromosome. Using a methylation array evaluating 1085 CpG sites across X chromosome and eleven CpG sites located at HUMARA locus, no differences in methylation levels and profiles emerged between all groups analysed, thus suggesting that age-associated epigenetic changes could not influence HUMARA results. In conclusion, the results presented herein highlight for the first time an interesting link between skewing of XCI and healthy aging and longevity. We speculate that the allelic imbalance produced by XCI skewing may compromise the cooperative and compensatory organization occurring between the two cell populations that make up the female mosaic