Maximal Sobolev regularity for solutions of elliptic equations in infinite dimensional Banach spaces endowed with a weighted Gaussian measure

Let $X$ be a separable Banach space endowed with a non-degenerate centered Gaussian measure $\mu$. The associated Cameron-Martin space is denoted by $H$. Let $\nu=e^{-U}\mu$, where $e^{-U}$ is a sufficiently regular weight and $U:X\rightarrow\mathbb{R}$ is a convex and continuous function. In this paper we are interested in the $W^{2,2}$ regularity of the weak solutions of elliptic equations of the type $$\lambda u-L_\nu u=f,$$ where $\lambda>0$, $f\in L^2(X,\nu)$ and $L_\nu$ is the self-adjoint operator associated with the quadratic form \[(\psi,\varphi)\mapsto \int_X\left\langle\nabla_H\psi,\nabla_H\varphi\right\rangle_Hd\nu\qquad\psi,\varphi\in W^{1,2}(X,\nu).\

Analysis of knee strength measurements performed by a hand-held multicomponent dynamometer and optoelectronic system

The quantification of muscle weakness is useful to evaluate the health status and performance of patients and athletes. In this paper, we proposed a novel methodology to investigate and to quantify the effects induced by inaccuracy sources occurring when using a hand-held dynamometer (HHD) for knee strength measurements. The validation methodology is based on the comparison between the output of a one-component commercial HHD and the outputs of a six-component load cell, comparable in dimension and mass. An optoelectronic system was used to measure HHD positioning angles and displacements. The setup allowed to investigate the effects induced by: 1) the operator's ability to place and to hold still the HHD and 2) ignoring the transversal components of the force exchanged. The main finding was that the use of a single component HHD induced an overall inaccuracy of 5% in the strength measurements if the angular misplacements are kept within the values found in this paper (≤15°) and with a knee range of motion ≤22°. Extension trials were the most critical due to the higher force exerted, i.e., 249.4 ± 27.3 versus 146.4 ± 23.9 N of knee flexion. The most relevant source of inaccuracy was identified in the angular displacement on the horizontal plane

An HI interstellar bubble surrounding WR85 and RCW118

We analyze the distribution of the interstellar matter in the environs of the Wolf-Rayet star LSS3982 (= WR85, WN6+OB?) linked to the optical ring nebula RCW118. Our study is based on neutral hydrogen 21cm-line data belonging to the Southern Galactic Plane Survey (SGPS). The analysis of the HI data allowed the identification of a neutral hydrogen interstellar bubble related to WR 85 and the 25' diameter ring nebula RCW118. The HI bubble was detected at a systemic velocity of -21.5 km/s, corresponding to a kinematical distance of 2.8+/-1.1 kpc, compatible with the stellar distance. The neutral stucture is about 25' in radius or 21+/-8 pc, and is expanding at 9+/-2 km/s. The associated ionized and neutral masses amount to 3000 Mo. The CO emission distribution depicts a region lacking CO coincident in position and velocity with the HI structure. The 9'.3 diameter inner optical nebula appears to be related to the approaching part of the neutral atomic shell. The HI void and shell are the neutral gas counterparts of the optical bubble and have very probably originated in the action of the strong stellar wind of the central star during the O-type and WR phases on the surrounding interstellar medium. The HI bubble appears to be in the momentun conserving stage.Comment: 9 pages, 7 figures, accepted in MNRA

Il Rinascimento degli acquedotti

Dopo il buio Medio Evo rifiorirono le arti nel Rinascimento. Anche sotto terra, negli acquedotti, si verificò qualcosa di analogo ma è ben poco noto. Ora si presentano qui quattro esempi di importanti acquedotti creati nell’Evo Moderno per alimentare castelli e ville della regione Lazio. L’acquedotto che conduce l’acqua dal fiume Aniene alle fontane del giardino della Villa d’Este a Tivoli fu compiuto nella seconda metà del XVI secolo e consentì la realizzazione di uno dei più famosi parchi “all’italiana”, tuttora aperto e frequentato da migliaia di visitatori. L’Acqua Farnesiana è un acquedotto creato alla fine del XVI secolo per alimentare la villa e il palazzo dei Farnese a Caprarola, nasce da un capofonte ipogeo in comune di Canepina, è lungo circa 9 km, con lunghi tratti scavati nella roccia. L’acquedotto del castello Ruspoli di Vignanello presenta un percorso ipogeo sottostante l’antico abitato, è lungo circa 2 km e fu creato dalla contessa Ottavia Orsini all’inizio del XVII secolo. L’acquedotto Aldobrandini fu realizzato tra il 1603 e il 1605, in parte riutilizzando le captazioni e i condotti dell’antica Aqua Julia, con un condotto di almeno 9,5 km; esso alimentava i giochi d’acque della villa Belvedere degli Aldobrandini e in parte anche altre ville, una mola e l’Abbazia di S. Nilo a Grottaferrata. È tuttora in piena efficienza.The fall of the Roman Empire brought into a rapid drop the population of the main towns; many crashes followed as well as the discontinuance of the extraordinary network of aqueducts that supported the survival in many conurbations. The resumption of the way of life after the twelfth. century fostered the revival of the fine arts and the architecture: the Renaissance was born. Somewhat similar took place in the undergrounds, where drinking waters flow in the ducts. A few examples of important aqueducts that were set up in the Modern Era are presented: they provided drinking water to castles and magnificent country houses. The aqueduct that takes the waters from river Aniene to the fountains of the Villa d’Este garden in Tivoli has been achieved in the second half of the 16th century, following the instructions of Cardinal Ippolito II d’Este: one of the most famous “italian” gardens was attained; the fountains are still perfectly effective and enjoy thousands visitors every year. “Acqua Farnesiana” is an aqueduct set up towards the end of the 16th century, 9 km ca. long; it sucks up water from an hypogean source in Canepina (VT) commune and, through a few underground tunnels, it feeds the Farnese palace, villa and gardens in Caprarola. The Ruspoli aqueduct flows through an hypogean tunnel below the ancient built-up area of Vignanello (VT) and is nearly 2 km long. It was set up by countess Ottavia Orsini at the beginning of the 17th century, in order to supply the “Italian garden” below her castle. The Aldobrandini aqueduct was achieved from 1603 to 1605 on Pope’s Clemente VII will, in a large part by the recovery of the underground springs and ducts created by the Romans for the ancient aqueduct Aqua Julia and by adding a shorter tunnel leading straight to the Villa Belvedere in Frascati (RM). The aqueduct is on the whole 9,5 km long; it was feeding the “Italian garden” just above the Villa, but in part supported other country houses too, near Frascati, the Saint Nilo Abbey in Grottaferrata plus some public fountains. This aqueduct is still perfectly working

Technical quality assessment of an optoelectronic system for movement analysis

The Optoelectronic Systems (OS) are largely used in gait analysis to evaluate the motor performances of healthy subjects and patients. The accuracy of marker trajectories reconstruction depends on several aspects: the number of cameras, the dimension and position of the calibration volume, and the chosen calibration procedure. In this paper we propose a methodology to evaluate the eects of the mentioned sources of error on the reconstruction of marker trajectories. The novel contribution of the present work consists in the dimension of the tested calibration volumes, which is comparable with the ones normally used in gait analysis; in addition, to simulate trajectories during clinical gait analysis, we provide non-default paths for markers as inputs. Several calibration procedures are implemented and the same trial is processed with each calibration le, also considering dierent cameras congurations. The RMSEs between the measured trajectories and the optimal ones are calculated for each comparison. To investigate the signicant dierences between the computed indices, an ANOVA analysis is implemented. The RMSE is sensible to the variations of the considered calibration volume and the camera congurations and it is always inferior to 43 mm

Upper body balance control strategy during continuous 3D postural perturbation in young adults

We explored how changes in vision and perturbation frequency impacted upright postural control in healthy adults exposed to continuous multiaxial support-surface perturbation. Ten subjects were asked to maintain equilibrium in standing stance with eyes open (EO) and eyes closed (EC) during sinusoidal 3D rotations at 0.25 (L) and 0.50 Hz (H). We measured upper-body kinematics – head, trunk, and pelvis – and analyzed differences in horizontal displacements and roll, pitch, and yaw sways. The presence of vision significantly decreased upper-body displacements in the horizontal plane, especially at the head level, while in EC the head was the most unstable segment. H trials produced a greater segment stabilization compared to L ones in EO and EC. Analysis of sways showed that in EO participants stabilized their posture by reducing the variability of trunk angles; in H trials a sway decrease for the examined segments was observed in the yaw plane and, for the pelvis only, in the pitch plane. Our results suggest that, during continuous multiaxial perturbations, visual information induced: (i) in L condition, a continuous reconfiguration of multi-body-segments orientation to follow the perturbation; (ii) in H condition, a compensation for the ongoing perturbation. These findings were not confirmed in EC where the same strategy – that is, the use of the pelvis as a reference frame for the body balance was adopted both in L and H

Unveiling the molecular environment of the ring nebula RCW 78

We present a study of the ionized, neutral atomic, and molecular gas associated with the ring nebula RCW 78 around the WR star HD 117688 (= WR 55). We based our study on CO observations carried out with the SEST and NANTEN telescopes. We report the detection of molecular gas with velocities in the range -56 to -33 km/s. The CO emission is mainly connected to the western section, with a total molecular mass of 1.3 x 10^5 solar masses. The analysis of the HI gas distribution reveals the HI envelope of the molecular cloud, while the radio continuum emission shows a ring-like structure, which is the radio counterpart of the optical nebula. The gas distribution is compatible with the western section of RCW 78 having originated in the photodissociation and ionization of the molecular gas by HD 117688, and with the action of the stellar winds of the WR star. A number of infrared point sources classified as YSO candidates showed that stellar formation activity is present in the molecular gas linked to the nebula. The fact that the expansion of the bubble have triggered star formation in this region can not be discarded.Comment: 15 pages, 11 Postscript figures, to be published in A&