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).\

Meningkatkan Kompetensi Guru Menyusun Rencana Pelaksanaan Pembelajaran Berorientasi pada Keterampilan Berpikir Tingkat Tinggi (Higher Order Thinking Skill) dalam Pembelajaran Tematik Melalui Bimbingan dan Latihan pada Kelompok Kerja Guru (KKG)

Penelitian ini bertujuan mendeskripsikan kompetensi guru kelas menyusun rencana pelaksanaan pembelajaran yang berorientasi pada keterampilan berpikir tingkat tinggi (Higher Order Thinking Skill) dalam pembelajaran tematik di Sekolah Dasar di UPT SD Negeri 035 Awo-awo Kec. Baebunta Kab. Luwu Utara Tahun Pelajaran 2018/2019. Metode yang digunakan dalam penelitian ini adalah metode Penelitian Tindakan Sekolah (PTS). Subjek penelitian yaitu Sekolah Dasar di UPT SD Negeri 035 Awo-awo Kec. Baebunta Kab. Luwu Utara Tahun Pelajaran 2018/2019, dengan jumlah guru sebanyak 8 (delapan) orang. Pengumpulan data dilakukan dengan observasi. Penelitian ini dilakukan 2 siklus yaitu siklus pertama dilakukan Kelompok Kerja Guru (KKG) dapat meningkatkan kompetensi guru dalam menyusun rencana pelaksanaan pembelajaran berorientasi pada keterampilan berpikir tingkat tinggi (Higher Order Thinking Skill) dalam Pembelajaran Tematik. Guru menunjukkan keseriusan dalam memahami dan melakukan diskusi Kelompok Kerja Guru (KKG) dengan bimbingan dari peneliti. Kesimpulan akhir dari penelitian ini adalah dengan Kelompok Kerja Guru (KKG) dapat meningkatkan kompetensi guru dalam menyusun rencana pelaksanaan pembelajaran berorientasi pada keterampilan berpikir tingkat tinggi (Higher Order Thinking Skill) dalam Pembelajaran Tematik. Hal itu dapat dibuktikan dari hasil observasi/pengamatan yang memperlihatkan bahwa terjadi peningkatan kompetensi guru dari siklus ke siklus . yaitu terjadi peningkatan sebesar 16,00% dari siklus pertama  kesiklus kedua

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

Fundamental domains of cluster categories inside module categories

Let $H$ be a finite dimensional hereditary algebra over an algebraically closed field, and let $\mathcal{C}_{H}$ be the corresponding cluster category. We give a description of the (standard) fundamental domain of $\mathcal{C}_{H}$ in the bounded derived category $\mathcal{D}^{b}(H)$, and of the cluster-tilting objects, in terms of the category $\mod\Gamma$\ of finitely generated modules over a suitable tilted algebra $$ Furthermore, we apply this description to obtain (the quiver of) an arbitrary cluster-tilted algebra.Comment: 20 pages, 9 figure

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

Rôle des fluides dans le comportement hydromécanique des roches fracturées hétérogènes : Caractérisation in situ et modélisation numérique

17 pagesNational audienceLes processus de couplages hydromécaniques dans un massif rocheux fracturé sont étudiés à travers des expérimentations in situ et des simulations numériques. L'approche expérimentale consiste à mesurer simultanément la pression de fluide et le déplacement mécanique en différents points d'un réservoir carbonaté tout en contrôlant les conditions aux limites hydrauliques. Ces mesures sont analysées par modélisation couplée hydromécanique. A l'échelle du massif, mesures et modèles montrent que le couplage hydromécanique est contrôlé par un comportement hydraulique de double perméabilité de fractures associé à un comportement mécanique de double rigidité de fractures. A l'échelle de la fracture unique, des mesures dynamiques par capteurs à fibre optique réalisées lors d'un pulse de pression montrent une réponse pression/déplacement présentant une boucle caractéristique dont l'évolution est différente entre les phases d'augmentation et de chute de pression. A partir de ces données in situ, les paramètres hydromécaniques des fractures et de la matrice rocheuse sont rétro analysés par les modèles numériques. Ces modélisations montrent que la sensibilité de la réponse hydromécanique de la fracture pressurisée est fortement dépendante de la raideur normale et de l'ouverture hydraulique de la fracture, de la raideur de la matrice rocheuse et de la géomé trie du réseau de fractures