A Weighted POD Method for Elliptic PDEs with Random Inputs

In this work we propose and analyze a weighted proper orthogonal decomposition method to solve elliptic partial differential equations depending on random input data, for stochastic problems that can be transformed into parametric systems. The algorithm is introduced alongside the weighted greedy method. Our proposed method aims to minimize the error in a L2 norm and, in contrast to the weighted greedy approach, it does not require the availability of an error bound. Moreover, we consider sparse discretization of the input space in the construction of the reduced model; for high-dimensional problems, provided the sampling is done accordingly to the parameters distribution, this enables a sensible reduction of computational costs, while keeping a very good accuracy with respect to high fidelity solutions. We provide many numerical tests to assess the performance of the proposed method compared to an equivalent reduced order model without weighting, as well as to the weighted greedy approach, in both low and high dimensional problems. \ua9 2018, Springer Science+Business Media, LLC, part of Springer Nature

Delle cose antiche della citta di Roma [Texto impreso]

El nombre del autor precede al titPie de imp. tomado del colofónSign.: *4, A-Z4, AA-ZZ4, AAA-ZZZ4, AAAA-MMMM

Sulla nuova edizione del «Giornale di guerra e di prigionia», «Il castello di Udine» e altre questioni gaddiane

Il saggio prende in esame la recente edizione del Giornale di guerra e di prigionia di Carlo Emilio Gadda (Adelphi 2023), a cura di Paola Italia, mettendone in luce le novità e le differenze rispetto al testo critico procurato da Dante Isella (Garzanti 1992). I quaderni riemersi nel 2019, redatti da Gadda nel novembre-dicembre 1918 durante la prigionia a Celle Lager, rivelano dati cruciali sul suo rapporto conflittuale con Ugo Betti e sulle connessioni tra il Giornale e le prose belliche del Castello di Udine (Edizioni di Solaria 1934).   Delving Into the New Edition of Carlo Emilio Gadda’s “Giornale di guerra e di prigionia”and its Relation to “Il castello di Udine” and Other Works The essay examines the latest edition of Carlo Emilio Gadda’s Giornale di guerra e di prigionia (Adelphi 2023), edited by Paola Italia, highlighting its innovations and differences compared to the critical text provided by Dante Isella (Garzanti 1992). The notebooks, unearthed in 2019 and penned by Gadda during his imprisonment in Celle Lager in November-December 1918, unveil crucial insights into his conflicted relationship with Ugo Betti and the interrelations between the Giornale and the war-related prose later collected in Il castello di Udine (Edizioni di Solaria 1934)

Tra permanenza e successione: il tempo nella prima Critica di Kant

The present work is focused on a specific question: is time permanent or not in Kant’s first Critique? I tried to find out my answer on the papers written by authors from Anglo-American tradition, who don’t seem so interested in this topic. Indeed, the former problem was to find remarks about it. Then I highlighted two different points of view: ones think that time is permanent. They tried to warrant this, using especially what Kant says about it in the second edition section dedicated to first Analogy. Others think that time flows, in particular when it’s considered as medi- ate external sense. Finally, I tried to explain why, on my point of view, it’s possible to find in Kant this two contrary position and how it is possible to get out from this situation

Gli odierni commentatori di Kant alla prova di Leibniz

During the Eighteenth century, in the way to consider time, mainly talking about external objects, there were two conflicting tradition inspired by Newton and Leibniz. To choose one of them meant too to choose a certain kind of relationship with cause and with succession. Kant made a choice. We will consider how the modern authors that examine the Kant texts or try to defend his point of view could answer if he made a wrong choice

Weighted reduced order methods for parametrized partial differential equations with random inputs

In this manuscript we discuss weighted reduced order methods for stochastic partial differential equations. Random inputs (such as forcing terms, equation coefficients, boundary conditions) are considered as parameters of the equations. We take advantage of the resulting parametrized formulation to propose an efficient reduced order model; we also profit by the underlying stochastic assumption in the definition of suitable weights to drive to reduction process. Two viable strategies are discussed, namely the weighted reduced basis method and the weighted proper orthogonal decomposition method. A numerical example on a parametrized elasticity problem is shown

Discovery of a radio relic in the low mass, merging galaxy cluster PLCK G200.9-28.2

Radio relics at the peripheries of galaxy clusters are tracers of the elusive cluster merger shocks. We report the discovery of a single radio relic in the galaxy cluster PLCK G200.9-28.2 ($z=0.22$, $M_{500} = 2.7\pm0.2 \times 10^{14} M_{\odot}$) using the Giant Metrewave Radio Telescope at 235 and 610 MHz and the Karl G. Jansky Very Large Array at 1500 MHz. The relic has a size of $\sim 1 \times 0.28$ Mpc, an arc-like morphology and is located at 0.9 Mpc from the X-ray brightness peak in the cluster. The integrated spectral index of the relic is $1.21\pm0.15$. The spectral index map between 235 and 610 MHz shows steepening from the outer to the inner edge of the relic in line with the expectation from a cluster merger shock. Under the assumption of diffusive shock acceleration, the radio spectral index implies a Mach number of $3.3\pm1.8$ for the shock. The analysis of archival XMM Newton data shows that PLCK G200.9-28.2 consists of a northern brighter sub-cluster, and a southern sub-cluster in a state of merger. This cluster has the lowest mass among the clusters hosting single radio relics. The position of the Planck Sunyaev Ze'ldovich effect in this cluster is offset by 700 kpc from the X-ray peak in the direction of the radio relic, suggests a physical origin for the offset. Such large offsets in low mass clusters can be a useful tool to select disturbed clusters and to study the state of merger.Comment: 10 pages, 7 figures, 4 tables. Accepted for publication in MNRA