198 research outputs found
Approximating real stability radii
No full textThe stability radius of an matrix (or distance to instability)
is a well-known measure of robustness of stability of the linear stable dynamical system
. Such a distance is commonly measured either in the -norm or in the
Frobenius norm.
Even if the matrix is real, the distance to instability is most often considered
with respect to complex valued matrices (in such case the two norms turn out to be
equivalent) and restricting the distance to real matrices makes the problem more complicated,
and in the case of Frobenius norm - to our knowledge - unresolved.
Here we present a novel approach to approximate real stability radii, particularly well-suited
for large sparse matrices.
The method consists of a two level iteration, the inner one aiming to compute the \eps-
pseudospectral abscissa of a low-rank ( or ) dynamical system, and the outer one
consisting of an exact Newton iteration.
Due to its local convergence property it generally provides upper bounds for the stability radii but in practice usually computes the correct values.
The method requires the computation of the rightmost eigenvalue of a sequence of matrices, each of them given by the sum of the original matrix and a low-rank one.
This makes it particularly suitable for large sparse problems, for which several existing methods become inefficient, due to the fact that they require to solve full Hamiltonian eigenvalue problems and/or compute multiple SVDs
Terracotta Imitation of Jewelry. Iconography and function
No full textBetween the end of the 4th and the beginning of the 3rd century B.C., the practice of reproducing jewellery and other objects used as personal ornament in the medium of gilded clay spread throughout the Greek world. The close comparisons drawn between such objects and prestigious artifacts of jewellery have led scholars to assign the former the function of "clay imitations of gold jewellery”, i.e. as reproductions of high quality items produced out of far "poorer" material with the intent to meet a wider demand. However, the data culled from the numerous ancient cemeteries discovered in northern Greece, Bulgarian Thrace, and Magna Graecia (Taras), as well as in many other sites that have yielded these products, offer a new interpretation.
The most significant results to emerge from the research can be summarized as follows:
1) For each of the aforementioned areas the records point to an overall scarcity of such products with respect to the other categories of clay artifacts and gold jewellery of similar date recovered in the same areas. This data is incongruent with any notion of mass production that the low cost would presumably have encouraged.
2) These gilded clay objects are chiefly found in funerary contexts, in either the most elite of monuments such as the tombs in Derveni and the Mound Tjulbe in the valley of Kazanluk (Bulgary) or more modest tombs, which stand out nonetheless for their sheer number and variety of materials together with the highly refined taste that choice items among their burial goods reflect. The latter tombs frequently boast valuables made out of gold, silver, ivory and alabaster that reveal the owners’ belonging to an emerging social class while confirming the luxury status to be assigned to these objects.
3) Though in some geographical areas the gilded terracotta objects are associated with the funerary rite of cremation, still others appear inside inhumation burials. The placement of these items in the tombs indicates, however, that their use is strictly connected to the funeral ritual and to be distinguished from the rest of the burial goods.
4) The use of these objects likely originated from a fad born in Macedonia, where a particular category of gilded pottery, serving analogous funerary purposes, was in vogue during the same period. This datum suggests that this region assigned a high value to the practice of gilding, whose open display together with that of other precious materials had become a status symbol
Marmi di reimpiego nella cosiddetta cripta dei SS. Eleuterio e Ponziano a Velletri
No full textL’intervento presenta i risultati dello studio degli elementi di decorazione architettonica – fino ad oggi pressoché inediti – reimpiegati nella cd. cripta dei Ss. Eleuterio e Ponziano, all’interno della cattedrale di San Clemente a Velletri. L’analisi formale di tali arredi rappresenta il prerequisito per avviare tentativi di ricontestualizzazione, nell’ambito di un più generale riesame della topografia della città veliterna in epoca romana. Variamente datati, gli spolia indagati appaiono, infatti, di estremo interesse in una duplice prospettiva di indagine: sia nel caso, cioè, che essi rappresentino una delle rare attestazioni degli originari apparati decorativi di edifici, oggi perduti, della città laziale, sia nel caso, peraltro non isolato nell’ambito della stessa città, che essi provengano, piuttosto, da altre località dei Colli Albani o del Lazio.This paper presents the results of a study of unpublished decorative architectural elements which have been re-used within the so-called crypt of St. Eleuterius and Ponzianus, in Saint Clement Cathedral, Velletri. The formal analysis of these marbles is a prerequisite for any attempt to re-contextualize them in the frame of a more general new examination of the topography of the city in Roman period. These spolia, which are variously dated, present two distinct and interesting research questions. The first of these involves the possibility that they represent one of the rare original decorative elements of Roman monuments which have not otherwise been preserved. The second involves the opportunity – elsewhere already observed in the same city – to examine whether the re-used
marbles come from different sites in the Alban Hills areas or in Latium
Updating the water budget of the Gran Sasso carbonate fractured/karstified aquifer (Central Italy) for a sustainable management of groundwater resources
No full textKarst aquifers are fundamental in the water supply of European countries, where outcrops of carbonate rocks are very common, providing abundant groundwater resources. The Gran Sasso karst aquifer, selected as representative study area for Italy in the EU-funded KARMA project, is characterized by both high percentage of withdrawals for drinking purposes and significant interaction between groundwater and underground works. The recharge evaluation of the aquifer has been carried out considering the 2001–2020 monitoring period, comparing three different methods: the Turc and APLIS methods, on annual scale, and the Thornthwaite method, on monthly scale, territorially distributed by 100 x 100 m cells on GIS basis. The total recharge considers not only rainfall but also the contribution of snow melting on infiltration. The results show similar mean recharge values in 2001–2020 for all methods, corresponding to 19.9, 18.5, and 19.4 m3/s, respectively, from Turc, Thornthwaite, and APLIS methods. A significant contribution to recharge from snowmelt has been confirmed (3.2 m3/s included in the above-mentioned values). These values can be considered reliable with respect to real discharge of the regional aquifer. The obtained results can be used to provide updated information to the drinking water companies for a suitable management of the available resource
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