1,721,569 research outputs found
An Empirical Test of Harrod’s Model
Full text linkAfter having illustrated in Chap. 13 the Harrod’s model and a chaotic specification of it, in this Chapter we are going to prove that (1) real data could be obtained by a suitable calibration of model’s parameters, (2) the calibrated model confirms theoretical predictions (Orlando and Della Rossa, Mathematics 7(6):524, 2019)
Isidoro di Pelusio, Ep. II 135, PG LXXVIII, col. 577: una nota testuale
No full textAt Isidorus of Pelusium, Ep. II 135, PG LXXVIII, col. 577, manuscripts and editions offer the following text: Ὅταν ... τις ... χρήματα ..., μᾶλλον δὲ ἁμαρτήματα, συνάγῃ ὡς ὁ κάνθαρος τὴν κάνθαρον. This can be translated as: «when ... someone ... collects riches, or rather I should say sins, like the dung-beetle (collects) the dung-beetle». The sentence does not make sense: dung-beetles do not collect other dung-beetles. The word κάνθαρον is therefore corrupted (A. Gargiulo). It substituted a word that meant «dung»: either κόπρον (F. Della Rossa) or ὄνθον (L. Battezzato)
A simple tree-based algorithm for deciding the stability of discrete-time switched linear systems
No full textWe re-evaluate the direct approach to study the stability of discrete-time switched systems with finitely many linear modes. We explore the tree of possible matrix products by pruning the paths leading to contractions and looking for unstable repeatable products. Generically, this simple strategy either terminates with all contracting leafs-showing the asymptotic stability of the system-or finds the shortest unstable matrix product. Although it behaves in the worst-case as the exhaustive search, we show that its performance is greatly enhanced by measuring contractiveness w.r.t. sum-of-squares polynomial norms, optimized to minimize the largest expansion among the system's modes. We test our approach on several benchmark examples proposed to test switched Lyapunov function methods. Although these methods are mathematically elegant and efficient, they are more involved to apply and cannot decide the system's instability. Moreover, our algorithm is flexible. Adding/removing system's modes, setting mode-independent dwell-times, and constraining switching to finite automata can all be easily implemented and exploited in control design
The Harrod Model
Full text linkAs mentioned in the Introduction, Sect. 1.2, the objective of this book is twofold: to provide a personal specification of a business cycle model within the Kaldor–Kalecki framework (see Chap. 16 ) and to choose a chaotic specification of the Harrod model (Sportelli and Celi (Metroeconomica 62:459–493, 2011)) to prove that (1) real data can be obtained by a suitable calibration of model’s parameters and (2) the calibrated model confirms theoretical predictions (Orlando and Della Rossa (Mathematics 7:524, 2019)). In this chapter, we first explain the Domar model and the Harrod model separately, and then we describe the mathematical foundation to the Harrod’s instability principle that will be tested then in Chap. 18
Atleti ed eroi bassi. Melisso ed Eracle nell’Istmica 4 di Pindaro
No full textQuesto articolo si propone di esaminare la presentazione di Melisso di Tebe nell’Istmica 4 di Pindaro. L’enfasi sulla bassa statura di Melisso e il paragone con Eracle, nell’ode eccezionalmente μορφὰν βραχύς, possono essere spiegati con una miglior comprensione della narrazione mitica e delle politeness strategies pindariche: Eracle, come Melisso, risulta «breve di statura» davanti agli avversari e il poeta non tiene conto solamente delle reazioni del vincitore, ma anche di quelle del pubblico umano e divino.This article aims to analyse how Melissus of Thebes is represented in Pindar’s Isthmian 4. The emphasis on Melissus’ short stature and the comparison with Heracles, who is unusually μορφὰν βραχύς in this ode, can be better explained if the mythical narrative and Pindar’s politeness strategies are properly understood: Heracles appears «short in stature» in front of his opponents, just as Melissus does, and the poet considers not only the reactions of the winner but also those of the human and divine audience
“Cosa diranno i signori dell’Istmo?”: l’umorismo di Pind. fr. 122 M.
No full textPindar’s fr. 122 M. celebrates a Corinthian rite dedicated to Aphrodite by Xenophon and numerous hetairai. At ll. 13-15, the speaker wonders how the Corinthian community will react to the ode’s opening, ‘companion of public women’ (ξυνάορον ξυναῖς γυναιξίν, l. 15). As a contribution to the study of laughter in Greek conviviality, this paper will examine humorous interpretations of this ode, with a particular focus on the hesitation expressed in ll. 13-15 and on other Pindaric passages where the narrator abruptly stops his train of thoughts to avoid unsuitable topics (as in Ol. 13.91, another ode for Xenophon). In the fragment, this well-known rhetorical device appears to be repurposed for a subject and a performative context that could provoke laughter from the audience
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