A normal form analysis in a finite neighborhood of a hopf bifurcation: on the center manifold dimension

The problem of determining the bounds of applicability of perturbation expansions in terms both of the system parameters and the state-space variable amplitude is a key point in the perturbation analysis of nonlinear systems. In the present paper an analysis in a finite neighborhood of a Hopf bifurcation is presented in order to analyze the conditions under which a Normal Form zero-divisors-based approach fails to describe the local dynamics and, therefore, a small divisor approach is required. The condition of “smallness” referred to the divisors is analyzed from both a qualitative and a quantitative point of view. Finally, a simple but effective analytical and numerical example is introduced to illustrate the theoretical issues along with an interpretation within a codimension-two framework

On the type of partial t-spreads in finite projective spaces

AbstractA partial t-spread in a projective space P is a set of mutually skew t-dimensional subspaces of P. In this paper, we deal with the question, how many elements of a partial spread L can be contained in a given d-dimensional subspace of P. Our main results run as follows. If any d-dimensional subspace of P contains at least one element of L, then the dimension of P has the upper bound d−1+(d/t). The same conclusion holds, if no d-dimensional subspace contains precisely one element of L. If any d-dimensional subspace has the same number m>0 of elements of L, then L is necessarily a total t-spread. Finally, the ‘type’ of the so-called geometric t-spreads is determined explicitely

Bruno Rizzi and Number Theory

Franco Eugeni remembers Bruno Rizzi: in this brief introduction, I would like to remember an afternoon spent in “Roma Tre” with Bruno, since we were both Ordinary Professors at that University. We passed it doing a dense program of work for the next three years. At 6.00 pm, I left for “Roseto degli Abruzzi”. At six o'clock a.m. of the next morning, I still have the voice in my ears. A phone call from the Headmaster Ciro d'Aniello, who told me "The Professor is dead" In that afternoon, Emilio Ambrisi and I went to Rome; we were stunned and desperate. Not many days later, a conference was held at the University of Teramo; it was the conference that we had prepared for Bruno, to celebrate his 60th birthday, but it was his memory. In the opening conference, Prof. Antonino Giambo, also fraternal friend of Bruno, burst into a tearful cry, which expressed in a moment, the senses of friendship and love that we all had for the missing friend! Starting from this work with Fabrizio Maturo, the study of some problems left open by the works of Eugeni and Rizzi will be investigated.SuntoRicordo di Franco Eugeni su Bruno Rizzi: in questa brevissima introduzione vorrei ricordare un pomeriggio passato a Roma Tre con Bruno, visto che allora eravamo entrambi Professori Ordinari in quella Università. Lo passammo a fare un denso programma di lavoro per i successivi tre anni. Alle 18.00 ripartii per Roseto degli Abruzzi. Alle sei del mattino successivo, ho ancora la voce nelle orecchie, una telefonata del Preside Ciro d’Aniello, che mi diceva “Il Professore è morto” Nel pomeriggio Emilio Ambrisi ed io ci recammo a Roma, eravamo attoniti e disperati. Non molti giorni dopo si tenne presso l’Università di Teramo un Convegno, era il Convegno che avevamo preparato per Bruno, per festeggiare i suoi 60 anni, fu invece il ricordo. Nella conferenza di apertura il prof. Antonino Giambò, anche lui, come noi, fraterno amico di Bruno, scoppiò in un pianto dirotto, che espresse in un attimo, i sensi dell’amicizia e dell’amore, che tutti noi avevamo per l’amico scomparso! A partire da questo lavoro con Fabrizio Maturo verrà approfondito lo studio di alcune problematiche rimaste aperte dai lavori di Eugeni e Rizzi

Is the golden section a key for understanding beauty? Part III

Our goal is to prove that the golden section, however important, is not the only key to understand a mathematical-formalizing approach to the idea of beauty. Having developed, from this point of view, reading keys linked to the post-modern, it is necessary to link together the multiple rivulets of knowledge that gather in this direction. Moreover the canons of the approaches presented up to now are very indicative for the understanding of many aspects of beauty, which however depends on the historical moment and the cultures created in the various civilizations. Therefore we can affirm that there is no effective definition of "beauty" that can be codified through fixed canons, but that the concept is expressed by a series of stratifications and interpretations that tend to link several major variations, expressing the various answers given by man to the question: what is the beauty

Is the Golden Section a Key for Understanding Beauty? - Part I

Our goal is to prove that the golden section, however important, is not the only key to understand a mathematical-formalizing approach to the idea of beauty. Having developed, from this point of view, reading keys linked to the post-modern, it is necessary to link together the multiple rivulets of knowledge that gather in this direction. Moreover the canons of the approaches presented up to now are very indicative for the understanding of many aspects of beauty, which however depends on the historical moment and the cultures created in the various civilizations. Therefore we can affirm that there is no effective definition of "beauty" that can be codified through fixed canons, but that the concept is expressed by a series of stratifications and interpretations that tend to link several major variations, expressing the various answers given by man to the question: what is the beauty

OMA analysis of a launcher under operational conditions with time-varying properties

The objective of the paper is the investigation of the capability of Operational Modal Analysis approaches to deal with time-varying system in the low-frequency domain. Specifically, the problem of the identification of the dynamic properties of a launch-vehicle, working under actual operative conditions, is studied. Two OMA methods are considered: the Frequency Domain Decomposition and the Hilbert Transform Method. It is demonstrated that both OMA approaches allow the time-tracking of modal parameters, namely, natural frequencies, damping ratios and mode shapes, from the response accelerations only recorded during actual flight tests of a launcher characterized by a large mass variation due to fuel burning typical of the first phase of the flight

Momenti significativi del mio approccio individuale tra pratica del calcolo e conquiste teoriche

Lavoro dedicato alla memoria della carissima amica, allieva e collega prof.ssa Pina Varone che le dure circostanze della vita e della morte ci hanno rapit

Digital design of medical replicas via desktop systems: shape evaluation of colon parts

In this paper, we aim at providing results concerning the application of desktop systems for rapid prototyping of medical replicas that involve complex shapes, as, for example, folds of a colon. Medical replicas may assist preoperative planning or tutoring in surgery to better understand the interaction among pathology and organs. Major goals of the paper concern with guiding the digital design workflow of the replicas and understanding their final performance, according to the requirements asked by the medics (shape accuracy, capability of seeing both inner and outer details, and support and possible interfacing with other organs). In particular, after the analysis of these requirements, we apply digital design for colon replicas, adopting two desktop systems. ,e experimental results confirm that the proposed preprocessing strategy is able to conduct to the manufacturing of colon replicas divided in self-supporting segments, minimizing the supports during printing. ,is allows also to reach an acceptable level of final quality, according to the request of having a 3D presurgery overview of the problems. ,ese replicas are compared through reverse engineering acquisitions made by a structured-light system, to assess the achieved shape and dimensional accuracy. Final results demonstrate that low-cost desktop systems, coupled with proper strategy of preprocessing, may have shape deviation in the range of ±1 mm, good for physical manipulations during medical diagnosis and explanation

Numeri q-perfetti e q-amicabili di seconda specie e altre generalizzazioni dei numeri perfetti di seconda specie

Nel presente lavoro si affronta, tra le curiosità matematiche, il problema deinumeri perfetti di seconda specie, riprendendo anche un lavoro del 1979 di FrancoEugeni e Bruno Rizzi, utilizzato come preambolo e spunto per le problematichelasciate aperte su tali concetti, e le loro generalizzazioni tra le quali quella deinumeri q-perfetti di 2 a specie. Il presente file si compone infatti di:1. Su alcune generalizzazioni dei numeri perfetti, tratto dal periodico dimatematiche serie V Volume 56 del 1980 riguardanti i numeri 1-perfetti di2 a specie e alcune problematiche dei numeri q-perfetti di 2 a specie. Il testoè corredato di note scritte in questa occasione.2. Un lavoro che appare qui per la prima volta in cui è trattato, per quanto siapossibile, il caso q > 1 per la suddetta generalizzazione dei numeri perfettidi 2 a specie e una diversa generalizzazione dei numeri perfetti di 2 a specieinsieme a risultati sul problema delle coppie di numeri amicabili diseconda specie, per entrambe le generalizzazioni

Strutture pseudo-euclidee su campi di Galois

In this paper we define an inner product in an affine plane AG(2, q). The odd case, in a canonical rapresentation, is connected with a geometry studied by Tallini. The even case is very new since, the inner product cannot be commutative and we have an ordered perpendicularity. Finally we applied theese questions to construct a criptographic authentication system