Il Club dei Volterriani: Il Volterriano Nr.8, 2000

• Giorgio T. Bagni
I fondamenti dell'Aritmetica: percorsi di ricerca per il XXI secolo
(Abstract. In this paper we propose a brief summary of the development of researches in Arithmetics and in Logics in XX century and present some important themes connected to the study of Mathematics' fundamental research.)

• Antonio Steiner, Fabrizio Pini, Martin J. Gander
Sistemi competitivi
(Abstract. The classical competition model of Vito Volterra always leads to the extinction of all the species except the strongest one. We show in this paper how to construct models of competition which permit the coexistence of several species in a competitive environment. We illustrate the new models with numerical examples and also present a model which can be solved analytically.)

• Antonio Steiner, Martin J. Gander
Erhaltung der Artenvielfalt durch Migration
(Abstract. We investigate the influence of migration on the evolution of one and two species living in regions under hunting conditions which keep the total number of individuals constant. Individuals migrate from an area with better living conditions to an area with worse living conditions, because in this way they minimize the hunting rate in both areas. At long term the populations approach a steady state.)

• Alberto Gandolfi
Due parole sui sistemi complessi
(Abstract. In this paper we explane with some examples the nature of complex systems.)

• Carmelo Basile, Alessandra Lenoci
Modelli stocastici della struttura per scadenza: i modelli di Vasiceck (1977) e Longstaff-Schwartz (1992)
(Abstract. Nell'ambito della modellizzazione dinamica della struttura per scadenza vengono esposti due modelli stocastici: il modello monofattoriale di Vasicek (1977) e quello a due fattori elaborato da Longstaff e Schwartz (1992). Nel primo di questi due modelli vengono calcolati i prezzi di alcuni derivati usando il principio di valutazione neutrale al rischio. Nel secondo viene utilizzato l'approccio di equilibrio generale per la determinazione della term structure. In particolare, dopo la risoluzione del problema individuale di ottimizzazione intertemporale vengono calcolati l'equilibrio finanziario ed il prezzo endogeno di mercato del rischio. Da queste grandezze si ottiene l'equazione fondamentale del prezzo di un valore contingente e formule esplicite per bonds e bond options.)

Quantum Excitations in Magnetic Clusters
(Abstract. The microscopic magnetic properties in solids are the results of true quantum mechanical interactions between the electrons. After a brief introduction, basic model predictions are developed for dimer clusters, and presented in the context of inelastic neutron scattering investigations. It is explained how the relevant microscopic information is extracted from the experimental outcomes.)

• Andrea Danani
Il Metodo Variazionale a Cluster per il quadrato MxM
(Abstract.  We present the formulation of the cluster variation method with the entropy expressed as a Möbius inversion. The method is then applied to the case of a square MxM as basic cluster for the approximation and the details of the calculations are given for the case M=3.)

• Luca Ortelli
Dalla distribuzione di Boltzmann in meccanica statistica alla distribuzione degli eventi sismici: ricerca di un'analogia formale
(Abstract.  Our aim is to point out some formal similarities between the derivation of the Boltzmann distribution in statistical mechanics and the derivation of the distribution of sismic events. We do this in two ways: one "classical" and one using the information theory.)

• Matteo Garzoni, Gabriele Janner
Il nucleo di deuterio
(Abstract.  This article is issued from our high school project in mathematics. A rather artificial but very simple model of the nucleus of deuterium is considered, with the strong interaction between proton and neutron represented as a rectangular potential well. Spin effects are neglected. The Schrödinger equation is solved in the case of zero orbital angular momentum. The depth of the potential is computed from the known experimental value of the sole energy level. The mean distance between the nucleons is also computed as well as the probability that this distance is greater than the range of the interaction.)