Maria Antonietta Lepellere

Modular functions: Uniform boundedness and compactness

We prove the Nikodym Boundedness, Brooks-Jewett and Vitali-Hahn-Saks theorems for modular functions on orthomodular lattices with SIP and on particular complemented or sectionally complemented lattices, and the equivalence, for any complemented or sectionally complemented lattice, between the Brooks-Jewett and Vitali-Hahn-Saks theorems for group-valued modular functions. As consequence, we obtain characterizations of relative, sequential and weak compactness in spaces of modular functions.

Pricing And Hedging American Barrier Options By A Modified Binomial Method

The aim of this work is to present a modification of the standard binomial method which allows to price American barrier options improving the efficiency of the trinomial methods. Our approach is based on a suitable interpolation of binomial values and allows to price and hedge such options also in the critical case of near barriers. All the different types of single barrier options are considered, in the case of knock-in barriers a new implementation of the binomial method is provided.

FROM LINGUISTIC REPRESENTATION TO FUZZY MATHEMATICS IN GROWN UP PEOPLE

The aim of this note is to give some critical examples where even the use of the same clustering rules lead to fuzziness. It starts from poor numerical systems and compares them with the expanded Sergeyev model, where the grossone is used, as an infinite terminal element. It can be compared with terminal elements of the ancient languages, such as the Greek myriad and the Chinese wan. On them some propositions that hold in the arithmetic of the grossone are similar, while they are not meaningful for the countable system of infinity. The note shows that both the upward and downward trend are actually present in human language and in conceptual arrangements. The note then goes on to sketch the model of evolution of Bak-Sneppen, showing two significant applications: the case of the evolution and study of foreign languages and, according to the model of Lloyd, the territorial analysis. In both cases it is highlighted how the Bak-Sneppen model becomes more stable when the universe is segmented, as already proven by the authors in previous works. The third part examines some cases of false probabilistic intuition due to incomplete perception of the phenomena, what could therefore be defined as hidden conditional probability. Interesting is the classic application of the theory of games to lotteries and ternary games, such as Chinese morra.

The assessment of consumer sensitivity to animal welfare: An application of Rasch Model

The sensitivity has become a mass phenomenon, still in expansion. The Euro-pean Commission, during last decade, carried out several surveys on food quality and animal welfare. This research, using data from a survey conducted on 320, respondents and applying the Rasch model on 14 selected questions (items), wants to develop a measure that appears representative of a latent variable defined as ‘Sensitivity towards Animal Welfare’. The ability to measure the individual level of this ‘Sensitivity’ therefore represents an interesting and important result, especially if there are correlations between this variable and other variables characterizing the opinions and habits of individuals, both in general and in relation to consumer decisions.