Nicolas Goze

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In this paper we present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any cases. This approach allows to give a notion of divisibility and in some cases an euclidian division. 1. Intervals and generalized intervals An interval is a connected closed subset(More)
In a previous paper, we have given an algebraic model to the set of intervals. Here, we apply this model in a linear frame. We define a notion of diagonalization of square matrices whose coefficients are intervals. But in this case, with respect to the real case, a matrix of order n could have more than n eigenvalues (the set of intervals is not factorial).(More)
On étudie les algèbres définies par une multiplication n-aire donnée par les produits de Gerstenhaber. On montre que dans le cas où n est impair, il n’existe pas de cohomologie de type Hochschild (ou opéradique). On définit donc un nouveau complexe de cohomologie. On étudie également l’algèbre libre sur un espace vectoriel de dimension finie ce qui permet(More)
In this paper we propose some very promissing results in interval arithmetics which permit to build well-defined arithmetics including distributivity of multiplication and division according addition and substraction. Thus, it allows to build all algebraic operations and functions on intervals. This will avoid completely the wrapping effects and data(More)
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