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- Arithmetic for closed ballsPublication . Beites, P. D.; Nicolás, A. P.; Vitoria, JoseInspired by circular complex interval arithmetic, an arithmetic for closed balls in Rn is pursued. In this sense, the properties of certain operations on closed balls in Rn, some of which related either to the Hadamard product of vectors or to the 2-fold vector cross product when n ∈ {3, 7}, are studied. In particular, known results for operations on closed balls in C, which can be identified with R2, are extended to closed balls in Rn.
- Bounds for the zeros of unilateral octonionic polynomialsPublication . Serôdio, Rogério; Beites, P. D.; Vitoria, JoséIn the present work it is proved that the zeros of a unilateral octo- nionic polynomial belong to the conjugacy classes of the latent roots of an appropriate lambda-matrix. This allows the use of matricial norms, and matrix norms in particular, to obtain upper and lower bounds for the zeros of unilateral octonionic polynomials. Some results valid for complex and/or matrix polynomials are extended to octonionic polyno- mials.