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On the dominance relation between ordinal sums of conjunctors

Susanne Saminger, Bernard De Baets, Hans De Meyer (2006)

Kybernetika

This contribution deals with the dominance relation on the class of conjunctors, containing as particular cases the subclasses of quasi-copulas, copulas and t-norms. The main results pertain to the summand-wise nature of the dominance relation, when applied to ordinal sum conjunctors, and to the relationship between the idempotent elements of two conjunctors involved in a dominance relationship. The results are illustrated on some well-known parametric families of t-norms and copulas.

On the existence of solutions of some second order nonlinear difference equations

Małgorzata Migda, Ewa Schmeidel, Małgorzata Zbąszyniak (2005)

Archivum Mathematicum

We consider a second order nonlinear difference equation Δ 2 y n = a n y n + 1 + f ( n , y n , y n + 1 ) , n ∈ N . ( E ) The necessary conditions under which there exists a solution of equation (E) which can be written in the form y n + 1 = α n u n + β n v n , are given. Here u and v are two linearly independent solutions of equation Δ 2 y n = a n + 1 y n + 1 , ( lim n → ∞ α n = α < ∞ and lim n → ∞ β n = β < ∞ ) . A special case of equation (E) is also considered.

On the extension of exponential polynomials

László Székelyhidi (2000)

Mathematica Bohemica

Exponential polynomials are the building bricks of spectral synthesis. In some cases it happens that exponential polynomials should be extended from subgroups to whole groups. To achieve this aim we prove an extension theorem for exponential polynomials which is based on a classical theorem on the extension of homomorphisms.

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