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On the uniqueness of periodic decomposition

Viktor Harangi (2011)

Fundamenta Mathematicae

Let a , . . . , a k be arbitrary nonzero real numbers. An ( a , . . . , a k ) -decomposition of a function f:ℝ → ℝ is a sum f + + f k = f where f i : is an a i -periodic function. Such a decomposition is not unique because there are several solutions of the equation h + + h k = 0 with h i : a i -periodic. We will give solutions of this equation with a certain simple structure (trivial solutions) and study whether there exist other solutions or not. If not, we say that the ( a , . . . , a k ) -decomposition is essentially unique. We characterize those periods for which essential uniqueness...

On the weak robustness of fuzzy matrices

Ján Plavka (2013)

Kybernetika

A matrix A in ( max , min ) -algebra (fuzzy matrix) is called weakly robust if A k x is an eigenvector of A only if x is an eigenvector of A . The weak robustness of fuzzy matrices are studied and its properties are proved. A characterization of the weak robustness of fuzzy matrices is presented and an O ( n 2 ) algorithm for checking the weak robustness is described.

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