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Properties of - compositions of fuzzy relations were first examined in Goguen [8] and next discussed by many authors. Power sequence of fuzzy relations was mainly considered in the case of matrices of fuzzy relation on a finite set. We consider - powers of fuzzy relations under diverse assumptions about operation. At first, we remind fundamental properties of - composition. Then, we introduce some manipulations on relation powers. Next, the closure and interior of fuzzy relations are examined....
In this paper we present new identities for the Radić’s determinant of a rectangular matrix. The results include representations of the determinant of a rectangular matrix as a sum of determinants of square matrices and description how the determinant is affected by operations on columns such as interchanging columns, reversing columns or decomposing a single column
We present a weak parametrix of the operator of the CFIE equation. An interesting feature of this parametrix is that it is compatible with different discretization strategies and hence allows for the construction of efficient preconditioners dedicated to the CFIE. Furthermore, one shows that the underlying operator of the CFIE verifies an uniform discrete Inf-Sup condition which allows to predict an original convergence result of the numerical solution of the CFIE to the exact one.
On exhibe dans cette note une paramétrix (au sens faible) de l'opérateur
sous-jacent à l'équation CFIE de l'électromagnétisme. L'intérêt de cette
paramétrix est de se prêter à différentes stratégies de discrétisation
et ainsi de pouvoir être utilisée comme préconditionneur de la CFIE.
On montre aussi que l'opérateur sous-jacent à la CFIE satisfait une condition
Inf-Sup discrète uniforme, applicable aux espaces de discrétisation usuellement rencontrés
en électromagnétisme, et qui permet d'établir...
We study the extent to which the pseudospectra of a matrix determine other aspects of its behaviour, such as the growth of its powers and its unitary equivalence class.
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