The vectorial extension of the Ribaucour transformation for the Lamé equations of orthogonal conjugates nets in multidimensions is given. We show that the composition of two vectorial Ribaucour transformations with appropriate transformation data is again a vectorial Ribaucour transformation, from which it follows the permutability of the vectorial Ribaucour transformations. Finally, as an exam...

In this paper, we introduce a vectorial conception of dFCSRs to build these registers over any finite field. We describe the structure of d-vectorial FCSRs and we develop an analysis to obtain basic properties like periodicity and the existence of maximal length sequences. To illustrate these vectorial d-FCSRs, we present simple examples and we compare with those of Goresky, Klapper and Xu.

The standard explanation for multiple filamentation of laser pulses is that it is caused by noise in the input beam. We propose an alternative explanation that is based on deterministic vectorial (polarization) effects. We present numerical simulations in support of the vectorial-effects explanation and suggest a simple experiment for deciding whether multiple filamentation is due to vectorial ...

Recently, one of the hot topics on vectorial Boolean bent functions is to construct vectorial Boolean bent functions in the form Tr m(P (x)) from Boolean bent functions in the form Tr 1 (P (x)), where P (x) ∈ F2n [x]. This paper first presents three constructions of vectorial Boolean bent functions in the form Tr m(P (x)), where two of them give answers to two open problems proposed by Pasalic ...