A lifting map from cuspidal automorphic representations of the Jacobi group G J to cuspidal auto-morphic representations of the group PGL(2) is constructed. The lifting also has a local deenition, and the local and global versions are compatible. The local lifts can be described in terms of equivalence classes of local representations. The main idea in the construction is to exploit the close r...

In the present paper, we introduce an alternative notion of the primitivity of words, that – unlike the standard understanding of this term – is not based on the power (and, hence, the concatenation) of words, but on morphisms. For any alphabet Σ, we call a word w ∈ Σ∗ morphically imprimitive provided that there are a shorter word v and morphisms h, h′ : Σ∗ → Σ∗ satisfying h(v) = w and h′(w) = ...

The aim of this paper is to show several iso morphic structures between fuzzy relations and operators from the family of fuzzy sets into itself In particular we prove that the preorders family is able to embed itself in the class of fuzzy consequence operators by way of a lattice monomorphism

In this paper we introduce and study a new property of infinite words: An infinite word x ∈ A, with values in a finite set A, is said to be k-self-shuffling (k ≥ 2) if x admits factorizations: x = ∏∞ i=0 U (1) i · · ·U (k) i = ∏∞ i=0 U (1) i = · · · = ∏∞ i=0 U (k) i . In other words, there exists a shuffle of k-copies of x which produces x. We are particularly interested in the case k = 2, in w...

Streams are infinite sequences. The simplest streams that are not ultimately periodic are morphic streams: fixed points of particular morphisms mapping single symbols to strings of symbols. A most basic way to visualize a stream is by a turtle curve: for every alphabet symbol fix an angle, and then proceed the stream elements by drawing unit segments and turn the corresponding angle. This paper...

An alphabet reduction is a 1-uniform morphism that maps a word to an image that contains a smaller number of different letters. In the present paper we investigate the effect of alphabet reductions on morphically primitive words, i. e., words that are not a fixed point of a nontrivial morphism. Our first main result answers a question on the existence of unambiguous alphabet reductions for such...