Simon (Theoret. Comput. Sci. 72 (1990) 65–94) has proved that every morphism from a free semigroup to a $nite semigroup S admits a Ramseyan factorization forest of height at most 9|S|. In this paper, we prove the same result of Simon with an improved bound of 7|S|. We provide a simple algorithm for constructing a factorization forest. In addition, we show that the algorithm cannot be improved s...

We count the number of occurrences of certain patterns in given words. We choose these words to be the set of all finite approximations of a sequence generated by a morphism with certain restrictions. The patterns in our considerations are either classical patterns 1-2, 2-1, 1-1· · · -1, or arbitrary generalized patterns without internal dashes, in which repetitions of letters are allowed. In p...

We show that the symmetric product of a flat affine scheme over a commutative ring can be embedded into the quotient by the general linear group of the scheme of commuting matrices. We also prove that the symmetric product of the affine space is isomorphic to the above quotient when the base ring is a characteristic zero field. Over an infinite field of arbitrary characteristic the quotient of ...

We start by showing that (1) is injective. Take an u ∈ Hom (A,B)⊗ Zl that maps to zero in HomΓ (Tl(A), Tl(B)). Write u = ∑∞ j=0 l uj , uj ∈ Hom(A,B), and [u]n for ∑n j=0 l uj . Note that since Hom (A,B) is a Z-module [u]n is in Hom (A,B). Now (since u maps to zero) [u]n is the zero morphism A[l ] → B[l], so it kills the ltorsion. As it is well known, this implies the existence of a certain ψn ∈...

In their book Rapoport and Zink constructed rigid analytic period spaces F for Fontaine’s filtered isocrystals and period morphisms from moduli spaces of p-divisible groups to some of these period spaces. They conjectured the existence of an étale bijective morphism F → F of rigid analytic spaces and of interesting local systems of Qp-vector spaces on F. For those period spaces possessing perio...

We prove that any (real or complex) analytic horizontally conformal submersion from a three-dimensional conformal manifold (M, cM ) to a twodimensional conformal manifold (N, cN ) can be, locally, ‘extended’ to a unique harmonic morphism from the H(eaven)-space (H, g) of (M, cN ) to (N, cN ). Moreover, any positive harmonic morphism with two-dimensional fibres from (H, g) is obtained this way.

The main purpose of this paper is to introduce the notion of vague h-morphism on vague graphs and regular vague graphs. The action of vague h-morphism on vague strong regular graphs are studied. Some elegant results on weak and co weak isomorphism are derived. Also, [Formula: see text]-complement of highly irregular vague graphs are defined.

In this paper we introduce the notion of intuitionistic fuzzy f morphism on intutionistic fuzzy graphs and regular intutionistic fuzzy graph. We study the action of intuitionistic fuzzy f morphism on intuitionistic fuzzy strong regular graphs. We derive some simple but elegent results on weak and coweak isomophisms. Mathematics Subject Classification: 03E72, 03F55