A run in a string is a periodic substring which is extendable neither to the left nor to the right with the same period. Strings containing many runs are of interest. In this paper, we focus on the series of strings {ψ(φ(a))}i≥0 generated by two kinds of morphisms, φ : {a, b, c} → {a, b, c}∗ and ψ : {a, b, c} → {0, 1}∗. We reveal a simple morphism φr plays a critical role to generate run-rich s...

A morphism h is called ambiguous for a string s if there is another morphism that maps s to the same image as h; otherwise, it is called unambiguous. In this paper, we examine some fundamental problems on the ambiguity of erasing morphisms. We provide a detailed analysis of so-called ambiguity partitions, and our main result uses this concept to characterise those strings that have a morphism o...

In this note we consider different versions of coinduction functors between categories of comodules for corings induced by a morphism of corings. In particular we introduce a new version of the coinduction functor in the case of locally projective corings as a composition of suitable “Trace” and “Hom” functors and show how to derive it from a more general coinduction functor between categories ...

Almost split sequences lie in the heart of Auslander-Reiten theory. This paper deals with structure almost certain ending terms morphism category an Artin algebra Λ. Firstly we try to interpret translates particular objects translations within Λ-modules, and then use them calculate sequences. In classical representation theory algebras, it is quite important recognize middle term As such, anoth...

Using an old example of Nagata, we construct a Noetherian ring prime characteristic p, whose Frobenius morphism is locally finite, but not finite.

Let $\pi: X \longrightarrow C$ be a fibration with reduced fibers over curve $C$ and consider polarization $H$ on the surface $X$. $E$ stable vector bundle of rank $2$ $C$. We prove that pullback $\pi^*E$ is $H-$stable This result allows us to relate corresponding moduli spaces bundles $\mathcal{M}_C(2,d)$ $\mathcal{M}_{X,H}(2,df,0)$ through an injective morphism. study induced morphism at leve...

Let X be a smooth projective variety of dimension n over an algebraically closed field k with char(k) = p > 0 and F : X → X1 be the relative Frobenius morphism. For any vector bundle W on X , we prove that instability of F∗W is bounded by instability of W ⊗ T(Ω X ) (0 ≤ l ≤ n(p − 1))(Corollary 4.8). When X is a smooth projective curve of genus g ≥ 2, it implies F∗W being stable whenever W is st...

In 1982, Séébold showed that the only overlap-free binary words that are the fixed points of non-identity morphisms are the Thue-Morse word and its complement. We strengthen Séébold’s result by showing that the same result holds if the term ‘overlapfree’ is replaced with ‘ 3 -power-free’. Furthermore, the number 7 3 is best possible.

Recently, Main [3] and Main, Bucher and Haussler [4] disproved quite a lot of conjectures about various classes of context-free languages by showing that the complement of the set of left factors of the T h u e M o r s e sequence and of other related infinite words is context-free. The aim of this article is to extend the latter result by showing, with almost the same proof technique, that, for...