If, for a morphism σ : ∆∗ → Σ∗ (where ∆ and Σ are arbitrary alphabets) and a word α ∈ ∆∗, there exists another morphism τ mapping α to σ(α), then σ is called ambiguous with respect to α ; if such a τ does not exist, then σ is unambiguous. For example, the morphism σ0 : {A,B,C}∗ → {a,b}∗ – given by σ0(A) := a, σ0(B) := a, σ0(C) := b – is ambiguous with respect to the word α0 := ABCACB, since the...

We give a characterization of all the sets X such that any morphism h on fa; bg is overlap-free ii for all x in X , h(x) is overlap-free. As a consequence, we observe the particular case X = fbbabaag which improves the previous characterization of Berstel-S e ebold 2]. R esum e Nous donnons une caract erisation de tous les ensembles X tels qu'un morphisme h sur fa; bg est sans chevauchement si ...

Let K be a discrete valuation field with ring of integers OK . Let f :X → Y be a finite morphism of curves overK . In this article, we study some possible relationships between the models over OK of X and of Y . Three such relationships are listed below. Consider a Galois cover f :X→ Y of degree prime to the characteristic of the residue field, with branch locus B. We show that if Y has semi-st...

Hitchin [Duke Math. J. 54(1), 91–114 (1987)] introduced a proper morphism from the moduli space of stable G-Higgs bundles [[Formula: see text] and [Formula: text]] over curve to vector invariant polynomials, he described generic fibers that morphism. In this paper, we first describe for parabolic projective symplectic/orthogonal Higgs without fixing determinant. We also when determinant is triv...

In this article we explore to what extend the techniques of Piunikhin, Salamon and Schwarz in [PSS96] can be carried over to Lagrangian Floer homology. In [PSS96] the authors establish an isomorphism between Hamiltonian Floer homology and singular homology of the underlying symplectic manifold. In general, Lagrangian Floer homology is not isomorphic to the singular homology of the Lagrangian su...

This article is the expanded version of a talk given at the conference: Algebraic geometry in East Asia 2008. In this notes, I intend to give a brief survey of results on the behavior of semi-stable bundles under the Frobenius pullback and direct images. Some results are new.

This paper deals with questions relating to Haghverdi and Scott’s notion of partially traced categories. The main result is a representation theorem for such categories: we prove that every partially traced category can be faithfully embedded in a totally traced category. Also conversely, every symmetric monoidal subcategory of a totally traced category is partially traced, so this characterize...

With the formal study of natural languages, we have obtained some residual results which greatly increase our power of logical manipulation. Coupled with a computer, our language extends enormously the external logic of our computing device. This paper is concerned with a well-defined symbolic list processing language and a set of operators for this language. These operators, which we call morp...

We introduce a notion of morphism of CohFT algebras, based on the analogy with A∞ morphisms. We outline the construction of a “quantization” of the classical Kirwan morphism to a morphism of CohFT algebras from the equivariant quantum cohomology of a Gvariety to the quantum cohomology of its geometric invariant theory or symplectic quotient, and an example relating to the orbifold quantum cohom...

New representation results for three families of regular languages are stated, using a special kind of shuue operation, namely the synchronized shuue. First, it is proved that the family of regular star languages is the smallest family containing the language (a + bc) and closed under synchronized shuue and length preserving morphism. The second representation result states that the family of "...