Browsing by Subject "Arf ring"

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    A fast algorithm for constructing Arf closure and a conjecture
    (Academic Press, 2014) Arslan, F.; Şahin, N.
    In this article, we give a fast and an easily implementable algorithm for computing the Arf closure of an irreducible algebroid curve (or a branch). Moreover, we study the relation between the branches having the same Arf closure and their regularity indices. We give some results and a conjecture, which are steps towards the interpretation of Arf closure as a specific way of taming the singularity.
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    On Arf rings
    (1994) Arslan, Sefa Feza
    In this thesis, we worked with curves which have cusp type singularities. We described the Arf theory, which solves the problem of understanding and finding the multiplicity sequence of a curve branch algebraically. We proposed an algorithm for finding the Arf characters of a given curve branch. We also faced the problem of Frobenius, and proposed an algorithm for the solution of problem of Frobenius in the most general case.