1,720,971 research outputs found
On type sequences and Arf rings
No full textIn this article we explicitly give a description to compute
the type sequence t_1, . . . , t_n of a semigroup S generated by an arithmetic sequence explicitly ; we show that the i-th term t_i is equal to 1 or to the type , depending on its position. Further, for analytically irreducible ring R with the branch sequence R_j ,we give a characterization of the “Arf” property using the type sequence of R and of the rings R_j .
Further, we prove some relations among the integers l*(R) and
l*(R_j ) . These relations allow us to obtaina new charaterization of semigroup rings of minimal multiplicity with l*(R)≤ type (R) in terms of the Arf property, type sequences and relations between
l*(R) and l*(Rj )
On the type sequence of some one dimensional rings
No full textIn this article we describe the holes and their positions of a numerical semigroup and use this description to compute the type sequence of the semigroup generated by an arithmetic explicitly
CM defect and Hilbert function of monomial curves
No full textIn this article we consider a semigroup ring R = K[[Γ ]] of a numerical semigroup Γ
and study the Cohen–Macaulayness of the associated graded ring G(Γ ) := grm(R) :=
⊕n∈N mn/mn+1 and the behaviour of the Hilbert function HR of R.Wedefine a certain (finite)
subset B(Γ ) ⊆ Γ and prove that G(Γ ) is Cohen–Macaulay if and only if B(Γ ) = ∅.
Therefore the subset B(Γ ) is called the Cohen–Macaulay defect of G(Γ ). Further, we prove
that if the degree sequence of elements of the standard basis of Γ is non-decreasing,
then B(Γ ) = ∅ and hence G(Γ ) is Cohen–Macaulay. We consider a class of numerical
semigroups Γ =
Σ3
i=0 Nmi generated by 4 elements m0,m1,m2,m3 such that m1 +m2 =
m0+m3—so called ‘‘balanced semigroups’’. We study the structure of the Cohen–Macaulay
defect B(Γ ) of Γ and particularly we give an estimate on the cardinality |B(Γ , r)| for
every r ∈ N. We use these estimates to prove that the Hilbert function of R is nondecreasing.
Further, we prove that every balanced ‘‘unitary’’ semigroup Γ is ‘‘2-good’’ and
is not ‘‘1-good’’, in particular, in this case, G(Γ ) is not Cohen–Macaulay. We consider a
certain special subclass of balanced semigroups Γ . For this subclass we try to determine
the Cohen–Macaulay defect B(Γ ) using the explicit description of the standard basis of Γ ;
in particular, we prove that these balanced semigroups are 2-good and determine when
exactly G(Γ ) is Cohen–Macaulay
On the Cohen–Macaulayness of some graded rings
No full textLet (R,m) be a 1-dimensional Cohen-Macaulay local ring of multiplicity e and embedding dimension v ≥2 . Let B denote the blowing-up of R along m and let I be the conductor of R in B. Let x be a superficial element in m of degree 1 and I' = (I +xR)/xR . We assume that the length l(I') = 1 . This class of local rings contains the class of 1-dimensional Gorenstein local rings . In section 1, we prove that if the associated graded ring G = gr(R) is Cohen-Macaulay, then I is contained in m^s + xR , where s is the degree of the h-polynomial h(R) of R. In section 2, we give necessary and sufficient conditions for the Cohen-Macaulayness of G.
These conditions are numerical conditions on the h-polynomial h(R) , particularly on its coefficients and the degree in comparison with the difference e − v . In section 3, we give some conditions for the Gorensteinness of G. In section 4, we give a characterisation (see 4.3) of numerical semigroup rings which satisfy the condition l(I') =
On the length equalities for one–dimensional rings
No full textIn this article we characterize noetherian local one-dimensional analytically irreducible and residually rational domains (R,m) which are non-Gorenstein, the non-negative integer l*(R)=t(R).l(R/C) – l(S/R) is equal to t(R)–1 and l(R/(C+xR))=2, where t(R) is the Cohen–Macaulay type of R , C is the conductor of R in the integral closure S of R in its quotient field Q(R) and xR is a minimal reduction of, by giving some conditions on the numerical semi-group v(R) of R
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
- …
