1,720,957 research outputs found
The regularity index of up to 2n−1 equimultiple fat points of P^n
Get PDFAbstract. Let X = mP_1 + +mP_n+k be a fat point subscheme of P^n, where Supp(X) consists
of n + k distinct points which generate P^n: We study the regularity index tau (X) of X, which is the
least degree in which the Hilbert function of X equals its Hilbert polynomial. We prove that the
generalized Segre's bound for tau (X) holds if n>=4 and there are k+3 points of Supp(X) on a linear 3-dimensional
subspace. We assume Supp(X) is not in general position and call d the least integer for
which there exists a linear subspace of dimension d containing at least d+2 points of Supp(X).
We prove that the generalized Segre's bound holds for simple points when either 3<=k<=n+1
and d>k-3 or k = 4 with no restriction on d. For m greater than or equal to 2 we prove the generalized Segre's bound
when Supp(X) consists of n+4 points and either there are at least 3 points on a line or at least
5 points on a plane or at least 6 points on a linear 3-dimensional subspace. Finally we prove that, in
general, 2m-1<=tau(X) <= 2m when 3<=k<=n-1 and d > k-1; and we extend this result to
the non-equimultiple case. We also provide cases in which the previous bound gives the generalized
Segre's bound
On Hadamard product of linear varieties
No full textIn this paper, we address the Hadamard product of linear varieties not necessarily in general position. In P2, we obtain a complete description of the possible outcomes. In particular, in the case of two disjoint finite sets X and X′ of collinear points, we get conditions for X X′ to be either a collinear finite set of points or a grid of |X||X′| points. In P3, under suitable conditions (which we prove to be generic), we show that X X′ consists of |X||X′| points on the two different rulings of a nondegenerate quadric and we compute its Hilbert function in the case |X| = |X′|
The Hilbert function of some Hadamard products
No full textIn this paper we address the Hadamard product of not necessarily generic linear varieties, looking in particular at its Hilbert function. We find that the Hilbert function of the Hadamard product X⋆Y of two varieties, with dim(X),dim(Y)≤ 1, is the product of the Hilbert functions of the original varieties X and Y . Moreover, the same result is obtained for generic linear varieties X and Y as a consequence of our showing that their Hadamard product is projectively equivalent to a Segre embedding
The Hilbert function of some Hadamard products
No full textIn this paper we address the Hadamard product of not necessarily generic linear varieties, looking in particular at
its Hilbert function. We find that the Hilbert function of the
Hadamard product X *Y of two varieties, with dim(X); dim(Y )
1, is the product of the Hilbert functions of the original varieties
X and Y . Moreover, the same result is obtained for generic linear
varieties X and Y as a consequence of our showing that their
Hadamard product is projectively equivalent to a Segre embedding
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
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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