1,720,997 research outputs found
IDEALS OF THE FORM
No full textThe second author is the corresponding author who has been supportedby the research project EMR/2015/000776, sponsored by the SERB, Governmentof India. The third author thanks SERB for the post-doctoral fellowshipunder the said project. The third author thanks CSIR for the SeniorResearch Fellowship for Ph.D. The authors thank the anonymous refereesfor their valuable comments and for drawing their attention to the references[5] and [18], extremely pertinent to this work.International audienceIn this paper we compute Gröbner bases for determinantal ideals of the form , where X and Y are both matrices whose entries are indeterminates over a field K. We use the Gröbner basis structure to determine Betti numbers for such ideals
Betti Numbers, Grobner Basis And Syzygies For Certain Affine Monomial Curves
No full textLet e > 3 and mo,... ,me_i be positive integers with gcd(m0,... ,me_i) = 1, which form an almost arithmetic sequence, i.e., some e - 1 of these form an arithmetic progression. We further assume that m0,... ,mc_1 generate F := Σ e-1 I=0 Nmi minimally. Note that any three integers and also any arithmetic progression form an almost arithmetic sequence.
We assume that 0 , Y,T be indeterminates. Let p denote the kernel of the if-algebra homomorphism η: K[XQ, ..., XV) Y) -* K^T], defined by r){Xi) = Tm\.. .η{Xp) = Tmp, η](Y) = Tn. Then, p is the defining ideal for the affine monomial curve C in A^, defined parametrically by Xo = Trr^)...)Xv = T^}Y = T*. Furthermore, p is a homogeneous ideal with respect to the gradation on K[X0)... ,XP,F], given by wt(Z0) = mo, • • •, wt(Xp) = mp, wt(Y) = n. Let 4 := K[XQ> ...,XP) Y)/p denote the coordinate ring of C.
With the assumption ch(K) = 0, in Chapter 1 we have derived an explicit formula for μ(DerK(A)), the minimal number of generators for the A-module DerK(A), the derivation module of A. Furthermore, since type(A) = μ(DerK(A)) — 1 and the last Betti number of A is equal to type(A), we therefore obtain an explicit formula for the last Betti number of A as well
A minimal set of binomial generatorsG for the ideal p had been explicitly constructed by PatiL In Chapter 2, we show that the set G is a Grobner basis with respect to grevlex monomial ordering on K[X0)..., Xp, Y]. As an application of this observation, in Chapter 3 we obtain an explicit minimal free resolution for affine monomial curves in A4K defined by four coprime positive integers mo,.. m3, which form a minimal arithmetic progression.
(Please refer the pdf file forformulas
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe 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
Full text link“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
Full text linkWe 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
Full text linkWe 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
- …
