1,720,952 research outputs found
Nilpotent and abelian Hopf-Galois structures on field extensions
Get PDFThis is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.Let L/K be a finite Galois extension of fields with group Γ . When Γ is nilpotent, we show that the problem of enumerating all
nilpotent Hopf–Galois structures on L/K can be reduced to the corresponding problem for the Sylow subgroups of Γ . We use this to enumerate all nilpotent (resp. abelian) Hopf–Galois structures on a cyclic extension of arbitrary finite degree. When Γ is abelian, we give conditions under which every abelian Hopf–Galois structure on L/K has type Γ . We also give a criterion on n such that every Hopf–Galois structure on a cyclic extension of degree n has cyclic type
Galois scaffolds and Galois module structure in extensions of characteristic p local fields of degree p2
Get PDFThis is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.A Galois scaffold, in a Galois extension of local fields with perfect residue fields, is an adaptation of the normal basis to the valuation of the extension field, and thus can be applied to answer questions of Galois module structure. Here we give a sufficient condition for a Galois scaffold to exist in fully ramified Galois extensions of degree p2 of characteristic p local fields. This condition becomes necessary when we restrict to p = 3. For extensions L/K of degree p2 that satisfy this condition, we determine the Galois module structure of the ring of integers by finding necessary and sufficient conditions for the ring of integers of L to be free over its associated order in K[Gal(L/K)]
Hopf-Galois structures of squarefree degree
Get PDFThis is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordLet n be a squarefree natural number, and let G, Γ be
two groups of order n. We determine the number of Hopf-Galois
structures of type G admitted by a Galois extension of fields with
Galois group isomorphic to Γ. We give some examples, including
a full treatment of the case where n is the product of three primes
Counting Hopf-Galois structures on cyclic field extensions of squarefree degree
Get PDFThis is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.We investigate Hopf-Galois structures on a cyclic field extension L/K of squarefree degree n. By a result of Greither and Pareigis, each such Hopf-Galois structure corresponds to a group of order n, whose isomorphism class we call the type of the Hopf-Galois structure. We show that every group of order n can occur, and we determine the number of Hopf-Galois structures of each type. We then express the total number of Hopf-Galois structures on L/K as a sum over factorisations of n into three parts. As examples, we give closed expressions for the number of Hopf-Galois structures on a cyclic extension whose degree is a product of three distinct primes. (There are several cases, depending on congruence conditions between the primes.) We also consider one case where the degree is a product of four primes.The first-named author acknowledges support from The Higher Committee for Education Development in Iraq
Hopf-Galois structures on non-normal extensions of degree related to Sophie Germain primes
Get PDFThis is the author accepted manuscript. The final version is available from Elsevier via the DOI in this recordWe consider Hopf-Galois structures on separable (but
not necessarily normal) field extensions L/K of squarefree degree
n. If E/K is the normal closure of L/K then G = Gal(E/K) can
be viewed as a permutation group of degree n. We show that G
has derived length at most 4, but that many permutation groups
of squarefree degree and of derived length 2 cannot occur. We
then investigate in detail the case where n = pq where q ≥ 3 and
p = 2q + 1 are both prime. (Thus q is a Sophie Germain prime
and p is a safeprime). We list the permutation groups G which can
arise, and we enumerate the Hopf-Galois structures for each G.
There are six such G for which the corresponding field extensions
L/K admit Hopf-Galois structures of both possible types.London Mathematical SocietyUniversity of Exete
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
On the mixing properties of piecewise expanding maps under composition with permutations
Get PDFThis is the author accepted manuscript. The final version is available from American Institute of Mathematical Sciences via the DOI in this record.We consider the effect on the mixing properties of a piecewise smooth interval map f when its domain is divided into N equal subintervals and f is composed with a permutation of these. The case of the stretch-and-fold map f(x)=mxmod1 for integers m≥2 is examined in detail. We give a combinatorial description of those permutations σ for which σ∘f is still (topologically) mixing, and show that the proportion of such permutations tends to 1 as N→∞. We then investigate the mixing rate of σ∘f (as measured by the modulus of the second largest eigenvalue of the transfer operator). In contrast to the situation for continuous time diffusive systems, we show that composition with a permutation cannot improve the mixing rate of f, but typically makes it worse. Under some mild assumptions on m and N, we obtain a precise value for the worst mixing rate as σ ranges through all permutations; this can be made arbitrarily close to 1 as N→∞ (with m fixed). We illustrate the geometric distribution of the second largest eigenvalues in the complex plane for small m and N, and propose a conjecture concerning their location in general. Finally, we give examples of other interval maps f for which composition with permutations produces different behaviour than that obtained from the stretch-and-fold map
- …
