1,721,009 research outputs found
Non-solvability for a class of left-invariant second-order differential operators on the Heisenberg group
No full textWe study the question of local solvability for second-order, left-invariant differential operators on the Heisenberg group , of the form
where is a complex matrix. Such operators never satisfy a cone condition in the sense of Sjöstrand and Hörmander. We may assume that cannot be viewed as a differential operator on a lower-dimensional Heisenberg group. Under the mild condition that and their commutator are linearly independent, we show that is not locally solvable, even in the presence of lower-order terms, provided that . In the case we show that there are some operators of the form described above that are locally solvable. This result extends to the Heisenberg group a phenomenon first observed by Karadzhov and Müller in the case of It is interesting to notice that the analysis of the exceptional operators for the case turns out to be more elementary than in the case When the analysis of these operators seems to become quite complex, from a technical point of view, and it remains open at this time
L^p-spectral multipliers for the Hodge Laplacian acting on 1-forms on the Heisenberg group
No full textWe prove that, if Δ_1 is the Hodge Laplacian acting on differential 1-forms on the (2n+1)-dimensional Heisenberg group, and if m is a Mihlin-Hörmander multiplier on the positive half-line, with L^2-order of smoothness greater than n+1/2, then m(Δ_1) is L^p-bounded for 1 < p < infinity. Our approach leads to an explicit description of the spectral decomposition of Δ_1 on the space of L^2-forms in terms of the spectral analysis of the sub-Laplacian L and the central derivative T, acting on
scalar-valued functions
On local solvability for complex coefficient differential operators on the Heisenberg group
No full textWe discuss the problem of solvability for some classes of complex coefficient second order left-invariant operators on the Heisenberg group Hn. We give several examples of operators that are not locally solvable for all choices of certain parameters, even if one allows the addition of lower order terms, in some cases also non-invariant ones. This is in striking contrast with the phenomenona known so far in the theory of local solvability of invariant second-order differential operators on nilpotent Lie groups. In order to disprove local solvability we use two different technical tools. The first one is a criterion by Hormander [Ho1]. The second one is an extension of a criterion for local non-solvability in [CR]. This extension, which is of interest in its own right, allows us to deal with non-homogeneous invariant differential operators.
Our analysis of the differential operators is based on the classification of normal forms for involutive complex Hamiltonians under the action of the real symplectic group
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
koamabayili/VECTRON-author-checklist: VECTRON author checklist
No full textWe have done our best to complete the author checklist relating to the use of animals in the hut study. Note that the objective for the hut study was to evaluate the IRS treatment applications for residual efficacy against Anopheles mosquitoes, including the local An. coluzzii mosquito population. Cows were only used to attract mosquitoes into the huts and no tests were carried out directly on the cows. The author checklist is intended for use with studies where experiments are carried out on animals, which is why we have had such difficulty in completing this for the hut study, as many of the questions do not relate to how the cows were used
- …
