1,720,960 research outputs found
Bifurcation and symmetry breaking for the Henon equation
No full textIn this paper, we consider the henon problem
in the unit ball of R^N, N≥3, with Dirchlet boundery conditions. We prove the existence of (at least) one branch of non-radial solutions that bifurcate from the radial ones and that this branch is unbounded
On a singular eigenvalue problem and its applications in computing the Morse index of solutions to semilinear PDE's, Part II
No full textBy using a characterization of the Morse index and the degeneracy in terms of
a singular one dimensional eigenvalue problem given in a previous paper, we
give a lower bound for the Morse index of radial solutions to H'enon type
problems
[ left{egin{array}{ll}
-Delta u = |x|^alpha f(u) qquad & ext{ in } Omega,
u= 0 & ext{ on } partial Omega,
end{array}
ight. ]
where is a bounded radially symmetric domain
of (), alpha>0 and is a real function. From this
estimate we get that the Morse index of nodal radial solutions to this problem
goes to as . Concerning the real H'enon problem,
, we prove radial nondegeneracy, we show that the radial
Morse index is equal to the number of nodal zones and we get that a least
energy nodal solution is not radial
On a singular eigenvalue problem and its applications in computing the Morse index of solutions to semilinear PDE's (preprint)
No full textWe investigate nodal radial solutions to semilinear problems of type
{−Δu=f(|x|,u) in Ω,u=0 on ∂Ω,
where Ω is a bounded radially symmetric domain of RN (N≥2) and f is a real function. We characterize both the Morse index and the degeneracy in terms of a singular one dimensional eigenvalue problem, and describe the symmetries of the eigenfunctions. Next we use this characterization to give a lower bound for the Morse index; in such a way we give an alternative proof of an already known estimate for the autonomous problem and we furnish a new estimate for H\'enon type problems with f(|x|,u)=|x|αf(u). Concerning the real H\'enon problem, f(|x|,u)=|x|α|u|p−1u, we prove radial nondegeneracy and show that the radial Morse index is equal to the number of nodal zones
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
A complete scenario on nodal radial solutions to the Brezis Nirenberg problem in low dimensions
No full textIn this paper we consider nodal radial solutions of the problem -?u = |u|2*-2u + ?u in B, u =0 on B where 2*= 2N N-2 with 3 N 6 and B is the unit ball of IRN. We compute the asymptotics of the solution u as well as u8, its first zero and other relevant quantities as ? goes to a critical value .?. Also the sign of ? - .? is established in all cases. This completes an analogous analysis for N 7 given in [12]
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
Morse index computation for radial solutions of the Hénon problem in the disk
Full text linkWe compute the Morse index m(up) of any radial solution up of the semilinear problem: −Δu=|x|α|u|p−1uinBu=0on∂Bwhere B is the unit ball of R2 centered at the origin, α≥0 is fixed and p>1 is sufficiently large. In the case α=0, i.e. for the Lane–Emden problem, this leads to the following Morse index formula m(up)=4m2−m−2,for p large enough, where m is the number of nodal domains of u
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
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