1,722,178 research outputs found
Threshold phenomena for symmetric decreasing solutions of reaction-diffusion equations
No full textWe study the long time behavior of solutions of the Cauchy problem for nonlinear reaction-diffusion equations in one space dimension with the nonlinearity of bistable, ignition or monostable type. We prove a one-to-one relation between the long time behavior of the solution and the limit value of its energy for symmetric decreasing initial data in L (2) under minimal assumptions on the nonlinearities. The obtained relation allows to establish sharp threshold results between propagation and extinction for monotone families of initial data in the considered general setting
THRESHOLD PHENOMENA FOR SYMMETRIC-DECREASING RADIAL SOLUTIONS OF REACTION-DIFFUSION EQUATIONS
No full textWe study the long time behavior of positive solutions of the Cauchy problem for nonlinear reaction-diffusion equations in R-N with bistable, ignition or monostable nonlinearities that exhibit threshold behavior. For L-2 initial data that are radial and non-increasing as a function of the distance to the origin, we characterize the ignition behavior in terms of the long time behavior of the energy associated with the solution. We then use this characterization to establish existence of a sharp threshold for monotone families of initial data in the considered class under various assumptions on the nonlinearities and spatial dimension. We also prove that for more general initial data that are sufficiently localized the solutions that exhibit ignition behavior propagate in all directions with the asymptotic speed equal to that of the unique one-dimensional variational traveling wave
On some nonlinear PDEs with Sobolev-hardy critical exponents and a Li-Lin open problem
No full textLet Ω be a C1 open bounded domain in RN, N ≥ 3, with (Formula presented.). We consider the following problem involving Hardy–Sobolev critical exponents: (Formula presented.), where 0 ≤ s1 < 2, 0 ≤ s2 < 2, 2 *(s2) ≠ λ ∈ R, 1 ≤ p ≤ 2*(s1) - 1 and with choices of exponents and parameters corresponding to cases in which (P) has not been before investigated. We prove the existence of positive solutions, which, in some cases, are also shown to be ground states. We remark that we give a first partial answer to a question proposed by Li and Lin (Arch Ration Mech Anal 203(3):943–968, 2012). © 2015, Springer-Verlag Berlin Heidelberg
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
A sharp stability result for the Gauss mean value formula
Full text linkWe prove a quantitative stability result for the Gauss mean value formula. We also show by an example that the estimate proved here is sharp
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