1,721,406 research outputs found
Energy instability and overdetermined elliptic problems in cones and cylinders: an approach via domain variations
Full text linkIn this thesis, we study semilinear elliptic problems in domains
that are constrained to be inside a fixed unbounded open set C, with appropriate boundary
conditions. Our aim is to understand how the geometry of C selects domains in which
positive solutions of the equation have special properties, mainly related to notions of
symmetry. Our arguments are primarily based on analyzing how the energy of a positive
solution in a domain varies when the domain moves inside C. We first consider the case
where C is generic. We show how to define an energy functional T when the equation
possesses more than one solution and compute the domain derivative of T. In the case
when C is a cone or a cylinder, we show that some special domains may be unstable
as critical points to the energy shape functional. This opens room for the search for
nonsymmetric domains with the same special properties, to be found, for example, by
local minimization of the energy functional. This is done by analyzing the sign of the
second derivative of the energy functional to understand the stability/instability of its
critical domains. Furthermore, we show that in a special class of domains, namely bounded
cylinders, solutions other than the one-dimensional ones do exist, under fairly general
assumptions on the nonlinearity. This is accomplished by means of bifurcation theory
and Morse index comparison
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
A particular mechanism for the retrieval of the spatial trace, II: an experimental study of 300 children
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Twelve angry men: A dynamic-epistemic study of awareness, implicit and explicit information
No full textBy moving from a suggestive example, the paper analyzes how information flows among agents involved in a deliberation. By interchanging information, agents become aware of details, draw the attention of the group to some issues, perform inferences and announce what they know. The proposed framework, based on the paradigm of dynamic epistemic logic, captures how knowledge results from step-wise multi-agent interaction
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