DSpace Communidade:
http://www.repositorio.ufop.br/handle/123456789/551
Tue, 17 Jul 2018 23:27:30 GMT20180717T23:27:30ZTorsion functions and the Cheeger problem : a fractional approach.
http://www.repositorio.ufop.br/handle/123456789/9844
Título: Torsion functions and the Cheeger problem : a fractional approach.
Autor(es): Bueno, Hamilton Prado; Ercole, Grey; Macedo, Shirley da Silva; Pereira, Gilberto A.
Resumo: Let Ω be a Lipschitz bounded domain of ℝN, N ≥ 2. The fractional Cheeger constant hs(Ω),
0 < s < 1, is defined by
hs(Ω) = inf
E⊂Ω
Ps(E)
E
, where Ps(E) = ∫
ℝN
∫
ℝN
χE(x) − χE(y)
x − y
N+s
dx dy,
with χE denoting the characteristic function of the smooth subdomain E. The main purpose of this paper is
to show that
lim
p→1
+
ϕ
s
p

1−p
L∞(Ω)
= hs(Ω) = lim
p→1
+
ϕ
s
p

1−p
L
1(Ω)
,
where ϕ
s
p
is the fractional (s, p)torsion function of Ω, that is, the solution of the Dirichlet problem for the
fractional pLaplacian: −(∆)
s
p u = 1 in Ω, u = 0 in ℝN \ Ω. For this, we derive suitable bounds for the first
eigenvalue λ
s
1,p
(Ω) of the fractional pLaplacian operator in terms of ϕ
s
p
. We also show that ϕ
s
p minimizes the
(s, p)Gagliardo seminorm in ℝN, among the functions normalized by the L
1
norm.Fri, 01 Jan 2016 00:00:00 GMThttp://www.repositorio.ufop.br/handle/123456789/984420160101T00:00:00ZAsymptotic behavior of the ptorsion functions as p goes to 1.
http://www.repositorio.ufop.br/handle/123456789/9261
Título: Asymptotic behavior of the ptorsion functions as p goes to 1.
Autor(es): Bueno, Hamilton; Ercole, Grey; Macedo, Shirley da Silva
Resumo: Let Ω be a Lipschitz bounded domain of RN, N ≥ 2, and let
up ∈ W1,p
0 (Ω) denote the ptorsion function of Ω, p > 1. It is observed
that the value 1 for the Cheeger constant h(Ω) is threshold with respect
to the asymptotic behavior of up, as p → 1+, in the following sense:
when h(Ω) > 1, one has limp→1+ up
L∞(Ω) = 0, and when h(Ω) < 1,
one has limp→1+ up
L∞(Ω) = ∞. In the case h(Ω) = 1, it is proved that
lim supp→1+ up
L∞(Ω) < ∞. For a radial annulus Ωa,b, with inner radius
a and outer radius b, it is proved that limp→1+ up
L∞(Ωa,b) = 0 when
h(Ωa,b) = 1.Fri, 01 Jan 2016 00:00:00 GMThttp://www.repositorio.ufop.br/handle/123456789/926120160101T00:00:00ZMetastable localization of diseases in complex networks.
http://www.repositorio.ufop.br/handle/123456789/9260
Título: Metastable localization of diseases in complex networks.
Autor(es): Ferreira, Ronan Silva; Costa, Rui A. da; Dorogovtsev, Sergey; Mendes, José Fernando Ferreira
Resumo: We describe the phenomenon of localization in the epidemic susceptibleinfectivesusceptible model on highly
heterogeneous networks in which strongly connected nodes (hubs) play the role of centers of localization. We
find that in this model the localized states below the epidemic threshold are metastable. The longevity and scale
of the metastable outbreaks do not show a sharp localization transition; instead there is a smooth crossover from
localized to delocalized states as we approach the epidemic threshold from below. Analyzing these longlasting
local outbreaks for a random regular graph with a hub, we show how this localization can be detected from the
shape of the distribution of the number of infective nodes.Fri, 01 Jan 2016 00:00:00 GMThttp://www.repositorio.ufop.br/handle/123456789/926020160101T00:00:00ZVulnerability of tropical soils to heavy metals : a PLSDA classification model for Lead.
http://www.repositorio.ufop.br/handle/123456789/9259
Título: Vulnerability of tropical soils to heavy metals : a PLSDA classification model for Lead.
Autor(es): Soares, Liliane Catone; Binatti, Júnia de Oliveira Alves; Linhares, Lucília Alves; Egreja Filho, Fernando Barboza; Fontes, Maurício P. F.
Resumo: One of themost important components of the soil vulnerability to heavy metals is related to a situationwhere the
critical load of the soil be exceeded, causing the releasing of retained metals. Soil vulnerability to a metal is a function
mainly of the interaction forces between the metal and the soil matrix, which depends on the physical and
chemical soil characteristics. This study aims to classify the soils as vulnerable or nonvulnerable for lead as a
function of the soil characteristics using Partial Least Squares Discriminant Analysis (PLSDA). The vulnerability
was assessed by the determination of available fraction metal (AF), after a treatmentwith Pb2+. Percent AF, evaluated
by extractionwith KNO3 solution,was used as reference only to separate the samples into two classes (vulnerable
and nonvulnerable) before the model construction. The data about soil characteristics were treated by
PLSDA aiming to discriminate the abovementioned classes, i.e. vulnerable and nonvulnerable. The employed
PLSDA model was built with 20 and 10 samples for the training and test sets, respectively, and in all cases
they were properly separated. The developed methodology shows high sensitivities (rate of true positives) and
specificities (rate of true negatives) for the two classes. Finally, it can be envisaged that this approach has potential
to be applied in classification of the soil vulnerability to lead, just based on soil characteristics.Sun, 01 Jan 2017 00:00:00 GMThttp://www.repositorio.ufop.br/handle/123456789/925920170101T00:00:00Z