NOTIZIARIO SETTIMANALE DEI SEMINARI DI MATEMATICA
2012-07-21
Seminari della settimana dal 16 al 20 luglio 2012 (se non specificato i seminari si tengono presso il Dip. di Matematica di Roma La Sapienza)
Lunedi' 16 luglio 2012
Ore 15:00, Aula di Consiglio
Seminario di Topologia Algebrica e Differenziale
Roberto De Leo (Universita' di Cagliari)
Partially isometric immersions and free maps
We investigate the existence of "partially" isometric immersions,
namely maps f:M -> R^q which, for a given Riemannian manifold M, are
isometries on some sub-bundle H of TM. The concept of free maps, which
is essential in the Nash-Gromov theory of isometric immersions, is
replaced here by that of H-free maps, i.e. maps whose restriction to H
is free. We prove that, under suitable conditions on the dimension q
of the Euclidean space, H-free maps are generic and we provide, for
the smallest possible value of q, explicit expressions for H-free maps
in the following three settings: 1-dimensional distributions in R^2,
Lagrangian distributions of completely integrable systems, Hamiltonian
distributions of a particular kind of Poisson Bracket.
Martedi' 17 luglio 2012
Ore 9:00, Aula di Consiglio
Gastao Coelho Gomes (Universita' di Rio de Janeiro)
Exploratory data analysis applied to the evaluation of aphasic
patients
n order to evaluate the degree of disease of aphasic patients, a study
was carried out by submitting to them a sample of images, selected
among a set of internationally adopted ones for this purpose. The
selection was performed according to i) the ease of recognition of the
represented items; and ii) the supposed familiarity of people with the
items' names. To check the first, the images were submitted to a set
of judges (without disease) and the images were retained provided that
90% of the judges recognised it. To check the second, the familiarity
of the used names was evaluated by asking one set of judges to declare
in which class of age (among 7) they got in touch with the name itself
and by asking the second set to choose the names degree of primitivity
on a 1-7 ordinal scale. The resulting data set have been submitted to
multidimensional exploratory data analysis, according to the nature of
the data and the results will be shown during the seminar.
Giovedi' 19 luglio 2012
Ore 12:00, Aula di Consiglio
Augusto Ponce (Universite' Catholique de Louvain)
LINK: http://www.mat.uniroma1.it/ricerca/notiziario.htmlOre 15:00, Aula di Consiglio
Seminario di Topologia Algebrica e Differenziale
Roberto De Leo (Universita' di Cagliari)
Partially isometric immersions and free maps
We investigate the existence of "partially" isometric immersions,
namely maps f:M -> R^q which, for a given Riemannian manifold M, are
isometries on some sub-bundle H of TM. The concept of free maps, which
is essential in the Nash-Gromov theory of isometric immersions, is
replaced here by that of H-free maps, i.e. maps whose restriction to H
is free. We prove that, under suitable conditions on the dimension q
of the Euclidean space, H-free maps are generic and we provide, for
the smallest possible value of q, explicit expressions for H-free maps
in the following three settings: 1-dimensional distributions in R^2,
Lagrangian distributions of completely integrable systems, Hamiltonian
distributions of a particular kind of Poisson Bracket.
Martedi' 17 luglio 2012
Ore 9:00, Aula di Consiglio
Gastao Coelho Gomes (Universita' di Rio de Janeiro)
Exploratory data analysis applied to the evaluation of aphasic
patients
n order to evaluate the degree of disease of aphasic patients, a study
was carried out by submitting to them a sample of images, selected
among a set of internationally adopted ones for this purpose. The
selection was performed according to i) the ease of recognition of the
represented items; and ii) the supposed familiarity of people with the
items' names. To check the first, the images were submitted to a set
of judges (without disease) and the images were retained provided that
90% of the judges recognised it. To check the second, the familiarity
of the used names was evaluated by asking one set of judges to declare
in which class of age (among 7) they got in touch with the name itself
and by asking the second set to choose the names degree of primitivity
on a 1-7 ordinal scale. The resulting data set have been submitted to
multidimensional exploratory data analysis, according to the nature of
the data and the results will be shown during the seminar.
Giovedi' 19 luglio 2012
Ore 12:00, Aula di Consiglio
Augusto Ponce (Universite' Catholique de Louvain)
The divergence of continuous vector fields
I will explain some results concerning the existence of continuous
vector fields in the Euclidean space of dimension N when the
divergence is prescribed. Up to an L^1 perturbation of the data, this
is always the case if the divergence does not charge sets of finite
Hausdorff measure of dimension N-1. This characterization is
reminiscent of a decomposition of measures which do not charge sets of
zero capacity due to Boccardo, Gallouet and Orsina.
I will explain some results concerning the existence of continuous
vector fields in the Euclidean space of dimension N when the
divergence is prescribed. Up to an L^1 perturbation of the data, this
is always the case if the divergence does not charge sets of finite
Hausdorff measure of dimension N-1. This characterization is
reminiscent of a decomposition of measures which do not charge sets of
zero capacity due to Boccardo, Gallouet and Orsina.
