Quaderni di Dipartimento
Collezione dei preprint del Dipartimento di Matematica.
La presenza del full-text è lacunosa per i prodotti antecedenti maggio 2006.
Trovati 868 prodotti
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QDD195 - 25/02/2015
Catino, G.; Mazzieri, L.
Connected sum construction for sigma_k-Yamabe metrics | Abstract | | In this paper we produce families of Riemannian metrics with positive constant sigma_k-curvature equal to 2^{?k}(n k) by performing the connected sum of two given compact non degenerate n--dimensional solutions (M1,g1) and (M2,g2) of the (positive) sigmak-Yamabe problem, provided 2<=2k
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QDD194 - 25/02/2015
Catino, G.
Complete gradient shrinking Ricci solitons with pinched curvature | Abstract | | We prove that any n--dimensional complete gradient Ricci soliton with pinched Weyl curvature is a finite quotient of R^n, R×S^{n?1} or S^n. In particular, we do not need to assume the metric to be locally conformally flat. |
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QDD193 - 15/02/2015
Catino, G.; Mantegazza C.; Mazzieri, L.; Rimoldi M.
Locally Conformally Flat Quasi-Einstein Manifolds | Abstract | | In this paper we prove that any complete locally conformally flat quasi-Einstein manifold of dimension n?3 is locally a warped product with (n?1)-dimensional fibers of constant curvature. This result includes also the case of locally conformally flat gradient Ricci solitons. |
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QDD192 - 15/02/2015
Catino, G.
Generalized quasi-Einstein manifolds with harmonic Weyl tensor | Abstract | | In this paper we introduce the notion of generalized quasi--Einstein manifold, which generalizes the concepts of Ricci soliton, Ricci almost soliton and quasi--Einstein manifolds. We prove that a complete generalized quasi--Einstein manifold with harmonic Weyl tensor and with zero radial Weyl curvature, is locally a warped product with (n?1)--dimensional Einstein fibers. In particular, this implies a local characterization for locally conformally flat gradient Ricci almost solitons, similar to the one proved for gradient Ricci solitons. |
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QDD190 - 13/01/2015
Finotelli, P.;Dulio, P.
A Mathematical Model for Evaluating the Functional Connectivity Strongness in Healthy People | Abstract | | The human brain is a really complex organization of connectivity whose principal elements are neurons,
synapses and brain regions. Up to now this connectivity is not fully understood, and recent impulse
in investigating its structure has been given by Graph Theory. However, some points remain unclear,
mainly due to possible mismatching between the Mathematical and the Neuroscienti c approach. It
is known that neural connectivity is classi ed into three categories: structural (or anatomical) connectivity,
functional connectivity and e ective connectivity. The point is that these categories demand
di erent kinds of graphs, except in the case of the resting state, and sometimes topological and metrical
parameters are involved simultaneously, without a speci c distinction of their roles.
In this paper we propose a mathematical model for treating the functional connectivity, based
on directed graphs with weighted edges. The function W(i; j; t), representing the weight of the edge
connecting nodes i; j at time t, is obtained by splitting the model in two parts, where di erent parameters
have been introduced step by step and rigorously motivated. In particular, there is a double role
played by the notion of distance, which, according to the di erent parts of the model, assumes a
discrete or an Euclidean meaning. Analogously, the time t appears both from a local and from a global
perspective. The local aspect relates to a speci c task submitted to an health volunteer (in view of
possible future applications also to subjects a ected by neurological diseases), while the global one
concerns the di erent periods in the human life that characterize the main changes in the neural brain
network. In the particular case of the resting state, we have shown that W reduces to the usually
employed probabilistic growth laws for the edge formation. We tested the correctness of our model by
means of synthetic data, where the selection of all involved parameters has been motivated according
to what is known from the available literature. It turns out that simulated outputs t well with the
expected results, which encourages further analysis on real data, and possible future applications to
neurological pathologies. |
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QDD191 - 13/01/2015
Beretta, E.; Cerutti, M.C.; Manzoni, A.; Pierotti, D.
On a semilinear elliptic boundary value problem arising in cardiac electrophysiology | Abstract | | In this paper we provide a representation formula for boundary voltage perturbations caused
by internal conductivity inhomogeneities of low volume fraction in a simpli ed monodomain model
describing the electric activity of the heart. We derive such a result in the case of a nonlinear
problem. Our long-term goal is the solution of the inverse problem related to the detection of regions
a ected by heart ischemic disease, whose position and size are unknown. We model the presence
of ischemic regions in the form of small inhomogeneities. This leads to the study of a boundary
value problem for a semilinear elliptic equation. We rst analyze the well-posedness of the problem
establishing some key energy estimates. These allow us to derive rigorously an asymptotic formula
of the boundary potential perturbation due to the presence of the inhomogeneities, following an
approach similar to the one introduced by Capdeboscq and Vogelius in [7] in the case of the linear
conductivity equation. Finally, we propose some ideas of the reconstruction procedure that might
be used to detect the inhomogeneities. |
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QDD189 - 27/11/2014
Pagani, C.D.; Pierotti,D.; Verzini, G.; Zilio, A.
A nonlinear Steklov problem arising in corrosion modeling | Abstract | | We investigate the existence of pairs (?, u), with ? > 0 and u harmonic function in the unit ball B ? R3 , such that the nonlinear boundary condition ?? u = ? sinh u holds on ?B. This type of exponential boundary condition arises in corrosion modeling (Butler-Volmer condition). We prove existence of global branches of nontrivial solutions in the framework of analytic bifurcation theory and investigate their properties both analytically and numerically.
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QDD188 - 11/11/2014
Maluta, E.; Papini, P.L.
Diametrically complete sets and normal structure | Abstract | | We prove that in some classes of reflexive Banach spaces every maximal diametral set must be diametrically complete, thus showing that diametrically complete sets may have empty interior also in reflexive spaces. As a consequence, we prove that, in those spaces, normal structure is equivalent to the weaker property that, for every bounded set, the absolute Chebyshev radius is strictly smaller than the diameter. Moreover we prove that, in any normed space, the two classes of diametrically complete sets and of sets of constant radius from the boundary coincide if and only if the space has normal structure. |
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