DSpace Collection:
http://hdl.handle.net/10077/10600
2023-02-05T10:16:16ZOn quotient orbifolds of hyperbolic 3-manifolds of genus two
http://hdl.handle.net/10077/10642
Title: On quotient orbifolds of hyperbolic 3-manifolds of genus two
Authors: Bruno, Annalisa; Mecchia, Mattia
Abstract: We analyse the orbifolds that can be obtained as quotients of genus two hyperbolic 3-manifolds by their orientation preserving isometry groups. The genus two hyperbolic 3-manifolds are exactly the hyperbolic2-fold branched coverings of 3-bridge links. If the3-bridge link is a knot, we prove that the underlying topological space of the quotient orbifold is either the 3-sphere or a lens space and we describe the combinatorial setting of the singular set for each possible isometry group. In the case of 3-bridge links with two or three components, the situation is more complicated and we show that the underlying topological space is the3-sphere, a lens space or a prism manifold. Finally we present an infnite family of hyperbolic 3-manifolds that are simultaneously the 2-foldbranched covering of three inequivalent knots, two with bridge number three and the third one with bridge number strictly greater than three.
Description: Annalisa Bruno and Mattia Mecchia, "On quotient orbifolds of hyperbolic -manifolds of genus two", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 46 (2014), pp.271-2992014-12-23T00:00:00ZNon resonance conditions for radial solutions of non linear Neumann elliptic problems on annuli
http://hdl.handle.net/10077/10641
Title: Non resonance conditions for radial solutions of non linear Neumann elliptic problems on annuli
Authors: Sfecci, Andrea
Abstract: An existence result to some nonlinear Neumann elliptic problems defined on balls has been provided recently by the author in [21]. We investigate, in this paper, the possibility of extending such a result to annuli.
Description: Andrea Sfecci, "Non resonance conditions for radial solutions of non linear Neumann elliptic problems on annuli", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 46 (2014), pp.255-2702014-12-23T00:00:00ZOn Grothendieck's counterexample to the Generalized Hodge Conjecture
http://hdl.handle.net/10077/10640
Title: On Grothendieck's counterexample to the Generalized Hodge Conjecture
Authors: Portelli, Dario
Abstract: For a smooth complex projective variety X, let $N^p$ and $F^p$ denote
respectively the coniveau filtration on $H^i(X,Q)$ and the Hodge filtration
on $H^i(X,C).$ Hodge proved that $N^p H^i(X,Q )\subset F^p H^i(X,C )\cap H^i(X,Q ),$ and conjectured that equality holds. Grothendieck exhibited a threefold X for which the dimensions of $N^{1}H^{3}(X,Q )$ and $F^{1} H^{3}(X,C )\cap H^{3}(X,Q )$
differ by one. Recently the point of view of Hodge was somewhat refined
(Portelli, 2014), and we aimed to use this refinement to revisit
Grothendieck's example.
We explicitly compute the classes in this second space which
are not in $N^{1}H^{3}(X,Q ).$
We also get a complete clarification that the representation of
the homology customarily used for complex tori does not allow to apply the
methods of (Portelli, 2014) to give a different proof of $N^{1} H^{3}(X,Q )\subsetneq F^{1} H^{3}(X,C )\cap H^{3}(X,Q ).$
Description: Dario Portelli, "On Grothendieck's counterexample to the Generalized Hodge Conjecture", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 46 (2014), pp.237-2542014-12-23T00:00:00ZOn an inequality from Information Theory
http://hdl.handle.net/10077/10639
Title: On an inequality from Information Theory
Authors: Horst, Alzer
Abstract: We prove that the inequalities
$$
\sum_{j=1}^n \frac{q_j (q_j-p_j)^2}{q_j^2 +m_j^{\alpha} M_j^{1-\alpha}}
\leq
\sum_{j=1}^n p_j \log \frac{p_j}{q_j}
\leq
\sum_{j=1}^n \frac{q_j (q_j-p_j)^2}{q_j^2 +m_j^{\beta} M_j^{1-\beta}}
\quad{(\alpha, \beta \in \mathbb{R})},
$$
where
$$
m_j=\min(p_j^2, q_j^2)
\quad\mbox{and}
\quad{M_j=\max(p_j^2, q_j^2)}
\quad(j=1,...,n),
$$
hold for all positive real numbers
$p_j, q_j$ $(j=1,...,n; n\geq 2)$ with
$\sum_{j=1}^n p_j=\sum_{j=1}^n q_j$ if and
only if $\alpha\leq 1/3$ and $\beta\geq 2/3$.
This refines a result of Halliwell and Mercer, who showed that the inequalities
are valid with $\alpha=0$ and $\beta=1$.
Description: Horst Alzer, "On an inequality from Information Theory", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 46 (2014), pp.231-2352014-12-23T00:00:00Z