http://www.openstarts.units.it:80/dspace/handle/10077/4127 2013-05-22T17:19:49Z http://www.openstarts.units.it:80/dspace/handle/10077/4138 Title: On some Semilinear Periodic Parabolic Problems Authors: Godoy, Tomas; Kaufmann, Uriel Abstract: Let $\Omega \subset \mathbb R^N$ a smooth bounded domain. We study existence and nonexistence of positive solutions for some semilinear Dirichlet periodic parabolic problems of the form $Lu = h(x,t,u)$ in $\Omega\times \mathbb R$ for a class of Caratheodory functions $h : \Omega\times \mathbb R \times [0,\infty) \rightarrow \mathbbR$ such that h (., 0) = 0 and $\lim_{\xi\rightarrow 0^+}\xi^{ −1}h (.,\xi) = 0$ or $-\infty$. All results remain true for the corresponding elliptic problems. Type: Articolo 2006-01-01T00:00:00Z http://www.openstarts.units.it:80/dspace/handle/10077/4137 Title: A Note on Gevrey Well-Posedness for the Operator $\partial^2_t - a(t)\partial _x(b(t,x)\partial_x)$ Authors: Del Santo, Daniele Abstract: We use a Littlewood-Paley decomposition to obtain a Gevrey-well-posedness result for a weakly hyperbolic equation in one space variable with coefficients depending also on x. Type: Articolo 2006-01-01T00:00:00Z http://www.openstarts.units.it:80/dspace/handle/10077/4136 Title: Algebraic Aspects of Commutation of Linear Operators up to a Factor Authors: Bellonotto, B.; Teppati, Giancarlo Abstract: When representing projective geometry by means of a vector space, commutativity can be replaced by commutativity up to a factor. This feature was investigated by F. Cecioni under very weak assumptions, but it is hard to generalize the methods of [4] to a wider algebraic context. In this note, we develop the independent treatment of H. Weyl, and extend the approach of to non-commutative rings under suitable assumptions on the endomorphisms. From this point of view, we show that commutativity of operators up to a non-trivial factor is an exceptional phenomenon in comparison to strict commutativity. Type: Articolo 2006-01-01T00:00:00Z http://www.openstarts.units.it:80/dspace/handle/10077/4135 Title: Hyperbolic Knots and Links with a Common Cyclic Branched Covering: Known Results and Open Problems Authors: Zimmermann, Bruno P. Abstract: We give a survey on recent progress and remaining open problems on the number and the geometry of knots and links which have a hyperbolic 3-manifold M as a common cyclic branched covering. This is strongly related to the algebra and the geometry of the finite isometry group G of M, and it naturally divides into the two cases G solvable and G non-solvable. The solvable case is relatively well understood whereas the non- solvable case remains somewhat mysterious. Type: Articolo 2006-01-01T00:00:00Z