Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
Not a member yet
1189 research outputs found
Sort by
Orlicz spaces and endpoint Sobolev-Poincaré inequalities for differential forms in Heisenberg groups
Full text linkIn this paper we prove Poincar´e and Sobolev inequalities for differential forms in the Rumin’s contact complex on Heisenberg groups. In particular, we deal with endpoint values of the exponents, obtaining finally estimates akin to exponential Trudinger inequalities for scalar function. These results complete previous results obtained by the authors away from the exponential case. From the geometric point of view, Poincaré and Sobolev inequalities for differential forms provide a quantitative formulation of the vanishing of the cohomology. They have also applications to regularity issues for partial differential equations
On the Shannon entropy of the number of vertices with zero in-degree in randomly oriented hypergraphs
Full text linkSuppose that you have colours and mutually independent dice, each of which has sides. Each dice lands on any of its sides with equal probability. You may colour the sides of each die in any way you wish, but there is one restriction: you are not allowed to use the same colour more than once on the sides of a die. Any other colouring is allowed. Let be the number of different colours that you see after rolling the dice. How should you colour the sides of the dice in order to maximize the Shannon entropy of ? In this article we investigate this question. It is shown that the entropy of is at most and that the bound is tight, up to a constant additive factor, in the case of there being equally many coins and colours. Our proof employs the differential entropy bound on discrete entropy, along with a lower bound on the entropy of binomial random variables whose outcome is conditioned to be an even integer. We conjecture that the entropy is maximized when the colours are distributed over the sides of the dice as evenly as possible
On graph energy, maximum degree and vertex cover number: On graph energy, maximum degree and vertex cover number
Full text linkFor a simple graph with vertices and edges having adjacency eigenvalues , the energy of is defined as . We obtain the upper bounds for in terms of the vertex covering number , the number of edges , maximum vertex degree and second maximum vertex degree of the connected graph . These upper bounds improve some recently known upper bounds for . Further, these upper bounds for imply a natural extension to other energies like distance energy and Randi\\u27{c} energy associated to a connected graph
A short proof for a determinantal formula for generalized Fibonacci numbers
Full text linkThe aim of this note is to provide a short proof for a recent determinantal formula of generalized Fibonacci numbers
Canonical reduction for quadratic quotients of the Rees algebra.
Full text linkIn this paper, we characterize when a quadratic quotient of the Rees algebra, obtained starting with a one-dimensional local ring, has a canonical reduction, generalizing a similar result obtained for Nagata idealization
On the existence of mild solutions for nonlocal impulsive partial integrodifferential equations in Banach spaces
No full textIn this work, we study the existence and uniqueness of mild and classical solutions for a nonlinear impulsive partial integrodiifential equation with nonlocal conditions. We need the compactness of the resolvent operator of the integrodifferential equations. We give a framework on the existence of solutions for some integrodiffential equations. An example is provided for illustrations of these new results
Sobolev inequalities via Muramatu\u27s integral formula
Full text linkFor the Sobolev space Wmp(Rn) with positive integer m and 1<p<infty, sometimes replaced by 1<=p<infty, we consider the case m-n/p<0 and the case m-n/p=0, and give new proofs of the Sobolev embedding theorems by Muramatu\u27s integral formula. When m-n/p<0, the embedding into Lq(Rn) with q satisfying m-n/p=-n/q is derived without the Hardy-Littlewood-Sobolev inequality by incorporating the method to prove it. When m-n/p=0, we prove the embedding into the BMO space or the VMO space as well as Trudinger\u27s inequality. 
Fixed points for non-expansive set-valued mappings
Full text linkLet E be a Banach space and F : E --> E be a 1-Lipschitz set-valued mapping with closed convex non-empty values. We study the set of fixed points Fix(F)={ x in E : x in F(x)} and provide in any space E with dim(E) > 2 an example of such a mapping F such that Fix(F) is not connected
On the Chow ring of certain hypersurfaces in a Grassmannian
Full text linkThis note is about Pl\"ucker hyperplane sections of the Grassmannian . Inspired by the analogy with cubic fourfolds, we prove that the only non-trivial Chow group of is generated by Grassmannians of type contained in . We also prove that a certain subring of the Chow ring of (containing all intersections of positive-codimensional subvarieties) injects into cohomology
Extensions of rings over 2-primal rings
Full text linkFor a set of endomorphisms and derivations , we first introduce -compatible ideals which are a generalization of -rigid ideals and study the connections of the prime radical and the upper nil radical of with the prime radical and the upper nil radical of the skew PBW extension.
Let be an injective skew PBW extension of an
-compatible ring . (i) It is shown that if
is a (semi)prime ring, then is a (semi)prime ring. (ii)
If is a completely (semi)prime ring, then is a
completely (semi)prime ring. (iii) If is a strongly
(semi)prime ring, then is a strongly (semi)prime ring.
Also, we prove that is -primal if and only if the
injective skew PBW extension is -primal if and only if
if and only if if and only if every minimal -prime
ideal of is completely prime