Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.45 (2013)https://www.openstarts.units.it/handle/10077/95942024-06-20T09:07:15Z2024-06-20T09:07:15Z111Compact groups with a dense free abelian subgroupDikranjan, DikranGiordano Bruno, Annahttps://www.openstarts.units.it/handle/10077/96052019-03-02T06:59:13Z2013-01-01T00:00:00Zdc.title: Compact groups with a dense free abelian subgroup
dc.contributor.author: Dikranjan, Dikran; Giordano Bruno, Anna
dc.description.abstract: The compact groups having a dense infinite cyclic subgroup (known as monothetic compact groups) have been studied by many authors for their relevance and nice applications. In this paper we describe in full details the compact groups $K$ with a dense free abelian subgroup $F$ and we describe the minimum rank $r_t(K)$ of such a subgroup $F$ of $K$. Surprisingly, it is either finite or coincides with the density character $d(K)$ of $K$.}
2013-01-01T00:00:00ZMetrizability of hereditarily normal compact like groupsDikranjan, DikranImpieri, DanieleToller, Danielehttps://www.openstarts.units.it/handle/10077/96042019-03-02T06:55:13Z2013-01-01T00:00:00Zdc.title: Metrizability of hereditarily normal compact like groups
dc.contributor.author: Dikranjan, Dikran; Impieri, Daniele; Toller, Daniele
dc.description.abstract: Inspired by the fact that a compact topological group is
hereditarily normal if and only if it is metrizable, we prove that various
levels of compactness-like properties imposed on a topological group G
allow one to establish that G is hereditarily normal if and only if G is
metrizable (among these properties are locally compactness, local minimality
and \omega-boundedness). This extends recent results from [4] in the
case of countable compactness.
2013-01-01T00:00:00ZOn a coefficient concerning an ill-posed Cauchy problem and the singularity detection with the wavelet transformFukuda, NaohiroKinoshita, Tamotuhttps://www.openstarts.units.it/handle/10077/96032019-03-02T07:04:05Z2013-01-01T00:00:00Zdc.title: On a coefficient concerning an ill-posed Cauchy problem and the singularity detection with the wavelet transform
dc.contributor.author: Fukuda, Naohiro; Kinoshita, Tamotu
dc.description.abstract: We study the Cauchy problem for 2nd order weakly hyperbolic
equations. F. Colombini, E. Jannelli and S. Spagnolo showed a
coefficient degenerating at an infinite number of points, with which the Cauchy problem is ill-posed Gevrey classes. Moreover, we olso report numerical results of the singularity detection with wavelet trasform for coefficient functions.
2013-01-01T00:00:00ZRecent progress on characterizing lattices C(X) and U(Y )Hušek, MiroslavPulgarín, Antoniohttps://www.openstarts.units.it/handle/10077/96022019-03-02T07:04:03Z2013-01-01T00:00:00Zdc.title: Recent progress on characterizing lattices C(X) and U(Y )
dc.contributor.author: Hušek, Miroslav; Pulgarín, Antonio
dc.description.abstract: Our effort to weaken algebraic assumptions led us to obtain
characterizations of C(X) as Riesz spaces, real l-groups, semi-affine
lattices and real lattices by using different techniques. We present a unified
approach valid for any “convenient” category. By setting equivalent
conditions to equi-uniform continuity, we obtain a characterization of
the lattice U(Y ) in parallel with that of C(X).
2013-01-01T00:00:00ZIncreasing chains and discrete reflection of cardinalitySpadaro, Santihttps://www.openstarts.units.it/handle/10077/96012019-03-02T07:04:01Z2013-01-01T00:00:00Zdc.title: Increasing chains and discrete reflection of cardinality
dc.contributor.author: Spadaro, Santi
dc.description.abstract: Combining ideas from two of our previous papers ([26]
and [27]), we refine Arhangel’skii Theorem by proving a cardinal inequality
of which this is a special case: any increasing union of strongly
discretely Lindelöf spaces without uncountable free sequences and with
countable pseudocharacter has cardinality at most continuum. We then
give a partial positive answer to a problem of Alan Dow on reflection
of cardinality by closures of discrete sets.
2013-01-01T00:00:00ZA note on secants of GrassmanniansBoralevi, Adahttps://www.openstarts.units.it/handle/10077/96002019-03-02T06:59:10Z2013-01-01T00:00:00Zdc.title: A note on secants of Grassmannians
dc.contributor.author: Boralevi, Ada
dc.description.abstract: Let $\GG(k,n)$ be the Grassmannian of $k$-subspaces in an $n$-dimensional complex vector space, $k \ge 3$. Given a projective variety $X$, its $s$-secant variety $\sigma_s(X)$ is defined to be the closure of the union of linear spans of all the $s$-tuples of independent points lying on $X$. We classify all defective $\sigma_s(\GG(k,n))$ for $s \le 12$.}
2013-01-01T00:00:00ZClassification of polarized manifolds by the second sectional Betti number, IIFukuma, Yoshiakihttps://www.openstarts.units.it/handle/10077/95992019-03-02T06:54:56Z2013-01-01T00:00:00Zdc.title: Classification of polarized manifolds by the second sectional Betti number, II
dc.contributor.author: Fukuma, Yoshiaki
dc.description.abstract: Let X be an n-dimensional smooth projective variety defined
over the field of complex numbers, let L be a very ample line
bundle on X. Then we classify (X,L) with b_2(X,L) = h^2(X,C) + 2,
where b_2(X,L) is the second sectional Betti number of (X,L).; Let $X$ be an $n$-dimensional smooth projective variety defined over the field of complex numbers, let $L$ be a very ample line bundle on $X$.
Then we classify $(X,L)$ with $b_{2}(X,L)=h^{2}(X,\mathbb{C})+2$, where $b_{2}(X,L)$ is the second sectional Betti number of $(X,L)$.}
2013-01-01T00:00:00ZA Lewy-Stampacchia estimate for variational inequalities in the Heisenberg groupPinamonti, AndreaValdinoci, Enricohttps://www.openstarts.units.it/handle/10077/95982019-03-02T06:54:54Z2013-01-01T00:00:00Zdc.title: A Lewy-Stampacchia estimate for variational inequalities in the Heisenberg group
dc.contributor.author: Pinamonti, Andrea; Valdinoci, Enrico
dc.description.abstract: We consider an obstacle problem in the
Heisenberg group framework, and we prove that the
operator on the obstacle
bounds pointwise the operator on the solution.
More explicitly,
if~$\bar u$ minimizes
the functional
$$ \int_\Omega |\nabla_{\H^n}u|^2$$
among the functions with prescribed Dirichlet boundary
condition that stay below a smooth obstacle~$\psi$, then
$$
0\leq \Delta_{\H^n} \bar u\leq \Big(\Delta_{\H^n}\psi\Big)^{+}.
$$
Moreover, we discuss how it could be possible to generalize the
previous
bound to a quasilinear setting once some regularity issues for the
equation
$$
\div_{\H^n}\Big(|\nabla_{\H^n}u|^{p-2}\nabla_{\H^n}u\Big)=f
$$
are satisfied.}
2013-01-01T00:00:00ZManifolds over Cayley-Dickson algebras and their immersionsLudkowski, Sergey V.https://www.openstarts.units.it/handle/10077/95972019-03-02T06:55:09Z2013-01-01T00:00:00Zdc.title: Manifolds over Cayley-Dickson algebras and their immersions
dc.contributor.author: Ludkowski, Sergey V.
dc.description.abstract: Weakly holomorphic manifolds over Cayley-Dickson algebras
are defined and their embeddings and immersions are studied.
2013-01-01T00:00:00ZRH-regular transformation of unbounded double sequencesPatterson, Richard F.https://www.openstarts.units.it/handle/10077/95962019-03-02T07:03:31Z2013-01-01T00:00:00Zdc.title: RH-regular transformation of unbounded double sequences
dc.contributor.author: Patterson, Richard F.
dc.description.abstract: At the Ithaca meeting in 1946 it was conjectured that it is possible to construct a two-dimensional regular summability matrix $A=\{a_{n,k}\}$ with the property that, for every real sequence $\{s_{k}\}$, the transformed sequence $$t_{n}=\sum_{k=0}^{\infty}a_{n,k}s_{k}$$ possesses at least one limit point in the finite plane. It was also counter-conjectured that, for every regular summability matrix $A$, there exists a single sequence $\{s_{k}\}$ such that the transformed sequence $t_{n}$ tends to infinity monotonically. In 1947 Erdos and Piranian presented answers to these conjectures. The goal of this paper is to present a multidimensional version of the above conjectures. The first conjecture is the following:
A four-dimensional RH-regular summability matrix $A=\{a_{m,n,k,l}\}$ can be constructed with the property that every double sequence $\{s_{k,l}\}$ transformed into the double sequence $$t_{m,n}=\sum_{k,l=0,0}^{\infty,\infty}a_{m,n,k,l}s_{k,l}$$ possesses at least one Pringsheim limit point in the finite plane.
The multidimensional counter-conjecture is the following. For every RH-regular summability matrix $A$ there exists a double sequence $\{s_{k,l}\}$ such that the four-dimensional transformed double sequence $\{t_{m,n}\}$ tends to infinity monotonically Pringsheim sense. This paper established that both multidimensional conjectures are false.}
2013-01-01T00:00:00Z