Expand all Collapse all | Results 1 - 5 of 5 |
1. CMB Online first
Cover products and Betti polynomials of graphs For disjoint graphs $G$ and $H$, with fixed
vertex covers
$C(G)$ and $C(H)$, their cover product is the graph $G
\circledast
H$ with vertex set
$V(G)\cup V(H)$ and edge set $E(G)\cup E(H)\cup\{\{i,j\}:i\in
C(G), j\in
C(H)\}$. We describe the graded Betti numbers of $G\circledast
H$ in terms of those of
$G$ and $H$. As applications we obtain: (i) For any positive
integer $k$ there
exists a connected bipartite graph $G$ such that $\operatorname{reg}
R/I(G)=\mu_S(G)+k$, where,
$I(G)$ denotes the edge ideal of $G$, $\operatorname{reg} R/I(G)$
is the Castelnuovo--Mumford
regularity of $R/I(G)$ and $\mu_S(G)$ is the induced or strong
matching number of
$G$; (ii) The graded Betti numbers of the complement of a tree
only depends upon
its number of vertices; (iii) The $h$-vector of $R/I(G\circledast
H)$ is described in
terms of the $h$-vectors of $R/I(G)$ and $R/I(H)$. Furthermore,
in a different
direction, we give a recursive formula for the graded Betti numbers
of chordal
bipartite graphs.
Keywords:Castelnuovo--Mumford regularity, chordal bipartite graph, edge ideal, graded Betti number, induced matching number, monomial ideal Categories:13D02, 05E45 |
2. CMB Online first
On the Regularity of the Multisublinear Maximal Functions This paper is concerned with the study of
the regularity for the multisublinear maximal operator. It is
proved that the multisublinear maximal operator is bounded on
first-order Sobolev spaces. Moreover, two key point-wise
inequalities for the partial derivatives of the multisublinear
maximal functions are established. As an application, the
quasi-continuity on the multisublinear maximal function is also
obtained.
Keywords:regularity, multisublinear maximal operator, Sobolev spaces, partial deviative, quasicontinuity Categories:42B25, 46E35 |
3. CMB 2013 (vol 57 pp. 546)
Compact Operators in Regular LCQ Groups We show that a regular locally compact quantum group $\mathbb{G}$ is discrete
if and only if $\mathcal{L}^{\infty}(\mathbb{G})$ contains non-zero compact operators on
$\mathcal{L}^{2}(\mathbb{G})$.
As a corollary we classify all discrete quantum groups among
regular locally compact quantum groups $\mathbb{G}$ where
$\mathcal{L}^{1}(\mathbb{G})$ has the Radon--Nikodym property.
Keywords:locally compact quantum groups, regularity, compact operators Category:46L89 |
4. CMB 2011 (vol 54 pp. 472)
A Semiregularity Map Annihilating Obstructions to Deforming Holomorphic Maps We study infinitesimal deformations of holomorphic maps of
compact, complex, KÃ¤hler manifolds. In particular, we describe a
generalization of Bloch's semiregularity map that annihilates
obstructions to deform holomorphic maps with fixed codomain.
Keywords:semiregularity map, obstruction theory, functors of Artin rings, differential graded Lie algebras Categories:13D10, 14D15, 14B10 |
5. CMB 2000 (vol 43 pp. 25)
Subdifferential Regularity of Directionally Lipschitzian Functions Formulas for the Clarke subdifferential are always expressed in the
form of inclusion. The equality form in these formulas generally
requires the functions to be directionally regular. This paper
studies the directional regularity of the general class of
extended-real-valued functions that are directionally Lipschitzian.
Connections with the concept of subdifferential regularity are also
established.
Keywords:subdifferential regularity, directional regularity, directionally Lipschitzian functions Categories:49J52, 58C20, 49J50, 90C26 |