Search results for "Clos"

Spatial reasoning withRCC8and connectedness constraints in Euclidean spaces

2014

The language RCC 8 is a widely-studied formalism for describing topological arrangements of spatial regions. The variables of this language range over the collection of non-empty, regular closed sets of n-dimensional Euclidean space, here denoted RC + ( R n ) , and its non-logical primitives allow us to specify how the interiors, exteriors and boundaries of these sets intersect. The key question is the satisfiability problem: given a finite set of atomic RCC 8 -constraints in m variables, determine whether there exists an m-tuple of elements of RC + ( R n ) satisfying them. These problems are known to coincide for all n � 1 , so that RCC 8 -satisfiability is independent of dimension. This c…

Ordering and Convex Polyominoes

2005

We introduce a partial order on pictures (matrices), denoted by ≼ that extends to two dimensions the subword ordering on words. We investigate properties of special families of discrete sets (corresponding to {0,1}-matrices) with respect to this partial order. In particular we consider the families of polyominoes and convex polyominoes and the family, recently introduced by the authors, of L-convex polyominoes. In the first part of the paper we study the closure properties of such families with respect to the order. In particular we obtain a new characterization of L-convex polyominoes: a discrete set P is a L-convex polyomino if and only if all the elements Q≼P are polyominoes. In the seco…

Fixed point theory for a class of generalized nonexpansive mappings

2011

AbstractIn this paper we introduce two new classes of generalized nonexpansive mapping and we study both the existence of fixed points and their asymptotic behavior.

Closedness and lower semicontinuity of positive sesquilinear forms

2009

The relationship between the notion of closedness, lower semicontinuity and completeness (of a quotient) of the domain of a positive sesquilinear form defined on a subspace of a topological vector space is investigated and sufficient conditions for their equivalence are given.

Fitting classes and lattice formations I

2004

AbstractA lattice formation is a class of groups whose elements are the direct product of Hall subgroups corresponding to pairwise disjoint sets of primes. In this paper Fitting classes with stronger closure properties involving F-subnormal subgroups, for a lattice formation F of full characteristic, are studied. For a subgroup-closed saturated formation G, a characterisation of the G-projectors of finite soluble groups is also obtained. It is inspired by the characterisation of the Carter subgroups as the N-projectors, N being the class of nilpotent groups.

Finite Groups with Only One NonLinear Irreducible Representation

2012

Let 𝕂 be an algebraically closed field. We classify the finite groups having exactly one irreducible 𝕂-representation of degree bigger than one. The case where the characteristic of 𝕂 is zero, was done by G. Seitz in 1968.

Resolvent Estimates for Non-Selfadjoint Operators via Semigroups

2009

We consider a non-selfadjoint h-pseudodifferential operator P in the semiclassical limit (h → 0). If p is the leading symbol, then under suitable assumptions about the behavior of p at infinity, we know that the resolvent (z–P)–1 is uniformly bounded for z in any compact set not intersecting the closure of the range of p. Under a subellipticity condition, we show that the resolvent extends locally inside the range up to a distance \(\mathcal{O}(1)((h\ln \frac{1}{h})^{k/(k + 1)} )\) from certain boundary points, where \(k \in \{ 2,4, \ldots \} \). This is a slight improvement of a result by Dencker, Zworski, and the author, and it was recently obtained by W. Bordeaux Montrieux in a model sit…

A Uniform Way to Control Chief Series in Finite p -Groups and to Construct the Countable Algebraically Closed Locally Finite p -Groups

1986

Multi-valued $$F$$ F -contractions in 0-complete partial metric spaces with application to Volterra type integral equation

2013

We study the existence of fixed points for multi-valued mappings that satisfy certain generalized contractive conditions in the setting of 0-complete partial metric spaces. We apply our results to the solution of a Volterra type integral equation in ordered 0-complete partial metric spaces.

Star-polynomial identities: computing the exponential growth of the codimensions

2017

Abstract Can one compute the exponential rate of growth of the ⁎-codimensions of a PI-algebra with involution ⁎ over a field of characteristic zero? It was shown in [2] that any such algebra A has the same ⁎-identities as the Grassmann envelope of a finite dimensional superalgebra with superinvolution B. Here, by exploiting this result we are able to provide an exact estimate of the exponential rate of growth e x p ⁎ ( A ) of any PI-algebra A with involution. It turns out that e x p ⁎ ( A ) is an integer and, in case the base field is algebraically closed, it coincides with the dimension of an admissible subalgebra of maximal dimension of B.