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• 1.
Arak Univ, Arak, Iran.
COFINITENESS AND COASSOCIATED PRIMES OF LOCAL COHOMOLOGY MODULES2009Ingår i: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 105, nr 2, s. 161-170Artikel i tidskrift (Refereegranskat)

Let R be a noetherian ring, alpha an ideal of R such that dim R/alpha = 1 and M a finite R-module. We will study cofiniteness and some other properties of the local cohomology modules H-alpha(i)(M). For an arbitrary ideal alpha and an R-module M (not necessarily finite), we will characterize alpha-cofinite artinian local cohomology modules. Certain sets of coassociated primes of top local cohomology modules over local rings are characterized.

• 2.
Linköpings universitet, Matematiska institutionen, Matematik och tillämpad matematik. Linköpings universitet, Tekniska fakulteten. National University of Rwanda, Rwanda.
THE ALGEBRA OF SEMIGROUPS OF SETS2015Ingår i: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 116, nr 2, s. 161-170Artikel i tidskrift (Refereegranskat)

We study the algebra of semigroups of sets (i.e. families of sets closed under finite unions) and its applications. For each n greater than 1 we produce two finite nested families of pairwise different semigroups of sets consisting of subsets of R" without the Baire property.

• 3. Costa, AF
On real trigonal Riemann surfaces2006Ingår i: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 98, nr 1, s. 53-68Artikel i tidskrift (Refereegranskat)

A closed Riemann surface X which can be realized as a 3-sheeted covering of the Riemann sphere is called trigonal, and such a covering will be called a trigonal morphism. A trigonal Riemann surface X is called real trigonal if there is an anticonformal involution (symmetry) a of X commuting with the trigonal morphism. If the trigonal morphism is a cyclic regular covering the Riemann surface is called real cyclic trigonal. The species of the symmetry or is the number of connected components of the fixed point set Fix(sigma) and the orientability of the Klein surface X/(sigma). We characterize real trigonality by means of Fuchsian and NEC groups. Using this approach we obtain all possible species for the symmetry of real cyclic trigonal and real non-cyclic trigonal Riemann surfaces.

• 4.
On the existence of connected components of dimension one in the branch locus of moduli spaces of Riemann surfaces2012Ingår i: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 111, nr 1, s. 53-64Artikel i tidskrift (Refereegranskat)

Let g be an integer >= 3 and let B-g = {X is an element of mu(g) : Aut(X) not equal Id} be the branch locus of mu(g), where mu(g) denotes the moduli space of compact Riemann surfaces of genus g. The structure of B-g is of substantial interest because B-g corresponds to the singularities of the action of the modular group on the Teichmuller space of surfaces of genus g (see [14]).

Kulkarni ([15], see also [13]) proved the existence of isolated points in the branch loci of the moduli spaces of Riemann surfaces. In this work we study the isolated connected components of dimension 1 in such loci. These isolated components of dimension one appear if the genus is g = p - 1 with p prime >= 11. We use uniformization by Fuchsian groups and the equisymmetric stratification of the branch loci.

• 5.
Pointwise regularity for solutions of double obstacle problems on metric spaces2011Ingår i: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 109, nr 2, s. 185-200Artikel i tidskrift (Refereegranskat)

We study continuity at a given point for solutions of double obstacle problems. We obtain pointwise continuity of the solutions for discontinuous obstacles. We also show Hölder continuity for solutions of the double obstacle problems if the obstacles are Hölder continuous.

• 6.
On the stability of Sobolev spaces with zero boundary values1999Ingår i: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 85, nr 2, s. 245-258Artikel i tidskrift (Refereegranskat)

In this note we characterize the open sets Omega for which W-1.p (Omega) boolean AND (q>p)boolean AND W-0(1,q) (Omega) = W-0(1.p) (Omega). We apply our result to establish the stability of the first eigenvalues of the p-laplacians with varying p.

• 7.
Uniform bounds for limited sets and applications to bounding sets.2000Ingår i: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 86, nr 2, s. 223-243Artikel i tidskrift (Refereegranskat)

A set D in a Banach space E is limited if lim sup(k-->infinity) sup(z epsilon D)\phi k(z)\ > 0 double right arrow sup(\\z\\=1) lim sup(k-->infinity) \phi k(z)\ > 0 for every sequence (phi k) subset of E*. It is studied how this implication can be quantified, for example if there exists a constant C > 0 such that lim sup(k-->infinity)sup(z epsilon D)\phi k(z)\ = 1 double right arrow sup\\z\\ = 1 lim sup(k-->infinity) \phi k(z)\ greater than or equal to C for every sequence (phi k) subset of E*, is studied. Relatively compact sets and limited sets in l(infinity) - among others the unit vectors - have uniform bounds in this sense. A fundamental example of a limited set without any uniform bounds is constructed. A set D is called bounding if f (D) is bounded for every entire function on E. That bounding sets are uniformly limited and that strongly bounding sets are limited in the strongest sense are proved. Examples show that the convex hull of bounding sets in general are not bounding and that bounding sets in general does not have Grothendieck's incapsulating property as relatively weakly compact sets have.

• 8.
Newtonian spaces based on quasi-Banach function lattices2016Ingår i: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 119, nr 1, s. 133-160Artikel i tidskrift (Refereegranskat)

In this paper, first-order Sobolev-type spaces on abstract metric measure spaces are defined using the notion of (weak) upper gradients, where the summability of a function and its upper gradient is measured by the “norm” of a quasi-Banach function lattice. This approach gives rise to so-called Newtonian spaces. Tools such as moduli of curve families and Sobolev capacity are developed, which allows us to study basic properties of these spaces. The absolute continuity of Newtonian functions along curves and the completeness of Newtonian spaces in this general setting are established.

• 9.
Department of Mathematics, Chalmers University of Technology and University of Göteborg, Göteborg, Sweden.
Extensions of Fatou theorems in products of upper half-spaces1995Ingår i: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 76, nr 1, s. 139-151Artikel i tidskrift (Refereegranskat)

We consider a multi-parameter maximal function and give a necessary and sufficient condition for its boundedness on Lp, P > 1. We also prove that the maximal function with suitable restriction parameters is of weak type (1,1).

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