Morita equivalences between some blocks for -solvable groups

We prove that any Morita equivalence between some blocks with Abelian defect groups and cyclic inertia quotients for -solvable groups is basic.

     

The vanishing of implies that is regular

Let be an excellent local ring of positive prime characteristic. We show that if , then is regular. This improves a result of Schoutens, in which the additional hypothesis that was an isolated singularity was required for the proof.

     

``Beurling type' subspaces of and

In this note we extend the ``Beurling type' characterizations of subspaces of and to and , respectively.

     

-actions with

Suppose that is a smooth -action on a closed smooth -dimensional manifold such that all Stiefel-Whitney classes of the tangent bundle to each connected component of the fixed point set vanish in positive dimension. This paper shows that if 2^k\dim F$"> and each -dimensional part possesses the linear independence property, then bounds equivariantly, and in particular, is the best possible upper bound of if is nonbounding.

     

-invariant subspaces of

In this note, we give a new proof of the characterization of the -invariant subspaces of for in using ideas from approximation theory.     

The number of planar central configurations for the -body problem is finite when mass positions are fixed

In the -body problem a central configuration is formed when the position vector of each particle with respect to the center of mass is a common scalar multiple of its acceleration vector. Lindstrom showed for and for 4$"> that if masses are located at fixed points in the plane, then there are only a finite number of ways to position the remaining th mass in such a way that they define a central configuration. Lindstrom leaves open the case . In this paper we prove the case using as variables the mutual distances between the particles.

     

A -sampling theorem related to the -Hankel transform

A -version of the sampling theorem is derived using the -Hankel transform introduced by Koornwinder and Swarttouw. The sampling points are the zeros of the third Jackson -Bessel function.

     

Real

The famous problem involves applying two maps: and to positive integers. If is even, one applies , if it is odd, one applies . The conjecture states that each trajectory of the system arrives to the periodic orbit . In this paper, instead of choosing each time which map to apply, we allow ourselves more freedom and apply both and independently of . That is, we consider the action of the free semigroup with generators and on the space of positive real numbers. We prove that this action is minimal (each trajectory is dense) and that the periodic points are dense. Moreover, we give a full characterization of the group of transformations of the real line generated by and .

     

Decomposability of graph -algebras

We give conditions on an arbitrary directed graph for the associated Cuntz-Krieger algebra to be decomposable as a direct sum. We describe the direct summands as certain graph algebras.

     

Tietze extension theorem for Hilbert -modules

We prove the following generalization of the noncommutative Tietze extension theorem: if is a countably generated Hilbert -module over a -unital -algebra, then the canonical extension of a surjective morphism of Hilbert -modules to extended (multiplier) modules, , is also surjective.