We discuss issues related to constructing an orthomodular structure from an object in a category. In particular, we consider axiomatics related to Baer *-semigroups, partial semigroups, and various constructions involving dagger categories, kernels, and biproducts.

We present a characterisation of { 1(q+1)+ 0, 1;n, q}-minihypers, q square, q = ph, p > 3 prime, h ≥ 2, q ≥ 1217, for 0+ 1 < q 7/12 2 − q1/4 2 . This improves a characterisation result of S. Ferret and L. Storme [6], involving more Baer subgeometries contained in the minihyper.

We extend the Billera–Ehrenborg–Readdy map between the intersection lattice and face lattice of a central hyperplane arrangement to affine and toric hyperplane arrangements. For toric arrangements, we also generalize Zaslavsky’s fundamental results on the number of regions. Résumé. Nous étendons l’opérateur de Billera–Ehrenborg–Readdy entre la trellis d’intersection et la trellis de faces d’un ...

Overlapping Schwarz methods form one of two major families of domain decomposition methods. We consider a two-level overlapping Schwarz method for Raviart-Thomas vector fields. The coarse part of the preconditioner is based on the energy-minimizing extensions and the local parts are based on traditional solvers on overlapping subdomains. We show that the condition number grows linearly with the...