The investigation of symmetric designs is of central interest in design theory. Another class of important incidence structures are projective and affine geometries. A projective geometry gives rise to two symmetric designs, namely the point-hyperplane designs and their complements. It is a remarkable property of these classical symmetric designs that we will investigate in this paper. For the ...

Let X be any partially ordered set, R any commutative ring, and T = I * (X,R) the weak incidence algebra of X over R. Let Z be a finite nonempty subset of X, L(Z) = {x ∈ X : x z for some z ∈ Z}, and M = Te Z. Various chain conditions on M are investigated. The results so proved are used to construct some classes of right perfect rings that are not left perfect.

Symmetry is defined as correspondence in size, shape and relative position of parts on opposite sides of a dividing line or median plane. Although the human body has a symmetrical appearance when viewed externally, most internal organs are asymmetrical with respect to the left and right sides. Human body shows anatomical as well as functional asymmetries: some of these are of great clinical sig...

If φ is a nontrivial automorphism of a thick building ∆ of purely infinite type, we prove that there is no bound on the distance that φ moves a chamber. This has the following group-theoretic consequence: If G is a group of automorphisms of ∆ with bounded quotient, then the center of G is trivial.

It is well known in cluster randomised trials with a binary outcome and a logistic link that the population average model and cluster specific model estimate different population parameters for the odds ratio. However, it is less well appreciated that for a log link, the population parameters are the same and a log link leads to a relative risk. This suggests that for a prospective cluster rand...

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