We provide a full description of congruence relations of convex, positive convex, and totally convex algebras. As a consequence of this result we obtain that finitely generated convex (positive convex, totally convex) algebras are finitely presentable. Convex algebras, in particular positive convex algebras, are important in the area of probabilistic systems. They are the Eilenberg-Moore algebr...

More than 40 years ago, Leo Moser stated a geometry problem on the plane asking for the least-area set that contains a congruent copy of every unit arc. The smallest set known, by Norwood and Poole in 2004, has area 0.26043. One interesting related problem is to focus on a set that contains a congruent copy of every convex unit arc. Such a set is called a cover for convex unit arcs. The smalles...

The deviation of a general convex body with twice differentiable boundary and an arbitrarily positioned polytope given number vertices is studied. paper considers the case where measured in terms surface areas involved sets, more precisely, by what called area deviation. proof uses arguments constructions from probability, integral geometry. bound closely related to p-affine areas.

BACKGROUND The effect of reaming on bone volume and surface area of the glenoid is not precisely known. We hypothesize that (1) convex reamers create a larger surface area than flat reamers, (2) flat reamers cause less bone loss than convex reamers, and (3) the amount of bone loss increases with the amount of version correction. METHODS Reaming procedures with different types of reamers are p...