In this work, we present a family of exact self-similar solutions for the distribution of enclosed areas under mean curvature flow on the union of disjoint closed curves in the plane. To our knowledge, this is the first example of closed-form exact self-similar solutions for the mean curvature flow. We perform numerical simulations for large sets of initial data obtained as the zero level set o...

In this article, we study a particular example of general random tessellation, the dead leaves model. This model, first studied by the Mathematical Morphology school, is defined as a sequential superimposition of random closed sets, and provides the natural tool to study the occlusion phenomenon, essential ingredient in the formation of visual images. We generalize results from G. Matheron, and...

in this paper a particular case of z-ideals, called strongly z-ideal, is defined by introducing zero sets in pointfree topology. we study strongly z-ideals, their relation with z-ideals and the role of spatiality in this relation. for strongly z-ideals, we analyze prime ideals using the concept of zero sets. moreover, it is proven that the intersection of all zero sets of a prime ideal of c(l),...