An involutive Stone algebra (IS-algebra) is simultaneously a De Morgan and (i.e., pseudo-complemented distributive lattice satisfying the identity $$\mathop {\sim }x \vee \mathop }\mathop \approx 1$$ ). IS-algebras have been studied algebraically topologically since 1980s, but corresponding logic (here denoted $$\mathcal {IS}_{\le }$$ ) has introduced only very recently. This departing point of...

Dendriform algebras are certain splitting of associative and arise naturally from Rota-Baxter operators, shuffle planar binary trees. In this paper, we first consider involutive dendriform algebras, their cohomology homotopy analogs. The an algebra splits the Hochschild algebra. next, introduce a more general notion oriented algebras. We develop theory for that closely related to extensions gov...

A polyhedron is a graph G which simple, planar and 3-connected. In this note, we classify the family of strongly involutive self-dual polyhedra. The latter done by using well-known result due to Tutte characterizing 3-connected graphs. We also show that special class polyhedra self-duality behaves topologically as antipodal mapping. These are related with several problems in convex discrete geo...

We prove that differentials of lattice coordinate functions x must be algebraically independent of their involutive conjugate, else no correct continuum limit exists. PACS: 02.40.Gh, 11.15.Ha

The structure group and the involutive differential system that characterize the pseudo-group of contact transformations on a jet space are determined.