The Abelian Sandpile Model is a diffusion process on (directed) graphs, studied, under various names, in statistical physics, discrete dynamical systems, theoretical computer science, algebraic graph theory, and other fields. The model takes a directed multigraph X with a sink accessible from all nodes; associates a configuration space with X and defines transition rules between the configurati...

Objectives: Social development in children is influenced by several factors, including family, school friends, television, gender, race, socioeconomic status, and locomotor activity, and depending on the situation and how they react to it, social development and maturity might get accelerated or get undermined. Therefore, in this study, we aimed to investigate the relationship between fine moto...

We show that the least genus of any compact Riemann surface S, admitting a simple Suzuki group G = Sz(^) as a group of automorphisms, is equal to 1 +|G|/40. We compute the number of such surfaces S as the number of normal subgroups of the triangle group A(2,4,5) with quotient-group G, and investigate the associated regular maps of type {4,5}.

We consider a version of the AdSd+1/CFTd correspondence, in which the bulk space is taken to be the quotient manifold AdSd+1/Γ with a fairly generic discrete group Γ acting isometrically on AdSd+1. We address some geometrical issues concerning the holographic principle and the UV/IR relations. It is shown that certain singular structures on the quotient boundary S/Γ can affect the underlying ph...

If we consider the quotient space of each tangent plane with respect to this equivalence relation, and the related quotient tangent bundle TS/∼1, a field FD : S −→ TS/∼1 maps each point on the surface to a direction. It is customary to take unit-length vectors as representatives of their equivalence classes, so that a direction field can be regarded as a vector field where the length of all vec...

For a proper action of a Lie group on a co-oriented contact manifold which preserves the contact structure, we show that the classical Marsden-Weinstein-Meyer symplectic reduction procedure extends naturally to the contact category, continuing the work of H. Geiges ([Ge]). With a certain regularity assumption in place, the contact quotient is shown to be naturally a contact manifold. More gener...