A graph $Gamma$ is said to be vertex-transitive or edge‎- ‎transitive‎ ‎if the automorphism group of $Gamma$ acts transitively on $V(Gamma)$ or $E(Gamma)$‎, ‎respectively‎. ‎Let $Gamma=Cay(G,S)$ be a Cayley graph on $G$ relative to $S$‎. ‎Then, $Gamma$ is said to be normal edge-transitive‎, ‎if $N_{Aut(Gamma)}(G)$ acts transitively on edges‎. ‎In this paper‎, ‎the eigenvalues of normal edge-tra...

We prove that, for a positive integer n and subgroup H of automorphisms of a cyclic group Z of order n, there is up to isomorphism a unique connected circulant digraph based on Z admitting an arc-transitive action of ZzH. We refine the Kovács–Li classification of arc-transitive circulants to determine those digraphs with automorphism group larger than ZzH. As an application we construct, for ea...

We prove the topological entropy remains constant inside class of partially hyperbolic diffeomorphisms with simple central bundle (that is, when it decomposes into one dimensional sub-bundles controlled geometry) and such that their induced action on is hyperbolic. In absence simplicity condition we construct a robustly transitive counter-example.

There is strong evidence that we automatically simulate observed behavior in our motor system. Previous research suggests that this simulation process depends on whether we observe a human or a non-human agent. Measuring a motor priming effect, this study investigated the question of whether agent-sensitivity of motor simulation depends on the specific action observed. Participants saw pictures...

Abstract We consider a finite, connected and simple graph Γ that admits vertex-transitive group of automorphisms

A finite group amalgam of index (k,m) is a 5-tuple (L,φ,B, ψ,R) where L, B, and R are finite groups, φ : B → L and ψ : B → R are monomorphisms, and the indices of B and B in L and R are k and m, respectively. The amalgam is faithful if N ≤ B, N C L, and N C R implies N = 1. It is well known that the finite faithful amalgams of index (k, 2) are in a bijective correspondence with (the conjugacy c...

a new base isolation method for reducing the destructive effect of earthquake is proposed in this method mushroom shaped basements are used under structures as base isolation. these basements have spherical surface and are located on foundations. basements have pinned arms that are connected. when the length of the arm is less then the radius of spherical surface, the action of them is similar ...