We prove the optimality of the move-to-front rule in the class of on-line selforganizing sequential search heuristics for data structures, taking advantage of the fact that the sequence of requested items is a Markov chain F whose symmetry group GF acts transitively on the set S of items (F is then said to be state-transitive ). We state corresponding general results on controlled Markov chains...

A regular covering projection ℘: X̃ → X of connected graphs is G-admissible if G lifts along ℘. Denote by G̃ the lifted group, and let CT(℘) be the group of covering transformations. The projection is called G-split whenever the extension CT(℘) → G̃ → G splits. In this paper, split 2-covers are considered, with a particular emphasis given to cubic symmetric graphs. Supposing that G is transitive o...

For two normal edge-transitive Cayley graphs on groups H and K which have no common direct factor and $gcd(|H/H^prime|,|Z(K)|)=1=gcd(|K/K^prime|,|Z(H)|)$, we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.

darafsheh and assari in [normal edge-transitive cayley graphs onnon-abelian groups of order 4p, where p is a prime number, sci. china math. {bf 56} (1) (2013) 213$-$219.] classified the connected normal edge transitive and $frac{1}{2}-$arc-transitive cayley graph of groups of order$4p$. in this paper we continue this work by classifying theconnected cayley graph of groups of order $2pq$, $p > q...

 After the classification of the flag-transitive linear spaces, the attention has been turned to line-transitive linear spaces. In this article, we present a partial classification of the finite linear spaces $mathcal S$ on which an almost simple group $G$ with the socle $G_2(q)$ acts line-transitively.

We study positive shadowing and chain recurrence in the context of linear operators acting on Banach spaces or even normed vector spaces. show that for there is only one recurrent set, this set a closed invariant subspace. prove every transitive dynamical system with property frequently hypercyclic and, as corollary, we obtain hypercyclic.

Using representation theory, we obtain a necessary and sufficient condition for a discrete–time Markov chain on a finite state space E to be representable as ΨnΨn−1 · · ·Ψ1z, n ≥ 0, for any z ∈ E, where the Ψi are independent, identically distributed random permutations taking values in some given transitive group of permutations on E. The condition is particularly simple when the group is 2-tr...

We consider the transitive linear maps on the operator algebra $B(X)$for a separable Banach space $X$. We show if a bounded linear map is norm transitive on $B(X)$,then it must be hypercyclic with strong operator topology. Also we provide a SOT-transitivelinear map without being hypercyclic in the strong operator topology.