Using the Kac-Rice approach, we show that the mean number 〈Ntot〉 of all possible equilibria of an elastic line (directed polymer), confined in an harmonic well and submitted to a quenched random Gaussian potential, grows exponentially 〈Ntot〉 ∼ exp (r L) with its length L. The growth rate r is found to be directly related to the fluctuations of the Lyapunov exponent of an associated Anderson loc...

Let G = (V,E) be a locally finite graph, i.e. a graph in which every vertex has finitely many adjacent vertices. In this paper, we associate a topology to G, called graphic topology of G and we show that it is an Alexandroff topology, i.e. a topology in which intersec- tion of every family of open sets is open. Then we investigate some properties of this topology. Our motivation is to give an e...

in this paper, we introduce the concepts of right, left and product stabilizers on hoops and study some properties and the relation between them.  and we try to find that how they can be equal and investigate that under what condition they can be filter, implicative filter, fantastic and positive implicative filter. also, we prove that  right and product stabilizers are filters and if they are ...

In this paper, we introduce soft complete continuity as a strong form of and continuity. Several characterizations, compositions, restriction theorems are obtained. Moreover, several preservation regarding compactness, Lindelofness, connectedness, regularity, normality, almost mild near paracompactness, metacompactness addition to these, the study deals with correlation between our new concepts...

We study the transfinite sequence of topologies on the ordinal numbers that is obtained through successive closure under Cantor’s derivative operator on sets of ordinals, starting form the usual interval topology. We characterize the non-isolated points in the ξ-th topology as those ordinals that satisfy a strong iterated form of stationary reflection, which we call ξ-simultaneous-reflection. W...