let $g$ be a finite simple graph whose vertices and edges are weighted by two functions. in this paper we shall define and calculate entropy of a dynamical system on weights of the graph $g$, by using the weights of vertices and edges of $g$. we examine the conditions under which entropy of the dynamical system is zero, possitive or $+infty$. at the end it is shown that, for $rin [0,+infty]$, t...

Let $G$ be a finite simple graph whose vertices and edges are weighted by two functions. In this paper we shall define and calculate entropy of a dynamical system on weights of the graph $G$, by using the weights of vertices and edges of $G$. We examine the conditions under which entropy of the dynamical system is zero, possitive or $+infty$. At the end it is shown that, for $rin [0,+infty]$, t...

The full order-preserving transformation semigroup, the orderpreserving partial transformation semigroup and the order-preserving one-to-one partial transformation semigroup on a poset X are denoted by OT (X), OP (X) and OI(X), respectively. It is well-known that for any posets X and Y , OT (X) ∼= OT (Y ) if and only if X and Y are either order-isomorphic or order-anti-isomorphic. The purpose o...

Let  be an n-dimensional Riemannian manifold, and  be its tangent bundle with the lift metric. Then every infinitesimal fiber-preserving conformal transformation  induces an infinitesimal homothetic transformation on .  Furthermore,  the correspondence   gives a homomorphism of the Lie algebra of infinitesimal fiber-preserving conformal transformations on  onto the Lie algebra of infinitesimal ...

For a linearly ordered set X we consider the relative rank of the semigroup of all order preserving mappingsOX on X modulo the full transformation semigroup TX . In other words, we ask what is the smallest cardinality of a set A of mappings such that 〈OX ∪A 〉 = TX . When X is countably infinite or well-ordered (of arbitrary cardinality) we show that this number is one, while when X = R (the set...