we introduce a two generated weakly branch contracting automaton group $g$ which is generated by a two state automaton on a three letter alphabet. using its branch structure and the finiteness nature of a sequence of its factor groups we compute the order of some of these factors. furthermore some algebraic properties of $g$ are detected .

given a pair (semispray $s$, metric $g$) on a tangent bundle, the family of nonlinear connections $n$ such that $g$ is recurrent with respect to $(s, n)$ with a fixed recurrent factor is determined by using the obata tensors. in particular, we obtain a characterization for a pair $(n, g)$ to be recurrent as well as for the triple $(s, stackrel{c}{n}, g)$ where $stackrel{c}{n}$ is the canonical ...

Let G be a graph of sufficiently large order n, and let a and b be integers with 1 ≤ a ≤ b. Let h : E(G) → [0, 1] be a function. If a ≤ ∑x∈e h(e) ≤ b holds for any x ∈ V (G), then G[Fh] is called a fractional [a, b]-factor of G with indicator function h, where Fh = {e ∈ E(G) | h(e) > 0}. A graph G is fractional independent-set-deletable [a, b]-factor-critical (simply, fractional ID-[a, b]-facto...

A spanning subgraph of a graph G is called a [0,2]-factor of G, if 0 ( ) 2 d x   for ( ) x V G   . is a union of some disjoint cycles , paths and isolate vertices , that span the graph G. It is easy to get a [0,2]-factor of G and there would be many of [0,2]-factors for a G. A characteristic number for a [0,2]-factor, which reflect the number of the paths and isolate vertices in it,. The [0...

The present study aimed at investigating the beneficial effects of co-administering granulocyte colony–stimulating factor (G-CSF) and stem cell factor (SCF) in a model of chronic liver injury induced by thioacetamide (TAA). Biochemical and histopathology- cal examinations were performed on serum and liver specimens. At the end of the treatment period, the rats were anesthetized with ether, seru...

Background: Macrophage migration inhibitory factor (MIF) is a key pro-inflammatory cytokine that is secreted by active macrophages accumulated in ectopic tissue of endometriosis. It involves in pathophysiological events of endometriosis such as angiogenesis, cell proliferation and it can stimulate the synthesis of PGE2 that are necessary for survival and establishment of ectopic endometriosis t...

A Λ-factor of a graph G is a spanning subgraph of G whose every component is a 3-vertex path. Let v(G) be the number of vertices of G. A graph is clawfree if it does not have a subgraph isomorphic to K1,3. Our results include the following. Let G be a 3-connected claw-free graph, x ∈ V (G), e = xy ∈ E(G), and L a 3-vertex path in G. Then (c1) if v(G) = 0 mod 3, then G has a Λ-factor containing ...