The dead end depth of an element g of a group G with finite generating set A is the distance from g to the complement of the radius dA(1, g) closed ball, in the word metric dA defined with respect to A. We say that G has infinite dead end depth when dead end depth is unbounded, ranging over G. We exhibit a finitely presented group G with a finite generating set, with respect to which G has infi...

background; various industries produce and discharge wastes containing different heavy metals into the environment. apart from using living biomass, dead and dried biomasses have been introduced as a new field of biotreatment technology. method; the cadmium (cd) (ii) removal characteristics of live (growing), dead (autoclaved), and oven-dried biomasses of aspergillus versicolor were examined as...

It is known, that the existence of dead ends (of arbitrary depth) in the Cayley graph of a group depends on the chosen set of generators. Nevertheless there exist many groups, which do not have dead ends of arbitrary depth with respect to any set of generators. Partial results in this direction were obtained by Šunić and by Warshall. We improve these results by showing that abelian groups only ...

It is proved that the curve graph C(Σ) of a surface Σg,n has a local pathology that had not been identified as such: there are vertices α, β ∈ C (Σ) such that β is a dead end of every geodesic joining α to β. There are also double dead-ends. Every dead end has depth 1. Mathematical Subject Classification 57M99, 20F65

Background: Various industries produce and discharge wastes containing different heavy metals into the environment. Apart from using living biomass, dead and dried biomasses have been introduced as a new field of biotreatment technology. Method: The cadmium (Cd) (II) removal characteristics of live (growing), dead (autoclaved), and oven-dried biomasses of Aspergillus versicolor were examined a...