We explore the structure of the p-adic automorphism group Γ of the infinite rooted regular tree. We determine the asymptotic order of a typical element, answering an old question of Turán. We initiate the study of a general dimension theory of groups acting on rooted trees. We describe the relationship between dimension and other properties of groups such as solvability, existence of dense free...

The diurnal fluctuation of nitrate concentration in the foliage of three parsley subspecies (plain-leafed, curly-leafed and turnip rooted parsley) cultivated in the spring and autumn of two consecutive years was examined. Nitrogen was applied at 30 (Control), 75, 150, 300 mg kg-1 in both years, but with the addition of 450 mg kg-1 in year 2. Harvest was carried out at 08:30, 12:30 and 17:30 on ...

A biconnected plane graph G is called internally triconnected if any cut-pair consists of outer vertices and its removal results in only components each of which contains at least one outer vertex. In a rooted plane graph, an edge is designated as an outer edge with a specified direction. For given positive integers n ≥ 1 and g ≥ 3, let G3(n, g) (resp., Gint(n, g)) denote the class of all trico...

The problem A graph G consists of a set V G of vertices and a set E G of edges each of which is an ordered pair of vertices These objects despite their simple struc ture can be used to model important properties of a wide variety of math ematical and physical systems One of their most important applications is to the study of routing in networks Here the vertices represent sites cities computer...

We propose a new arithmetic for non-empty rooted unordered trees simply called trees. After discussing tree representation and enumeration, we define the operations of tree addition, multiplication, and stretch, prove their properties, and show that all trees can be generated from a starting tree of one vertex. We then show how a given tree can be obtained as the sum or product of two trees, th...

The graph G contains a graph H as a minor if there exist pair-wise disjoint sets {Si ⊆ V (G)|i = 1, . . . , |V (H)|} such that for every i, G[Si] is a connected subgraph and for every edge uv in H, there exists an edge of G with one end in Su and the other end in Sv. A rooted H minor in G is a minor where each Si of minor contains a predetermined xi ∈ V (G). We prove that if the constant c is s...

The problem of computing a minimum cost subgraph D′ = (V,A′) of a directed graph D = (V,A) so that D′ contains k edge-disjoint paths from a specified root r ∈ V to every other node in V is known to be nicely solvable since it can be formulated as a matroid intersection problem. A corresponding problem when openly disjoint paths are requested rather than edge-disjoint was solved in [12] with the...

introduction a large number of orthodontists prefer to rebond the failed bonded brackets or use recycled brackets in some instances. the aim of this study was to compare the shear bond strength of rebonding with using recycled brackets on enamel surface. methods bonding of brackets on the surface of extracted first bicuspids was tested in five different groups to compare their shear bond streng...