In this study, we examine the dual expression of Valeontis’ concept parallel p-equidistant ruled surfaces well known in Euclidean 3-space, according to Study mapping. Furthermore, show that part angle on unit sphere corresponds p-distance. We call these obtained “dual equidistant surfaces” and briefly denote them with “DPERS”. find Blaschke vectors, invariants striction curves DPERS give relati...

We consider simply generated trees, where the nodes are equipped with weakly monotone labellings with elements of {1,2, . . . ,r}, for r fixed. These tree families were introduced in Prodinger and Urbanek (1983) and studied further in Kirschenhofer (1984), Blieberger (1987), and Morris and Prodinger (2005). Here we give distributional results for several tree statistics (the depth of a random n...

A se t of points, called consumers, and another point called central supplier, are located i n a Euclidean plane. The cost of constructing a connection between two points i s proportional t o the distance between them. The minimum cost required for connecting a l l the consumers t o the supplier i s given by a minimal Steiner tree. An example i s given i n which for every allocation of the tota...

The Steiner tree problem asks for a minimum cost tree spanning a given set of terminals S ⊆ V in a weighted graph G = (V, E, c), c : E → R. In this paper we consider a generalization of the Steiner tree problem, so called Polymatroid Steiner Problem, in which a polymatroid P = P (V ) is defined on V and the Steiner tree is required to span at least one base of P (in particular, there may be a s...

Social and psychological concerns, improved function, appearance, self-esteem encourages a patient to pursue Orthodontic treatment, for which extraction may or not be needed. Conventionally steiner stick analysis tweed head plate correction is followed decide during fixed orthodontic treatment desirable outcome. This study was designed compare predicted position angulation of maxillary mandibul...

Let G be a connected graph of order n . The Steiner distance d ( S ) set vertices is the minimum size subgraph that contains all For k ≤ , -diameter sdiam maximum among sets generalises classical diameter, which coincides with 2-diameter. problem determining given order, diameter and degree was first studied by Erdös Rényi. In this paper we consider corresponding for -diameter. Δ ∈ N define e a...

We consider the vertex-weighted version of the undirected Steiner tree problem. In this problem, a cost is incurred both for the vertices and the edges present in the Steiner tree. We completely describe the associated polytope by linear inequalities when the underlying graph is series-parallel. For general graphs, this formulation can be interpreted as a (partial) extended formulation for the ...

The line planning problem in public transport deals with the construction of a system of lines that is both attractive for the passengers and of low costs for the operator. In general, the computed line system should be connected, i.e., for each two stations there have to be a path that is covered by the lines. This subproblem is a generalization of the well-known Steiner tree problem; we call ...

As a consequence of the classification of the finite simple groups, it has been possible in recent years to characterize Steiner t-designs, that is t-(v, k,1) designs, mainly for t = 2, admitting groups of automorphisms with sufficiently strong symmetry properties. However, despite the finite simple group classification, for Steiner t-designs with t > 2 most of these characterizations have rema...

The Euclidean Steiner tree problem is to find the tree with minimal Euclidean length spanning a set of fixed points in the plane, allowing the addition of auxiliary points to the set (Steiner points). The problem is NP-hard, so polynomial-time heuristics are desired. We present two such heuristics, both of which utilize an efficient method for computing a locally optimal tree with a given topol...