This paper develops techniques for computing the minimum weight Steiner triangulation of a planar point set. We call a Steiner point P a Steiner reducing point of a planar point set X if the weight (sum of edge lengths) of a minimum weight triangulation of X ∪{P} is less than that of X. We define the Steiner reducing set St(X) to be the collection of all Steiner reducing points of X. We provide...

A set S of vertices of a connected graph G is a geodetic set if every vertex of G lies on an x−y geodesic for some elements x and y in S. The minimum cardinality of a geodetic set ofG is the geodetic number ofG, denoted by g(G). A set S of vertices of a graph G is an edge geodetic set if every edge of G lies on an x − y geodesic for some elements x and y in S. The minimum cardinality of an edge...

A graph   is called integral if all eigenvalues of its adjacency matrix  are integers.  Given a subset $S$ of a finite group $G$, the bi-Cayley graph $BCay(G,S)$ is a graph with vertex set $Gtimes{1,2}$ and edge set ${{(x,1),(sx,2)}mid sin S, xin G}$.  In this paper, we classify all finite groups admitting a connected cubic integral bi-Cayley graph.

Let G(V, E, W) be a graph n vertices and m edges, where each edge e is associated with a positive distance W(e). The traditional p-Center problem is to locate some kind of facilities at p vertices of G to minimize the maximum distance between any vertex and its nearest facility. This paper proposes a practical constraint: the subgraph induced by the p facility vertices must be connected and the...

Let Ω be a bounded simply connected domain in the complex plane, C. Let N be a neighborhood of ∂Ω, let p be fixed, 1 < p < ∞, and let û be a positive weak solution to the p Laplace equation in Ω ∩N. Assume that û has zero boundary values on ∂Ω in the Sobolev sense and extend û to N \ Ω by putting û ≡ 0 on N \ Ω. Then there exists a positive finite Borel measure μ̂ on C with support contained in ...

Recently, Brushless Cascaded Doubly Fed Induction Generator (BCDFIG) has been considered as an attractive choice for grid-connected applications due to its high controllability and reliability. In this paper, a Finite Control Set Model Predictive Control (FCS-MPC) method with active and reactive power control capability in grid-connected mode is proposed for controlling the BCDFIG in a way that...

We describe all connected components of the space of pairs (P, s), where P is a hyperbolic Riemann surface with finitely generated fundamental group and s is an m-spin structure on P . We prove that any connected component is homeomorphic to a quotient of R by a discrete group. Our method is based on a description of an m-spin structure by an m-Arf function, that is a map σ : π1(P, p) → Z/mZ wi...

The goal of the present paper is to calculate the limit of spectrum of the Hodge-de Rham operator under the perturbation of collapse of one part of a connected sum. It takes place in the general problem of blowing up conical singularities introduced in [Maz06] and [Row08]. Le but de ce travail est de calculer la limite du spectre de l’opéateur de Hodgede Rham dans la perturbation obtenue par ef...