Elementary proofs are presented for two graph theoretic results, originally proved by H. Shirazi and J. Verstraëte using the combinatorial Nullstellensatz. In an undirected graph G = (V, E) we denote by dG(v) the degree of v ∈ V . If F (v) ⊆ N is a set of forbidden degrees for every v ∈ V , then a subgraph G = (V, E) of G is called F -avoiding if dG′(v) / ∈ F (v) for all v ∈ V . Theorem 1 (Shir...

In this follow-up work, we extend the discontinuous Galerkin (DG) methods previously developed on rectangular meshes [18] to triangular meshes. The DG schemes in [18] are both optimally convergent and energy conserving. However, as we shall see in the numerical results section, the DG schemes on triangular meshes only have suboptimal convergence rate. We prove the energy conservation and an err...

Decentralized Generation (DG) is expected to play a vital role in the future of electric power system. The power electronics interfaced microturbine generation systems are currently attracting lot of attention to meet different needs both at end consumers and the distribution utility levels. Dynamic modelling of the microturbine is a challenging process because manufacturers do not readily prov...

162 CUNICAL CHEMISTRY, Vol.40, No. 1, 1994 6. Hahn G,J,Meeker WQ. Statistical intervals: a guide for practitioners. New York: John Wiley, 1991. 7. Bailar JC, Mosteller F. Guidelines for statistical reporting in articles for medical journals: amplifications and explanations. In: Bailar JC, Mosteller F, eds. Medical uses of statistics, 2nd ed. Boston: NEJM Books, 1992:313-31. 8. Altman DG, Gore S...

It is now more than a decade since distributed generation (DG) began to excite major interest amongst electric power system planners and perators, energy policy makers and regulators as well as developers. This paper presents an overview of the key issues concerning the integration f distributed generation into electric power systems that are of most interest today. The main drivers behind the ...

A super edge-magic labeling of a graph G = (V, E) of order p and size q is a bijection f : V ∪E → {i} i=1 such that (1) f(u)+ f(uv)+ f(v) = k ∀uv ∈ E and (2) f(V ) = {i}pi=1. Furthermore, when G is a linear forest, the super edge-magic labeling of G is called strong if it has the extra property that if uv ∈ E(G), u′, v′ ∈ V (G) and dG(u, u′) = dG(v, v′) < +∞, then f(u) + f(v) = f(u′) + f(v′). I...

Let G be a simple undirected graph. A broadcast on G is a function f : V (G) → N such that f(v) ≤ eG(v) holds for every vertex v of G, where eG(v) denotes the eccentricity of v in G, that is, the maximum distance from v to any other vertex of G. The cost of f is the value cost(f) = ∑ v∈V (G) f(v). A broadcast f on G is independent if for every two distinct vertices u and v in G, dG(u, v) > max{...