We generalize some results of Ford and Roman constraining the possible behaviors of the renormalized expected stressenergy tensor of a free massless scalar field in two dimensional Minkowski spacetime. Ford and Roman showed that the energy density measured by an inertial observer, when averaged with respect to the observers proper time by integrating against some weighting function, is bounded ...

We consider two infinite games, played on a countable graph G given with an integer vertex labelling. One player seeks to construct a ray (a one-way infinite path) in G, so that the ray’s labels dominate or elude domination by an integer sequence being constructed by another player. For each game, we give a structural characterization of the graphs on which one player or the other can win, prov...

Let G = (V,E) be a graph. A subset S of V is called a dominating set if each vertex of V −S has at least one neighbor in S. The domination number γ(G) equals the minimum cardinality of a dominating set in G. A minus dominating function on G is a function f : V → {−1, 0, 1} such that f(N [v]) = ∑ u∈N [v] f(u) ≥ 1 for each v ∈ V , where N [v] is the closed neighborhood of v. The minus domination ...

Let $G$ be a graph with vertex set $V(G)$. For any integer $kge 1$, a signed (total) $k$-dominating functionis a function $f: V(G) rightarrow { -1, 1}$ satisfying $sum_{xin N[v]}f(x)ge k$ ($sum_{xin N(v)}f(x)ge k$)for every $vin V(G)$, where $N(v)$ is the neighborhood of $v$ and $N[v]=N(v)cup{v}$. The minimum of the values$sum_{vin V(G)}f(v)$, taken over all signed (total) $k$-dominating functi...

Temperature cables restrained from lateral movement, were measured as a function of grain height, cable location and surface coating. For the restrained conditions, the cable forces were one to nine times those previously measured for unrestrained cables. The large load increase on the restrained cables is believed to be caused by the flow profile which existed at each of the three different ca...

etant donné le rapport réciproque entre la société et la littérature, et vu la dominance extraordinaire du roman, à l'état actuel, sur les autres expressions littéraires, on ne peut s'empêcher de s'interroger sur la cause et l'origine de la primauté du genre romanesque. certes, le roman ne date pas du xixe siècle; il est l'un des héritages des siècles précédents. néanmoins, son déploiement est ...

A function f : V (G) → {+1,−1} defined on the vertices of a graph G is a signed dominating function if for any vertex v the sum of function values over its closed neighborhood is at least 1. The signed domination number γs(G) of G is the minimum weight of a signed dominating function on G. By simply changing “{+1,−1}” in the above definition to “{+1, 0,−1}”, we can define the minus dominating f...

Let G = (V,E) be a simple graph. For any real function g : V −→ R and a subset S ⊆ V , we write g(S) = ∑ v∈S g(v). A function f : V −→ [0, 1] is said to be a fractional dominating function (FDF ) of G if f(N [v]) ≥ 1 holds for every vertex v ∈ V (G). The fractional domination number γf (G) of G is defined as γf (G) = min{f(V )|f is an FDF of G }. The fractional total dominating function f is de...

A three-valued function f defined on the vertices of a graph G = (V,E), f : V , ( 1 , 0 , 1), is a minus dominating function if the sum of its function values over any closed neighborhood is at least one. That is, for every v E V, f(N[v])>~ 1, where N[v] consists of v and every vertex adjacent to v. The weight of a minus dominating function is f ( V ) = ~ f (v) , over all vertices v E V. The mi...