Let G be a finite and simple graph with vertex set V (G), and let f : V (G) → {−1, 1} be a two-valued function. If k ≥ 1 is an integer and ∑x∈N(v) f(x) ≥ k for each v ∈ V (G), where N(v) is the neighborhood of v, then f is a signed total k-dominating function on G. A set {f1, f2, . . . , fd} of signed total k-dominating functions on G with the property that ∑d i=1 fi(x) ≤ k for each x ∈ V (G), ...

Top-k queries allow end-users to focus on the most important (top-k) answers amongst those which satisfy the query. In traditional databases, a user defined score function assigns a score value to each tuple and a top-k query returns k tuples with the highest score. In uncertain database, top-k answer depends not only on the scores but also on the membership probabilities of tuples. Several top...

Let G = (V, E) be an undirected graph with a set V of nodes and a set E of edges, |V | = n. A node v is said to distance-k dominate a node w if w is reachable from v by a path consisting of at most k edges. A set D ⊆ V is said a distance-k dominating set if every node can be distance-k dominated by some v ∈ D. The size of a minimum distance-k dominating set, denoted by γk(G), is called the dist...

The VC-dimension of a family P of n-permutations is the largest integer k such that the set of restrictions of the permutations in P on some k-tuple of positions is the set of all k! permutation patterns. Let rk(n) be the maximum size of a set of n-permutations with VC-dimension k. Raz showed that r2(n) grows exponentially in n. We show that r3(n) = 2 Θ(nα(n)) and for every t ≥ 1, we have r2t+2...

The VC-dimension of a family P of n-permutations is the largest integer k such that the set of restrictions of the permutations in P on some k-tuple of positions is the set of all k! permutation patterns. Let rk(n) be the maximum size of a set of n-permutations with VCdimension k. Raz showed that r2(n) grows exponentially in n. We show that r3(n) = 2 Θ(n logα(n)) and for every t ≥ 1, we have r2...

For a d-tuple of commuting operators S := (S1,..., Sd) ? B[X]d, m N and p (0,?), we define Q(p) (S;u) 0?k?m (-1)k (m k) (???Nd0 |?| = k k!/? ||S?u||p). As natural extension the concepts (m,p)-expansive (m,p)-contractive for tuple operators, introduce study (m,?)-expansive (m,?)-contractive acting on Banach space. We say that is (resp. (m,?)- contractive d-tuple) if Q(p)m 0 u X ?) . These extend...

The edge-domsaturation number ds′(G) of a graph G = (V,E) is the least positive integer k such that every edge of G lies in an edge dominating set of cardinality k. The connected edge-domsaturation number dsc(G) of a graph G = (V,E) is the least positive integer k such that every edge of G lies in a connected edge dominating set of cardinality k. In this paper, we obtain several results connect...

We limit our discussion to graphs that are simple and finite of order . Although 8 we often identify a graph with its set of vertices, in cases where we need to be K explicit we write . A set of vertices of is said to Z ÐKÑ Q K dominate K provided each vertex of is either in or adjacent to a vertex of . K Q Q The domination number of is the minimum order of a dominating set. A K dominating prov...

In this paper we deal with the problem of obtaining the set of k-additive measures dominating a fuzzy measure. This problem extends the problem of deriving the set of probabilities dominating a fuzzy measure, an important problem appearing in Decision Making and Game Theory. The solution proposed in the paper follows the line developed by Chateauneuf and Jaffray for dominating probabilities and...