For a graph G that models a facility, various detection devices can be placed at the vertices so as to identify the location of an intruder such as a thief or saboteur. Here we introduce the open neighborhood locating-dominating set problem. We seek a minimum cardinality vertex set S with the property that for each vertex v its open neighborhood N(v) has a unique non-empty intersection with S. ...

In this paper we present two principal results. In Theorem 1 we show that if r¡ denotes the open set of (conservative) matrices which map some subspace of c of infinite deficiency isomorphically onto c and if A denotes the closed set of matrices which sum some bounded divergent sequence, then [r']~=A. In Theorem 2 we produce a class of triangular matrices with the property that no triangular ma...

This derivation of (2) is not valid, because this duality applies to inferences and theorems only, not to definitions. In fact, (1) should be treated as an axiom. Accordingly, the duality of Lemma 3.3.1 would not be valid until the dual (2) of (1) is proved independently, as we do below. Our new proof will make use of Proposition 3.3.3, the original proof of which is based on duality. So, we mu...

Answering a recent question posed by Gregori, Morillas and Sapena (“On a class of completable fuzzy metric spaces”, Fuzzy Sets and Systems, 161 (2010), 2193–2205) we present two examples of non strong fuzzy metrics (in the sense of George and Veeramani).

......An instruction set architecture (ISA) is one of the most important interfaces in a computer system because it divides software from hardware. Most widely used ISAs were developed decades ago and are proprietary. This may make sense because hardware implementations were and are mostly proprietary and most software was proprietary when these ISAs were developed. Today, however, we appreciat...

The notions of pre-local function, semi-local functions and α-local functions with respect to a topology and an ideal are introduced, and several properties are investigated. Also, the concept of P -I-open sets and P -I-closed sets in ideal topological spaces are discussed. Relations between I-open sets and P -I-open sets are provided, and several properties related to P -I-open sets, pre-local...

We provide an extension of the notion of chain-valued frame introduced by Pultr and Rodabaugh in [Category theoretic aspects of chain-valued frames: parts I and II, Fuzzy Sets and Systems 159 (2008) 501–528 and 529–558] by relaxing the assumption that L be a complete chain. As a result of this investigation we formulate the category L-Frm of L-frames under the weaker assumption that L is a comp...

 Abstract: In many applications we have to encountered with bounded dependent variables. Beta regression model can be used to deal with these kinds of response variables. In this paper we aim to study spatially correlated responses in the unit interval. Initially we introduce spatial beta generalized linear mixed model in which the spatial correlation is captured through a random effect. T...