We take another look at two compounds which have been discussed as possible realizations of ‘‘spin ice,’’ namely holmium titanate and dysprosium titanate. As we have earlier observed, holmium titanate does not display icelike behavior at low temperatures because the long-ranged dipolar interactions between spins are strong compared to the nearest-neighbor interactions. We show, exactly, that th...

The partial functions under disjoint-domain sums and functional composition do not form a field, and thus conventional linear algebra is not applicable. However they can be regarded as a so-ring, an algebraic structure possessing a natural partial ordering, an infinitary partial addition and a binary multiplication, subject to a set of axioms. In this paper, we introduce the notions of 2-absorb...

Our first job was to adapt the causal partial order of events to the new context of object oriented distributed applications. We want to order method invocations, method executions and blocks of code. By this way we adopt an approach based on a logic of action where only two events are needed : the begin and the end of the action. Then the causal ordering of distributed objects applications is ...

We give an exposition of Herrmann’s proof that there is an infinite computable partial ordering with no infinite Σ 2 chains or

We deened an extension of Kowalski and Sergot's Event Calculus (EC) 2] to deal with incomplete information about event ordering. Given a set of events, EC allows to derive maximal time intervals (MVIs) over which the properties they initiate or terminate hold. When only partial knowledge on event ordering is given, EC is neither able to derive all admissible MVIs nor to distinguish which of the...

Deciding whether one probability distribution is more informative (in the sense of representing a less indeterminate situation) than another one is typically done using well-established information measures such as, e.g., the Shannon entropy or other dispersion indices. In contrast, the relative specificity of possibility distributions is evaluated by means of fuzzy set inclusion. In this paper...

The cutwidth of a graph G is defined to be the smallest integer k such that the vertices of G can be arranged in a vertex ordering [v1, . . . , vn] in a way that, for every i = 1, . . . , n− 1, there are at most k edges with one endpoint in {v1, . . . , vi} and the other in {vi+1, . . . , vn}. We examine the problem of computing in polynomial time the cutwidth of a partial w-tree with bounded d...

AbStXlWt Some simple assumptions about prior ignorance, and the idea that a sticiently arresting contrast in the likelihoods of evidence will elicit belief that one proposition is at least as belief-worthy as another, lead to a partial ordering of propositions without the use of any hind of prior probability. The partial ordering is mt a posterior probability distribution, but does share some i...

The cutwidth of a graph G is defined to be the smallest integer k such that the vertices of G can be arranged in a vertex ordering [v1, . . . , vn] in a way that, for every i = 1, . . . , n−1, there are at most k edges with the one endpoint in {v1, . . . , vi} and the other in {vi+1, . . . , vn}. We examine the problem of computing in polynomial time the cutwidth of a partial w-tree with bounde...