An ordering of multidimensional alternatives is separable on a set of dimensions if fixing values on the complementary dimensions always produces the same induced ordering. Most often, studies of separability assume continuous alternative spaces; as we show, separability has different properties when alternative spaces are discrete. For instance, two well-known theorems of Gorman—that common se...

Suppose we are given the conditional proba­ bility of one variable given some other vari­ ables. Normally the full joint distribution over the conditioning variables is required to determine the probability of the conditioned variable. Under what circumstances are the marginal distributions over the conditioning variables sufficient to determine the probabil­ ity of the conditioned variable? Su...

Perceptual separability is a foundational concept in cognitive psychology. A variety of research questions in perception - particularly those dealing with notions such as "independence," "invariance," "holism," and "configurality" - can be characterized as special cases of the problem of perceptual separability. Furthermore, many cognitive mechanisms are applied differently to perceptually sepa...

Knowing whether a household behaves according to separability or non-separability is needed for the correct modeling of production decisions. We propose a superior test to those found in the literature on separability by using a mixture distribution approach to estimate the probability that a farm household behaves according to non-separability, and test that the determinants of consumption aff...

We provide axiomatic characterizations of two natural families of rules for aggregating equivalence relations: the family of join aggregators and the family of meet aggregators. The central conditions in these characterizations are two separability axioms. Disjunctive separability, neutrality, and unanimity characterize the family of join aggregators. On the other hand, conjunctive separability...

in this article‎, ‎we have characterized ideals in $c(x)$ in which‎ ‎every ideal is also an ideal (a $z$-ideal) of $c(x)$‎. ‎motivated by‎ ‎this characterization‎, ‎we observe that $c_infty(x)$ is a regular‎ ‎ring if and only if every open locally compact $sigma$-compact‎ ‎subset of $x$ is finite‎. ‎concerning prime ideals‎, ‎it is shown that‎ ‎the sum of every two prime (semiprime) ideals of e...

In this paper, we study separability of graded field extensions. In particular, without restriction to torsion free of the grade group, we show that some separability results of graded field extensions given in [7] hold. On the other hand, the separability notions defined in [1] do not cover many situations, for example group algebras. We show that these notions are simple cases of separability...

Recently, Laplacian matrices of graphs are studied as density matrices in quantum mechanics. We continue this study and give conditions for separability of generalized Laplacian matrices of weighted graphs with unit trace. In particular, we show that the Peres-Horodecki positive partial transpose separability condition is necessary and sufficient for separability in C2 ⊗ C. In addition, we pres...