The cycling operation endows the super summit set Sx of any element x of a Garside group G with the structure of a directed graph Γx. We establish that the subset Ux of Sx consisting of the circuits of Γx can be used instead of Sx for deciding conjugacy to x in G, yielding a faster and more practical solution to the conjugacy problem for Garside groups. Moreover, we present a probabilistic appr...

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...

We show that under some simple conditions a topological conjugacy h between two holomorphic self-maps f1 and f2 of complexn-dimensional projective space Pn lifts canonically to a topological conjugacy H between the two corresponding polynomial self-maps of Cn+1, and this conjugacy relates the two Green functions of f1 and f2. These conjugacies are interesting because their geometry is not inher...

emph{The (undirected) power graph on the conjugacy classes} $mathcal{P_C}(G)$ of a group $G$ is a simple graph in which the vertices are the conjugacy classes of $G$ and two distinct vertices $C$ and $C'$ are adjacent in $mathcal{P_C}(G)$ if one is a subset of a power of the other. In this paper, we describe groups whose associated graphs are $k$-regular for $k=5,6$.

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...

In this paper, we consider the conjugacy problem for HNNextensions of groups with solvable conjugacy problem for which the associated subgroups are cyclic. An example of such a group with unsolvable conjugacy problem is constructed. A similar construction is given for free products with amalgamation.

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...

fullerene chemistry is nowadays a well-established field of both theoretical and experimental investigations‎. this study considers the symmetry of small fullerenes cage c24 and c28‎. ‎using pm3 program for c24 and c28 fullerenes, oh and td symmetry were confirmed, respectively‎. ‎ the mentioned algorithm to compute the automorphism group of these fullerenes with connectivity and geometry of th...