Gent and Prosser proposed the first constraint model for the Stable Marriage problem with Ties and Incomplete preference lists (SMTI). Their model was based upon the simple Stable Marriage (SM) model proposed by Gent et al, in which for each man woman pair a constraint is posted consisting of a set of no good pairs of values. Prosser and Unsworth proposed a specialised binary constraint for SM ...

Background and objectives: Plants are usually used for treatment of different diseases according to their traditional application. The use of the plant based medications is increasingly becoming popular all over the world. Traditional herbal medicines should be transformed into new forms to make better acceptance and more comfortable use by patients. The aim of the present stud...

Popular matching and was extensively studied in recent years as an alternative to stable matchings. Both type of matchings are defined in the framework of Stable Marriage (SM) problem: in a given bipartite graph G = (A,B;E) each vertex u has a strict order of preference on its neighborhood. A matching M is popular, if for every matching M ′ of G, the number of vertices that prefer M ′ to M is a...

Nowadays, plants have been considered as powerful agents for treatment of disorders regarding to their traditional use. In Iranian Traditional Medicine (ITM), plants have a special role in the treatment of various diseases. Burns with their devastating outcomes have been discussed in ITM as well. In the present study, a polyherbal ointment (PHO), retrieved from ITM, was formulated for burn heal...

We consider the Stable Marriage Problem and the Stable Roommates Problem, two well-known types of the general class of Stable Matching Problems. They are combinatorial problems which can be solved by centralized algorithms in polynomial time. This requires to make public lists of preferences which agents would like to keep private. With this aim, we define the distributed version of these probl...

We consider instances of the Stable Roommates problem that arise from geometric representation of participants preferences: a participant is a point in a metric space, and his preference list is given by sorted distances to the other participants. We observe that, unlike in the general case, if there are no ties in the preference lists, there always exists a unique stable matching; a simple gre...

For examining vitamins, exact quantitations in natural matrices are essential. Up to date, one of the most accurate quantitation methods is the stable isotope dilution assay (SIDA), which is based on the use of isotopically labelled analogues of the analytes as internal standards. The merits of SIDA include the ideal compensation for losses, superior specificity and enhanced sensitivity due to ...

In this paper we describe an efficient algorithm that decides if a stable matching exists for a generalized stable roommates problem, where, instead of linear preferences, agents have partial preference orders on potential partners. Furthermore, we may forbid certain partnerships, that is, we are looking for a matching such that none of the matched pairs is forbidden, and yet, no blocking pair ...

It is known that there may not exist any stable matching for a given instance of the stable roommates problem. A stable partition is a structure that generalizes the notion of a stable matching; Tan (1991) proved that every instance of the stable roommates problem contains at least one such structure. In this paper we propose a new algorithm for finding a stable partition, and hence a new algor...

Let B be a σ–unital C–algebra. We show that every strongly continuous E0–semigroup on the algebra of adjointable operators on a full Hilbert B–module E gives rise to a full continuous product system of correspondences over B. We show that every full continuous product system of correspondences over B arises in that way. If the product system is countably generated, then E can be chosen countabl...