Over time, there have been refinements in the way that probability distributions are used for representing beliefs. Models which rely on single probability distnlnrti ons depict a complete ordering among the propositions of interest, yet human beliefs are sometimes not completely ordered. Non-singleton sets of probability distributions can represent partially ordered beliefs. Convex sets are pa...

In this paper we examine compensation schemes that prevent a threat of secession by all country’s regions and in the same time provide no incentives for citizens’ migration within the country. We prove that, under quite general assumptions on the distribution of citizens’ preferences, there exist transfer schemes that are both secession-proof and migration-proof. Moreover, we show that these co...

Partial actions of groups appeared independently in various areas of mathematics, in particular, in the study of operator algebras. The formal definition of this concept was given by Exel in 1998 [1]. Later in 2003, Abadie [2] introduced the notion of enveloping action and found that any partial action possesses an enveloping action. The study of partial actions on arbitrary rings was initiated...

As the problems of interest in large-scale science are ever more complex or intertwined, scientists can benefit from machinery to manage hypotheses and their interconnection in the context of a large-scale research project. A partial order is assumed to model hypothesis interconnectivity, meaning that hypotheses may be ‘based on or equal to’ one another. Then we investigate lattices as a mathem...

Let f(n) be a totally multiplicative function such that |f(n)| ≤ 1 for all n, and let F (s) = ∑∞ n=1 f(n)n−s be the associated Dirichlet series. A variant of Halász’s method is developed, by means of which estimates for ∑N n=1 f(n)/n are obtained in terms of the size of |F (s)| for s near 1 with 1. The result obtained has a number of consequences, particularly concerning the zeros of the p...

The complexity of the present data-centric world finds its expression in the increasing number of multi-indicator systems. This has led to the development of multicriteria ranking systems based on partial order. Partial order is a main pillar of structural mathematics. Partial order helps reveal why an object of interest holds a certain ranking position and how much it is subject to change if a...

the positions 0 = B0 ≤ B1 ≤ B2 ≤ ... ≤ Bn ≤ ... In this last case it moves necessarily up : Bn denotes the position of the nth reflecting barrier. The barriers are assumed to be thrown at random on N, and more precisely the intervals Xn between the barriers are assumed to be i.i.d.. We prove, giving thus a complete answer to a question of Molchanov, that there is homogeneization for xt iff (q/p...

The notion of functionality is not cast in stone, but depends upon what we have as types in our language. With partial equivalence relations (pers) as types we show that the functional relations are precisely those satisfying the simple equation f = f ◦ f∪ ◦ f , where “∪” is the relation converse operator. This article forms part of “A calculational theory of pers as types” [1].

We describe a distributed partial order reduction algorithm for security protocols. Some experimental results using an implementation of the algorithm in the distributed μCRL toolset are also reported.

In this essay I present a general characterization of qualitative probability, including a partial taxonomy of possible approaches. I discuss some of these in further depth, identify central issues, and suggest some general comparisons.