Quotient rings and Fountain-Gould left orders by the local approach

We study Fountain-Gould left orders in semiprime rings coinciding with their socles by means of local rings at elements.     

Compatible Poisson Brackets on Lie Algebras

We discuss the relationship between the representation of an integrable system as an L-A-pair with a spectral parameter and the existence of two compatible Hamiltonian representations of this system. We consider examples of compatible Poisson brackets on Lie algebras, as well as the corresponding integrable Hamiltonian systems and Lax representations.     

A setup heuristic for interval orders

The setup minimization problem for linear extensions of interval orders is considered and a simple greedy heuristic is shown to be never worse than twice the optimum.     

IDENTIFICATION OF MULTIVARIATE ARMA MODELS

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Arrow's theorem: unusual domains and extended codomains

In this paper we establish Arrow's theorem in a general ordinal case. When some configurations are allowed in the domain and if this domain is included in the codomain, the only social functions satisfying the independence condition and the weak Pareto Principle are the absolute dictatorships or the absolute oligarchies.     

Properties of four partial orders on standard Young tableaux

Let SYTn be the set of all standard Young tableaux with n cells. After recalling the definitions of four partial orders, the weak, KL, geometric and chain orders on SYTn and some of their crucial properties, we prove three main results:

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Intervals in any of these four orders essentially describe the product in a Hopf algebra of tableaux defined by Poirier and Reutenauer.

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The map sending a tableau to its descent set induces a homotopy equivalence of the proper parts of all of these orders on tableaux with that of the Boolean algebra ²[n−1]. In particular, the Möbius function of these orders on tableaux is (−1)ⁿ⁻³.

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For two of the four orders, one can define a more general order on skew tableaux having fixed inner boundary, and similarly analyze their homotopy type and Möbius function.

     

Countable linear orders with disjoint infinite intervals are mutually orthogonal

Two linear orderings of a same set are perpendicular if the only self-mappings of this set that preserve them both are the identity and the constant mappings. Two linear orderings are orthogonal if they are isomorphic to two perpendicular linear orderings. We show that two countable linear orderings are orthogonal as soon as each one has two disjoint infinite intervals. From this and previously known results it follows in particular that each countably infinite linear ordering is orthogonal to itself.     

Ruin-based risk measures in discrete-time risk models

For an insurance company, effective risk management requires an appropriate measurement of the risk associated with an insurance portfolio. The objective of the present paper is to study properties of ruin-based risk measures defined within discrete-time risk models under a different perspective at the frontier of the theory of risk measures and ruin theory. Ruin theory is a convenient framework to assess the riskiness of an insurance business. We present and examine desirable properties of ruin-based risk measures. Applications within the classical discrete-time risk model and extensions allowing temporal dependence are investigated. The impact of the temporal dependence on ruin-based risk measures within those different risk models is also studied. We discuss capital allocation based on Euler’s principle for homogeneous and subadditive ruin-based risk measures.     

Extensions of the prudence principle to exploit a valued outranking relation

In many outranking methods, the alternatives are first compared pairwise to build a valued outranking relation, which is then exploited to derive a recommendation for the decision maker. This paper proposes extensions of Arrow and Raynaud’s prudence principle to exploit a valued outranking relation, even in cases where the outranking values have an ordinal interpretation. The idea is to build a ranking that maximizes the weakest support for its implicit pairwise comparisons. We present a family of exploitation models providing three types of solutions, depending on the decision maker’s request: a linear order, a weak order, or a partial preorder. An algorithm is provided which solves the exploitation models. Relations between these models and some of their properties are also discussed.