Multivariate measures of positive dependence

In this paper a set of desirable properties for measures of positive dependence of ordered n-tuples of continuous random variables (n >= 2) is proposed and a class of multivariate positive dependence measures is introduced. We consider the comonotonicity dependence structure as the strong dependency structure and so the class consists of measures that take values in the range [0, 1] and are defined in such a way that they equal 1 in case the random vector is comonotonic and equal 0 in case it is independent.

Preference Rapresentation for Multicriteria Decision Making

In this note we consider a multicriteria decision problem where the decision maker know the the state of the world but the set of consequences is multidimensional. We suppose that a value function is specified over the attribute of the decision problem and we analyze some classes of non additive functions that can represent interaction between criteria.Multicriteria decision making, value functions, Choquet signed integral, Schur decreasing functions. functions

Pontryagin Maximum Principle and Stokes Theorem

We present a new geometric unfolding of a prototype problem of optimal control theory, the Mayer problem. This approach is crucially based on the Stokes Theorem and yields to a necessary and sufficient condition that characterizes the optimal solutions, from which the classical Pontryagin Maximum Principle is derived in a new insightful way. It also suggests generalizations in diverse directions of such famous principle.Comment: 21 pages, 7 figures; we corrected a few minor misprints, added a couple of references and inserted a new section (Sect. 7); to appear in Journal of Geometry and Physic

Quasi-geostrophic kinematic dynamos at low magnetic Prandtl number

Rapidly rotating spherical kinematic dynamos are computed using the combination of a quasi geostrophic (QG) model for the velocity field and a classical spectral 3D code for the magnetic field. On one hand, the QG flow is computed in the equatorial plane of a sphere and corresponds to Rossby wave instabilities of a geostrophic internal shear layer produced by differential rotation. On the other hand, the induction equation is computed in the full sphere after a continuation of the QG flow along the rotation axis. Differential rotation and Rossby-wave propagation are the key ingredients of the dynamo process which can be interpreted in terms of $\alpha\Omega$ dynamo. Taking into account the quasi geostrophy of the velocity field to increase its time and space resolution enables us to exhibit numerical dynamos with very low Ekman (rapidly rotating) and Prandtl numbers (liquid metals) which are asymptotically relevant to model planetary core dynamos

Finite Mechanical Proxies for a Class of Reducible Continuum Systems

We present the exact finite reduction of a class of nonlinearly perturbed wave equations, based on the Amann-Conley-Zehnder paradigm. By solving an inverse eigenvalue problem, we establish an equivalence between the spectral finite description derived from A-C-Z and a discrete mechanical model, a well definite finite spring-mass system. By doing so, we decrypt the abstract information encoded in the finite reduction and obtain a physically sound proxy for the continuous problem.Comment: 15 pages, 3 figure