We define a binary relation (qualitative uncertainty assessment (QUA)) to describe a decision-maker’s subjective assessment of likelihoods on a collection of events. To model ambiguity, we permit incompleteness. Our axioms yield a representation according to which A is more likely than B if an only if a capacity, called uncertainty measure (UM) assigns a higher value to A than to B and a higher...

We show how to use numerical methods within the framework of successive scaling to analyse the microstructure of turbulence, in particular to find inertial range exponents and structure functions. The methods are first calibrated on the Burgers problem and are then applied to the 3D Euler equations. Known properties of low order structure functions appear with a relatively small computational o...

We study brane recombination for supersymmetric configurations of intersecting branes in terms of the world-volume field theory. This field theory contains an impurity, corresponding to the degrees of freedom localized at the intersection. The Higgs branch, on which the impurity fields condense, consists of vacua for which the intersection is deformed into a smooth calibrated manifold. We show ...

We present an algorithm for parameter identification in combustion problems modelled by partial differential equations. The method includes local mesh refinement controlled by a posteriori error estimation with respect to the error in the parameters. The algorithm is applied to two types of combustion problems. The first one deals with the identification of Arrhenius parameters, while in the se...

We say that a function F (τ) obeys WDVV equations, if for a given invertible symmetric matrix η and all τ ∈ T ⊂ R, the expressions c α β γ(τ) = η cλβγ(τ) = η∂λ∂β∂γF can be considered as structure constants of commutative associative algebra; the matrix ηαβ inverse to η αβ determines an invariant scalar product on this algebra. A function x(z, τ) obeying ∂α∂βx (z, τ) = zc ε α β∂εx (z, τ) is call...

We study convex Hamilton-Jacobi equations H(x,Du) = a and ut+H(x,Du) = a in a bounded domain Ω of R with the Neumann type boundary condition Dγu = g in the viewpoint of weak KAM theory, where γ is a vector field on the boundary ∂Ω pointing a direction oblique to ∂Ω. We establish the stability under the formations of infimum and of convex combinations of subsolutions of convex HJ equations, some...

The absolute visual magnitude as function of the observed color (B-V) , also named Hertzsprung-Russell diagram can be described through five equations; that in presence of calibrated stars means eight constants. The developed framework allows to deduce the remaining physical parameters that are mass , radius and luminosity. This new technique is applied to the first 10 PC , the first 50 pc , th...