In this paper we discuss the problem of approximating a belief function (b.f.) with a possibility measure of consonant belief function (co.b.f.) from a geometric point of view. We focus in particular on outer consonant approximations, i.e. co.b.f.s less committed than the original b.f. in terms of degrees of belief. We show that for each specific chain of focal elements the set of outer consona...

Let Q be an infinite subset of Z, let Ψ : Z→ [0,∞), and let θ ∈ R. Define E(Q,Ψ, θ) = {x ∈ R : ‖qx− θ‖ ≤ Ψ(q) for infinitely many q ∈ Q}. We prove a lower bound on the Fourier dimension of E(Q,Ψ, θ). This generalizes theorems of Kaufman and Bluhm and yields new explicit examples of Salem sets. We give applications to metrical Diophantine approximation, including determining the Hausdorff dimens...

We give an explicit formula (i.e., an explicit expression for the formal stationary phase formula) for the local Fourier-Laplace transform of a formal germ of meromorphic connection of one complex variable with a possibly irregular singularity. Introduction We will denote by C((t)) (resp. C({t})) the field C[[t]][t] (resp. C{t}[t]) of formal (resp. convergent) Laurent series of the variable t, ...

Let ρ(x) = x− [x], χ = χ(0,1), λ(x) = χ(x) logx, and M(x) = ∑ k≤x μ(k), where μ is the Möbius function. Norms are in Lp(0,∞), 1 < p < ∞. For M1(θ) = M(1/θ) it is noted that ζ(s) ≠ 0 in s > 1/p is equivalent to ‖M1‖r < ∞ for all r ∈ (1,p). The space is the linear space generated by the functions x ρ(θ/x) with θ ∈ (0,1]. Define Gn(x)= ∫ 1 1/nM1(θ)ρ(θ/x)θ−1dθ. For all p ∈ (1,∞) we prove the two ar...

We present tight bounds on the spanning ratio of a large family of ordered θ-graphs. A θ-graph partitions the plane around each vertex into m disjoint cones, each having aperture θ = 2π/m. An ordered θ-graph is constructed by inserting the vertices one by one and connecting each vertex to the closest previously-inserted vertex in each cone. We show that for any integer k ≥ 1, ordered θ-graphs w...

A nested sequence of projectors and corresponding braid matricesˆR(θ): (1) Odd dimensions. Abstract A basis of N 2 projectors, each an N 2 × N 2 matrix with constant elements, is implemented to construct a class of braid matricesˆR(θ), θ being the spectral parameter. Only odd values of N are considered here. Our ansatz for the projectors P α appearing in the spectral decomposition ofˆR(θ) leads...

Following [3] we confirm a conjecture of Yde Venema by piecing together results from various authors. Specifically, we show that if A is a residually finite, finitely generated modal algebra such that HSP(A) has equationally definable principal congruences, then the profinite completion of A is the MacNeille completion of A, and ♦ is smooth. Specific examples of such modal algebras are the free...

A pseudo-primitive word with respect to an antimorphic involution θ is a word which cannot be written as a catenation of occurrences of a strictly shorter word t and θ(t). Properties of pseudo-primitive words are investigated in this paper. These properties link pseudo-primitive words with essential notions in combinatorics on words such as primitive words, (pseudo)-palindromes, and (pseudo)-co...

Let (M,F) be a foliated m + n-dimensional manifold M with n-dimensional foliation F . Let V be a finite dimensional vector space over R. We describe all canonical (Folm,n-invariant) V -valued 1-forms Θ: TP r(M,F) → V on the r-th order adapted frame bundle P r(M,F) of (M,F). All manifolds and maps are assumed to be of class C∞. A definition of foliations can be found in [2]. Let Folm,n be the ca...

1 Bayesian Interpretation of Mutual Information Recall that the mutual information I(θ; X) between two random variables θ and X is defined as the Kullback-Leibler divergence between their joint distribution and the product of their marginal distributions. The following Bayesian interpretation of I(θ; X) well captures its intuitive interpretation as the amount of information that X contains abou...