2014/12/15 by Jean B. Lasserre, Lasserre, Jean B. · 1 citation
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Advanced Statistical Methods and Models #FOS: Mathematics #Mathematical functions and polynomials #Optimization and Control (math.OC) #math.OC
paper · pdf · doi:10.48550/arxiv.1412.4617
arxiv created 2014/12/15 · openalex publication_date 2014/12/15 · arxiv updated 2014/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a vector a ∈ Rn, we provide an alternative and direct proof for the formula of the volume of sections delta ∩ x : a T x \textless= t and slices ∩ x : a T x = t, t ∈ R, of the simplex delta. For slices the formula has already been derived but as a by-product of the construction of univariate B-Splines. One goal of the paper is to also show how simple and powerful can be the Laplace transform technique to derive closed form expression for some multivariate integrals. It also complements some previous results obtained for the hypercube [0, 1] n .