Consider the supposedly simple problem of computing a point in a convex set that is conveyed by a separation oracle with no further information (e. g., no domain ball containing or intersecting the set, etc.). The authors' ...

We define in the space of n×m matrices of rank n, n ≤ m, the condition Riemannian structure as follows: For a given matrix A the tangent space at A is equipped with the Hermitian inner product obtained by multiplying the ...

Given a C∗-algebra A with trace τ, we compute the first and second variation formulas for the p-energy functional Fp of the unitary group UA of A, for p = 2n an even integer, namely: Fp(γ) = Z b a τ([ ˙γ∗γ˙ ] n)dt, where ...

This paper is the third and final part of a trilogy dealing with the concept of k-convexity in various geometries.

We present in this work two strategies to calculate the volume of some convex polyhedra of the following classes: Platonic polyhedra, Archimedean polyhedra, Catalan’s polyhedra and Johnson’s polyhedra. These strategies ...