Let X be a set. Let K(x, y) > 0 be a measure of the affinity between the data points x and y. We prove that K has the structure of a Newtonian potential K(x, y) = φ(d(x, y)) with φ decreasing and d a quasi-metric on X under ...

In this paper we construct two free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus Omega(R)/dR where R = C[t. t(-1), u vertical bar u(2) = t(3) - 2bt(2) + t]. The first realization provides an ...

In the early 1990s, three research groups simultaneously developed continuous macroporous rod-shaped polymeric systems to eliminate the problem of flow through the interparticle spaces generally presented by the chromatography ...

We study the relationship between maps and convexity, particularly from the following viewpoint: when does a desired property result from another weaker one? See Propositions 11, 15, 19, 20, 22 and 28.

We prove the existence of an associated family of G-structure preserving minimal immersions into semi-Riemannian manifolds endowed with a compatible infinitesimally homogeneous G-structure. We will study in more details ...