we study the support sets of sub-topical functions‎ ‎and investigate their maximal elements in order to establish a necessary and sufficient condition‎ ‎for the global minimum of the difference of two sub-topical functions‎.

A new approach to the question of the existence of small-amplitude, uniformly translating, two-dimensional capillary-gravity water waves was proposed by Kirchgässner (1988), who suggested writing the governing equations as an infinite-dimensional, quasilinear dynamical system in which the horizontal coordinate is the time-like variable. The centre-manifold reduction theorem of Mielke (1988) may...

The Legendre-Fenchel transform is a classical piece of mathematics with many applications. In this paper we show how it arises in the context of category theory using categories enriched over the extended real numbers R := [−∞,+∞]. A key ingredient is Pavlovic’s “nucleus of a profunctor” construction. The pairing between a vector space and its dual can be viewed as an R-profunctor; the construc...

We prove general uniqueness results for radial solutions of linear and nonlinear equations involving the fractional Laplacian (−∆) with s ∈ (0, 1) for any space dimensions N > 1. By extending a monotonicity formula found by Cabré and Sire [9], we show that the linear equation (−∆)u+ V u = 0 in R has at most one radial and bounded solution vanishing at infinity, provided that the potential V is ...

Suppose that K is a closed, total cone in a real Banach space X, that A :X!X is a bounded linear operator which maps K into itself, and that A« denotes the Banach space adjoint of A. Assume that r, the spectral radius of A, is positive, and that there exist x ! 1 0 and m& 1 with Am(x ! ) ̄ rmx ! (or, more generally, that there exist x ! a (®K ) and m& 1 with Am(x ! )& rmx ! ). If, in addition, A...