For k even, let Pk denote the vector space of polynomials in 2 real variables of degree at most k. A linear functional L : Pk −→ R is positive if p ∈ Pk, p|R2 ≥ 0 =⇒ L(p) ≥ 0. Hilbert’s theorem on sums of squares (cf. [15]) implies that L : P4 −→ R is positive if and only if the moment matrix associated to L is positive semidefinite. In this note, using k = 6, we exhibit the first families of p...

We provide finite-sample analysis of a general framework for using k-nearest neighbor statistics to estimate functionals of a nonparametric continuous probability density, including entropies and divergences. Rather than plugging a consistent density estimate (which requires k → ∞ as the sample size n → ∞) into the functional of interest, the estimators we consider fix k and perform a bias corr...

If K is a pre-compact subset of a normed space X and > 0, the quantity logN(K, BX) describes the complexity of K at the level of resolution . A 1972 conjecture of A. Pietsch – originally stated in the operatortheoretic laguage – asserts that the two “metric entropy functionals,” → logN(K, BX) and → logN(BX∗ , K◦), are equivalent in the appropriate sense, uniformly over normed spaces X and over ...

In the free energy of hydration of a solute, the chemical contribution is given by the free energy required to expel water molecules from the coordination sphere and the packing contribution is given by the free energy required to create the solute-free coordination sphere (the observation volume) in bulk water. With the simple point charge/extended (SPC/E) water model as a reference, we examin...

Let 〈X ,Y〉 be a pair of Banach spaces in separating duality [18, Chapter IV]. A convex set M ⊂ X is called cone if λx ∈M for any x ∈M, λ ≥ 0. A cone M is called pointed if M∩ (−M)= {0}. Suppose that X is endowed with a locally convex topology τ, which is always assumed to be compatible with the duality 〈X ,Y〉, and K ⊂ X is a τ-closed pointed cone. An element ξ ∈ Y is called strictly positive if...

We report on the energetics of intercalation of lithium, sodium and potassium in graphite by density functional theory using recently developed van der Waals (vdW) density functionals. First stage intercalation compounds are well described by conventional functionals like GGA, but van der Waals functionals are crucial for higher stage intercalation compounds and graphite, where van der Waals in...

‎in this paper we study the existence of nontrivial‎ solutions for a variational inequality on the half-line‎. ‎our‎ ‎approach is based on the non-smooth critical point theory‎ ‎for szulkin-type functionals.

We study random convex cones defined as positive hulls of d-dimensional walks and bridges. compute expectations various geometric functionals these such the number k-dimensional faces sums conic quermassintegrals their faces. These are expressed in terms Stirling numbers both kinds B-analogues.

The paper aims at finding widely and smoothly defined nonparametric location and scatter functionals. As a convenient vehicle, maximum likelihood estimation of the location vector μ and scatter matrix Σ of an elliptically symmetric t distribution on R with degrees of freedom ν > 1 extends to an M-functional defined on all probability distributions P in a weakly open, weakly dense domain U . Her...