We have computed the entropy of liquid water using a two-phase thermodynamic model and trajectories generated by ab initio molecular dynamics simulations. We present the results obtained with semilocal, hybrid, and van der Waals density functionals. We show that in all cases, at the experimental equilibrium density and at temperatures in the vicinity of 300 K, the computed entropies are underes...

Using a coupling argument, we establish a general weak law of large numbers for functionals of binomial point processes in d-dimensional space, with a limit that depends explicitly on the (possibly non-uniform) density of the point process. The general result is applied to the minimal spanning tree, the k-nearest neighbors graph, the Voronoi graph, and the sphere of influence graph. Functionals...

Let *3* be the algebra of polynomials in one indeterminate x over the complex field C. Suppose || • || is a norm on 9 such that the coefficient functionals c,: X a.oc' —* a, (j = 0,1,2, • • •) are all continuous with respect to || • ||, and let K CC be the set of characters on 9> which are || • ||-continuous. Then K is compact, C\K is connected, and 0 G K. Let A be the completion of 9 with resp...

the existence of infinitely many solutions is established for a class of nonlinear functionals involving the p-biharmonic operator with nonhomoge- neous neumann boundary conditions. using a recent critical-point theorem for nonsmooth functionals and under appropriate behavior of the nonlinear term and nonhomogeneous neumann boundary conditions, we obtain the result.

The existence of infinitely many solutions for an anisotropic discrete non-linear problem with variable exponent according to p(k)–Laplacian operator with Dirichlet boundary value condition, under appropriate behaviors of the non-linear term, is investigated. The technical approach is based on a local minimum theorem for differentiable functionals due to Ricceri. We point out a theorem as a spe...

This paper deals with the quantitative normal approximation of non-linear functionals of Poisson random measures, where the quality is measured by the Kolmogorov distance. Combining Stein’s method with the Malliavin calculus of variations on the Poisson space, we derive a bound, which is strictly smaller than what is available in the literature. This is applied to sequences of multiple integral...

We prove the following result: there is a family R = ⟨ 0 , 1 … ⟩ of subsets ω such that for every stable coloring c : [ ] 2 → k hyperarithmetical in and finite collection Turing functionals, an infinite homogeneous set H none finitely many functionals map ⊕ to cohesive R. This provides partial answer question computable combinatorics, whether COH omnisciently computably reducible SRT .

Plan: 0. Introduction and Notation. 1. Preliminaries. 2. A logarithmic characterization of C∗-algebras with WEP. 3. Pusz/Woronowicz’ formula and the operator space OH. 4. The projection constant of the operator space OHn. 5. Norm calculations in a quotient space. 6. K-functionals associated to a states and conditional expectations. 7. Sums of free mean zero variables. 8. Appendix: Concrete real...