The ordinary type of information data for approximation of functions f or functionals of them in the univariate case consists of function values {f(x1), . . . , f(xm)}. The classical Lagrange interpolation formula and the Gauss quadrature formula are famous examples. The simplicity of the approximation rules, their universality, the elegancy of the proofs and the beauty of these classical resul...

In a companion paper, the authors obtained some Fubini type identities in law for quadratic functionals of Brownian motion, and, more generally, for certain functionals of symmetric stable processes, the function: x -* x2 then being replaced by: x e IxIa. In this paper, discrete analogues of such identities in law, which involve a sequence of independent standard symmetric stable r.v.'s of inde...

In this paper we study the lower semicontinuous envelope with respect to the L-topology of a class of isotropic functionals with linear growth defined on mappings from the n-dimensional ball into RN that are constrained to take values into a smooth submanifold Y of RN . Let B be the unit ball in R and Y a smooth Riemannian manifold of dimension M ≥ 1, isometrically embedded in R for some N ≥ 2....

We introduce equity forward variance term-structure models and derive the respective HJM-type arbitrage conditions. We then discuss finitedimensional Markovian representations of the infinite-dimensional fixed time-to-maturity forward variance swap curve and analyse examples of such variance curve functionals. The results are then applied to show that the speed of mean-reversion in standard sto...

In 1958 Gödel published his Dialectica interpretation, which reduces classical arithmetic to a quantifier-free theory T axiomatizing the primitive recursive functionals of finite type. Here we extend Gödel’s T to theories Pn of “predicative” functionals, which are defined using MartinLöf’s universes of transfinite types. We then extend Gödel’s interpretation to the theories of arithmetic induct...

Let (Ω,A, μ) be a σ-finite nonatomic measure space and let Λw,φ be the Orlicz-Lorentz space. We study the Gateaux differentiability of the functional Ψw,φ(f) = ∞ ∫ 0 φ(f∗)w. More precisely we give an exact characterization of those points in the Orlicz-Lorentz space Λw,φ where the Gateaux derivative exists. This paper extends known results already on Lorent spaces, Lw,q , 1 < q <∞. The case q =...

in this work, we dissect the performance of  two modern perdew-burke-ernzerhof (pbe)-based double-hybrid (dh) density functionals to predict the isotropic and anisotropic polarizabilities of water nanoclusters (h2o)n [n = 2-6]. the considered models include the cubic integrand (ci) and quadratic integrand (qi) functions as well as the spin-opposite-scaled (sos) scheme for perturbative correlati...