Abstract In this paper, we prove the equivalence between a K-functional and modulus of smoothness generated by Laguerre-Bessel operator on

Many exchange-correlation functionals of the generalized gradient approximation GGA are available in the literature. More particularly, during the last few years several research groups have proposed GGA functionals for solids, which very often perform better especially for the lattice constant than the standard GGA functional of Perdew, Burke, and Ernzerhof PBE J. P. Perdew, K. Burke, and M. E...

We discuss the difficulties of estimating quadratic functionals based on observations Y (t) from the white noise model Y (t) = Jf (u )du + cr W (t), t E [0,1], o where W (t) is a standard Wiener process on [0, 1]. The optimal rates of convergence (as cr -> 0) for estimating quadratic functionals under certain geometric constraints are 1 found. Specially, the optimal rates of estimating J[f (k)(...

The problem of optimal estimation of the linear functionals Aξ = ∑∞ k=0 a(k)ξ(k) and AN ξ = ∑N k=0 a(k)ξ(k) which depend on the unknown values of a stochastic sequence ξ(m) with stationary nth increments is considered. Estimates are obtained which are based on observations of the sequence ξ(m) + η(m) at points of time m = −1,−2, . . ., where the sequence η(m) is stationary and uncorrelated with...

We prove a homogenization theorem for non-convex functionals depending on vector-valued functions, defined on Sobolev spaces with respect to oscillating measures. The proof combines the use of the localization methods of Γ-convergence with a ‘discretization’ argument, which allows to link the oscillating energies to functionals defined on a single Lebesgue space, and to state the hypothesis of ...

exists and can be expressed in terms of K and K ′. The functionals F under consideration are derived from the mixed volume or the mixed area measure functional. Analogous questions are treated for the motion group instead of the translation group. The resulting relations can be regarded as dual counterparts to various versions of the principal kinematic formula. Motivation for our investigation...