in hilbert space l2(rn), we prove the equivalence between the mod-ulus of smoothness and the k-functionals constructed by the sobolev space cor-responding to the fourier transform. for this purpose, using a spherical meanoperator.

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...

In Hilbert space L2(Rn), we prove the equivalence between the mod-ulus of smoothness and the K-functionals constructed by the Sobolev space cor-responding to the Fourier transform. For this purpose, Using a spherical meanoperator.

 ‎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.

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...

A general scheme for systematically modeling long-range corrected (LC) hybrid density functionals is proposed. Our resulting two LC hybrid functionals are shown to be accurate in thermochemistry, kinetics, and noncovalent interactions, when compared with common hybrid density functionals. The qualitative failures of the commonly used hybrid density functionals in some "difficult problems," such...

‎We extend the notion of approximately multiplicative to approximately n-multiplicative maps between locally multiplicatively convex algebras and study some properties of these maps‎. ‎‎W‎e prove that every approximately n-multiplicative linear functional on a functionally continuous locally multiplicatively convex algebra is continuous‎. ‎We also study the relationship between approximately mu...

We define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital Banach algebra A and show that the δ-approximate spectrum σ_δ (a) of a is compact. The relation between the δ-approximate spectrum and the usual spectrum is investigated. Also an analogue of the classical Gleason-Kahane-Zelazko theorem is established: For each ε>0, there is δ>0 such that if ϕ is...

We introduce the notion of bilinear moment functional and study their general properties. The analogue of Favard’s theorem for moment functionals is proven. The notion of semiclassical bilinear functionals is introduced as a generalization of the corresponding notion for moment functionals and motivated by the applications to multi-matrix random models. Integral representations of such function...

We define notions of resource-bounded continuity and sequentiality for type-two functionals with total inputs, and prove that there are continuous functionals which cannot be efficiently simulated by sequential functionals. We also show that for some naturally-defined classes of continuous functionals, an efficient simulation is possible.