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, an equation of state has been utilized for thermodynamic modeling of aqueous electrolyte solutions. The proposed equation of state is a combination of simplified statistical associating fluid theory (SAFT) equation of state (similar to simplified PC-SAFT) to describe the effect of short-range interactions and mean spherical approximation (MSA) term to describe the effect of long-r...

In this paper we establish a multiscale approximation for random fields on the sphere using spherical needlets — a class of spherical wavelets. We prove that the semidiscrete needlet decomposition converges in mean and pointwise senses for weakly isotropic random fields on Sd, d ≥ 2. For numerical implementation, we construct a fully discrete needlet approximation of a smooth 2-weakly isotropic...