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 the context of adaptive nonparametric curve estimation a common assumption is that a function (signal) to estimate belongs to a nested family of functional classes. These classes are often parametrized by a quantity representing the smoothness of the signal. It has already been realized by many that the problem of estimating the smoothness is not sensible. What can then be inferred about the...

the basic type of assembly line balancing (alb) problem is the allocation of work elements to a set of production work stations considering cycle time, precedence constraints, and assembly diagram to achieve predefined performance criteria such as line efficiency and smoothness index. in this paper, a mixed integer programming model for solving multiple product alb problems with processing time...

Recently ([21]), a new meshfree approximation method for Darcy’s problem has been introduced and analyzed. This method is based on a symmetric collocation approach using radial basis functions producing solutions with an analytically divergence-free velocity part. However, the error analysis provided in [21] works only for smooth solutions, where the smoothness is intrinsically linked to the sm...