The main purpose of the paper is to study sharp estimates of approximation of periodic functions in the Hölder spaces H p for all 0 < p ≤ ∞ and 0 < α ≤ r. By using modifications of the classical moduli of smoothness, we give improvements of the direct and inverse theorems of approximation and prove the criteria for the precise order of decrease of the best approximation in these spaces. Moreove...

The paper presents upper estimates of the error of weighted and unweighted simultaneous approximation by the Bernstein operators and their iterated Boolean sums. The estimates are stated in terms of the Ditzian-Totik modulus of smoothness or appropriate K-functionals. AMS classification: 41A10, 41A17, 41A25, 41A28, 41A35, 41A36.

Interrelations between smoothness of a continuum at a point, pointwise smoothness, the property of Kelley at a point and local connectedness are studied in the paper.

PVC frame cutting process by guillotine is a common method that attracted attention of car parts and PVC decorating furniture producers. In this paper, the effects of main parameters such as cutting speed, lubricants and cutting frame holder pressure force on PVC frame section surface smoothness is investigated by experimental methods on a specified PVC frame sample and then by FEM simulation u...

The exterior sphere condition is compared to proximal smoothness, and examples are provided, which show that the two properties are not necessarily equivalent. Then conditions are given under which equivalence holds, and an open question involving the union of uniform closed balls property is stated in the form of a conjecture.

The purpose of this present paper is to give an equivalent theorem on Lupaş operators with ω φλ(f, t), where ω r φλ(f, t) is Ditzian-Totik modulus of smoothness for linear combination of Lupaş operators.

Surface smoothness of ceramic glazes is always an important characteristic of ceramic glazes as a point of surface engineering studies. Surface roughness affects chemical resistivity, glossiness and stainabiliy of glazes. In fact, less surface roughness improves cleanability of the surface by the least usage amount of detergents. In this investigation, surface topography of two common opaque gl...

We consider reheating after inflation with a non-standard kinetic term. We show that the difference in the kinetic term in different Hubble patches inherited from the long-wavelength moduli inhomogeneities may generate a significant level of non-Gaussianity after inflation.