Approximation Functionals and Their Application

The purpose of this work is to obtain local estimates, and to calculate the constants of approximation of smooth functions. To achieve this goal, the trajectory of functionals, the concept of an approximation families of functionals, the tape of the trajectory of functionals and the width of the tape are considered. For this, the concepts of approximation functionals and their trajectories in the conjugate space are introduced, and the concepts of the trajectory tape and the tape width at a given point are discussed. The resulting overall evaluation of the approximation is applied to multidimensional cases, namely, to approximations by the Courant and Zlamal elements.

Arens simultaneously factorization

Let X be a Banach bimodule over a Banach algebra 𝒜. We shall seek conditions under which (1) X and its dual factorize on the same side or (2) X factors on the left (or right) if and only if its second conjugate space has a left (or right) unit.

Geometric Modeling for Five-Axis CNC Machining of Mold Surface with Flat-End Tool

This paper taken the flat-end tool and machined surface as a pair of mutually conjugate space contact tooth envelope surface and used the Frenet frame of differential geometry to describe the NC machining tool path in five-axis CNC machining of mold surface with flat-end tool. Thus the geometric model in five-axis CNC machining of mold surface with flat-end tool was established.