Zbigniew Walczak

A note on the convergence of Baskakov type operators

In the present paper, we estimate the rate of convergence on functions of polynomial type for some variant of the Baskakov operators. The form of the operator discussed in the present paper makes results helpful from the computational point of view.

Approximation theorems for a general class of truncated operators

Abstract In this paper we give direct approximation theorems for a general family of truncated operators. We discuss the linear and nonlinear cases.

Bending of five-layer beams with crosswise corrugated main core

The subject of the study is one orthotropic thin-walled sandwich beam with trapezoidal core and two-layer facings. The outer layers of facings are flat, but inner layers are trapezoidal corrugated. The main core of the beam is also trapezoidal corrugated – in perpendicular direction to the corrugation of inner layers of facings. The beam is with lengthwise corrugated layers and crosswise corrugated main core. The mathematical and physical model of this beam is formulated, and also the field of displacements. The system of equilibrium equations is analytically derived using the energy method. The obtained solutions will be verified numerically (FEM).

Some approximation theorems for a general class of discrete type operators in spaces with a polynomial weight

The paper is devoted approximation of real-valued functions defined on an unbounded interval by linear and non-linear operators. The publication pays special attention to defining class of operators and examining their certain approximation properties. The form of the class of operators given in the present paper makes the achieved results more helpful from the computational point of view.

Mathematical Modeling of Three-layer Circular Plate under Uniformly Distributed Load (Pressure)

The paper is devoted to a three-layer circular plate consisting of two facings and a core with variable mechanical properties. The simply supported plate is subjected to pressure. The mathematical model of the plate is formulated, in particular the field of displacements. The nonlinear hypothesis is proposed. Basing on the principle of the total potential energy the system of equilibrium equations is derived. Then the system is solved using the method of Bubnov-Galerkin. The maximal deflections, normal stresses and shear stresses are calculated.