Showing papers in "Applications of Mathematics in 1970"

Conformal mapping of the halfplane onto a strip with variable width

Abstract: By using Schwarz-Christoffel theorem the author deduces the conformal mapping of a halfplane onto an infinitely long strip whose one boundary id a straight line while the other one is a polygonal line consisting of two half lines parallel to the first boundary and connected by a segment whose slope angle is a fractional multiple of $\pi$. This mapping is expressed by means of elementary functions distinguishing the cases when $\pi$ is divided by odd or even integer; some important properties of this mapping are shown.

Solution of linear algebraic equations with 3-diagonal ill-conditioned system matrix

Abstract: Certain methods for the solution of system of linear algebraic equations with ill-conditioned system matrix are compared with the Gaussian method. The considered methods were modified for 3-diagonal systems.

Torsion of a composite beam of rectangular cross-section consisting of $n$ isotropic media with interfaces parallel to one of the sides

Abstract: In this paper the torsion problem of a composite beam of rectangular cross-section composed of $n$ different isotropic media with interfaces parallel to one side is solved adopting a procedure based on the use of Green's function for a composite body and Fourier sine transform. An example of a composite beam formed of three media is considered and dependence of the position of occurrence of maximum stress on the ration of rigidity moduli is observed.