Showing papers in "Applications of Mathematics in 1980"
TL;DR: In this article, it was shown that the problem of finding a minimum $k$-basis, the $n$-center problem, and the $p$-median problem are NP-complete even in the case of such communication networks as planar graphs with maximum degree 3.
Abstract: It is shown that the problem of finding a minimum $k$-basis, the $n$-center problem, and the $p$-median problem are $NP$-complete even in the case of such communication networks as planar graphs with maximum degree 3. Moreover, a near optimal $m$-center problem is also $NP$-complete.
44 citations
TL;DR: An example of a finite set of projectors in $E_3$ for which no 0-1 measure exists can be found in this article, where the authors show how to construct a projector with no 0 -1 measure.
Abstract: An example of a finite set of projectors in $E_3$ is exhibited for which no 0-1 measure exists.
26 citations
TL;DR: In this article, the authors considered the problem of a unilateral contact between bounded bodies without friction within the range of two-dimensional linear elastostatics, and two classes of problems were distinguished: those with a bounded contact zone and with an enlargign contact zone.
Abstract: Problems of a unilateral contact between bounded bodies without friction are considered within the range of two-dimensional linear elastostatics. Two classes of problems are distinguished: those with a bounded contact zone and with an enlargign contact zone. Both classes can be formulated in terms of displacements by means of a variational inequality. The proofs of existence of a solution are presented and the uniqueness discussed.
24 citations
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TL;DR: In this article, an evolutionary variational inequalities and its applications to the traction boundary value problems of elastoplasticity are studied, using the penalty method to prove the existence of a solution.
Abstract: An abstract theory of evolutionary variational inequalities and its applications to the traction boundary value problems of elastoplasticity are studied, using the penalty method to prove the existence of a solution.
3 citations
TL;DR: In this paper, it is shown that in practice it is possible to work with a matrix of the system the bandwidth of which is reduced, and a simple numerical example illustrates the discussion.
Abstract: The matrix of the system of linear algebraic equations, arising in the application of the finite element method to one-dimensional problems, is a bandmatrix. In approximations of high order, the band is very wide but the elements situated far from the diagonal of the matrix are negligibly small as compared with the diagonal elements.
The aim of the paper is to show on a model problem that in practice it is possible to work with a matrix of the system the bandwidth of which is reduced. A simple numerical example illustates the discussion.