Showing papers by "Norbert Sauer published in 1977"
TL;DR: Chvátal as mentioned in this paper proved that if in a packing of translates of a square each square has at least six neighbours, then the density of the packing is at least 11/15.
Abstract: As a contribution to various investigations [1-11] about packing of convex bodies with certain conditions imposed on the number of neighbours of each body, V. Chvátal [12] recently proved the following theorem: If in a packing of translates of a square each square has at least six neighbours then the density of the packing is at least 11/15.
4 citations
TL;DR: In this article, it was shown that the unique solution to a system ζ of functional equations can be found in a semigroup of functions, provided that each function is endowed with a collection of finitary operations, such that each operation admits a homomorphism.
Abstract: A semigroup of functionsS υAA isalgebraic providedA can be endowed with some collection of (finitary) operations to produce an algebraU withS = EndU, the endomorphisms ofU. Thealgebraic closure ofS is\(\bar S\)=End,Us, whereUs is the algebra of all finitary operations which admit eachf σS as a homomorphism. Here we prove, for A finite, thatg σ\(\bar S\) iffg is the unique solution to a system ζ of functional equations each of the formfx=h orfx=y with, coefficientsf, h σS. For A infinite a similar local condition holds. Applications to related problems are given.
2 citations
TL;DR: The algebraic closure off as mentioned in this paper is the sum of all maps which admit algebraic operations on a set A which admit all powers off and certain other maps as well, and is defined in terms of algebraic closures.
Abstract: The algebraic operations on a set A which admit (as a homomorphism) a particular mapf∈AA, admit all powers off and certain other maps as well The algebraic closure off,\(\bar f\), is the totality of all maps which admit the algebraic operations thatf does The purpose of this paper is to characterize\(\bar f\) in terms off, both forA finite and forA infinite
2 citations