FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 1, PAGES 133-142

**On the lifetime of configurations in homogeneous structures**

A. S. Doumov

Abstract

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The paper deals with the relationship between
the lifetime of configurations and the number of states of
a cell in homogeneous structures.
For $K$_{V}(n), which is
a class of all homogeneous structures with $n$ states of
the cell and the neighbourhood $V$ that includes all the
vectors no longer than one, and $L$_{V}(x), which is
the reverse function for $xx|V|$, it has been established that the
number $n$~ L_{V}(D) of
states of the cell is necessary and sufficient in order that for any
positive integer $d$, $d$£
D, in the mentioned class of homogeneous
structures, a structure $S$ could be found in which
the lifetime of a certain one-cell configuration
equals $d$.

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Last modified: April 11, 2000