We prove an asymptotic analog of the classical Hurewicz theorem on mappings that lower dimension. This theorem allows us to find sharp upper bound estimates for the asymptotic dimension of groups acting on finitedimensional metric spaces and allows us to prove a useful extension theorem for asymptotic dimension. As applications we find upper bound estimates for the asymptotic dimension of nilpo...

In rewriting theory, termination of a rewrite system by Kruskal's theorem implies a theoretical upper bound on the complexity of the system. This bound is, however, far from having been reached by known examples of rewrite systems. All known orderings used to establish termination by Kruskal's theorem yield a multiply recursive bound. Furthermore, the study of the order types of such orderings ...

For a non-autonomous dynamics with discrete time defined by tempered sequence of upper-triangular matrices, we obtain lower and upper bounds for the Grobman regularity coefficients. We also give two applications these results: an bound coefficients exterior powers sequence, simple proof Oseledets' multiplicative ergodic theorem cocycles over measure-preserving transformation without using Kingm...

The discontinuous slip-line form of upper bound plasticity analysis is considered using an equilibrium forces approach. It demonstrated that the underlying basis approach can be written in terms stress functions provide a continuum state interpretation solution. An alternative proof theorem, applicable to both associative and non-associative materials, presented. broader nature strict condition...