We provide an enhancement of Shipley's algebraicization theorem which behaves better in the context commutative algebras. This involves defining flat model structures as Shipley and Pavlov-Scholbach, showing that functors still Quillen equivalences this refined context. The use allows one to identify algebraic counterparts change groups functors, demonstrated forthcoming work author.

The study of matrix inequalities in a dimension-free setting is in the realm of free real algebraic geometry (RAG). In this paper we investigate constrained trace and eigenvalue optimization of noncommutative polynomials. We present Lasserre’s relaxation scheme for trace optimization based on semidefinite programming (SDP) and demonstrate its convergence properties. Finite convergence of this r...

In this paper, we introduce the concept of x-maximal flatness. A control system is x-maximally flat if the number of new states gained by each successive derivation of the flat output is the largest possible. Firstly, we show that the only control-linear systems that are xmaximally flat are those that are static feedback equivalent to the m-chained form. Secondly, we generalize that result from...