We study the first order theory of Bezout difference rings. In particular we show that rings of sequences very rarely have decidable theories as difference rings, or even decidable model completions. MSC: 03C60, 03B25, 12H10, 13L05

In this paper, we show that recovery of a function from its averages over squares in the plane is closely related to a problem of recovery of bandlimited functions from samples on unions of regular lattices. We use this observation to construct explicit solutions to the Bezout equation which can be easily implemented in software. We also show that these sampling results give a new proof of the ...

— Let N and D be two matrices over the algebra H∞ of bounded analytic functions in the disk, or its real counterpart H∞ R . Suppose that N and D have the same number n of columns. In a generalisation of the notion of topological stable rank 2, it is shown that N and D can be approximated (in the operator norm) by two matrices e N and e D, so that the Aryabhatta-Bezout equation X e N + Y e D = I...

This paper shows that if one designs an LQG system by combining the reduced order controlcontroller using the conventional technique of loop transfer ler and the high order therefore, it is quite recovery (LTR), then two frequency weighted controller reduction methods, the Enns' frequency weighted balanced that in truncation (Enns, 1984a, Ph.D. Thesis, Stanford University, problems, one should ...