We call the function / described in the theorem a coprime mapping. Theorem 1 settles in the affirmative a conjecture of D. J. Newman. The special case when / = {JV + l.JV + 2, ...,2Af} was proved by D. E. Daykin and M. J. Baines [2]. V. Chvatal [1] established Newman's conjecture for each JV ^ 1002. We prove Theorem 1 constructively by giving an algorithm for the construction of a coprime mappi...

This report discusses ltering and parametrization issues involved in the usage of fractional representations in multivariable, approximate and feedback relevant identi-cation of a possibly unstable plant operating under closed loop conditions. It will be shown that the access to any stable right coprime factorization of the plant can be gained by employing the knowledge of the controller and to...

A numerically reliable state space algorithm is proposed for computing normalized coprime factorizations of periodic descriptor systems. A preprocessing step is used in the algorithm to convert the initial problem for possibly non-causal systems into a simpler problem for causal periodic systems. The main computational ingredient here is the computation of a coprime factorization with causal fa...

Listings Sparse and Coprime Sampling: Benefits, Challenges and Future Directions Piya Pal University of Maryland, College Park 2305 A V Williams University of Maryland College Park MD 20742 [email protected] Coprime and nested sampling have been recently introduced as powerful sparse deterministic sampling techniques that can exploit statistical properties of signals to sample them at rates sign...

This note establishes a result linking algebraically coprime factorizations of transfer matrices of delay systems to approximately coprime factorizations in the sense of distributions. The latter have been employed by the second author in the study of function-space controllability for such systems.

A multivariable model reference adaptive control system (MRACS) design method for a plant with m inputs and p outputs is proposed (m # p). Using an interactor matrix the coprime factorization of the plant for (1) m > p case, and (2) m < p case is derived. Further, using this coprime factorization the structure of MRACS is established.

We show, if p is prime, that the equation xn + yn = 2pz2 has no solutions in coprime integers x and y with |xy| ≥ 1 and n > p132p , and, if p 6= 7, the equation xn + yn = pz2 has no solutions in coprime integers x and y with |xy| ≥ 1 and n > p12p .

In this paper we consider MISO fractional systems with delays that are given by their transfer function. For a large class of such systems, we determine left coprime factorizations as well as associated Bézout factors, and guarantee the existence of right coprime factorizations.