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Let [mu](x) be a monic polynomial over Z of least degree such that [mu]([theta]) [member of] P.

On the ring of integers of real cyclotomic fields

However, there is one special case which is amenable to solution for any value of n, namely the one in which all the coefficients equal zero except [a.sub.n] = 1 and [a.sub.0] = -1; then, the following reduced monic polynomial results:

Adding some perspective to de Moivre's theorem: visualising the n-th roots of unity

Then q(z) is a monic polynomial of degree m such that, by the Cayley-Hamilton theorem, q(T) = 0.

Cyclic convolution operators on the hardy spaces

Then every monic polynomial f(X) in R[X] of degree relatively prime to p has OA.

OPTIMAL APPROXIMATION IN HENSELIAN FIELDS

where [B.sup.+] is a monic polynomial whose zeros are stable and so well damped that they can be canceled by the controller and [B.sup.-] corresponds to the unstable or poorly damped factors that cannot be canceled.

Self tuning regulators for a liquid level process

This can be further processed to obtain the monic polynomial (9) and the non-null solutions (8).

A Novel Chaotic System for Random Pulse Generation

[alpha](s) is a monic polynomial of unknown coefficients, while [beta](s) is a monic polynomial of known coefficients that are determined by poles [[lambda].sub.1], [[lambda].sub.2], ..., [[lambda].sub.n-m]}.

Partial pole placement in LMI region

Since [c.sub.m](z) is arbitrary monic polynomial of degree [v.sub.m], the linear space V over R spanned by the rows of polynomial vector [a(z)-d(z)], consists of all polynomials [lambda](z) over R[z] with

Dynamics assignment by output feedback

Let [a.sup.n] (z) be a monic polynomial of degree n with real coefficients [a.sub.i] [member of] R, i = 0, ..., n - 1

Stability of discrete-time systems via polytopes of reflection vector sets/Diskreetaja susteemide stabiilsuspiirkonna lahendid peegeldusvektorite polutoopide kaudu