BAUER, On certain methods for expanding the

characteristic polynomial, Numer.

To study the damping properties of EMS on the basis of the structural circuit, the transfer functions are obtained for the control and disturbing actions, of which, as in the source [10], the

characteristic polynomial (CP) is used:

We give a conjecture about the growth rate of M([[??].sup.[infinity].sub.n]), and the growth rates (maximal roots of the

characteristic polynomial [D.sub.n]([lambda])) are computed using the softwares Drive6 and Mathematica.

Then the dynamic model of the spindle is established and the

characteristic polynomial is obtained.

According to the Schur-Cohn stability criterion [12], when all the eigenvalues of the

characteristic polynomial corresponding to the Jacobian matrix (10) are in the unit circle on the complex plane, that is, the modulus of any eigenvalue is less than 1, the equilibrium point ([x.sub.1], [x.sub.2], [I.sub.1], [I.sub.2]) is asymptotically stable.

Let [psi](A(G);x) = det(x[I.sub.n] - A(g)), or simply [psi](A(G)) ([psi](L(G)) and [psi](Q(G)), resp.), be the adjacency (Laplacian and signless Laplacian, resp.)

characteristic polynomial of G and its roots be the adjacency (Laplacian and signless Laplacian, resp.) eigenvalues of G, denoted by [[lambda].sub.1] (G) [greater than or equal to] [[lambda].sub.2](G) [greater than or equal to] ...

A final section describes physical visualizations of eigenvectors--for mirror reflections, rotations, row reductions, and circulant matrices--before turning to the issue of their calculation through the

characteristic polynomial. ([umlaut] Ringgold, Inc., Portland, OR)

The

characteristic polynomial of G is a polynomial of degree n , defined as (G, ) = det (In Eqs.

Then [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the

characteristic polynomial which determines the recurrence relation that [h.sub.m](n) satisfies.

Then [[chi].sub.m](t) = [t.sup.dm] [q.sub.m](1/t) is the

characteristic polynomial which determines the recurrence relation that [h.sub.m](n) satisfies.

Thus, the closed loop

characteristic polynomial is (for simplicity, the operator [q.sup.-1] is omitted)