Often to detect the behavior in a small neighborhood of the equilibrium, instead of the Hamiltonian H one considers the

normal form truncated to some order

Now, by setting [K.sub.kl], k + l = 2, ..., 2[n.sub.r] + 1 equal to zero we define the coefficients [h.sup.kl] of transformation (B.1), while the rest of the resonant terms of the odd order, [c.sub.i] = [K.sub.i+1,i], i = 1, ..., [n.sub.r], constitute the desirable

normal form of (29).

be the Smith

normal form of matrix A, where U [member of] GL(m, R) and V [member of] GL(n, R).

The classification of the student answer (

normal form) in the form of waterfall model.

Proposition 1 There exists an algorithm that, given a sword [sigma] of height h, returns a

normal form of [sigma].

In Section 3, by using an extended method of multiple scales, we obtained the

normal form of the Hopf bifurcation.

The

normal form method and the center manifold theory are used to analyze the double Hopf bifurcation for system.

Previous studies showed that the

normal form of the protein is an enzyme that maintains the structure and integrity of a person's DNA.

Jandad Spinghar, the Election Watch Afghanistan's (EWA) chief, said the electoral process was not in its

normal form that's why initial results had to be delayed.

A

normal form could be printed for ` 200, the committee held.

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are homogeneous polynomials of degree j in [??] and [epsilon], after dropping the hats for simplification of notations, system (42) can be put into the

normal formIn this subsection, we will determine the direction and stability of Hopf bifurcations by calculating explicitly the

normal form of system (2) on the associated two-dimensional (2D) center manifold.