A Riemannian metric g is said to be associated with a contact manifold if there exist a (1, 1) tensor ield [phi] and a contravariant global vector field [xi], called the
characteristic vector field of the manifold such that
The projection of eigenvector [u.sup.i] is the largest on X, so when the
characteristic vector of X is the largest, it makes tr([S.sub.x]) the maximum value.
Hence, the input
characteristic vector for PNN is [[[sigma].sub.[theta]], [[sigma].sub.c], [[sigma].sub.t], [W.sub.et]].
According to the matrix theory, we can judgment that the weight coefficient of each factor is the
characteristic vector w of the judgment matrix.
(3) A warped product space R x [sub.[lambda]][C.sup.n] if k([??], X) < 0; where k([??], X) denotes the sectional curvature of the plane section containing the
characteristic vector field [??] and an arbitrary vector field X.
Every time, t, in which a j state is input, a
characteristic vector [o.sub.t] is generated, according to the probability density [b.sub.j]([o.sub.t]).
According to the
characteristic vector H = [[H.sub.c], [H.sub.t]] extracted in part 2, the
Clearly the set X = {v: [phi]'(v) = k + 1} is independent in G (since 0 [member of] t(e) for all e [member of] E) and therefore its
characteristic vector p belongs to P.