Applying Minkowski's theorem we infer the existence ofsome

extremal points [e.sub.1], ..., [e.sub.n] of the set A and [[lambda].sub.i] > 0, i = 1, ..., n, with [[summa].sup.n.sub.i=1] [[lambda].sub.i] = 1 such that

which implies that the curve of G([r.sub.+]) has the same distributions of the extremal points and inflexion points as that of [T.sub.H] ([r.sub.+]) (see Figure 5), apart from the extreme configuration with zero entropy.

In this case, the two points can be proven to be the only pair of extremal points of [T.sub.H] where the numerator of [T'.sub.H] vanishes.

The distances between the extremal points and the centroid indicate the extents to which the hands and legs are extended in motion.

The rate of change of distance is a measure of the speed with which the extremal points are moving.

SAFF, Potential and discrepancy estimates for weighted

extremal points, Constr.

(2) If an interpolatory quadrature formula exists, then is it necessarily based on the

extremal points for some discretized energy problem?

(1.1)) if, and only if, there exist r

extremal points [z.sub.1], [z.sub.2] ..., [z.sub.r] [member of] {z [member of] R : [absolute value of (f - g*)(z)] = [[parallel]f - g*[parallel].sub.R]} and positive numbers [[mu].sub.1], [[mu].sub.2], ..., [[mu].sub.r] [member of] [R.sub.+] (r [less than or equal to] 2n + 1 in the complex case and r [less than or equal to] n + 1 in the real case) such that