1) is not completely integrable (nonholonomic system), then for any point a G D does exist some integral curves at a only and it is possible that integral manifolds of maximum dimension do not exist at certain points.

The idea to consider constrained extremals by a family of integral curves of a Pfaff system allows to approach the problem of convexity for a nonholonomic hypersurface using a method similar to those in [section][section]4.

All the integral curves passing through the point a are contained in the same "level set" F (x) = F (a).

Key words: roughnes of the cut surface, differential equation, integral curves

The mathematical description of the dependency of the maximum roughness of the cut surface of the feed is possible formulated with the diferential equation and integral curves.

Paper topics include studies of a singularly perturbed Riccati equation, asymptotic differential algebra, non- oscillating

integral curves and o-minimal structures, topological construction of transseries and an introduction of generalized Borel summability, higher-order norms for the Moivre-Laplace theorem, matching the similarities of canard values, and generalizing surreal numbers.

These maxima correspond to the plateaux on the

integral curves of strength distribution (Fig.

From this theorem it follows that the notions of extremum constrained by integral manifolds and extremum constrained by integral curves are equivalent.

XQ] be the union of all integral curves at of the Pfaff system (*).

j] the derivatives are continuous functions on the domain D for every j [member of] {1,2}, than the one and only one

integral curves [?

1) is referred to as a phase trajectory, and (y([lambda]), [lambda]) as an integral curve.

Thus, in the PC homotopy continuation framework, this integral curve (y([lambda]), [lambda]) is the path determined by the homotopy