Indirect encoding of the genes of a

closed curve for interactively create innovative car silhouettes.

The s-v phase diagram is made up by many

closed curves combining with Poincaree section, and it can be indicated that the response of pipe wall is the quasiperiodic motion.

A borderline

closed curve of any figure at the plane consists of either three or four kinds of colored points.

alpha]] is a simple, smooth

closed curve, symmetric with respect to the real axis, starlike with respect to z = 0, which passes through [z.

2] = [partial derivative]B contains a

closed curve which is invariant under the antipodal map, then the Euler characteristic of M is odd.

20 A space is said to be simply connected if every

closed curve in the space may be contracted to a point without leaving the space.

i] does not contain a simple

closed curve and (3) [F.

n] curve, thereby producing the following

closed curve [[?

Quite naturally, all counterparts of a

closed curve are interpreted by any assignment on the same set.

John showed that a finite-length

closed curve in the plane can be made convex in a continuous manner, and without bringing any two points of the curve closer together.

Our methods introduce circular and spherical images of parametric curves and surfaces, leading to results on the tangential degree of a

closed curve in the plane, and the Hopf Theorem on the normal degree of a surface in three-space.

To a topologist, a knot in a formal sense is any simple

closed curve embedded in a three-dimenstional space.