A new index is proposed for describing the degree of folding of a planar curve segment. Based on a basic concept from integral geometry, the Curve Folding Index (CFI) of a curve segment is defined to be the expected number of intersections that a random line has with the curve. The CFI provides a simple measure to characterize planar curves in terms of the degree of folding, and is shown to be ...

In this paper, we deal with the reverse isoperimetric inequality for a closed and strictly convex curve in the Euclidean plane R2 involving the following geometric functionals associated to the given convex curve: length, areas of the region respectively included by the curve and the locus of curvature centers, and the integral of the radius of curvature. In fact, a stronger and sharp version o...

We give an affirmative answer to a 1976 question of M. Rosen: every abelian group is isomorphic to the class group of an elliptic Dedekind domain R. We can choose R to be the integral closure of a PID in a separable quadratic field extension. In particular, this yields new and – we feel – simpler proofs of theorems of L. Claborn and C.R. Leedham-Green. Luther Claborn received his PhD from U. Mi...

This paper studies the discontinuity in the behavior of neighboring integral curves. Discontinuity is measured by a number of selected attributes of the integral curves. A variety of attribute fields are defined. The attribute value at any given spatio-temporal point in these fields is assigned the attribute of the integral curve that passes through this point. This encodes the global behavior ...

In this paper, we discuss some necessary and sufficient conditions for a curve to be arithmetically Cohen-Macaulay, in terms of its general hyperplane section. We obtain a characterization of the degree matrices that can occur for points in the plane that are the general plane section of a non arithmetically Cohen-Macaulay curve of P. We prove that almost all the degree matrices with positive s...

Motion trajectories provide a key and informative clue in motion characterization of humans, robots and moving objects. In this paper, we propose some new integral invariants for space motion trajectories, which benefit effective motion trajectory matching and recognition. Integral invariants are defined as the line integrals of a class of kernel functions along a motion trajectory. A robust es...