A geometric invariant of a space curve, the writhing number, is defined and studied. For the central curve of a twisted cord the writhing number measures the extent to which coiling of the central curve has relieved local twisting of the cord. This study originated in response to questions that arise in the study of supercoiled double-stranded DNA rings.

Managing large volume points clouds data generated from laser scanner is a challenging problem in Geographic Information System (GIS) and spatial database. Based on analyzing the pros and cons of the existing management methods, this paper presents a method to manage lidar data in databases based on the Hilbert space-filling curve. Each lidar data point (X, Y, and Z) is encoded (indexed) by the...

Reliable segmentation of actions performed by objects, is critical to the understanding of semantic content in a video. Deciding which portion of object motion sequence is a distinct action unit, however, is often d@@ult, even for humans. We seem to hierarchically compose actions By noting characteristic changes in the nature of motion. This paper present an action segmentation algorithm that m...

This paper extends the previous work of generating monotonic-rhythm log-aesthetic space curve segments so that compound-rhythm log-aesthetic space curve segments are interactively generated. A compound-rhythm log-aesthetic space curve segment is composed of two monotonic-rhythm log-aesthetic space curve segments whose logarithmic curvature and torsion graphs are represented by two connected lin...

We prove that if every hyperbolic group is residually finite, then every quasi-convex subgroup of every hyperbolic group is separable. The main tool is relatively hyperbolic Dehn filling.

We prove that Dehn filling a small link exterior with a non-degenerate boundary slope row produces a 3-manifold which is either Haken and ∂-irreducible or one of very restricted typies of reducible manifolds (Theorem 2), generalizing a result of Culler, Gordon, Luecke and Shalen in the case of a knot exterior (Theorem 1). The result provides some interesting applications on exceptional Dehn fil...

The main purpose of this paper is to show that ideas of deformation theory can be applied to “infinite dimensional geometry”. We develop the deformation theory of Brody curves. Brody curve is a kind of holomorphic map from the complex plane to the projective space. Since the complex plane is not compact, the parameter space of the deformation can be infinite dimensional. As an application we pr...