ISOTROPIC MATERIALS WHOSE DEFORMATION AND DISTORTION ENERGIES ARE EXPRESSIBLE BY SCALAR INVARIANTS

New Topological Invariants Expressible as Tensors.

Knot Energies and Knot Invariants

To record what has happened, ancient people tie knots. | I ching, the Chinese classic of 1027{771 B.C. Knots are fascinating objects. When fastening a rope, the distinction between a knot and a \slip-knot" (one that can be undone by pulling) must have been recognized very early in human history. We even developed a subconscious about knots: When we are puzzled or troubled, we have a feeling of ...

Modules whose direct summands are FI-extending

‎A module $M$ is called FI-extending if every fully invariant submodule of $M$ is essential in a direct summand of $M$‎. ‎It is not known whether a direct summand of an FI-extending module is also FI-extending‎. ‎In this study‎, ‎it is given some answers to the question that under what conditions a direct summand of an FI-extending module is an FI-extending module?

Spacetimes characterized by their scalar curvature invariants

In this paper we determine the class of four-dimensional Lorentzian manifolds that can be completely characterized by the scalar polynomial curvature invariants constructed from the Riemann tensor and its covariant derivatives. We introduce the notion of an I-non-degenerate spacetime metric, which implies that the spacetime metric is locally determined by its curvature invariants. By determinin...

Rectifying Perspective Distortion into Affine Distortion Using Variants and Invariants

For user convenience, document image processing captured with a digital camera instead of a scanner has been researched. However, existing methods of document image processing are not usable for a perspective document image captured by a digital camera because most of them are designed for the one captured by a scanner. Thus, we have to rectify the perspective of the document image and obtain t...