A real n-dimensional homogeneous polynomial f (x) of degree m and a real constant c define an algebraic hypersurface S whose points satisfy f (x) = c. The polynomial f can be represented by Axm where A is a real mth order n-dimensional supersymmetric tensor. In this paper, we define rank, base index and eigenvalues for the polynomial f , the hypersurface S and the tensor A. The rank is a nonneg...

We discuss a simple parameter degeneracy in lens models which follows directly from the well known mass sheet degeneracy and prevents determining the radial mass distribution from lensing alone for many systems. For cosmological important systems like 1115+080 it is shown that no exact value of H0 can be determined without assuming a mass index β. 1. The mass sheet degeneracy The degeneracies e...

W e quantify the observation by Kender and Freudenstein [6] that degenerate views occupy a significant fraction of the viewing sphere surrounding an object. This demonstrates that systems for recognition must explicitly account f o r the possibility of view degeneracy. W e show that view degeneracy cannot be detected f rom a single camera viewpoint. As a result, systems designed to recognize ob...

A dynamic definition of a first-order phase transition is given. It is based on a master equation description of the time evolution of a system. When the operator generating that time evolution has an isolated near degeneracy there is a first-order phase transition. Conversely, when phenomena describable as first-order phase transitions occur in a system, the corresponding operator has near deg...

Interpolating diffusion tensor fields is a key technique to visualize the continuous behaviors of biological tissues such as nerves and muscle fibers. However, this has been still a challenging task due to the difficulty to handle possible degeneracy, which means the rotational inconsistency caused by degenerate points. This paper presents an approach to interpolating 3D diffusion tensors in 2D...