The generalized Killing equations for the configuration space of spinning particles (spinning space) are analysed. Solutions of these equations are expressed in terms of Killing-Yano tensors. In general the constants of motion can be seen as extensions of those from the scalar case or new ones depending on the Grassmann-valued spin variables. Spinning particles, such as Dirac fermions, can be d...

The adjacency algebra of an association scheme is defined over an arbitrary field. In general, it is always semisimple over a field of characteristic zero but not always semisimple over a field of positive characteristic. The structures of adjacency algebras over fields of positive characteristic have not been sufficiently studied. In this paper, we consider the structures of adjacency algebras...

In this paper, we propose a method for recognizing three-dimensional (3D) objects using multi-view depth images. To derive the essential 3D shape information extracted from these images for stable and accurate 3D object recognition, we need to consider how to integrate partial shapes of a 3D object. To address this issue, we introduce two ideas. The first idea is to represent a partial shape of...

This paper considers the quantization problem on the Grassmann manifold with dimension n and p. The unique contribution is the derivation of a closed-form formula for the volume of a metric ball in the Grassmann manifold when the radius is sufficiently small. This volume formula holds for Grassmann manifolds with arbitrary dimension n and p, while previous results are only valid for either p = ...

— We study subsets of Grassmann varieties G(l, m) over a field F , such that these subsets are unions of Schubert cycles, with respect to a fixed flag. We study such sets in detail, and give applications to coding theory, in particular for Grassmann codes. For l = 2 much is known about such Schubert unions with a maximal number of Fq-rational points for a given spanning dimension. We study the ...

There are nontrivial dualities and parallels between polynomial algebras and the Grassmann algebras. This paper is an attempt to look at the Grassmann algebras at the angle of the Jacobian conjecture for polynomial algebras (which is the question/conjecture about the Jacobian set – the set of all algebra endomorphisms of a polynomial algebra with the Jacobian 1 – the Jacobian conjecture claims ...