Generalized Zk-graded Grassmann variables are used to label coherent states related to the nilpotent representation of the q-oscillator of Biedenharn and Macfarlane when the deformation parameter is a root of unity. These states are then used to construct generalized Grassmann representatives of state vectors. Recently in [1] we have constructed coherent states for k-fermions using Kerner’s [2]...

Let V be an n-dimensional vector space (4 ≤ n < ∞) and let Gk(V ) be the Grassmannian formed by all k-dimensional subspaces of V . The corresponding Grassmann graph will be denoted by Γk(V ). We describe all isometric embeddings of Johnson graphs J (l,m), 1 < m < l − 1 in Γk(V ), 1 < k < n − 1 (Theorem 4). As a consequence, we get the following: the image of every isometric embedding of J (n, k...

This paper shows that the Grassmann Manifolds GF(n,N) can all be imbedded in an Euclidean space MF(N) naturally and the imbedding can be realized by the eigenfunctions of Laplacian △ on GF(n,N). They are all minimal submanifolds in some spheres of MF(N) respectively. Using these imbeddings, we construct some degenerate Morse functions on Grassmann Manifolds, show that the homology of the comple...

The present paper considers distributed consensus algorithms that involve N agents evolving on a connected compact homogeneous manifold. The agents track no external reference and communicate their relative state according to a communication graph. The consensus problem is formulated in terms of the extrema of a cost function. This leads to efficient gradient algorithms to synchronize (i.e. max...

Two distinct projections of finite rank m are adjacent if their difference is an operator two or, equivalently, the intersection images (m−1)-dimensional. We extend this adjacency relation on other conjugacy classes finite-rank self-adjoint operators which leads to a natural generalization Grassmann graphs. Let C be class formed by with eigenspaces dimension greater than 1. Under assumption tha...

Let V be an n-dimensional left vector space over a division ring R. We write Gk(V ) for the Grassmannian formed by k-dimensional subspaces of V and denote by Γk(V ) the associated Grassmann graph. Let also V ′ be an n′-dimensional left vector space over a division ring R′. Isometric embeddings of Γk(V ) in Γk′ (V ′) are classified in [13]. A classification of J(n, k)-subsets in Gk′ (V ′), i.e. ...

A short review on infinite-dimensional Grassmann-Banach algebras (IDGBA) is presented. Starting with the simplest IDGBA over K = R with l 1-norm (suggested by A. Rogers), we define a more general IDGBA over complete normed field K with l 1-norm and set of generators of arbitrary power. Any l 1-type IDGBA may be obtained by action of Grassmann-Banach functor of projective type on certain l 1-spa...

Image super-resolution remains an important research topic to overcome the limitations of physical acquisition systems, and to support the development of high resolution displays. Previous example-based super-resolution approaches mainly focus on analyzing the co-occurrence properties of lowresolution and high-resolution patches. Recently, we proposed a novel single image super-resolution appro...

In this paper,The concept of a (∈,∈ ∨q)-fuzzy ideal in an ordered Abel-Grassmann groupoid is introduced. In partcicular, left regular ordered Abel-Grassmann groupoids are characterized by using the (∈ ,∈ ∨q)-fuzzy ideals.