Fusion frames are valuable generalizations of discrete frames. Most concepts of fusion frames are shared by discrete frames. However, the dual setting is so complicated. In particular, unlike discrete frames, two fusion frames are not dual of each other in general. In this paper, we investigate the structure of the duals of fusion frames and discuss the relation between the duals of fusion fram...

We consider the space FE k,n of all spherical tight frames of k vectors in the n–dimensional Hilbert space E (k > n), for E = R or E = C, and its orbit space GE k,n = FE k,n/O n under the obvious action of the group OE n of structure preserving transformations of E. We show that the quotient map FE k,n → GE k,n is a locally trivial fiber bundle (also in the more general case of ellipsoidal tigh...

A classification of self-dual ZZk-codes of modest lengths is known for small k. For k = 4, 6, 8, 9 and 10, the classification of self-dual ZZk-codes is extended to lengths 19, 12, 12, 12 and 10, respectively, by considering k-frames of unimodular lattices.

A Stiefel manifold VkR n is the set of orthonormal k-frames inR, and it is diffeomorphic to the homogeneous space SO(n)/SO(n−k). We study SO(n)-invariant Einstein metrics on this space. We determine when the standard metric on SO(n)/SO(n−k) is Einstein, and we give an explicit solution to the Einstein equation for the space V2R.

In this article, we consider pair frames in Banach spaces and   introduce Banach pair frames. Some various concepts in the frame theory such as frames, Schauder frames, Banach frames and atomic decompositions are considered as   special kinds of (Banach) pair frames.  Some frame-like inequalities  for (Banach)  pair frames are presented. The elements that participant  in the construction of (Ba...

We apply the holographic principle to the Brans-Dicke cosmology. We analyze the holographic bound in both the Jordan and Einstein frames. The holographic bound is satisfied for both the k = 0 and k = −1 universe, but it is violated for the k = 1 matter dominated universe. 04.50.+h, 98.80.Hw Typeset using REVTEX 1

A necessary condition for existence of a (v, k, k−1) near resolvable BIBD is v ≡ 1 (mod k). In this paper, we update earlier known existence results when k ∈ {9, 12, 16}, and show this necessary condition is sufficient, except possibly for 26, 37 and 149 values of v for k = 9, 12, 16 respectively. Some new results for existence of (9, 8)-frames of type 9 are also obtained; in particular, we sho...

In this paper we introduce generalized Darboux frame of a spacelike curve $\alpha$ lying on lightlike surface in Minkowski space $\mathbb{E}_{1}^{3}$. We prove that has two such frames and obtain frame's equations. find the relations between curvature functions $k_g$, $k_n$, $\tau_g$ with respect to its $\tilde{k}_{g}$, $\tilde{k}_{n}$, $\tilde{\tau}_{g}$ frames. show exist along straight line ...