A holey perfect Mendelsohn design of type h n 1 1 h n 2 2 h n k k (HPMD(h n 1 1 h n 2 2 h n k k) with block size four is equivalent to a frame idempotent quasigroup satisfying Stein's third law with the same type, where a frame quasigroup of type h n 1

Let H be a Hilbert space. Given a bounded positive definite operator S on H, and a bounded sequence c = {ck}k∈N of non negative real numbers, the pair (S, c) is frame admissible, if there exists a frame {fk}k∈N on H with frame operator S, such that ‖fk‖ 2 = ck, k ∈ N. We relate the existence of such frames with the Schur-Horn theorem of majorization, and give a reformulation of the extended ver...

$K$-frames as a generalization of frames were introduced by L. Gu{a}vruc{t}a to study atomic systems on Hilbert spaces which allows, in a stable way, to reconstruct elements from the range of the bounded linear operator $K$ in a Hilbert space. Recently some generalizations of this concept are introduced and some of its difference with ordinary frames are studied. In this paper, we give a new ge...

$K$-frames which are generalization of frames on Hilbert spaces‎, ‎were introduced‎ ‎to study atomic systems with respect to a bounded linear operator‎. ‎In this paper‎, ‎$*$-$K$-frames on Hilbert $C^*$-modules‎, ‎as a generalization of $K$-frames‎, ‎are introduced and some of their properties are obtained‎. ‎Then some relations‎ ‎between $*$-$K$-frames and $*$-atomic systems with respect to a...

this paper is a continuation of [uniformities and covering properties for partial frames (i)], in which we make use of the notion of a partial frame, which is a meet-semilattice in which certain designated subsets are required to have joins, and finite meets distribute over these. after presenting there our axiomatization of partial frames, which we call $sels$-frames, we added structure, in th...

In this paper, we propose a video summarization algorithm by multiple extractions of key frames in each shot. This algorithm is based on the k partition algorithms. We choose the ones based on k-medoid clustering methods so as to find the best representative object for each partitions. In order to find the number of partition (i.e. the number of representative frames of each shot), we introduce...

In this paper, we introduce the concepts of $ast$-K-g-Frames in Hilbert $mathcal{A}$-modules and we establish some results.

The K correction “corrects” for the fact that sources observed at different redshifts are, in general, compared with standards or each other at different rest-frame wavelengths. It is part of the relation between the emittedor rest-frame absolute magnitude of a source in one broad photometric bandpass to the observed-frame apparent magnitude of the same source in another broad bandpass. This sh...

The multipeg Towers of Hanoi problem consists of k pegs mounted on a board together with n disks of different sizes. Initially these disks are placed on one peg in the order of their size, with the largest at the bottom. The rules of the problem allow disks to be moved one at a time from one peg to another as long as a disk is never placed on top of a smaller disk. The goal of the problem is to...