Fusion frame theory is an emerging mathematical theory that provides a natural framework for performing hierarchical data processing. A fusion frame is a frame-like collection of subspaces in a Hilbert space, thereby generalizing the concept of a frame for signal representation. In this paper, we study the existence and construction of fusion frames. We first present a complete characterization...

A group divisible design is resolvable if there exists a partition n = {P,, Pz, . .} of p such that each part Pi is itself a partition of X. In this paper we investigate the existence of resolvable group divisible designs with K = {3}, M a singleton set, and all A. The case where M = { 1) has been solved by Ray-Chaudhuri and Wilson for I = 1, and by Hanani for all h > 1. The case where M is a s...

If an operator t transforms a group G into itself without being commutative with each operator of G, and if t2 is commutative with each operator of G, then t is said to transform the operators of G according to an automorphism of order two. Moreover, every automorphism of G which is of order 2 may be obtained by transforming G by operators having the given properties of t.f Let s be any operato...

This study examines the acoustic correlates of the singleton and geminate consonants in Tripolitanian Libyan Arabic (TLA). Several measurements were obtained including target segment duration, preceding vowel duration, RMS amplitude for the singleton and geminate consonants, and F1, F2 and F3 for the target consonants. The results confirm that the primary acoustic correlate that distinguishes s...

In this paper, we describe a procedure for constructing q– ary [N, 3, N−2]–MDS codes, of length N ≤ q+1 (for q odd) or N ≤ q+2 (for q even), using a set of non–degenerate Hermitian forms in PG(2, q).

A new class of full diversity space-time codes is proposed that leads to a significantly smaller Peak-to-Mean Envelope Power Ratio (PMEPR) compared to the recently invented Diagonal Algebraic SpaceTime (DAST) and Threaded Algebraic Space-Time (TAST) codes. Moreover, the proposed “Low PMEPR Space-Time” (LPST) codes exhibit identical performance and decoding complexity compared to the TAST codes....

Given a real and invertible d×d matrix C, we define for k ∈ Zd a generalized translation operator TCk acting on f ∈ L 2(Rd) by (TCkf)(x) = f(x − Ck), x ∈ R . A generalized shift-invariant system is a system of the type {TCjkφj}j∈J,k∈Zd , where {Cj}j∈J is a countable collection of real invertible d×d matrices, and {φj}j∈J ⊂ L 2(Rd). Generalized shift-invariant systems contain the classical wavel...

OBJECTIVE We compared the performance of the 50-g glucose challenge test (GCT) in singleton versus twin pregnancies and investigated the need for adjusting GCT cutoff values for gestational diabetes mellitus (GDM) in twin pregnancies among Korean women. METHODS A retrospective chart review was performed in women who underwent GCT at 24 to 28 weeks' gestation and delivered in our department be...

Fusion frames, and, more generally, operator-valued frame sequences are generalizations of classical frames, which are today a standard notion when redundant, yet stable sequences are required. However, the question of stability of duals with respect to perturbations has not been satisfactorily answered. In this paper, we quantitatively measure this stability by considering the associated devia...