Let p > 7 be a prime, let G = Z/pZ, and let S1 = ∏p i=1 gi and S2 = ∏p i=1 hi be two sequences with terms from G. Suppose that the maximum multiplicity of a term from either S1 or S2 is at most 2p+1 5 . Then we show that, for each g ∈ G, there exists a permutation σ of 1, 2, . . . , p such that g = ∑p i=1(gi · hσ(i)). The question is related to a conjecture of A. Bialostocki concerning weighted...

If G is a finite Abelian group, let MZS(G, k) denote the set of minimal zero sequences of G of length k. In this paper we investigate the structure of the elements of this set, and the cardinality of the set itself. We do this for the class of groups G = Zn for k both small (k ≤ 4) and large (k > 2n 3 ).

Let Cn be the cyclic group of n elements, and let S = (a1, · · · , ak) be a sequence of elements in Cn. We say that S is a zero sequence if ∑k i=1 ai = 0 and that S is a minimal zero-sequence if S is a zero sequence and S contains no proper zero subsequence. In this paper we prove, among other results, that if S is a minimal zero sequence of elements in Cn and |S| ≥ n − [ 3 ] + 1, then there ex...

AbstmctMultiresolution analysis via decomposition on wavelet bases has emerged as an important tool in the analysis of signals and images when these objects are viewed as sequences of complex or real numbers. An important class of multiresolution decompositions are the so-called Laplacian pyramid schemes, in which the resolution is successively halved by recursively lowpass filtering the signal...

Abstract The concept of spin model is due to V. F. R. Jones. The concept of nonsymmetric spin model, which generalizes that of the original (symmetric) spin model, is defined naturally. In this paper, we first determine the diagonal matrices T satisfying the modular invariance or the quasi modular invariance property, i.e., (PT) = s/rnP or (PT) = m%I (respectively), for the character table P of...