Watermark recovery is often based on cross-correlating images with pseudo-noise sequences, as access to un-watermarked originals is not required. Successful recovery of these watermarks is determined by the (periodic or aperiodic) sequence autoand cross-correlation properties. This paper presents several methods of extending the dimensionality of 1D sequences in order to utilise the advantages ...

We define a notion of unitarizability for weight modules over a generalized Weyl algebra (of rank one, with commutative coeffiecient ring R), which is assumed to carry an involution of the form X∗ = Y , R∗ ⊆ R. We prove that a weight module V is unitarizable iff it is isomorphic to its finitistic dual V . Using the classification of weight modules by Drozd, Guzner and Ovsienko, we obtain necess...

We relate the semiclassical asymptotics of the 6j symbols for the quantized enveloping algebra Uq(sl2) at q a root of unity (resp. q real positive) to the geometry of spherical (resp. hyperbolic) tetrahedra.

A sequence a = (a0, a1, a2, · · · , an) is said to be an almost p-ary sequence of period n + 1 if a0 = 0 and ai = ζ bi p for 1 ≤ i ≤ n, where ζp is a primitive p-th root of unity and bi ∈ {0, 1, · · · , p − 1}. Such a sequence a is called perfect if all its out-of-phase autocorrelation coefficients are zero; and is called nearly perfect if its out-of-phase autocorrelation coefficients are all 1...

Wolfmann [Wolfmann, 1992] introduced the idea of ZCZ binary sequences with the so-called almost perfect sequences, which have one non-zero off-peak autocorrelation value. Non-binary ZCZ sequences over roots of unity were first constructed by Suehiro [Suehiro, 1994]. Other types of ZCZ sequences have been constructed based on the existence of complementary pairs [Suehiro, 1994][Fan, 1999a][Matsu...

There exists a number of known constructions for perfect sequences over roots of unity. These include Frank sequences of length n over n roots of unity [Heimiller, 1961][Frank, 1962], Chu sequences of length n over n roots of unity for n odd and length n over 2n roots of unity for n even [Chu, 1972], Milewski sequences of length m overm roots of unity [Milewski, 1983], Liu-Fan sequences of leng...

At the 1991 West Coast Number Theory Conference, Emma Lehmer asked for proofs of the formulas on semi-symmetric cyclotomic sums that appeared without proof in D. H. Lehmer's last notebook. This note is the result. Furthermore, we show how to determine signs which Lehmer had left ambiguous. Classical cyclotomy defined the cyclotomic classes of degree e and prime conductor p = ef + 1 to be (1) C ...

For prime power q = p and a field F containing a root of unity of order q we show that the Galois cohomology ring H∗(GF , Z/q) is determined by a quotient G [3] F of the absolute Galois group GF related to its descending q-central sequence. Conversely, we show that G [3] F is determined by the lower cohomology of GF . This is used to give new examples of pro-p groups which do not occur as absol...

Abstract. Concerning the uniqueness and sharing values of meromorphic functions, many results about meromorphic functions that share more than or equal to two values have been obtained. In this paper, we shall study meromorphic functions that share only one value, and prove the following result: For n ≥ 11 and two meromorphic functions f(z) and g(z) , if ff ′ and gg share the same nonzero and f...