D-optimal designs are n x n ±l-matrices where n == 2 mod 4 with maximum determinant. D-optimal designs obtained via circulant matrices are equivalent to 2-{ v; kl i k2 i k1 + k2 ~(v 1)} supplementary difference sets, where v = ~. We use cyclotomy to construct D-optimal designs, where v is a prime. We give a generalisation of cyclotomy and extend the cyclotomic techniques which enables use to fi...

In Hegel’s philosophy, both truth and genuine freedom belong to the domain of Idea. Life, as it is categorized in Science Logic, first form stage Idea, therefore essential for a comprehension self-determination. this paper, I explore why what extent Life self-determining true. Considering Hegel considers be three fundamental features all life, explain how life with respect its organic unity, re...

In this paper, for solving the finite-dimensional variational inequality problem ðx x ÞFðx ÞP0; 8x 2 X; where F is a C ðr > 1Þ mapping from X to R, X 1⁄4 fx 2 R : gðxÞO0g is nonempty (not necessarily bounded) and gðxÞ :R ! R is a convex Crþ1 mapping, a homotopy method is presented. Under various conditions, existence and convergence of a smooth homotopy path from almost any interior initial poi...

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...

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...