We show that the action of universal R-matrix of affine U q sl 2 quantum algebra, when q is a root of unity, can be renormalized by some scalar factor to give a well defined nonsingular expression, satisfying Yang-Baxter equation. It reduced to intertwining operators of all representations , corresponding to Chiral Potts, if the parameters of these representations lie on well known algebraic cu...

Let P = f" + (I ,,) , the direct sum of the p x p identity matrix and the negative of the q x q ident ity matrix. The fo llowing theorem is proved. TH EOHEM: If X = cZ where Z is a 4 x 4 P-orthogonal , P-skew-symmetric matrix and Ie I .;;; 2, there exist matrices A an.d B, both of which are P-orthogollal and P-skew-symmetric, sach that X = AB BA. Methods for o btaining certain matrices which sa...

by a quasi-permutation matrix we mean a square matrix over the complex field c with non-negative integral trace. thus, every permutation matrix over c is a quasipermutation matrix. for a given finite group g, let p(g) denote the minimal degree of a faithful permutation representation of g (or of a faithful representation of g by permutation matrices), let q(g) denote the minimal degree of a fai...

It is known that extremal doubly-even self-dual codes of length n ≡ 8 or 0 (mod 24) yield 3or 5-designs respectively. In this paper, by using the generator matrices of bordered double circulant doubly-even self-dual codes, we give 3-(n, k; m)-SEEDs with (n, k, m) ∈ {(32, 8, 5), (56, 12, 9), (56, 16, 9), (56, 24, 9), (80, 16, 52)}. With the aid of computer, we obtain 22 generator matrices of bor...

We prove a super-linear lower bound on the size of a bounded depth bilinear arithmetical circuit computing cyclic convolution. Our proof uses the strengthening of the Donoho-Stark uncertainty principle [DS89] given by Tao [Tao05], and a combinatorial lemma by Raz and Shpilka [RS03]. This combination and an observation on ranks of circulant matrices, which we use to give a much shorter proof of ...

In this paper we present a new method to construct a polynomial u(x) ∈ Z[x] which will make Φk(u(x)) reducible. We construct a finite separable extension of Q(ζk), denoted as E. By primitive element theorem, there exists a primitive element θ ∈ E such that E = Q(θ). We represent the primitive k-th root of unity ζk by θ and get a polynomial u(x) ∈ Q[x] from the representation. The resulting u(x)...

We introduce the class of skew-circulant lattice rules. These are s-dimensional lattice rules that may be generated by the rows of an s×s skewcirculant matrix. (This is a minor variant of the familiar circulant matrix.) We present briefly some of the underlying theory of these matrices and rules. We are particularly interested in finding rules of specified trigonometric degree d. We describe so...

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus, every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fa...

In this paper a new approach to the modelling of ATM-traffic is proposed. The traffic is measured and characterised by its first and second order statistic moments. A Markov Modulated Poisson Process (MMPP) is used to capture the information in these two stochastic moments. Instead of a general MMPP, a circulant MMPP is used to reduce the computational cost. A circulant MMPP (CMMPP) is an MMPP ...