The nth detour chromatic number, χn(G) of a graph G is the minimum number of colours required to colour the vertices of G such that no path with more than n vertices is monocoloured. The number of vertices in a longest path of G is denoted by τ (G) . We conjecture that χn(G) ≤ d τ(G) n e for every graph G and every n ≥ 1 and we prove results that support the conjecture. We also present some suf...

Consider a sequence of N x N random nonnegative matrices in which each element depends on a vector u of parameters. The nth partial product is the random matrix formed by multiplying, from right to left, the first n of these random matrices in order. Under certain conditions, the elements of the nth partial product grow asymptotically exponentially as n increases, and the logarithms of the disc...

We study some properties of the Askey-Wilson polynomials (AWP) when q is a primitive Nth root of unity. For general four-parameter AWP, zeros of the Nth polynomial and the orthogonality measure are found explicitly. Special subclasses of the AWP, e.g., the continuous q-Jacobi and big q-Jacobi polynomials, are considered in detail. A set of discrete weight functions positive on a real interval i...

The total number of noncrossing partitions of type Ψ is the nth Catalan number 1 n+1 (

We evaluate the impact of three auction mechanisms—the Becker-DeGroot-Marschak (BDM) mechanism, the second-price auction (SPA), and the random nth-price auction (NPA)—in the measurement of private willingness-to-pay and willingness-to-accept for a pure public good. Our results show that the endowment effect is lower with the BDM mechanism. In this market mechanism, the effect disappears after a...

Let A be an abelian variety over an algebraically closed field. The Chow group CH0(A) of zero-dimensional cycles modulo rational equivalence forms a ring under the Pontryagin product operation with respect to which the subset I of degree zero cycles is an ideal. The nth power of I is shown to agree with the nth power of the algebraic equivalence relation as defined by H. Saito. A result is also...

Let pn denote the nth prime. Goldston, Pintz, and Yıldırım recently proved that lim inf n→∞ (pn+1 − pn) log pn = 0. We give an alternative proof of this result. We also prove some corresponding results for numbers with two prime factors. Let qn denote the nth number that is a product of exactly two distinct primes. We prove that lim inf n→∞ (qn+1 − qn) ≤ 26. If an appropriate generalization of ...

This work proposes a high efficiency PRNG suitable for use in stream ciphers. It is based on hybrid cellular automata with nonlinear feedback to improve its resistance to attacks. It is shown that it can be designed with an arbitrary number N of cells as long as N>Nth with no need for designing a new polynomial like in traditional feedback shift registers (it is easily scalable). The space of t...

The following twelve poster abstracts were presented at the ANTS-8 poster session.1 ANTS-8 was held at the Banff Centre in Banff, Alberta Canada, May 17–22, 2008. The conference website, where many of the posters can be viewed online, is http://ants.math. ucalgary.ca/. Calculating Really Big Cyclotomic Polynomials Andrew Arnold and Michael Monagan, Simon Fraser University, ada26@ sfu.ca The nth...

We investigate the second-harmonic generation of the nth-order Bessel beam in the nonlinear medium. The analysis is based on the Khokhlov-Zabolotskaya-Kuznetsov wave equation under the second-order approximation in nonlinear acoustics. The theory indicates that for an nth-order Bessel beam, the second-harmonic beam is nearly diffraction-free in the radial direction and behaves as a Bessel beam ...