We consider Metropolis Glauber dynamics for sampling proper qcolourings of the n-vertex complete b-ary tree when 3 ≤ q ≤ b/2 ln(b). We give both upper and lower bounds on the mixing time. For fixed q and b, our upper bound is nO(b/ log b) and our lower bound is nΩ(b/q log(b)), where the constants implicit in the O() and Ω() notation do not depend upon n, q or b.

We let ω denote the least exponent such that two n× n matrices can be multiplied with O(nω+ ) arithmetic operations for every > 0. It is clear that ω ≥ 2, while Strassen showed that ω is strictly less than 3. Today it is widely believed that ω = 2, although the best upper bound is roughly 2.34 due Coppersmith and Winograd. We will see a somewhat worse upper bound based on a group theoretic appr...

We consider crack propagation in brittle non-linear elastic materials in the context of quasi-static evolutions of energetic type. Given a sequence of self-similar domains nΩ on which the imposed boundary conditions scale according to Bažant’s law, we show, in agreement with several experimental data, that the corresponding sequence of evolutions converges (for n → ∞) to the evolution of a crac...

Basic path-matchings, introduced by Cunningham and Geelen (FOCS 1996), are a common generalization of matroid intersection and non-bipartite matching. The main results of this paper are a new algebraic characterization of basic path-matching problems and an algorithm for constructing basic path-matchings in Õ(nω) time, where n is the number of vertices and ω is the exponent for matrix multiplic...

For n > 2 let In be the σ-ideal in P(nω) generated by all sets which do not contain n equidistant points in the usual metric on nω. For each n > 2 a set Sn is constructed in Rn so that the σ-ideal which is generated by the convex subsets of Sn restricted to the convexity radical K(Sn) is isomorphic to In. Thus cov(In) is equal to the least number of convex subsets required to cover Sn — the con...

We take into account the sigma meson cloud effect in the meson cloud model to calculate the distributions of light flavor sea quarks in the proton. Our calculation gives a better description of the data for d(x)/u(x). We also provide a picture that the probability of finding a physical proton in a Fock state |Nω〉 is reasonable small with a smaller cutoff Λω.

We study the one-dimensional discrete quasi-periodic Schrödinger equation −φ(n+ 1) − φ(n− 1) + λV (x+ nω)φ(n) = Eφ(n), n ∈ Z We introduce the notion of variations of potential and use it to define “typical” potential. We show that for “typical” C potential V , if the coupling constant λ is large, then for most frequencies ω, the Lyapunov exponent is positive for all energies E.

Aim: Acetylsalicylic acid (ASA, aspirin), which is one of the most frequently used drugs in the world, causes severe gastric mucosal injury. Nitric oxide (NO) is synthesized from L-arginine by nitric oxide synthase (NOS). NOS can be inhibited by Nω-nitro-L-arginine methyl ester (L-NAME) and stimulated by supplementing the diet with L-arginine (L-Arg). The aim of this study was to investigate th...