The critical exponent of an infinite word w is the supremum of all rational numbers α such that w contains an α-power. We resolve an open question of Krieger and Shallit by showing that for each α > 2 there is an infinite binary word with critical exponent α.

The paper deals with a degenerate and singular parabolic equation with nonlinear boundary condition. We first get the behavior of the solution at infinity, and establish the critical global existence exponent and critical Fujita exponent for the fast diffusive equation, furthermore give the blow-up set and upper bound of the blow-up rate for the nonglobal solutions.

We present simulations of the one-dimensional Oslo rice pile model in which the critical height at each site is randomly reset after each toppling. We use the fact that the stationary state of this sand-pile model is hyperuniform to reach system of sizes >10^{7}. Most previous simulations were seriously flawed by important finite-size corrections. We find that all critical exponents have values...

Y. Berkovich has proposed to classify nonabelian finite pgroups G of exponent > p which have exactly p maximal abelian subgroups of exponent > p and this was done here in Theorem 1 for p = 2 and in Theorem 2 for p > 2. The next critical case, where G has exactly p + 1 maximal abelian subgroups of exponent > p was done only for the case

The effect of columnar defects on the critical dynamics of superconducting Tl2Ba2CaCu2O8 (Tl2212) film has been investigated. The Tl-2212 film was irradiated at 0 C by 1.3 GeV U-ions along the normal of the film surface. The dose of 6.0 x 10 ions/cm of the Uion irradiation corresponds to a matching field of 1.2 T. The in-plane longitudinal resistivity of the irradiated Tl2212 has been measured ...