This paper is concerned with ground state solutions for the Hénon type equation −∆u(x) = |y|αup−1(x) in Ω, where Ω = B(0, 1) × Bn−k(0, 1) ⊂ R and x = (y, z) ∈ R × Rn−k. We study the existence of cylindrically symmetric and non-cylindrically symmetric ground state solutions for the problem. We also investigate asymptotic behavior of the ground state solution when p tends to the critical exponent...

The spin-glass-like behavior observed in mechanically alloyed Al49Fe30Cu21 is attributed to the collective freezing of ferromagnetic nanoclusters, i.e., the appearance of a superspin glass phase. The presence of the clusters and their estimated size (;1 nm) were inferred from magnetization measurements. The transition critical exponent zn513.860.4, extracted from ac-susceptibility data, is simi...

We apply the recently devised quasi-stationary simulation method to study the lifetime and order parameter of the contact process in the subcritical phase. This phase is not accessible to other methods because virtually all realizations of the process fall into the absorbing state before the quasi-stationary regime is attained. With relatively modest simulations, the method yields an estimate o...

We investigate powers of prefixes in Sturmian sequences. We obtain an explicit formula for ice(ω), the initial critical exponent of a Sturmian sequence ω, defined as the supremum of all real numbers p > 0 for which there exist arbitrary long prefixes of ω of the form u, in terms of its S-adic representation. This formula is based on Ostrowski’s numeration system. We characterize those irrationa...

A square is the concatenation of a nonempty word with itself. A word has period p if its letters at distance pmatch. The exponent of a nonempty word is the quotient of its length over its smallest period. In this article we give a proof of the fact that there exists an infinite binary word which contains finitely many squares and simultaneously avoids words of exponent larger than 7/3. Our infi...

Richomme, Saari and Zamboni (J. Lond. Math. Soc. 83: 79–95, 2011) proved that at every position of an infinite Sturmian word starts an abelian power of exponent k, for every positive integer k. Here, we improve on this result, studying the maximal exponent of abelian powers and abelian repetitions (an abelian repetition is the analogous of a fractional power in the abelian setting) occurring in...

We consider bond percolation on the d-dimensional hypercubic lattice. Assuming the existence of a single critical exponent, the exponent ρ describing the decay rate of point-to-plane crossings at the critical point, we prove that hyperscaling holds whenever critical rectangle crossing probabilities are uniformly bounded away from 1.

We consider bond percolation on the d-dimensional hypercubic lattice. Assuming the existence of a single critical exponent, the exponent ρ describing the decay rate of point-to-plane crossings at the critical point, we prove that hyperscaling holds whenever critical rectangle crossing probabilities are uniformly bounded away from 1.

The numerical solution of the nonlocal kinetic equation allows to simulate heavy ion reactions around Fermi energy. The expansion velocity and density profile show specific radial dependence which can be described with a Tsallis exponent of q = 5/3. This might be considered as an indication of a phase transition.

A surprising result of FitzGerald and Horn (1977) shows that A◦α := (aα ij) is positive semidefinite (p.s.d.) for every entrywise nonnegative n× n p.s.d. matrix A = (aij) if and only if α is a positive integer or α ≥ n− 2. Given a graph G, we consider the refined problem of characterizing the setHG of entrywise powers preserving positivity for matrices with a zero pattern encoded by G. Using al...