Distributive lattices determined by weighted double skeletons

Related to his S-glued sum construction, the skeleton S(L) of a finite lattice L was introduced by C. Herrmann in 1973. Our theorem asserts that if D is a finite distributive lattice and its second skeleton, S(S(D)), is the trivial lattice, then D is characterized by its weighted double skeleton, introduced by the second author in 2006. The assumption on the second skeleton is essential.Comment: 12 pages and 2 figure

Periodic orbits, basins of attraction and chaotic beats in two coupled Kerr oscillators

Kerr oscillators are model systems which have practical applications in nonlinear optics. Optical Kerr effect i.e. interaction of optical waves with nonlinear medium with polarizability $\chi^{(3)}$ is the basic phenomenon needed to explain for example the process of light transmission in fibers and optical couplers. In this paper we analyze the two Kerr oscillators coupler and we show that there is a possibility to control the dynamics of this system, especially by switching its dynamics from periodic to chaotic motion and vice versa. Moreover the switching between two different stable periodic states is investigated. The stability of the system is described by the so-called maps of Lyapunov exponents in parametric spaces. Comparison of basins of attractions between two Kerr couplers and a single Kerr system is also presented.Comment: 22 pages, 14 figures, submitted to Nonlinear Dynamic

Counting and Generating Terms in the Binary Lambda Calculus (Extended version)

In a paper entitled Binary lambda calculus and combinatory logic, John Tromp presents a simple way of encoding lambda calculus terms as binary sequences. In what follows, we study the numbers of binary strings of a given size that represent lambda terms and derive results from their generating functions, especially that the number of terms of size n grows roughly like 1.963447954. .. n. In a second part we use this approach to generate random lambda terms using Boltzmann samplers.Comment: extended version of arXiv:1401.037

Galvanomagnetic properties and noise in a barely metallic film of V2O3

We have measured the magnetotransport properties of a strained metallic V2O3 thin film. Most of the properties are similar to V2O3 single crystals that have been submitted to a large pressure. In addition, resistance noise analysis indicates that conductivity fluctuations are freezing out at T\approx 10K. Examination of a range of measurements leads to the conclusion that spins-configuration fluctuations dominate in the low temperature regime.Comment: accepted for publication in Phys Rev