On the size of the algebraic difference of two random Cantor sets

In this paper we consider some families of random Cantor sets on the line and investigate the question whether the condition that the sum of Hausdorff dimension is larger than one implies the existence of interior points in the difference set of two independent copies. We prove that this is the case for the so called Mandelbrot percolation. On the other hand the same is not always true if we apply a slightly more general construction of random Cantor sets. We also present a complete solution for the deterministic case.Comment: This replacement corrects an important omission in the proof of Theorem 1(a

Superconductivity near lattice instability: the case of NbC1−x_{1-x}Nx_x and NbN

Using density functional theory within the local density approximation we report a study of the electron-phonon coupling in NbC$_{1-x}$N$_x$ and NbN crystals in the rocksalt structure. The Fermi surface of these systems exhibits important nesting. The associated Kohn anomaly greatly increases the electron-phonon coupling and induces a structural instability when the electronic density of states reaches a critical value. Our results reproduce the observed rise in $T_{c}$ from 11.2 K to 17.3 K as the nitrogen doping is increased in NbC$_{1-x}$N$_x$. To further understand the contribution of the structural instability to the rise of the superconducting temperature, we develop a model for the Eliashberg spectral function in which the effect of the unstable phonons is set apart. We show that this model together with the McMillan formula can reproduce the increase of $T_{c}$ near the structural phase transition.Comment: 6 pages, 5 figures, submission PR

Quantum Communication with Quantum Dot Spins

Single electron spins in quantum dots are attractive for quantum communication because of their expected long coherence times. We propose a method to create entanglement between two remote spins based on the coincident detection of two photons emitted by the dots. Local nodes of several qubits can be realized using the dipole-dipole interaction between trions in neighboring dots and spectral addressing, allowing the realization of quantum repeater protocols. We have performed a detailed feasibility study of our proposal based on tight-binding calculations of quantum dot properties.Comment: 4 pages, 2 figures, new and improved version, explicit performance estimate

A statistical mechanics framework for the large-scale structure of turbulent von K{\'a}rm{\'a}n flows

In the present paper, recent experimental results on large scale coherent steady states observed in experimental von K{\'a}rm{\'a}n flows are revisited from a statistical mechanics perspective. The latter is rooted on two levels of description. We first argue that the coherent steady states may be described as the equilibrium states of well-chosen lattice models, that can be used to define global properties of von K{\'a}rm{\'a}n flows, such as their temperatures. The equilibrium description is then enlarged, in order to reinterpret a series of results about the stability of those steady states, their susceptibility to symmetry breaking, in the light of a deep analogy with the statistical theory of Ferromagnetism. We call this analogy "Ferro-Turbulence

Le vote des ouvriers, de l’alignement à gauche à une « droitisation » ?

Depuis un demi-siècle, les comportements électoraux et les attitudes politiques des ouvriers ont connu de profondes transformations. Les ouvriers constituent-ils un monde à part sur la scène politique ? Existe-t-il toujours une spécificité ouvrière ?Note publiée sur le site du Cevipof "Elections 2012" In "Le recueil des notes du Cevipof - Les électorats sociologiques

Los trotacalles de las ciudades

Se presentan los resultados de una investigación que tuvo como objetivo comprender las conductas, en particular amorosas y sexuales, de jóvenes de la calle de la ciudad de Quebec, Canadá, en relación con los factores de riesgo y los factores de protección concernientes a la transmisión de Infecciones de Transmisión Sexual o Sanguínea y del Virus de inmunodeficiencia Humana. Se utilizó un método cualitativo basado en la recopilación de relatos de experiencias de vida. Tal aproximación ha permitido cernir las experiencias de estos jóvenes a partir de los significados que tenían para ellos y ellas. Las cincuenta entrevistas individuales realizadas para esta investigación involucraron a treinta varones y veinte mujeres con una edad media de poco más de veinte años. Hemos identificado rápidamente dos tipos de jóvenes. El primer tipo es el del "sobreviviente" y el segundo el del "aventurero". El "sobreviviente" de la calle es aquel que sobrevive a la adversidad a través de una historia de vida dolorosa (en particular con su familia). 2El aventurero" ha escogido romper, provisoriamente, con su medio familiar, con el cual no vive, pero con quien mantiene vínculos. En sus prácticas amorosas y sexuales hemos descubierto en los jóvenes seis diferentes estrategias para evitar el uso del condón. Concluimos en que es importante replantear la prevención del SIDA y de las ITSS adaptando el discurso a la realidad vivida por los jóvenes de la calle; es decir, la búsqueda, ante todo, del placer

On Disjoint hypercubes in Fibonacci cubes

The {\em Fibonacci cube} of dimension $n$, denoted as $\Gamma\_n$, is the subgraph of $n$-cube $Q\_n$ induced by vertices with no consecutive 1's. We study the maximum number of disjoint subgraphs in $\Gamma\_n$ isomorphic to $Q\_k$, and denote this number by $q\_k(n)$. We prove several recursive results for $q\_k(n)$, in particular we prove that $q\_{k}(n) = q\_{k-1}(n-2) + q\_{k}(n-3)$. We also prove a closed formula in which $q\_k(n)$ is given in terms of Fibonacci numbers, and finally we give the generating function for the sequence $\{q\_{k}(n)\}\_{n=0}^{ \infty}$