Infinite products of 2×22\times2 matrices and the Gibbs properties of Bernoulli convolutions

We consider the infinite sequences (A\_n)\_{n\in\NN} of $2\times2$ matrices with nonnegative entries, where the $A\_n$ are taken in a finite set of matrices. Given a vector V=\pmatrix{v\_1\cr v\_2} with $v\_1,v\_2>0$, we give a necessary and sufficient condition for $\displaystyle{A\_1... A\_nV\over|| A\_1... A\_nV||}$ to converge uniformly. In application we prove that the Bernoulli convolutions related to the numeration in Pisot quadratic bases are weak Gibbs

Weak Gibbs property and system of numeration

We study the selfsimilarity and the Gibbs properties of several measures defined on the product space \Omega\_r:=\{0,1,...,\break r-1\}^{\mathbb N}. This space can be identified with the interval $[0,1]$ by means of the numeration in base $r$. The last section is devoted to the Bernoulli convolution in base $\beta={1+\sqrt5\over2}$, called the Erd\H os measure, and its analogue in base $-\beta=-{1+\sqrt5\over2}$, that we study by means of a suitable system of numeration

ISEL: An e-Taxation System for Employers

In 2008 the State of Geneva modified its regulation on taxation at source in order to collect electronic fiscal data from employers. Indeed the latter provide data on their employees directly to the tax administration (AFC) and furthermore pay taxes to the State on behalf of their employees. They subtract the corresponding amounts from employees' income and refund that money to the fiscal administration. The taxation at source system is applied to foreigners who work in Switzerland or who receive Swiss pensions, to people who live in Geneva but work in other Cantons, as well as to performers, artists or speakers who work occasionally in Geneva. More than 12'000 companies and 117'000 employees are concerned by the scheme, and large companies provide data on several thousand employees. In the past these files provided by employers were handled semi-automatically by the AFC (at best). The new system (called ISEL for Impôt à la Source En Ligne) offers employers two electronic channels to provide data on employees: file transfer (.XSD) and internet e-form. This case study describes the ISEL project and its context, and discusses the issues raised by the introduction of this e-taxation system. On the human side, our paper takes a qualitative approach, based on interviews of various stakeholders involved in the project. They were asked questions on ISEL's functionality, usability, performance, and so on. On the technical side, the paper presents the architecting principles of the e-government approach in Geneva (Legality, Responsibility, Transparency and Symmetry) and the workflow that was implemented on top of AFC's legacy system.private public partnership; tax collection; e-services; e-government; data exchange; architecture; usability

Singular inextensible limit in the vibrations of post-buckled rods: Analytical derivation and role of boundary conditions

In-plane vibrations of an elastic rod clamped at both extremities are studied. The rod is modeled as an extensible planar Kirchhoff elastic rod under large displacements and rotations. Equilibrium configurations and vibrations around these configurations are computed analytically in the incipient post-buckling regime. Of particular interest is the variation of the first mode frequency as the load is increased through the buckling threshold. The loading type is found to have a crucial importance as the first mode frequency is shown to behave singularly in the zero thickness limit in the case of prescribed axial displacement, whereas a regular behavior is found in the case of prescribed axial load.This publication is based in part upon work supported by Award no. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST) (A.G.). A.G. is a Wolfson/Royal Society Merit Award holder. Support from the Royal Society, through the International Exchanges Scheme (Grant IE120203), is also acknowledge

Thin-shell concentration for convex measures

We prove that for $s<0$, $s$-concave measures on ${\mathbb R}^n$ satisfy a thin shell concentration similar to the log-concave one. It leads to a Berry-Esseen type estimate for their one dimensional marginal distributions. We also establish sharp reverse H\"older inequalities for $s$-concave measures

Spectral Stability of Unitary Network Models

We review various unitary network models used in quantum computing, spectral analysis or condensed matter physics and establish relationships between them. We show that symmetric one dimensional quantum walks are universal, as are CMV matrices. We prove spectral stability and propagation properties for general asymptotically uniform models by means of unitary Mourre theory