Strengthened semidefinite programming bounds for codes

We give a hierarchy of semidefinite upper bounds for the maximum size A(n,d) of a binary code of word length n and minimum distance at least d. At any fixed stage in the hierarchy, the bound can be computed (to an arbitrary precision) in time polynomial in n; this is based on a result of de Klerk et al. (Math Program, 2006) about the regular ∗-representation for matrix ∗-algebras. The Delsarte bound for A(n,d) is the first bound in the hierarchy, and the new bound of Schrijver (IEEE Trans. Inform. Theory 51:2859–2866, 2005) is located between the first and second bounds in the hierarchy. While computing the second bound involves a semidefinite program with O(n ⁷) variables and thus seems out of reach for interesting values of n, Schrijver’s bound can be computed via a semidefinite program of size O(n ³), a result which uses the explicit block-diagonalization of the Terwilliger algebra. We propose two strengthenings of Schrijver’s bound with the same computational complexity. Supported by the Netherlands Organisation for Scientific Research grant NWO 639.032.203.     

An asymptotic-preserving well-balanced scheme for the hyperbolic heat equationsUn schema « équilibre » et « asymptotic-preserving » pour les equations de la chaleur hyperboliques

We propose here a well-balanced numerical scheme for the one-dimensional Goldstein–Taylor system which is endowed with all the stability properties inherent to the continuous problem and works in both rarefied and diffusive regimes. To cite this article: L. Gosse, G. Toscani, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 337–342.     

Méthode d'éléments finis avec hybridisation frontière pour les problèmes de contact avec frottementFinite element method with Lagrange multipliers for contact problems with friction

In this Note, we propose a finite element method with Lagrange multipliers in order to approximate contact problems with friction. The discretized normal and tangential constraints at the candidate contact interface are expressed by using continuous piecewise linear Lagrange multipliers in the saddle-point formulation. An optimal error estimate is established and several numerical studies corresponding to this choice of the discretized normal and tangential constraints are achieved. To cite this article: L. Baillet, T. Sassi, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 917–922.     

Up to isometries,a deformation is a continuous function of its metric tensorAux isométries près,une déformation est une fonction continue de son tenseur métrique

If the Riemann–Christoffel tensor associated with a field of class $\text{C}{}^2$ of positive definite symmetric matrices of order three vanishes in a connected and simply connected open subset $\text{Ω?}\text{R}{}^3$, then this field is the metric tensor field associated with a deformation of class $\text{C}{}^3$ of the set $\text{Ω}$, uniquely determined up to isometries of $\text{R}{}^3$. We establish here that the mapping defined in this fashion is continuous, for ad hoc metrizable topologies. To cite this article: P.G. Ciarlet, F. Laurent, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 489–493.     

Spatial trapping of short pulses in Ti-indiffused LiNbO(3) waveguides

We show numerically and experimentally that spatial trapping can be induced in quadratic media even if the pump pulse's duration is shorter than the group-delay mismatch between fundamental wave and second-harmonic components. The influence of phase mismatch and pulse power on the trapping effect is discussed. Spatial, temporal, and spectral behaviors that accompany self-trapped propagation are highlighted.     

The cut cone III: On the role of triangle facets

The cut polytopeP _n is the convex hull of the incidence vectors of the cuts (i.e. complete bipartite subgraphs) of the complete graph onn nodes. A well known class of facets ofP _n arises from the triangle inequalities:x _ij +x _ik +x _jk ≤ 2 andx _ij -x _ik -x _jk ≤ 0 for 1 ≤i,j, k ≤n. Hence, the metric polytope M_n, defined as the solution set of the triangle inequalities, is a relaxation ofP _n . We consider several properties of geometric type for P_n, in particular, concerning its position withinM _n . Strengthening the known fact ([3]) thatP _n has diameter 1, we show that any set ofk cuts,k ≤ log₂ n, satisfying some additional assumption, determines a simplicial face ofM _n and thus, also, ofP _n . In particular, the collection of low dimension faces ofP _n is contained in that ofM _n . Among a large subclass of the facets ofP _n , the triangle facets are the closest ones to the barycentrum of P_n and we conjecture that this result holds in general. The lattice generated by all even cuts (corresponding to bipartitions of the nodes into sets of even cardinality) is characterized and some additional questions on the links between general facets ofP _n and its triangle facets are mentioned.     

Nanotextured multicrystalline Al‐BSF solar cells reaching 18% conversion efficiency using industrially viable solar cell processes

We report recent achievements in adapting industrially used solar cell processes on nanotextured surfaces. Nanostructures were etched into c‐Si surfaces by dry exothermic plasma‐less reaction of F species with Si in atmospheric pressure conditions and then modified using a short post‐etching process. Nanotextured multicrystalline wafers are used to prepare Al‐BSF solar cells using industrially feasible solar cell proc‐ essing steps. In comparison to the reference acidic textured solar cells, the nanostructured cells showed gain in short circuit current (J_sc) of up to 0.8 mA/cm² and absolute gain in conversion efficiency of up to 0.3%. The best nanotextured solar cell was independently certified to reach the conversion efficiency of 18.0%. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)     

Indépendance algébrique sur les T-modules

We study the transcendence degree (of the values at algebraic points) of the coordinate functions of a given one parameter subgroup on a simple g dimensional T-module. In such a situation, we obtain a lower bound for this transcendence degree depending on g and on the growth order of the parameter subgroup. As a particular case, one gets the finite characteristic analogue of a result of Siegel on the algebraic independence for the values of the classical Bessel function.Résumé. Nous obtenons une minoration du degré de transcendance d'un ensemble de valeurs en des points algébriques des fonctions coordonnées d'un sous-groupe à un paramètre d'un T-module simple, en fonction de l'ordre de croissance de ces dernières et de la dimension du T-module. Un cas particulier de ce résultat permet d'obtenir en caractéristique finie un analogue d'un résultat de Siegel sur l'indépendance algébrique des valeurs de la fonction de Bessel usuelle.     

Suppression of radiative losses of surface polaritons on nanostructured thin metal films

The strong electromagnetic coupling between surface plasmon polariton modes on opposite interfaces of a finite thickness periodically nanostructured metal film has been studied. Surface polariton dispersion and associated electromagnetic field distributions have been analyzed. It was shown that at a frequency that corresponds to the crossing of film Bloch modes of different symmetries, the radiative losses of surface polaritons that are related to the polaritons' coupling to light during propagation on the structured surface are suppressed.     

Infrared and visible emission of Er in combustion-synthesized CaAl2O4 phosphors

New near-infrared luminescent, monoclinic CaAl₂O₄:Er³⁺ phosphor was prepared by using the combustion route at furnace temperatures as low as 500 °C in a few minutes. Combustion synthesized phosphor has been well characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy-dispersive analysis of X-ray (EDAX) mapping studies. The luminescence spectra of Er³⁺-doped calcium aluminate were studied at UV (380 nm), vis (488 nm) and IR (980 nm) excitation. Upon UV and vis excitation, the CaAl₂O₄:Er³⁺ phosphor exhibits emission bands at ~523 nm and at ~547 nm, corresponding to transitions from the ²H_11/2 and ⁴S_3/2 erbium levels to the ⁴I_15/2 ground state. A strong luminescence at 1.55 μm in the infrared (IR) region due to ⁴I_13/2→⁴I_15/2 transition has been observed in CaAl₂O₄:Er³⁺ phosphor upon 980 nm CW pumping. In the spectrum of IR-excited up-conversion luminescence, green (~523 and ~547 nm) and red (662 nm) luminescence bands were present, the latter associated with the ⁴F_9/2→⁴I_15/2 transitions of Er³⁺ ions. Both excited state absorption and energy transfer may be proposed as processes responsible for the population of the ⁴S_3/2 and ⁴F_9/2 erbium levels upon IR excitation. The mechanisms responsible for the up-conversion luminescence are discussed.