Synthesis of New Aminophosphonothiophene Derivatives

The reaction of n , n '-diphosphonylketones 1 with active methylenenitriles and sulfur in basic conditions led to the new 5-amino-2-(phosphonomethyl)-3-(phosphonoethyl)thiophenes 2 . These compounds were then used in the Horner-Wadsworth-Emmons reaction to give 5-amino-2-alkenyl-3-(phosphonoethyl)thiophenes 3 . The structure of all obtained products was confirmed by NMR ( 1 H, 31 P, 13 C) and IR spectroscopy.     

Performance Enhancement of Polymer Solar Cells by Using Two Polymer Donors with Complementary Absorption Spectra

Performance enhancement of polymer solar cells (PSCs) is achieved by expanding the absorption of the active layer of devices. To better match the spectrum of solar radiation, two polymers with different band gaps are used as the donor material to fabricate ternary polymer cells. Ternary blend PSCs exhibit an enhanced short‐circuit current density and open‐circuit voltage in comparison with the corresponding HD‐PDFC‐DTBT (HD)‐ and DT‐PDPPTPT (DPP)‐based binary polymer solar cells, respectively. Ternary PSCs show a power conversion efficiency (PCE) of 6.71%, surpassing the corresponding binary PSCs. This work demonstrates that the fabrication of ternary PSCs by using two polymers with complementary absorption is an effective way to improve the device performance.

     

Stationary Stokes, Oseen and Navier–Stokes Equations with Singular Data

The concept of very weak solution introduced by Giga (Math Z 178:287–329, 1981) for the Stokes equations has hardly been studied in recent years for either the Navier–Stokes equations or the Navier–Stokes type equations. We treat the stationary Stokes, Oseen and Navier–Stokes systems in the case of a bounded open set, connected of class C^1,1{\mathcal{C}^{1,1}} of \mathbbR³{\mathbb{R}^3}. Taking up once again the duality method introduced by Lions and Magenes (Problèmes aus limites non-homogènes et applications, vols. 1 & 2, Dunod, Paris, 1968) and Giga (Math Z 178:287–329, 1981) for open sets of class C^￥{\mathcal{C}^{\infty}} [see also chapter 4 of Necas (Les méthodes directes en théorie des équations elliptiques. (French) Masson et Cie, éd., Paris; Academia, éditeurs, Prague, 1967), which considers the Hilbertian case p = 2 for general elliptic operators], we give a simpler proof of the existence of a very weak solution for stationary Oseen and Navier–Stokes equations when data are not regular enough, based on density arguments and a functional framework adequate for defining more rigourously the traces of non-regular vector fields. In the stationary Navier–Stokes case, the results will be valid for external forces not necessarily small, which lets us extend the uniqueness class of solutions for these equations. Considering more regular data, regularity results in fractional Sobolev spaces will also be discussed for the three systems. All these results can be extended to other dimensions.     

Reduction of the adjoint representation of sl(2,1): generators of primitive ideals

We present a reduction of the adjoint representation of the Lie superalge-bra,sl(2,1) and a study of the quotient algebra B(^c,k)= u/u(C?c)+u(D?kc), where c,k are two complex numbers. Under some additional conditions, we prove that every irreducible infinite dimensional representation of B(^c,k) is faithful, and that B(^C,K) is a primitive algebra. We give explicitly a set of generators of primitive degenerate ideal of infinite codimension. Essentially we prove that any minimal primitive ideal of u(sl(2,1)) is generated, as a 2-sided ideal, by its intersection with the algebra of gg-iuvariants.     

Exterior Stokes problem in the half-space

The purpose of this work is to solve the exterior Stokes problem in the half-space . We study the existence and the uniqueness of generalized solutions in weighted L ^p theory with 1 < p < ∞. Moreover, we consider the case of strong solutions and very weak solutions. This paper extends the studies done in Alliot, Amrouche (Math. Methods Appl. 23:575–600, 2000) for an exterior Stokes problem in the whole space and in Amrouche, Bonzom (Exterior Problems in the Half-space, submitted) for the Laplace equation in the same geometry as here.      

Multiscale Lyapunov exponent for 2-microlocal functions

The Lyapunov exponent is an important indicator of chaotic dynamics. Using wavelet analysis, we define a multiscale representation of this exponent which we demonstrate the scale-wise dependence for functions belonging to spaces. An empirical study involving simulated processes and financial time series corroborates the theoretical findings.     

Synthesis,structural and complex impedance spectroscopy studies of Ni0.4Co0.4Mg0.2Fe2O4 spinel ferrite

Spinel ferrite having composition Ni_0.4Co_0.4Mg_0.2Fe₂O₄ was prepared by sol-gel method. X-ray diffraction result indicates that the ferrite sample has a cubic spinel type structure. FT-IR showed two absorption bands (ν₁ and ν₂) that are attributed to the stretching vibration of tetrahedral and octahedral sites. Complex impedance properties have been investigated in 200–420 K temperature range with varying frequency between 40 and 10⁷ Hz. Frequency and temperature dependency of imaginary part of permittivity (?″) and dielectric loss (tanδ) has been discussed in terms of hopping of charge carriers between Fe²⁺ and Fe³⁺ ions. Activation energy has been estimated from both temperature dependency of dc conductivity and relaxation time data, which indicates that the relaxation process and conductivity have the same origin. Nyquist plots of impedance show semicircle arcs for sample and an electrical equivalent circuit has been proposed to explain the impedance results.     

On Saint Venant's compatibility conditions and Poincaré's lemma

Saint Venant's theorem constitutes a classical characterization of smooth matrix fields as linearized strain tensor fields. This theorem has been extended to matrix fields with components in $L^2$ by the second author and P. Ciarlet, Jr. in 2005. One objective of this Note is to further extend this characterization to matrix fields whose components are only in $H^{\mathrm{?1}}$. Another objective is to demonstrate that Saint Venant's theorem is in fact nothing but the matrix analog of Poincaré's lemma. To cite this article: C. Amrouche et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Experimental observation of quantum confinement in the conduction band of CdSe quantum dots

X-ray absorption spectroscopy has been used to characterize the evolution in the conduction band (CB) density of states of CdSe quantum dots (QDs) as a function of particle size. We have unambiguously witnessed the CdSe QD CB minimum (CBM) shift to higher energy with decreasing particle size, consistent with quantum confinement effects, and have directly compared our results with recent theoretical calculations. At the smallest particle size, evidence for a pinning of the CBM is presented. Our observations can be explained by considering a size-dependent change in the angular-momentum-resolved states at the CBM.