Réception des messages biphase dans les systémes de télécommunications par fibres optiques

The author considers the problems relevant to the detection of unipolar split-phase signals in digital optical fiber communication systems. By use of simplifications concerning the fiber frequency response and the noise power spectrum, the error rate is computed in different kinds of signal processing. Compared to the theoretical optimum detection, the results are presented as a function of the practical receiver bandwidth.     

Rational Design of Poly(2,7‐Carbazole) Derivatives for Photovoltaic Applications

A reliable model that can be used to estimate the electronic properties (i.e., the HOMO, LUMO, and band gap energies) of conjugated polymers would be a great tool for applications in organic electronics such as light‐emitting diodes, field‐effect transistors, and photovoltaic cells. Recently, poly(2,7‐carbazole) derivatives have shown promising results when used as an active donor layer in bulk heterojunction photovoltaic cells with power conversion efficiency exceeding 7%. By using a simple correlation between density functional theory (DFT) theoretical calculations performed on six model compounds (using the repeating unit) and experimental data from the six corresponding polymers, an accurate estimation of the HOMO energy level, the LUMO energy levels, and the band gap of several poly(2,7‐carbazole) derivatives was obtained. According to the theoretical data obtained for more than one hundred repeating units, fourteen new copolymers that can be used as p‐type materials in bulk heterojunction solar cells were selected and synthesized. Experimental data obtained from these materials were then used to refine the correlation between DFT and experimental data of poly(2,7‐carbazole) derivatives.

     

Diffusion Crosslinking Kinetics of Thermoset Polymers

The problem of the delayed crosslinking arising due to the diffusion of a crosslinker molecule from a vector particle within a thermoset polymer matrix is discussed. The crosslinker molecules, initially embedded in the vector particles, diffuse from the particle to the polymer matrix and react with the functional groups grafted to polymer chains. The two‐step diffusion crosslink kinetics is studied theoretically on the example of polyethylene functionalized with anhydride groups reacting with 1,4‐butanediol as a crosslinker molecule. This provides the independent of time limiting distribution functions of the concentration of crosslinks, unreacted and intermediate functional groups, which are shown to be rather sensitive to system parameters as rates of chemical reactions, ratio of diffusion coefficients of matrix to vector particles, stoichiometric composition of the reactive groups, etc. The nonmonotonic distribution of the crosslink concentration around the vector particles at certain range of the parameters is revealed.

     

On the graph of a function in two variables over a finite field

We show that if the number of directions not determined by a pointset of , of size q² is at least p^e q then every plane intersects in 0 modulo p^e+1 points and apply the result to ovoids of the generalised quadrangles and .     

Stability of a Cubically Convergent Method for Generalized Equations

In Geoffroy et al, Acceleration of convergence in Dontchev's iterative method for solving variational inclusions Serdica Math. J. 29 (2003), pp. 45–54] we showed the convergence of a cubic method for solving generalized equations of the form 0 ∈ f(x) +- G(x) where f is a function and G stands for a set-valued map. We investigate here the stability of such a method with respect to some perturbations. More precisely, we consider the perturbed equation y ∈ f(x) +- G(x) and we show that the pseudo-Lipschitzness of the map (f +- G)⁻¹ is closely tied to the uniformity of our method in the sense that the attraction region does not depend on small perturbations of the parameter y. Finally, we provide an enhanced version of the convergence theorem established by Geoffroy, et al.     

Maharam's problem

We solve Maharam's problem [D. Maharam, An algebraic characterization of measure algebras, Ann. Math. 48 (1947) 154–167. [3]], also known as the Control Measure Problem. We construct a non-zero exhaustive submeasure on the algebra of clopen sets of the Cantor set that is not absolutely continuous with respect to a measure. To cite this article: M. Talagrand, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Photoinduced magnetism caused by charge-transfer excitations in tetracyanoethylene-based organic magnets

The photoinduced magnetism in Mn-tetracyanoethylene (TCNE) molecule-based magnets is ascribed to charge-transfer excitations from manganese to TCNE. Charge-transfer energies are calculated using density functional theory; photoinduced magnetization is described using a model Hamiltonian based on a double-exchange mechanism. Photoexciting electrons from the manganese core spins into the lowest unoccupied orbital of TCNE with photon energies around 3 eV increase the magnetization through a reduction of the canting angle of the manganese core spins for an average electron density on TCNE less than one. When photoexciting with a smaller energy, divalent TCNE molecules are formed. The delocalization of the excited electron causes a local spin flip of a manganese core spin.     

Entropy-driven formation of the gyroid cubic phase

We show, by computer simulation, that tapered or pear-shaped particles, interacting through purely repulsive interactions, can freely self-assemble to form the three-dimensionally periodic, gyroid cubic phase. The Ia3d gyroid cubic phase is formed by these particles on both compression of an isotropic configuration and expansion of a smectic A bilayer arrangement. For the latter case, it is possible to identify the steps by which the topological transformation from nonintersecting planes to fully interpenetrating, periodic networks takes place.     

Synthesis, crystal structure and reactivity of uranium(IV) complexes with p-tert-butylcalix[4]arene ligands

Reactions of UCl4 with 25,27-dimethoxy-5,11,17,23-tetra-tert-butylcalix[4]arene (H2Me2calix) in THF or pyridine at 80 degrees C gave [UCl2(Me2calix)L2] [L = THF (1) or pyridine (2)]. Similar treatment of U(acac)(4) (acac = MeCOCHCOMe) with H2Me2calix in THF or pyridine afforded [U(acac)2(Me2calix)] (3). The bis-calixarene compound [U(Me2calix)(H2calix)] (4) was obtained by reaction of U(OTf)4 or U(OTf)3 with H2Me2calix in pyridine at 110 degrees C. Treatment of UCl4 with H2Me2calix in pyridine at 110 degrees C gave [Mepy][UCl2(Hcalix)(py)2] (5) resulting from demethylation and acid cleavage of the methoxy groups of the calixarene ligand of 2. Adventitious traces of air were responsible for the formation of [Hpy][Mepy]4[{UCl(calix)}3(mu3-O)][UCl6] (6) during the reaction of UCl4 and H2Me2calix, and of [{U(Me2calix)(mu3-O)LiCl(THF)}2] (7) during the reaction of 2 with tBuLi. The X-ray crystal structures of 1.2THF, 2.2py, 3.0.25L (L = THF and py), 4.2py, 5, 6.3py and 7.THF have been determined.