From Multifractal Measures to Multifractal Wavelet Series

Given a positive locally finite Borel measure μ on R, a natural way to construct multifractal wavelet series is to set , where . Indeed, under suitable conditions, it is shown that the function F_μ inherits the multifractal properties of μ. The transposition of multifractal properties works with many classes of statistically selfsimilar multifractal measures, enlarging the class of processes which have self-similarity properties and controlled multifractal behaviors. Several perturbations of the wavelet coefficients and their impact on the multifractal nature of F_μ are studied. As an application, multifractal Gaussian processes associated with F_μ are created. We obtain results for the multifractal spectrum of the so-called W-cascades introduced by Arnéodo et al.     

Studies of the local structure in LixNi0.7Co0.3O2 (0.5≤x≤1.0) cathode materials

Among the Li_xNi_1−yCo_yO₂ system, LiNi_0.7Co_0.3O₂ is being considered one of the best cathode materials due to its small volume cell expansion upon charge-discharge cycling. In order to study the modifications of structural and physical properties occurring in the cathode materials during charge, different Li_xNi_0.7Co_0.3O₂ samples (0.5 ≥ x ≥ 1.0) were prepared by electrochemical lithium deintercalation in non-aqueous cells. During the first charge of the Li//Li_xNi_0.7Co_0.3O₂ cell, the structural change in the cathode lattice was followed by both x-ray powder diffraction and FTIR spectroscopy at room temperature. A good correlation is found between XRD data and the local environment of the host lattice. Paper presented at the 5th Euroconference on Solid State Ionics, Benalmádena, Spain, Sept. 13–20, 1998     

Physical properties of LiMn2O4 spinel prepared at moderate temperature

A moderate-temperature method of preparation of the spinel LiMn₂O₄ was developed around 500 °C. Physical features of the products were identified by X-ray photoelectron spectroscopy, X-ray diffractometry, Raman scattering and FTIR spectroscopy. The electronic conductivity of LiMn₂O₄ has been studied as a function of annealing temperature. The product LiMn₂O₄ is identified as a micron-sized powder and analysis of the local environment is in good accordance with the classical structural model of Fd3m space group. LiMn₂O₄ exhibits an electrical conductivity of 1.9×10⁻⁵ S/cm at room temperature with an activation energy of 0.16 eV which corresponds to an electron hopping mechanism between the two charge states of Mn³⁺ and Mn⁴⁺ ions. A first-order phase transition is observed at 292 K.     

Theoretical calculations and Raman spectrum of intercalation modes in LixInSe

By using an extended linear-chain model which includes the interlayer forces, we have calculated the new vibrational modes, of Li intercalated InSe. The dispersion curves along thek _z wavevector perpendicular to the layers for the -polytype are determined in the first Brillouin zone. Assuming that the interlayer interaction is not modified upon intercalation and the interaction between lithium atom and adjacent layers in the van der Waals plane has the same value than the interlayer one, the new modes are determined with the force constant given by the rigid layer mode of the, -polytype at 18 cm^–1. This model gives the variation of the acoustic branches and the appearance of two optical intercalation modes at higher frequencies. The Brillouin zone boundary modes of the acoustic branches at 18 and 41 cm^–1 in the pure material are calculated to be 22 and 50 cm^–1 respectively forx=1/2. The dispersion of the new optical branches is flat along thez-direction and frequencies are obtained at 96 cm^–1 for the Li mode perpendicular tok _z and at 218 cm^–1 for the Li mode parallel tok _z. We compare also our results with the Li mode frequencies obtained in a total energy calculation. Raman scattering experiments have been performed in intercalated sample in order to verify the proposed model.     

Adaptive instant record signals applied to detection with time reversal operator decomposition

Time reversal arrays are becoming common tools whether for detection or tomography. These applications require the measurement of the response from the array to one or several receivers. The most natural way to record the impulse responses for several sources is to generate pulses successively from each emitting point and record simultaneously the signals from the receivers. However, this method is very time consuming or inefficient in terms of signal-to-noise ratio. To overcome this limitation quasi-orthogonal pseudonoise signals like Kasami sequences can be used. For guided wave propagation, a very high degree of orthogonality between the signal is necessary to allow an accurate measure of the whole multipath structure of the transfer function. Hence, in this work, we propose a new family of pseudo-orthogonal signals that is adapted to the environment and more specifically, to highly dispersive media. These adaptive instant records signals are used experimentally to detect targets using the time reversal operator decomposition method. The accuracy of the 15 x 15 transfer functions acquired simultaneously, and therefore the detection capability, are demonstrated in an experimental ultrasonic waveguide as a small-scale model of shallow water propagation including bottom absorption and reverberation.     

Characterization Theorem for Best Polynomial Spline Approximation with Free Knots,Variable Degree and Fixed Tails

In this paper, we derive a necessary condition for a best approximation by piecewise polynomial functions of varying degree from one interval to another. Based on these results, we obtain a characterization theorem for the polynomial splines with fixed tails, that is the value of the spline is fixed in one or more knots (external or internal). We apply nonsmooth nonconvex analysis to obtain this result, which is also a necessary and sufficient condition for inf-stationarity in the sense of Demyanov–Rubinov. This paper is an extension of a paper where similar conditions were obtained for free tails splines. The main results of this paper are essential for the development of a Remez-type algorithm for free knot spline approximation.     

trans-cis Photoisomerization of the styrylpyridine Ligand in [Re(CO)3(2,2'-bipyridine)(t-4-styrylpyridine)]+: role of the metal-to-ligand charge-transfer excited states

The trans-cis isomerization of the styrylpyridine carbon-carbon double bond induced by visible light irradiation in fac-[Re(CO)(3)(bpy)(stpy)](+) (bpy = 2,2'-bipyridine; stpy = t-4-styrylpyridine) has been investigated by means of quantum-chemical methods. The structures of the various cis and trans conformers of [Re(CO)(3)(bpy)(stpy)](+) have been optimized at the density functional theory (DFT) level. Three rotational conformers for the most stable trans isomer lie within 2.3 kJ mol(-1) each other. The energy difference between the cis and trans isomers is 27.0 kJ mol(-1). The electronic spectroscopy of the most stable conformers has been investigated by time-dependent DFT (TD-DFT) and complete active space self-consistent field/CAS second order perturbation theory (CASSCF/CASPT2) calculations. The lowest absorption bands are dominated by metal-to-ligand charge-transfer (MLCT, d(Re)-->pi*(bpy)) transitions calculated at about 25,000 cm(-1) and by a strong intraligand (1)IL (pi(stpy)-->pi*(stpy)) transition in the near UV region. On the basis of CASSCF potential energy curves (PECs) calculated as a function of the torsion angle of the C=C bond of the styrylpyridine ligand, it is shown that the role of the low-lying MLCT states is important in the photoisomerization mechanism. In contrast to the free organic ligand, in which the singlet mechanism is operational via the (1)IL (S(1)) and electronic ground (S(0)) states, coordination to the rhenium steers the isomerization to the triplet PEC corresponding to the (3)IL state. From the (3)IL(t) (t = trans) the system evolves to the perpendicular intermediate (3)IL(p) (p = perpendicular) following a 90 degrees rotation around the styrylpyridine C=C bond. The metal center acts as a photosensitizer because of the presence of photoactive MLCT states under visible irradiation. The position of the crossing between the (3)IL and electronic ground state PEC determines the quantum yield of the isomerization process.     

Acid-induced degradation of phosphorescent dopants for OLEDs and its application to the synthesis of tris-heteroleptic iridium(III) bis-cyclometalated complexes

Investigations of blue phosphorescent organic light emitting diodes (OLEDs) based on [Ir(2-(2,4-difluorophenyl)pyridine)(2)(picolinate)] (FIrPic) have pointed to the cleavage of the picolinate as a possible reason for device instability. We reproduced the loss of picolinate and acetylacetonate ancillary ligands in solution by the addition of Br?nsted or Lewis acids. When hydrochloric acid is added to a solution of a [Ir(C^N)(2)(X^O)] complex (C^N = 2-phenylpyridine (ppy) or 2-(2,4-difluorophenyl)pyridine (diFppy) and X^O = picolinate (pic) or acetylacetonate (acac)), the cleavage of the ancillary ligand results in the direct formation of the chloro-bridged iridium(III) dimer [{Ir(C^N)(2)(μ-Cl)}(2)]. When triflic acid or boron trifluoride are used, a source of chloride (here tetrabutylammonium chloride) is added to obtain the same chloro-bridged iridium(III) dimer. Then, we advantageously used this degradation reaction for the efficient synthesis of tris-heteroleptic cyclometalated iridium(III) complexes [Ir(C^N(1))(C^N(2))(L)], a family of cyclometalated complexes otherwise challenging to prepare. We used an iridium(I) complex, [{Ir(COD)(μ-Cl)}(2)], and a stoichiometric amount of two different C^N ligands (C^N(1) = ppy; C^N(2) = diFppy) as starting materials for the swift preparation of the chloro-bridged iridium(III) dimers. After reacting the mixture with acetylacetonate and subsequent purification, the tris-heteroleptic complex [Ir(ppy)(diFppy)(acac)] could be isolated with good yield from the crude containing as well the bis-heteroleptic complexes [Ir(ppy)(2)(acac)] and [Ir(diFppy)(2)(acac)]. Reaction of the tris-heteroleptic acac complex with hydrochloric acid gives pure heteroleptic chloro-bridged iridium dimer [{Ir(ppy)(diFppy)(μ-Cl)}(2)], which can be used as starting material for the preparation of a new tris-heteroleptic iridium(III) complex based on these two C^N ligands. Finally, we use DFT/LR-TDDFT to rationalize the impact of the two different C^N ligands on the observed photophysical and electrochemical properties.