Functionalized polynorbornenes with fragments of cholic acid and luminophore complexes of iridium(III) and copper(I) in side chains. Synthesis and photophysical properties

Copolymers containing fragments of cholic acid and luminophore complexes of iridium(III) and copper(I) in the side chains have been synthesized by metathesis polymerization. Photophysical properties of the obtained compounds have been investigated. Iridium-containing copolymers demonstrate intense photoluminescence of green, bluish-green and red colors. Copper-containing copolymers generate radiation of green and yellow-green colors. The color of photoluminescence of the metal-containing polymers is determined by the nature of copper(I) and iridium(III) complexes bonded to polymer chain.     

On a Diophantine Inequality with Reciprocals

We generalize Chebotarev’s density theorem to Weil groups. Since the Artin–Weil conjecture on the integrality of the Artin–Hecke L-functions, constructed by A. Weil, has not been completely proved so far, we estimate the character sums both under and without the assumption of the validity of that conjecture.     

Lithium deintercalation/intercalation processes in cathode materials based on lithium iron phosphate with the olivine structure

This review describes the current state of the studies of lithium deintercalation/intercalation processes in cathode materials based on lithium iron phosphate with olivine structure. The limiting factors of LiFePO₄ charge/discharge processes, as well as the main methods for their acceleration are considered. A partial replacement of iron cations in the structure improves the electrochemical characteristics of the cathode materials, including the discharge capacity, charge/discharge rate, and, in some cases, changes the charge/discharge mechanism. The use of nanoscale phosphate LiFePO₄ with the olivine structure considerably increases the charge/discharge rate of cathode materials based on it by reducing the diffusion path length. Methods for LiFePO₄ surface modification are considered. Particular attention is paid to the development of composite materials with electron-conducting additives. Combining of various approaches to the modification of the material in question makes it possible to obtain materials with a discharge capacity close to the theoretical value (170 mA h g^–1) at a low charge/discharge rate and to considerably increase its capacity at high charge and discharge currents.     

3D microoptical elements formed in a photostructurable germanium silicate by direct laser writing

We present our investigations into the fabrication of three-dimensional microoptical elements by the direct femtosecond laser writing of a germanium–silicon photosensitive hybrid material. Germanium glass composites are very interesting for optical applications as they are photosensitive, and maintain high optical transparency in the visible and near-infrared bands of the spectrum. Here, we have used a germanium containing hybrid material to make nanophotonic structures and microoptical elements such as photonic crystal templates, prisms and spatial polarization plates, both on flat surfaces and fiber tips. Our results show that this germanium silicate composite is an excellent material for microoptics fabrication.     

Green’s functions for discrete mTH-order problems*

We investigate an mth-order discrete problem with additional conditions, described by m linearly independent linear functionals. We find the solution to this problem and present a formula and the existence condition of Green??s function if the general solution of a homogeneous equation is known. We obtain a relation between Green??s functions of two nonhomogeneous problems. It allows us to find Green??s function for the same equation, but with different additional conditions. The obtained results are applied to problems with nonlocal boundary conditions.     

Synthesis and optical properties of Ce-doped Y3Mg2AlSi2O12 phosphors

Y_3−xMg₂AlSi₂O₁₂:Ce_x³⁺ (x=0.015, 0.03 and 0.06) phosphors possessing garnet crystal structure were synthesized by the sol–gel combustion technique. The samples were characterized by application of powder X-ray diffraction (XRD), photoluminescence (PL) spectroscopy, thermal quenching (TQ) and scanning electron microscopy (SEM). Moreover, luminous efficacies (LE), color points and quantum efficiencies (QE) were calculated. Optical properties were studied as a function of Ce³⁺ concentration and annealing temperature. XRD analysis revealed that sintering of polycrystalline Y₃Mg₂AlSi₂O₁₂:Ce³⁺ powders at 1550 °C results in nearly single-phase garnet materials. Phosphors showed broad emission band in the range of 500–750 nm and had the maximum intensity at 600 nm, which results in strongly red-shifted phosphors compared with conventional YAG:Ce phosphors emitting at 560 nm. However, strong concentration quenching has also been observed, probably due to increased Stokes shift.     

An approximation property of lacunary sequences

Let f ₁ and f ₂ be two positive numbers of the field , and let f _n+2 = f _n+1 + f _n for each n ≥ 1. Let us denote by {x} the fractional part of a real number x. We prove that, for each ξ ∉ K, the inequality {ξf _n } > 2/3 holds for infinitely many positive integers n. On the other hand, we prove a result which implies that there is a transcendental number ξ such that {ξf _n } < 39/40 for each n ≥ 1. Moreover, it is shown that, for every a > 1, there is an interval of positive numbers that contains uncountably many numbers ξ such that {a ⁿ } 6 min 2/(a − 1), (34a ² − 32a + 7)/(9(2a − 1)²) for each n > 1. Here, the minimum is strictly smaller than 1 for each a > 1. In contrast, by an old result of Weyl, for any a > 1, the sequence {ξa ⁿ }, n = 1, 2, ..., is uniformly distributed in [0, 1] (and so everywhere dense in [0, 1]) for almost all real numbers ξ.     

Homologie cyclique,principe de Selberg et pseudo-coefficient

Sans résuméOblatum 8-VII-1992 & 14-VII-1993To Armand Borel     

Application of Statistical Rate Theory of Interfacial Transport to Study Solid Surface Heterogeneity from Controlled-rate Thermal Desorption

Controlled-rate thermodesorption (CRTD) spectra are obtained by adjusting the heating rate in such a way that the rate of desorption can be constant. A quantitative analysis of the obtained spectra is presented, based on application of the statistical rate theory of interfacial transport (SRTIT) to describe both adsorption and desorption kinetics. The SRTIT approach relates the rates of adsorption and desorption to the chemical potentials of the adsorbate in the gaseous and in the adsorbed phases. This quantitative analysis of the CRTD spectra yields the condensation approximation for the actual adsorption energy distribution. For the purpose of illustration, an analysis is made of water desorption from a synthetic apatite mineral under CRTD and classical TPD conditions. The influence of the adsorption and desorption rates is also discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Aqueous sol-gel synthesis route for the preparation of YAG: Evaluation of sol-gel process by mathematical regression model

Yttrium aluminium garnet (Y₃Al₅O₁₂, YAG) polycrystalline samples have been prepared by a simple aqueous sol-gel methodology. The influence of nineteen sol-gel processing variables on the formation of YAG has been investigated. Effects of different fabrication parameters on the phase purity and morphological properties of the compounds were studied by energy-dispersive spectrometry (EDS), X-ray powder diffraction (XRD) analysis and scanning electron microscopy (SEM). The parameters of the sol-gel processing such as pH of starting solution, concentration and nature of complexing ligand, temperature and duration of gelation, powder rehomogenization during annealing, duration and temperature of the final heat treatment were found to be the most significant. For the evaluation and verification of the experimental results the Brandon's model of a multiple regression was successfully used.