Inverse spectral problems for energy-dependent Sturm-Liouville equations

We study the inverse spectral problem of reconstructing energy-dependent Sturm-Liouville equations from their Dirichlet spectra and sequences of the norming constants. For the class of problems under consideration, we give a complete description of the corresponding spectral data, suggest a reconstruction algorithm, and establish uniqueness of reconstruction. The approach is based on connection between spectral problems for energy-dependent Sturm-Liouville equations and for Dirac operators of special form.Comment: AMS-LaTeX, 28 page

Enhanced reversible solid-state photoswitching of a cationic dithienylethene assembled with a polyoxometalate unit

International audienceThe first photochromic supramolecular assembly of a dithienylethene (DTE) cation with a polyoxometalate (POM) is elaborated. The POM unit modifies the photoswitching of the DTE in the solid state, via both steric and electronic effects, resulting in an increase of its cycloreversion rate, and an almost complete re-opening process. The crystal structure after exposure to UV light reveals a remarkable photocyclization yield of almost 28%. The structural model was greatly improved by theoretical calculations, and the absorption properties were nicely modeled from electronic structure calculations

Strong solid-state luminescence enhancement in supramolecular assemblies of polyoxometalate and "Aggregation-Induced Emission"-active phospholium

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Investigation of Ga substitution in ZnO powder and opto-electronic properties

Two sets of Ga-doped ZnO powders were synthesized via solid-state and Pechini routes with a substitution rate varying from 0 to 4 mol %. The gallium solubility limit is strongly dependent on the synthesis history. Indeed, a low temperature annealing allows incorporating about 1.5 mol % (X-ray diffraction (XRD), inductive coupled plasma spectroscopy (ICP), optical properties) whereas under 0.1% of dopant is introduced after thermal treatment at high temperature: 1500 °C (from XRD and pellets conductivity). The incorporation of gallium leads to an anisotropic distortion of the zincite crystal lattice (a and c parameters increase and decrease, respectively, versus the Ga content leading to a decrease of the c/a ratio) which can be explained from the valence bond model. XRD analysis, chemical titration by ICP, and conductivity measurements (on pellets obtained at high temperature) allow determining accurately the maximum Ga content in the zincite. The optical properties (IR absorption efficiency) linked to electron carriers are directly correlated to the gallium rate introduced in ZnO oxide; nevertheless, the non linear correlation between these two parameters tends to show that the concentration of charge carriers in the system is not equal to the amount of Ga3+ atoms inserted per ZnO volume unit. A saturation regime is observed and was here explained once again on the basis of the valence band model by the increase of inhibiting p type defects with the increase of (n-type donors) Ga3+ concentration

Drastic solid-state luminescence color tuning of an archetypal Ir( iii ) complex using polyoxometalates and its application as a vapoluminescence chemosensor

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