Directional Study of the Optical Properties of Tb3+‐ and Eu3+‐Doped Nanoparticles Embedded in Silica Photonic Crystals

The effects of the stop band (SB) in colloidal photonic crystals composed of silica spheres containing Eu³⁺‐ and Tb³⁺‐doped yttria nanoparticles are analysed. Reflection and transmission spectra indicate movement of the stop band, due to the 111 series of planes, towards shorter wavelengths with increasing angle of observation. The profile of the emission spectra is modified by the presence of the SB depending on the angle of measurement. Such a modification is more effective for a narrow emission band and it is thus more evident in the case of Tb³⁺ than Eu³⁺. An angular effect is also observed in the lifetime, which presents two maxima and one minimum. In the case of Tb³⁺ the maxima are at observation angles of 35 and 50°, and the minimum at 45°. We attribute this behaviour to penetration of the excitation beam at 475 nm modulated by the stop band. The ions excited in this way emit from different depths in the crystal, and therefore their lifetime will be affected differently by the same stop band, depending on the thickness of the crystal that must be crossed. Eu³⁺ shows a similar but less pronounced effect for two reasons: first, the main stop band (due to the 111 planes) is not effective at the excitation wavelength of 392 nm; second, the broadness of the Eu³⁺ emission is comparable to the width of the SB, and a decrease in the transition rate at the wavelength of the SB maximum is compensated by an increase at the sides of the SB.     

1,3,5-Triazepane-2,6-diones as structurally diverse and conformationally constrained dipeptide mimetics: identification of malaria liver stage inhibitors from a small pilot library

The development of the 1,3,5-triazepane-2,6-dione system as a novel, conformationally restricted, and readily accessible class of dipeptidomimetics is reported. The synthesis of the densely functionalized 1,3,5-triazepane-2,6-dione skeleton was achieved in only four steps from a variety of simple linear dipeptide precursors. To extend the practical value of 1,3,5-triazepane-2,6-diones, a general polymer-assisted solution-phase synthesis approach amenable to library production in a multiparallel format was developed. The conformational preferences of the 1,3,5-triazepane-2,6-dione skeleton were investigated in detail by NMR spectroscopy and X-ray diffraction. The ring exhibits a characteristic folded conformation which was compared to that of related dipeptide-derived scaffolds including the more planar 2,5-diketopiperazine (DKP). Molecular and structural diversity was increased further through post-cyclization appending operations at urea nitrogens. Preliminary biological screens of a small collection of 1,3,5-triazepane-2,6-diones revealed inhibitors of the underexplored malaria liver stage and suggest strong potential for this dipeptide-derived scaffold to interfere with and to modulate biological pathways.     

Analysis and Approximation of a Stochastic Growth Model with Extinction

We consider a stochastic growth model for which extinction eventually occurs almost surely. The associated complete Fokker–Planck equation describing the law of the process is established and studied. This equation combines a PDE and an ODE, connected one to each other. We then design a finite differences numerical scheme under a probabilistic viewpoint. The model and its approximation are evaluated through numerical simulations.     

Links between the Slater Index and the Ryser Index of Tournaments

Given a tournament T, the Slater index i(T) of T is the minimum number of arcs that must be reversed to make T transitive. The Ryser index (T) of T, defined from the out-degrees of T, measures a remoteness between T and the transitive tournaments of same order. In this paper, we study some links between i(T) and (T). More precisely, calling I(n, ) the maximum value of i(T) over the set of tournaments on n vertices and such that (T)=, we compute an upper bound of I(n,) for every value of . Then we use this upper bound to study a conjecture stated by J.-C. Bermond on the regularity (i.e., the fact that all the out-degrees are equal or almost equal) of the tournaments with a maximum Slater index by showing that the out-degrees of such tournaments cannot be too far from the ones of the regular tournaments.