The Weil-��tale fundamental group of a number field II

We define the fundamental group underlying the Weil-étale cohomology of number rings. To this aim, we define the Weil-étale topos as a refinement of the Weil-étale sites introduced by Lichtenbaum (Ann Math 170(2):657–683, 2009). We show that the (small) Weil-étale topos of a smooth projective curve defined in this paper is equivalent to the natural definition. Then we compute the Weil-étale fundamental group of an open subscheme of the spectrum of a number ring. Our fundamental group is a projective system of locally compact topological groups, which represents first degree cohomology with coefficients in locally compact abelian groups. We apply this result to compute the Weil-étale cohomology in low degrees and to prove that the Weil-étale topos of a number ring satisfies the expected properties of the conjectural Lichtenbaum topos.     

Attosecond resolved electron release in two-color near-threshold photoionization of N2

We have simulated two-color photoionization of N(2) by solving the time-dependent Schr?dinger equation with a simple model accounting for the correlated vibronic dynamics of the molecule and of the ion N(2)(+). Our results, in very good agreement with recent experiments [Haessler et al., Phys. Rev. A 80, 011404 (2009)], show how a resonance embedded in the molecular continuum dramatically affects the phases of the two-photon transition amplitudes. In addition, we introduce a formal relation between these measurable phases and the photoelectron release time, opening the way to attosecond time-resolved measurements, equivalent to double-slit experiments in the time domain.     

Mechanism of YF3 nanoparticle formation in reverse micelles

This article reports an investigation of the mechanism of YF(3) nanoparticle formation in two variants of the reverse microemulsion precipitation method. These two variants involve the addition of F(-), either as a microemulsion or directly as an aqueous solution, to Y(3+) dispersed in nonionic reverse micelles. The two methods yield amorphous and single-crystal nanoparticles, respectively. The kinetics of reagent mixing are studied by (19)F NMR and colorimetric model reactions, and the particle growth is monitored by TEM. Mixing and nucleation are shown to occur within seconds to minutes whereas particle growth continues for 4 to 48 h, depending on the particle type. Moreover, the growth rate remains constant during most of the growth period, indicating that Ostwald ripening is the most probable growth mechanism. The single-emulsion method also produces a minority amorphous population that exhibits significantly different growth kinetics, attributed to a coagulation mechanism. Secondary growth experiments, involving the addition of precursor ions to mature particles, have been conducted to evaluate the relative importance of nucleation and the competitive growth of existing particle populations. The key differences between the two methods reside in the nucleation step. In the case of the classical method, nucleation occurs upon intermicellar collisions and under conditions of comparable concentrations of Y(3+) and F(-). This method generates more numerous stable nuclei and smaller particles. In the single-microemulsion method, nucleation occurs in the presence of excess F(-) through the interaction of Y(3+)-containing micelles with microdroplets of aqueous F(-). These conditions lead to the formation of crystalline particles and a wider size distribution of unstable nuclei.     

Some Remarks on the Eigenvalue Multiplicities of the Laplacian on Infinite Locally Finite Trees

We consider the continuous Laplacian on an infinite uniformly locally finite network under natural transition conditions as continuity at the ramification nodes and the classical Kirchhoff flow condition at all vertices in a L ^∞-setting. The characterization of eigenvalues of infinite multiplicity for trees with finitely many boundary vertices (von Below and Lubary, Results Math 47:199–225, 2005, 8.6) is generalized to the case of infinitely many boundary vertices. Moreover, it is shown that on a tree, any eigenspace of infinite dimension contains a subspace isomorphic to ${\ell^\infty({\mathbb N})}$ . As for the zero eigenvalue, it is shown that a locally finite tree either is a Liouville space or has infinitely many linearly independent bounded harmonic functions if the edge lengths do not shrink to zero anywhere. This alternative is shown to be false on graphs containing circuits.     

On the finiteness of the Morse index for Schr?dinger operators

We show that if M is a complete Riemannian manifold and H = Δ + V is a Schr?dinger operator, then the existence of a positive solution of Hu?=?0 outside a compact set is equivalent to the finiteness of the Morse index of H.     

Helical γ-Peptide Foldamers as Dual Inhibitors of Amyloid-β Peptide and Islet Amyloid Polypeptide Oligomerization and Fibrillization

Type 2 diabetes (T2D) and Alzheimer's disease (AD) belong to the 10 deadliest diseases and are sorely lacking in effective treatments. Both pathologies are part of the degenerative disorders named amyloidoses, which involve the misfolding and the aggregation of amyloid peptides, hIAPP for T2D and Aβ_1-42 for AD. While hIAPP and Aβ_1-42 inhibitors have been essentially designed to target β-sheet-rich structures composing the toxic amyloid oligomers and fibrils of these peptides, the strategy aiming at trapping the non-toxic monomers in their helical native conformation has been rarely explored. We report herein the first example of helical foldamers as dual inhibitors of hIAPP and Aβ_1-42 aggregation and able to preserve the monomeric species of both amyloid peptides. A foldamer composed of 4-amino(methyl)-1,3-thiazole-5-carboxylic acid (ATC) units, adopting a 9-helix structure reminiscent of 3₁₀ helix, was remarkable as demonstrated by biophysical assays combining thioflavin-T fluorescence, transmission electronic microscopy, capillary electrophoresis and mass spectrometry.     

Parahydrogen-Induced Polarization of Diethyl Ether Anesthetic

The growing interest in magnetic resonance imaging (MRI) for assessing regional lung function relies on the use of nuclear spin hyperpolarized gas as a contrast agent. The long gas-phase lifetimes of hyperpolarized ¹²⁹Xe make this inhalable contrast agent acceptable for clinical research today despite limitations such as high cost, low throughput of production and challenges of ¹²⁹Xe imaging on clinical MRI scanners, which are normally equipped with proton detection only. We report on low-cost and high-throughput preparation of proton-hyperpolarized diethyl ether, which can be potentially employed for pulmonary imaging with a nontoxic, simple, and sensitive overall strategy using proton detection commonly available on all clinical MRI scanners. Diethyl ether is hyperpolarized by pairwise parahydrogen addition to vinyl ethyl ether and characterized by ¹H NMR spectroscopy. Proton polarization levels exceeding 8 % are achieved at near complete chemical conversion within seconds, causing the activation of radio amplification by stimulated emission radiation (RASER) throughout detection. Although gas-phase T₁ relaxation of hyperpolarized diethyl ether (at partial pressure of 0.5 bar) is very efficient, with T₁ of ca. 1.2 second, we demonstrate that, at low magnetic fields, the use of long-lived singlet states created via pairwise parahydrogen addition extends the relaxation decay by approximately threefold, paving the way to bioimaging applications and beyond.     

Bright Electrogenerated Chemiluminescence of a Bis‐Donor Quadrupolar Spirofluorene Dye and Its Nanoparticles

A series of symmetric fluorescent dyes built from a spirofluorene core bearing electroactive end groups and having different conjugated linkers were prepared with a view to their use as building blocks for the preparation of electrochemiluminescent (ECL) dyes and nanoparticles. Their electrochemical, spectroelectrochemical, and ECL properties were first investigated in solution, and structure/activity relationships were derived. The electrochemical and ECL properties show drastic variation that could be tuned by means of the nature of the π‐conjugated system, the end groups, and the core. In this series, highly fluorescent dye 1 based on a spirofluorene core and triphenylamine end groups connected via thiophene moieties shows the most promising and intriguing properties. Dye 1 is reversibly oxidized in three well‐separated steps and generates a very intense and large ECL signal. Its ECL efficiency is 4.5 times higher than that of the reference compound [Ru(bpy)₃]²⁺ (bpy=2,2′‐bipyridine). This remarkably high efficiency is due to the very good stability of the higher oxidized states and it makes 1 a very bright organic ECL luminophore. In addition, thanks to its molecular structure, this dye retains fluorescence after nanoprecipitation in water, which leads to fluorescent organic nanoparticles (FONs). The redox behavior of these FONs shows oxidation waves consistent with the initial molecular species. Finally, ECL from FONs made of 1 was recorded in water and strong ECL nanoemitters are thus obtained.