On extending existence theory from scalar ordinary differential equations to infinite quasimonotone systems of functional equations

In this paper we use Tarski's fixed point theorem to extend in a systematic way the existence of extremal solutions from scalar initial value problems to boundary value problems for infinite quasimonotone functional systems of differential equations.

     

Phase-averaged measurements of the turbulence properties in the near wake of a circular cylinder at high Reynolds number by 2C-PIV and 3C-PIV

The near wake of a circular cylinder at high Reynolds number is investigated by means of 2D-PIV and stereoscopic PIV. Phase-averaged measurements of the instantaneous fields have been performed. The linear stochastic estimation (LSE) has been adapted to estimate the phase-averaged quantities. This avoids the long time acquisition and the large storage needed for phase averaging. A good comparison is achieved between the results of the conditional sampling and those of LSE. Therefore, the estimation has been applied to the three-component datas and allowed evaluation of the whole phase-averaged turbulent stress tensor.     

Optical and structural characterization of iron oxide and cobalt oxide thin films at 800 nm

We report on optical and structural properties of α-Fe₂O₃ and Co₃O₄ thin films, grown by direct oxidation of pure metal films deposited on soda-lime glass. Structural characteristics and morphology of the films were investigated by X-ray diffraction, atomic force microscopy, and scanning electron microscopy. Linear optical absorption, and linear refraction as well as nonlinear optical properties were investigated. The third-order optical susceptibilities were measured applying the Thermally managed Z-scan technique using a Ti: sapphire laser (150 fs; 800 nm). The results obtained for the Co₃O₄ film were \( \text{Re} \chi^{\left( 3 \right)} \) = ?(5.7 ± 2.4) ×10^?9 esu and \( \text{Im} \chi^{(3)} \) = ?(1.8 ± 0.2) ×10^?8 esu while for the α-Fe₂O₃ film we determined \( \text{Re} \chi^{(3)} \) = +(6.6 ± 2.4) ×10^?10 esu and \( \text{Im} \chi^{(3)} \) = +(2.2 ± 0.4) ×10^?10 esu.     

When did Hermann Weyl pass away?

We show that in the existing bibliography there are many contradictory claims about the exact date of death of Hermann Weyl and, after a detailed exposition of the way we got our evidence, we demonstrate that Weyl died on 8 December 1955. The paper also shows up the fact that an authoritative intellectual biography on Weyl is yet to be written.     

A stepwise retro‐imino‐ene as a key step in the mechanism of allene formation via the Crabbé acetylene homologation

The mechanism of the acetylene homologation procedure accidentally discovered and further developed by Crabbé and coworkers is unknown. Kinetic isotope effect (KIE) experiments, however, suggest that an intramolecular hydrogen shift is the key step of the transformation. In this work, we present a computational study of this mechanism. We found that the reaction proceeds via an unexpected stepwise retro‐imino‐ene rearrangement. This mechanism justifies the role of Cu(I) as a reaction catalyst and is also compatible with the KIE experiments reported. © 2012 Wiley Periodicals, Inc.     

A Chiral Molecular Cage Comprising Diethynylallenes and N-Heterotriangulenes for Enantioselective Recognition

Chirality, a characteristic tool of molecular recognition in nature, is often a complement of redox active systems. Scientists, in their eagerness to mimic such sophistication, have designed numerous chiral systems based on molecular entities with cavities, such as macrocycles and cages. In an attempt to combine chirality and redox-active species, in this contribution we report the synthesis and detailed characterization of a chiral shape-persistent molecular cage based on the combination of enantiopure diethynylallenes and electron-rich bridged triarylamines, also known as N-heterotriangulenes. Its ability for chiral recognition in solution was revealed through UV/vis titrations with enantiopure helicenes.     

Random fiber laser

We investigate the effects of two-dimensional confinement on the lasing properties of a classical random laser system operating in the incoherent feedback (diffusive) regime. A suspension of 250 nm rutile (TiO2) particles in a rhodamine 6G solution was inserted into the hollow core of a photonic crystal fiber generating the first random fiber laser and a novel quasi-one-dimensional random laser geometry. A comparison with similar systems in bulk format shows that the random fiber laser presents an efficiency that is at least 2 orders of magnitude higher.