On second order differential equations with state-dependent delay

We study existence and uniqueness of solutions for a general class of second order abstract differential equations with state-dependent delay. Some examples related to partial differential equations with state dependent delay are presented.     

Stabilization of the uniform Timoshenko beam by one locally distributed feedback

In this article, we study the energy decay rate for an elastic Timoshenko system. This system consists of two coupled wave equations. Only the equation about the rotation angle is damped by one locally distributed feedback at the neighbourhood of the boundary. The equation for the transverse displacement of the beam is only indirectly damped through the coupling. First, we establish an exponential energy decay rate in the case of the same speed of propagation. Next, when the wave speeds are different, a polynomial-type decay rate is obtained. These results are proved by verifying the frequency domain conditions.     

Stabilization of the wave equations with localized Kelvin–Voigt type damping under optimal geometric conditions

The purpose of this note is to investigate the stabilization of the wave equation with Kelvin–Voigt damping in a bounded domain. Damping is localized via a non-smooth coefficient in a suitable subdomain. We prove a polynomial stability result in any space dimension, provided that the damping region satisfies some geometric conditions. The main novelty of this note is that the geometric situations covered here are richer than that considered in [25], [22], [16] and include in particular an example where the damping region is not localized in a neighborhood of the whole or a part of the boundary.     

Three polymorphic forms of the co-crystal 4,4'-bipyridine/pimelic acid and their structural, thermal, and spectroscopic characterization

Three crystal forms of the co-crystal 4,4'-bipy/pimelic acid (bipy: bipyridine), [NH(4)C(5)-C(5)H(4)N][HOOC(CH(2))(5)COOH], have been prepared and their relationship investigated by single-crystal X-ray diffraction, variable-temperature X-ray powder diffraction, differential scanning calorimetry and solid-state NMR spectroscopy. Both X-ray and NMR spectroscopic results indicate that no proton transfer takes place, that is, the three crystal forms are true co-crystals of neutral molecules. Forms I and II both convert into Form III at high temperature, Forms II and III being the thermodynamically stable forms at room and high temperature, respectively.     

Noncovalent interactions between ([18]crown-6)-tetracarboxylic acid and amino acids: electrospray-ionization mass spectrometry investigation of the chiral-recognition processes

Chiral recognition of enantiomers by host compounds is one of the most challenging topics in modern host-guest chemistry. Amongst the well-established methods, mass spectrometry (MS) is increasingly used nowadays, due to its low detection limit, short analysis time, and suitability for analyzing mixtures and for studying chiral effects in the gas phase. The development of electrospray-ionization (ESI) techniques provides an invaluable tool to study, in the gas phase, diastereoisomeric complex ions prepared from enantiomer ions and a chiral selector. This paper reports on an ESIMS and ESIMSMS study of the molecular mechanisms that intervene in the chiral-recognition phenomena observed between amino acids and a chiral crown ether. The modified crown ether, namely (+)-([18]crown-6)-2,3,11,12-tetracarboxylic acid, is used as the chiral selector when covalently bound on a stationary phase in liquid chromatography. This study was stimulated by the fact that, except with threonine and proline, consistent elution orders were observed, which indicates that the D enantiomers interact more strongly with the chiral selector than the L enantiomers. For proline, the lack of a primary amino group is likely to be responsible for the nonresolution of the two forms, whereas the second stereogenic center on threonine could explain the reversed elution order. In light of those observations, we performed mass spectrometry experiments to understand more deeply the enantiomeric recognition phenomena, both in solution by the enantiomer-labeled guest method and in the gas phase by gas-phase ligand-exchange ion/molecule reactions. The results have been further supported by quantum chemical calculations. One of the most interesting features of this work is the identification of a nonspecific interaction between proline and the crown ether upon ESIMS analysis.     

Electronic and infrared spectroscopy of jet-cooled (+/-)-cis-1-amino-indan-2-ol hydrates

The role of conformational isomerism in molecular interaction has been studied using the example of jet-cooled complexes of (+/-)-cis-1-amino-indan-2-ol with water. The two formerly evidenced conformers of (+/-)-cis-1-amino-indan-2-ol easily form hydrates and dihydrates, which have been studied by means of laser-induced fluorescence and IR/UV double resonance spectroscopy, as well as ab initio calculations. All the 1 : 1 and 1 : 2 complexes with water evidenced in this work involve "ring" structures, in which the water monomer or dimer acts as an acceptor from the NH(2) and a donor to the OH groups of (+/-)-cis-1-amino-indan-2-ol. However, the water lies externally to the indan frame in the hydrates of conformer I of (+/-)-cis-1-amino-indan-2-ol, which possesses axial NH(2) and equatorial OH groups, and above it for the hydrates with the less stable conformer II, with equatorial NH(2) and axial OH groups. Consequently, the different steric constraints which exist in the two conformers result in different hydrogen bond topologies, with an additional OH[dot dot dot]pi interaction for the hydrates of conformer II.     

The photophysical determination of the minimum hydrotrope concentration of aromatic hydrotropes

A method based on the aggregate to monomol emission ratio, I(aggr)/I(monomol), was used to determine the minimal hydrotropic concentration (MHC) of aromatic hydrotropes. The main advantage of this method is that it does not require the use of probes or other additives, which might disrupt the aggregation process. Also, it relies on spectrophotometric measurements, which are more sensitive and less arduous than others, like conductivity, light scattering and surface tension.