Hyers–Ulam Stability of Euler’s Differential Equation

We obtain a result on generalized Hyers–Ulam stability for Euler’s differential equation in Banach spaces. Our result extends and improves some recent results of Mortici, Jung and Rassias concerning the stability of Euler’s equation on a bounded domain.     

A competitive sensing system based on cyclobis(paraquat-p-phenylene) and a new β-cyclodextrin-tetrathiafulvalene derivative

We report the synthesis of 4,5-di(ethylthio)-4′-[6-deoxy-β-cyclodextrin-6-yl-aminocarbonyl]-tetrathiafulvalene (β-CD-DET-TTF) and its inclusion abilities towards cyclobis(paraquat-p-phenylene) (CBPQT⁴⁺ ) and 1-naphthol. The structure of the synthesised compound has been established by mass spectrometry and ¹H NMR spectra combined with a theoretical MM3 and AM1 study. The sensor affords a charge transfer (CT) complex with the CBPQT⁴⁺  and is able to include 1-naphthol in the cyclodextrin cavity. The complexes were characterised experimentally by UV–vis spectroscopy and simulated by a MM3 docking procedure. The sensing ability of the β-CD-DET-TTF/CBPQT⁴⁺  complex towards 1-naphthol has been investigated by a competitive spectral method.

The synthesis and characterisation of a new water soluble β-CD-DET-TTF derivative able to formed a CT complex with the CBPQT⁴⁺  acceptor is reported. The water soluble CT complex β-CD-DET-TTF/CBPQT⁴⁺  could be used as an efficient sensor towards aromatic guests prone to give inclusion complexes with the CBPQT⁴⁺  ring.     

Development of a competitive continuous variation plot for the determination of inclusion compounds stoichiometry

The spectral displacement method in presence of methyl orange has been coupled to the continuous variation plot to allow the determination of the stoichiometries for inclusion compounds. Such a “competitive continuous variation plot” (CCV plot) is especially useful for the study of substrates which are not directly observable by spectroscopy or which are too poorly soluble to give observable signals. Moreover, when a mixture of complexes is observed, the position of the maximum in the competitive continuous variation plot gives information on the relative affinities of the complexes, which is not the case in the classical Job plot which also depends of the intrinsic spectral characteristics of each complex. The method is not restricted to β-cyclodextrin inclusion compounds, and it may be applied to any complexes if an appropriate competitive system is available.     

Novel local free energy minimum on the Cu(001) surface

High-resolution LEED (low-energy electron diffraction) data of Cu(001) reveal an uniaxial in-plane lattice reconstruction by 1%. One-dimensional nanogrooves induced by ion bombardment involve the creation of steps that enable this reconstruction. This is the first verification of van der Merwe's prediction of step facilitated reconstruction. We confirm the predicted dependence on step orientation: <100> steps allow stress-relief and <110> steps do not, consistent with the known elastic anisotropy. Similar behavior is predicted for other nonreconstructed (001) surfaces of 3d and 4d metals.     

The electrochemically tuneable recognition properties of an electropolymerised flavin derivative

The electrochemically tuneable recognition properties between an electropolymerised flavin derivative and 2,6-diethylamidopyridine are reported.     

Study of the Inclusion Complexes of β-Cyclodextrin with the Sodium Salt of Trisulfonated Triphenylphosphine

The formation of inclusion complexesbetween the sodium salt of trisulfonatedtriphenylphosphine and -cyclodextrin has beeninvestigated at two temperatures by high field nuclearmagnetic resonance, electrospray mass and UV-visspectroscopies. At 268 K, titration experiments andJob's method suggest that the major species insolution is a 1 : 1 inclusion complex. The moleculargeometry of this inclusion complex was studied usingthe ROESY NMR technique complemented by molecularmodelling. All these methods converged towards thestructure attained by inserting one aromatic ring intothe hydrophobic cavity of the host from the side ofthe secondary hydroxyls. At 298 K, a higher proportionof 2 : 1 and 3 : 1 complexes induces strong alterations ofthe NMR signals, preventing an easy and reliabledetermination of association constants. Nevertheless,an apparent association constant can be determinedfrom UV-vis data by assuming a 1 : 1 equilibrium. Thegeometry of the 2 : 1 and 3 : 1 complexes is also brieflydiscussed from ROESY NMR experiments.     

Analytical Improvement in Measuring Formation Constants of Inclusion Complexes between β-Cyclodextrin and Phenolic Compounds

Inclusion complex formation betweensixteen para-substituted phenols and-cyclodextrin have been investigated in orderto establish Quantitative Structure AffinityRelationships. An analytical methodology is proposed,in order to obtain reliable evaluation of bindingaffinities. Potentiometry and circular dichroism havebeen applied to define experimental conditions and toconfirm postulated equilibriums. In addition, the useof algorithmic treatments and concentrationoptimisation to determine formation constants leads tocoherent values between ¹H NMR, direct UVSpectroscopy and the spectral displacement method. Theresults emphasise the contribution of van der Waalsinteractions, provided that no significant differencein the dipole of the molecule arises from thepara-substituent.     

1,2,4-triazolium-ylures—VI: Réactions des triazolium-phénacylures avec les alcynes symétriques

In the reaction of 4-aryl-1,2,4-triazolium-phenacylides with dimethyl acetylcnedicarboxylate, the initial cyclo-adducts 5 undergo C-N bond fission giving 6–9.