Sincov’s and other functional equations and negative interest rates

Aequationes mathematicae - Investigating the future value F(K, s, t) of a capital K invested between dates s and t, the “natural” condition $$F(K,s,t)ge K$$ has lost...     

Carboxylate Catalyzed Isomerization of β,γ-Unsaturated N-Acetylcysteamine Thioesters**

We demonstrate herein the capacity of simple carboxylate salts – tetrametylammonium and tetramethylguanidinium pivalate – to act as catalysts in the isomerization of β,γ-unsaturated thioesters to α,β-unsaturated thioesters. The carboxylate catalysts gave reaction rates comparable to those obtained with DBU, but with fewer side reactions. The reaction exhibits a normal secondary kinetic isotope effect (k_1H/k_1D=1.065±0.026) with a β,γ-deuterated substrate. Computational analysis of the mechanism provides a similar value (k_1H/k_1D=1.05) with a mechanism where γ-reprotonation of the enolate intermediate is rate determining.     

Development and characterization of ultra-porous silica films made by the sol–gel method. Application to biosensing

The aim of this work is to demonstrate the sensing ability of reverse-symmetry waveguides to investigate adsorption of casein and build-up of poly-L-lysine mediated casein multilayers. A first part of this study is dedicated to the elaboration and characterization of ultra-porous thin films with very low refractive indices by an appropriate sol–gel method. This will form the basis of our planar optical sensors. Optical waveguide light mode spectroscopy is a real-time and sensitive method to study protein adsorption kinetics and lipid bilayers. We used it to test the obtained waveguides for in-situ monitoring of biomolecule adsorption. As a result, significant changes in the incoupling peak position were observed during the layer-by-layer adsorption. Finally, refractive index and thickness of the adsorbed layers were established.     

Synthesis of hemilabile P,N-ligands with a pentane-2,4-diyl backbone

A general and convenient two-step synthetic method has been developed for the preparation of a novel class of aminoalkyl-phosphine type compounds, which involves nucleophilic ring-opening of cyclic sulfate esters. The ring-opening step was performed using several different aliphatic and aromatic amines to produce aminoalkyl sulfates that were reacted with LiPPh₂ to give the corresponding P,N-ligands. The desymmetrization procedure affords an easy route to synthesize enantiomerically pure pentane-2,4-diyl based P,N-ligands with a highly tunable structure. The ligands derived from primary amines have a stereogenic N-atom that can be useful in asymmetric catalytic syntheses.     

Evaluation of plasmon-loss spectra of molybdenum using elastic-peak electron spectroscopy

Plasmon-loss spectra of clean polycrystalline molybdenum surfaces have been determined in the primary energy range E_p = 50–3000 eV. Spectra a distributions (nonderivative mode). A simplified model is described for evaluating plasmon-loss spectra using elastic-peak electron spectroscopy, as de of elastically reflected electrons is determined by integrating the N(E) spectrum of secondary and backscattered electrons. The ratio of the ar (23–24 eV) to that of the elastic peak is Pλ, the product of the probability for creating a volume plasmon loss and the inelastic mean free pat second plasmon-loss peak is (Pλ)². Evaluation of our experimental plasmon-loss spectra gives Pλ = 0.4–0.5 for E_p > 500 eV. Th constitutes ～50% of all losses determining the IMFP, interband loss processes being important in the remainder. For the low energy range, E_p found. For E_p < 100 eV, no volume plasmon-loss peak could be detected in our N(E) spectra. The simplified model proves to be valid fo plasmon-loss peak (11–12 eV), i.e., such that N_pls/N_e ? 10^?2. Some results are presented concerning surface plasmon losses as molybdenum surface.     

On Hamiltonian Formulations of the Schrödinger System

We review and compare different variational formulations for the Schrödinger field. Some of them rely on the addition of a conveniently chosen total time derivative to the hermitic Lagrangian. Alternatively, the Dirac-Bergmann algorithm yields the Schrödinger equation first as a consistency condition in the full phase space, second as canonical equation in the reduced phase space. The two methods lead to the same (reduced) Hamiltonian. As a third possibility, the Faddeev-Jackiw method is shown to be a shortcut of the Dirac method. By implementing the quantization scheme for systems with second class constraints, inconsistencies of previous treatments are eliminated.     

Das tautomere Gleichgewicht des Bilirubins Kurze Mitteilung

The equilibrium between lactam and lactim forms of bilirubin was studied by means of optical pK-measurements of model compounds of the arylmethylidenepyrrolinone and pyrromethenone series as well as bilirubin, bilirubin dimethyl ester and dimethoxybilirubin dimethyl ester. The lactam form of bilirubin was found to be more stable by a factor of at least 10⁴ compared with the lactim form. Therefore the latter is not responsible for the spectroscopic anomalies of bilirubin.     

Optical resolution of a series of potential cholecystokinin antagonist 4(3H)-quinazolone derivatives by chiral liquid chromatography on alpha1-acid glycoprotein stationary phase

Optical resolution of the enantiomers of new 4(3H)-quinazolone derivatives is investigated using the alpha1-acid glycoprotein chiral stationary phase (Chiral-AGP). Stereoselective separation of the model compounds can be controlled by varying the pH and adding uncharged organic modifiers (acetonitrile and 2-propanol) to the mobile phase. For the majority of quinazolone derivatives, Chiral-AGP is proved to be an excellent enantioselector, because optimized chromatographic conditions allow for the baseline separation of the enantiomers. Separation factors between 1.19 and 1.85 are obtained. The effects of acetonitrile and 2-propanol on the chromatographic behavior of the model compounds are quite different because of their different hydrophobic- and hydrogen-bonding properties. The eluent pH and organic modifier concentration also contributes to the chiral recognition by altering the protein environment. The analysis of the experimental results leads to new information about the chromatographic mechanism on a Chiral-AGP surface.     

The Use of Principal Component Analysis for the Study of the Interaction of Anionic Surfactants with Hydroxypropyl-β- Cyclodextrin

The interaction of 11 sulfosuccinic acid ester anionic surfactants with hydroxypropyl--cyclodextrin (HPCD) were determined with reversed-phase thin-layer chromatography and the relative strength of interaction was calculated. The relationship between the strength of interaction and the physicochemical parameters of anionic surfactants was elucidated with principal component analysis (PCA). HPCD interacted with the anionic surfactants decreasing their hydrophobicity. The distribution of the points of the strength of interaction and physicochemical parameters on the two dimensional nonlinear map of PC loadings suggested that the strength of interaction between the anionic surfactants and HPCD is of mixed steric character, with hydrophobic and electronic forces being involved in the interaction.