Modular curves and Poncelet polygons

Parts of the results and the essential techniques of this note are taken from the Erlangen thesis (1991) of the second author. They were circulated as Nr. 122 of Schriftenreihe Komplexe Mannigfaltigkeiten. Our research was supported by DFG grant Ba 423/3-3 and the European Science Project Geometry of Algebraic Varieties SCI-0398-C(A)     

Negative ion mass spectra of some unsaturated C-glycosides following keV ion bombardment

A series of anomeric unsaturated C-glycosides were studied by negative ion mass spectrometry following keV ion bombardment The compounds bearing an acidic hydrogen show a prominent [M ? H]^? peak; in the other cases, the [M ? H]^? peak is of very low intensity. A retro-Diels–Alder fragmentation and the abstraction of a hydrogen atom from the aglycon residue are observed in all cases.     

Thermodynamics of mixtures of hexane and heptane isomers with normal and branched hexadecane

Molar excess mixing enthalpies h ^E , Gibbs free energies g ^E and hence entropies s ^E have been obtained using calorimetry and the vapor sorption method at 25°C for hexane isomers+2,2,4,4,6,8,8-heptamethylnonane, a highly branched C ₁₆ . The h ^E and g ^E are negative while Ts ^E are positive, but small. The values are explained by the Prigogine-Flory theory through negative free volume contributions to h ^E and Ts ^E , counterbalanced in the case of Ts ^E by the positive combinatiorial Ts ^E for mixing molecules of different size. No contribution is seen from the interaction between methyl and methylene groups. The excess quantities are also obtained for hexane and heptane isomers mixed with n-hexadecane. Values of h ^E and Ts ^E are now strongly positive, while those of g ^E are only slightly less negative. The interpretation requires two recently advanced contributions in addition to those of the Prigogine-Flory theory: 1) a decrease of order when correlations of orientations between n-C ₁₆ molecules in the pure liquid are replaced in the solution by weaker correlations whose strengths depend on the shapes of the lower alkane isomers. For lower alkane isomers of the same shape, but highly sterically hindered, h ^E and Ts ^E are small, manifesting, 2) a negative contribution, ascribed to a rotational ordering of n-C ₁₆ segments on the sterically-hindered molecule. Enthalpy-entropy compensation is observed for these new contributions, arising from their rapid fall-off with increase of temperature.     

Mécanisme de la réaction de cyclisation en milieu aqueux de carbanilates de propargyle en méthylène-4 oxazolidinones-2

The alkaline hydrolysis of propargyl 3-chlorocarbanilates was investigated kinetically using uv spectropotometry. The cyclization to 4-methoylene-2-oxazolisinones proceeds via the numcleophilic attack of the substrate anion concomitantly with that of the hydroxide ion on the triple bond. The nucleophilic attack leads directly to the heterocycle whereas the hydroxide ion attack gives rise to a ketocarbamate which is then cyclized to the oxazolidione.     

Two unexpected effects concerning perturbations of the B3Π0u+ state of molecular iodine

We present in this paper two new effects observed in the state of molecular iodine: a very high diamagnetic correction in the vibrational level υ′ = 62 and an important orientation of the optically excited molecules due to predissociation. Both effects can be interpreted by taking into consideration the perturbation of the B state by other electronic states.     

Matrix-assisted laser desorption/ionisation mass spectrometry for the direct analysis of enzymatically digested kappa- iota- and hybrid iota/nu-carrageenans

Enzymatically digested oligosaccharides of kappa-, iota- and hybrid iota/nu-carrageenans were analysed using matrix-assisted laser desorption/ionisation time-of-flight mass spectrometry in the negative-ion mode. nor-Harmane was used as matrix. Depending on the stock concentration and the laser intensity applied, the oligosaccharides exhibited losses of sulphate units (neutralised by the Na+ ion, and thus non-stable), leaving the primary backbone structure in most cases with only the deprotonated sulphate groups (carrying the negative charge, stable). This meant that kappa- and iota-oligosaccharides could not be easily distinguished from one another since they share the same primary backbone structure. However, for the hybrid iota/nu-oligosaccharides the primary backbone structure could be identified since the nu-carrageenan repeating unit differs from that of the kappa/iota-carrageenan unit. For all types of oligosaccharides, the results indicated cleavage of an anhydrogalactose unit from the non-reducing end. Specifically, for the hybrid oligosaccharides of iota/nu-carrageenans, this type of fragmentation means that the nu-carrageenan unit is not positioned on the non-reducing end of the hybrid oligosaccharides. Dehydration reactions, and exchange reactions of Na+ with K+ and Ca2+, were also observed.     

The Reaction of Singlet Oxygen with Adamantylideneadamantane Mediated by Rose Bengal

The photo-oxygenation of adamantylideneadamantane ( 1 ) on siliceous supports using admixed granules of ion-exchange resin fixed to methylene blue (MB) and rose bengal (RB) gave exclusively the corresponding dioxetane derivative 2 for the former sensitizer, while the latter gave 2 and traces of the epoxide 3. RB and the charge-transfer complex produced from N-ethylcarbazole and 2,4,5,6-tetranitrofluoren-9-one both reacted with chemically generated singlet oxygen to give superoxide radical anion. Trapping of the latter with 5,5-dimethyl-1-pyrroline 1-oxide gave an adduct exhibiting a characteristic ESR spectrum. The treatment of 1 in MeOH with 30% aqueous H₂O₂ for 22 h at 60° gave 3 in 100% yield. Repetition of this experiment in the presence of 2,6-di(tert-butyl)-p-cresol caused no significant change. These results indicate that singlet oxygen reacts with 1 , in the presence of RB, by two different processes. The first leads to dioxetane formation. The second process involves conversion of singlet oxygen by RB to superoxide radical anion which subsequently gives H₂O₂ so producing epoxide 3 from 1 .     

Intrinsic folding of small peptide chains: spectroscopic evidence for the formation of beta-turns in the gas phase

Laser desorption of model peptides coupled to laser spectroscopic techniques enables the gas-phase observation of genuine secondary structures of biology. Spectroscopic evidence for the formation of beta-turns in gas-phase peptide chains containing glycine and phenylalanine residues establishes the intrinsic stability of these forms and their ability to compete with other stable structures. The precise characterization of local minima on the potential energy surface from IR spectroscopy constitutes an acute assessment for the state-of-the-art quantum mechanical calculations also presented. The observation of different types of beta-turns depending upon the residue order within the sequence is found to be consistent with the residue propensities in beta-turns of proteins, which suggests that the prevalence of glycine in type II and II' turns stems essentially from an energetic origin, already at play under isolated conditions.