Rigorous and accurate enclosure of invariant manifolds on surfaces

Knowledge about stable and unstable manifolds of hyperbolic fixed points of certain maps is desirable in many fields of research, both in pure mathematics as well as in applications, ranging from forced oscillations to celestial mechanics and space mission design. We present a technique to find highly accurate polynomial approximations of local invariant manifolds for sufficiently smooth planar maps and rigorously enclose them with sharp interval remainder bounds using Taylor model techniques. Iteratively, significant portions of the global manifold tangle can be enclosed with high accuracy. Numerical examples are provided.     

Formazane als funktionelle Gruppen chelatbildender Ionenaustauscher. I

Zusammenfassung Die Darstellung substituierter Formazane und ihre chemische Fixierung an Cellulose, amino- und chlormethyliertem Polystyrol wird beschrieben. Die Kapazitäten der Austauscher liegen zwischen 0,05 mÄq/g (Cellulose) und 0,6 mÄq/g (Polystyrol). In neutralem Medium zeigen sie eine besondere Affinität zu Hg(II), Pd(II) und Ag(I), aber keine Affinität zu Cu(II). Weiterhin wurde eine spektrophotometrische Bestimmung von Hg(II) und Ag(I) mit dem wasserlöslichen Formazan (FII)-NO₂ ausgearbeitet [Hg(II): ₅₄₆=23 000 l Mol^–1 cm^–1, Ag(I): ₅₄₆ =38 000 l Mol^–1 cm^–1].Dem Land Nordrhein-Westfalen sowie dem Fond der Chemischen Industrie danken wir für die finanzielle Förderung dieser Untersuchungen.     

Massenspektrometrische Charakterisierung von Propyldazin und abgeleiteten Derivaten

Ohne Zusammenfassung

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Mass-spectrometric characterisation of propyldazine and derived compounds

     

pH-triggered assembly of organometallic receptors for lithium ions

The reaction of half-sandwich complexes of ruthenium, rhodium, and iridium with amino-substituted 3-hydroxy-2-pyridone ligands in aqueous solution gives monomeric O,O'-chelate complexes. Upon addition of base, the complexes assemble to form trimeric metallamacrocycles, as evidenced by NMR spectroscopy and single-crystal X-ray analyses. The macrocycles are able to act as highly selective receptors for lithium ions. The binding constants depend on the nature of the half-sandwich complex, the ligand, and the pH. With a commercially available (cymene)Ru complex, a receptor with a Li+ binding constant of K(a) = 5.8 (+/-1.0) x 10(4) M(-1) and a Li+-Na+ selectivity of 10 000:1 can be obtained. The fact that the assembly process of the receptor is pH-dependent can be used to detect the presence of lithium ions by a pH measurement. Furthermore, it is possible to transduce the binding of Li+ into a change of color by means of a chemical reaction with FeCl(3). This allows the detection of Li+ in the pharmacologically relevant concentration range of 0.5-1.5 mM by the "naked eye".     

Dominance of radiative coupling over disorder in resonance Rayleigh scattering in semiconductor multiple quantum-well structures

Resonance Rayleigh scattering by periodic semiconductor multiple quantum-well structures is studied experimentally and theoretically. Polaritonic effects are found to dominate disorder in the secondary emission dynamics. The coexistence of several radiant polaritonic modes with different radiative decay times leads to polarization beating between modes, strongly influences the rise times, and determines the fast decay times of the resonance Rayleigh scattered signals.     

Tartaric Acid Starch Ether: A Novel Biopolymer‐Based Polyelectrolyte

New tartaric acid starch ethers have been synthesized applying starch sources of different amylose content. The reactions were carried out heterogeneously in ethanol/water mixtures with cis‐disodiumepoxysuccinate as etherifying reagent leading to products of a degree of substitution (DS) up to 0.3. The molecular structure of the new starch ethers was evaluated by elemental analysis, FTIR and ¹³C NMR spectroscopy. Preliminary studies using a convenient titration method indicate a high binding capacity for Ca²⁺ ions which is dependent on the starch source and DS.

Tartaric acid starch ethers.     

Photochemical inactivation of Pseudomonas aeruginosa

Adaptability to a broad range of environments together with relatively high resistance to antibiotics and to disinfectants makes Pseudomonas aeruginosa a concern in hospitals and in public health. We investigated whether UVA-mediated photochemical inactivation of P. aeruginosa could be accomplished with high efficiency while at the same time preserving the sensitivity of subsequent diagnostic tests. We characterized dose responses and bactericidal kinetic rates of 5-iodonaphthyl 1-azide (INA) and of amotosalen (AMO) as these substances exposed to UVA are known to inactivate germs with minimal impact to blood products or to viral antigens. Neither UVA without photochemicals nor INA or AMO in the dark inactivated bacteria. We found that AMO was ca 1000-fold more effective in inactivating P. aeruginosa cells than INA under similar conditions. Photoinactivation with either INA or AMO at conditions that abolished bacterial infectivity did not impair polymerase chain reaction (PCR) and enzyme-linked immunosorbent assay (ELISA) testing. For comparison, similar titers of Bacillus atrophaeus spores (a surrogate for B. anthracis) remained unaffected at conditions that reduced the survival of P. aeruginosa below detection levels. The results presented in this study should assist in improved methods to inactivate P. aeruginosa in environmental, clinical and forensic samples without impairing subsequent nucleic acid- or immune-based analysis.     

Oxazolidine synthesis by complementary stereospecific and stereoconvergent methods

Complementary stereospecific and stereoconvergent reactions for enantioselective synthesis of 1,3-oxazolidines are reported. In the presence of a rhodium catalyst, reaction of enantioenriched butadiene monoxide with aryl imines is stereospecific (99% ee). Alternatively, the reaction of racemic butadiene monoxide, in the presence of a chiral palladium or nickel catalyst, provides an enantioselective synthesis of 1,3-oxazolidines (up to 94% ee). Synthesis of either the cis- or trans-1,3-oxazolidines is also accomplished under catalyst control.     

Diastereoselective synthesis of diketopiperazine bis-α,β-epoxides

Functionalized diketopiperazines (dioxopiperazines) are an important class of molecules in medicinal chemistry and material science. Herein we report a diastereoselective synthesis of diketopiperazine bis-α,β-epoxides via the oxidation of exocyclic olefins. Although six diastereomers may be formed by this approach, only one or two of them were observed.     

The missing link: triplet fluorocarbonyl nitrene FC(O)N

The elusive triplet fluorocarbonyl nitrene, FC(O)N (X³A′′), has been generated in high yield from matrix‐isolated FC(O)N₃ by ArF excimer laser photolysis (λ=193 nm). As a side product FNCO was formed. The novel nitrene was characterized by IR, UV/Vis, EPR spectroscopy, and quantum‐chemical calculations. All six fundamental vibrations of FC(O)N at 1681.3, 1193.8, 879.8, 646.5, 588.7, and 434.8 cm^?1 (argon matrix, 16 K), their ^12/13C, ^16/18O, and ^14/15N isotopic shifts, and four electronic transitions at T₀=13 890, 25 428, 29 166, and 30 900 cm^?1 that exhibit vibrational fine structures have been detected. Under visible‐light irradiation at λ≥495 nm, FC(O)N reacted with molecular N₂ in the matrix cage at 6 K to give back FC(O)N₃, whereas near‐UV irradiation at λ≥335 nm yielded FNCO. The singlet–triplet energy gaps of different carbonyl nitrenes are discussed.