Minimal length of two intersecting simple closed geodesics

On a hyperbolic Riemann surface, given two simple closed geodesics that intersect n times, we address the question of a sharp lower bound L _n on the length attained by the longest of the two geodesics. We show the existence of a surface S _n on which there exists two simple closed geodesics of length L _n intersecting n times and explicitly find L _n for . The first author was supported in part by SNFS grant number 2100-065270, the second author was supported by SNFS grant number PBEL2-106180.     

2-O-Substituted-3,6-per-anhydro-α-Cyclodextrin as Potential Biocompatible Agents for the Selective Complexation of Heavy Metal Ions with Special Attention to Lead

We report on the synthesis,characterization and ionic complexation properties ofhexakis (2-O-acetyl-3,6-anhydro)cyclomaltohexaose and hexakis (2-O-methyl-3,6-anhydro) cyclomaltohexaose usingthin-layer chromatography and Nuclear MagneticResonance spectroscopy. The selectivity towardscations depends on chemical modification of thehydroxyl groups and a very high specificity can beobtained in the case of lead for methylatedderivatives.     

Kondensationsreaktionen von α-Aminothionamiden und α-Oxothionamiden

Ohne Zusammenfassung64. Mitt.:F. Asinger, H. Offermanns undP. Krings, Ann. Chem. (im Druck). P. Müller, Teil der Diplomarbeit, Techn. Hochschule Aachen, 1967. H. Andree, Teil der Diplomarbeit, Techn. Hochschule Aachen, 1967.     

The FIGARO II experiment: a general outline of the mission and the principal scientific results

Summary The FIGARO II (French Italian Gamma-Ray Observatory) experiment has been launched successfully three times: in July 1986 from Milo (Trapani), in November 1988 from Charleville (Australia) and in July 1990 again from Milo. In the first flight the observational program was limited to the Crab pulsar PSR0531+21 only because of a telemetry failure: the high sensitivity of FIGARO II allowed an accurate study of the pulse shape as well as a phase-resolved spectroscopy. It was also possible to evaluate the dispersion measure of the Crab pulsar at the flight date from the time delay between gamma-ray and radio pulses. The major results of the second flight were a stringent upper limit to the low-energy gamma-ray flux from PSR 0833-45 (Vela pulsar)—well below the detection claimed by the UCR group —and the observation of a strong emission in the 0.511 MeV annihilation line from the inner region of our Galaxy. The data acquired in the third flight are still under analysis, but preliminary results suggest changes in the shape of the pulse profile. Paper presented at the V Cosmic Physics National Conference, S. Miniato, November 27–30, 1990.     

Applications of a theorem of Singerman about Fuchsian groups

Assume that we have a (compact) Riemann surface S, of genus greater than 2, with , where is the complex unit disc and Γ is a surface Fuchsian group. Let us further consider that S has an automorphism group G in such a way that the orbifold S/G is isomorphic to where is a Fuchsian group such that and has signature σ appearing in the list of non-finitely maximal signatures of Fuchsian groups of Theorems 1 and 2 in [6]. We establish an algebraic condition for G such that if G satisfies such a condition then the group of automorphisms of S is strictly greater than G, i.e., the surface S is more symmetric that we are supposing. In these cases, we establish analytic information on S from topological and algebraic conditions. Received: 4 April 2008     

Pants Decompositions of Random Surfaces

Our goal is to show, in two different contexts, that “random” surfaces have large pants decompositions. First we show that there are hyperbolic surfaces of genus g for which any pants decomposition requires curves of total length at least g ^7/6−ε . Moreover, we prove that this bound holds for most metrics in the moduli space of hyperbolic metrics equipped with the Weil–Petersson volume form. We then consider surfaces obtained by randomly gluing euclidean triangles (with unit side length) together and show that these surfaces have the same property.     

Capturing the multivariate extremal index: bounds and interconnections

The multivariate extremal index function is a direction specific extension of the well-known univariate extremal index. Since statistical inference on this function is difficult it is desirable to have a broad characterization of its attributes. We extend the set of common properties of the multivariate extremal index function and derive sharp bounds for the entire function given only marginal dependence. Our results correspond to certain restrictions on the two dependence functions defining the multivariate extremal index, which are opposed to Smith and Weissman’s (1996) conjecture on arbitrary dependence functions. We show further how another popular dependence measure, the extremal coefficient, is closely related to the multivariate extremal index. Thus, given the value of the former it turns out that the above bounds may be improved substantially. Conversely, we specify improved bounds for the extremal coefficient itself that capitalize on marginal dependence, thereby approximating two views of dependence that have frequently been treated separately. Our results are completed with example processes.      

Wirkungsweise polymerer Vergrauungsinhibitoren in Waschmitteln

Zusammenfassung Im Waschprozeß werden ölige Anschmutzungen von textilen Oberflächen abgelöst und dispergiert. Die Flotte soll darüber hinaus das Wideraufziehen (Redeposition) frei schwebender Schmutzanteile auf Textilfasern vermindern.Bei empfohlener Solldosierung eines Waschmittels entfalten Tenside, Komplexbildner, Builder und Zeolithe den größten Teil der erforderlichen Stabilisierungswirkung. Polymere Vergrauungsinhibitoren bewirken nur graduelle zusätzliche Verbesserungen. Mit fortschreitender Unterdosierung nimmt die stabilisierende Tensid-und Builder-Wirkung schnell ab und die Bedeutung polymerer Vergrauungsinhibitoren steigt.Der Wirkungsmechanismus weist ein hohes Maß an Selektivität gegenüber textilen Substraten auf. Auf polarem Gut (z. B. Baumwolle) wird oft mit Erfolg Carboxymethylcellulose eingesetzt. Die Wirkungsweise beruht in diesem Falle weitgehend auf der sterischen Polymerschutzwirkung adsorbierter Schichten.Auf hydrophoberen Polyesterfasern zeigen Celluloseether mit hydrophoben Seitenketten (z. B. Hydroxypropylcellulose) sehr gute Effekte. Dabei wird die sterische Komponente der Polymerschutzwirkung durch Erniedrigung der treibenden Kraft der Heterokoagulation (Hydrophilierung sämtlicher hydrophober Grenzflächen) verstärkt. An Mischgeweben werden daher oft Kombinationen mehrerer Vergrauungsinhibitoren genutzt.Die vergrauungsinhibierende Wirksamkeit polymerer Substanzen für Polyester kann durch deren Fähigkeit, ungeachtet der Konkurrenz mit restlichen Inhaltsstoffen des Waschmittels möglichst starke effektiv irreversible Hydrophilierungseffekte hervorzurufen, charakterisiert werden.

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In laundering, oily soils are detached from textile surfaces and dispersed. In addition, the washing solution should reduce the redeposition of free suspended soil particles onto the textile fibres.In the case of a recommended predetermined dosage of a detergent the main part of the required stabilizing effect is due to the surfactants, complexing agents, builders and zeolites. Polymeric antiredeposition agents cause only gradual additional improvements. In the case of a weak dosage the stabilizing effects of the surfactants and builders rapidly decrease and the effects of the polymeric antiredeposition agents increase.The mechanism of these effects is characterized by high selectivity of the textile substrates. In the case of polar textiles (for instance cotton) carboxy methyl cellulose is often successfully used. In this case the mode of action is mostly due to steric repulsion of the adsorbed layer.In the case of hydrophobic polyester fibres cellulose ethers with hydrophobic sidechains (for instance hydroxy propyl cellulose) show very good effects. In this case the steric component of the polymeric repulsion is supported by the decrease of the driving force of the heterocoagulation (hydrophilization of all hydrophobic interfaces). For this reason combinations of several antiredeposition agents are often used for mixed fabrics.The performenace of the polymeric agents for polyesters can be characterized by their ability to cause strong effective irreversible hydrophilization effects despite the competitive influences of the residual detergent ingrediences.

Vortrag anläßlich der Hauptversammlung der Kolloid-Gesellschaft in Berlin vom 2. bis 4. Oktober 1985.     

One pot synthesis of nitrogen-containing polycyclic delta-lactones by double nucleophilic addition of bis(trimethylsilyl)ketene acetals to pyridines

Pyridine and bis(TMS)ketene acetals (TMS = trimethylsilyl) react successively with methylchloroformate and iodine (or peracids) to give, via functionalized dihydropyridines, bicyclic nitrogen-containing lactones which have been characterized by X-ray crystallography.