Non-trivial simple poles at negative integers and mass concentration at singularity

Let (X,0) be the germ of a normal space of dimension n+1 and let f be the germ at 0 of a holomorphic function on X. Assume both X and f have an isolated singularity at 0. Denote by J the image of the restriction map , where F is the Milnor fibre of f at 0. We prove that the canonical Hermitian form on , given by poles of order at in the meromorphic extension of , passes to the quotient by J and is non-degenerate on . We show that any non-zero element in J produces a “mass concentration” at the singularity which is related to a simple pole concentrated at for (in a non-na?ve sense). We conclude with an application to the asymptotic expansion of oscillatory integrals , for , when . Received: 28 May 2001 / Published online: 26 April 2002     

Chemical Reactions in the Manufacture of Waveguides for Long Distance Optical Data Transmission

One of the modern high technologies which has advanced enormously in the last few years is glass fiber technology. This is used in the manufacture of glass fibers for lighting purposes and for the optical transfer of analog and digital data with a high transfer density. The technical demands made on the glass fibers required for data transfer, the optical waveguides, are extremely high and are already fulfilled to a large extent by industry. At present about four million kilometers of fiber, worth ca. 800 million DM are produced worldwide (10% in the Federal Republic of Germany). Numerous chemical processes take place during the manufacture of optical waveguides. However, in contrast both to the high and constantly growing demands on the quality and to the increasing production volume of such fibers, little is in fact known about the reactions involved. The present article will attempt to develop a picture of the multifarious reactions occurring in the course of this technical process on the basis of literature data and our own studies.     

Equilibrium studies of Mn(II), Mg(II), Ca(II), Sr(II) and Ba(II) withp-fluoro-,p-chloro-,p-bromo-,p-methyl-benzoylacetones and 1-(4-fluorophenyl)-1,3-pentanedione

The rawpH-data, obtained from the potentiometric titrations of the titled ligands with NaOH in 75% (v/v) dioxane-water mixture performed at 20, 30 and 40°C at constant ionic strength (=0.1M-NaClO₄), have been adequately corrected for dilution, and solvent effects in order to evaluate thermodynamic dissociation constants. Variance of the latter as a function of temperature has also been accounted for. The differing magnitudes of thermodynamic dissociation constants of the titled ligands have been explained on the basis of the non coplanar orientation of the phenyl ring in the ligands and a comparison has been made with those of unsubstituted benzoylacetone, dibenzoylmethane and acetylacetone.Following similar technique, thermodynamic stepwise and overall formation constants of the titled metal-ligand systems have been obtained and the results correlated with ligand basicity inverse metal crystal radii and second potentials of metals. Decrease in the free enthalpy (–G) of complexation reaction has also been evaluated.

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Untersuchung der Gleichgewichte von Mn(II), Mg(II), Ca(II), Sr(II) und Ba(II) mit p-Fluor-, p.-Chlor-, p-Brom-, p-Methyl-benzoylaceton und 1-(4-Fluorphenyl)-1,3-pentanedion

Zusammenfassung Aus der potenitometrischen Titration der Titelverbindungen mit NaOH in 75 (v/v) Dioxan—Wasser bei, 20, 30 und 40°C bei konstanter Ionenstärke (=0,1M-NaClO₄) wurden die thermodynamischen Dissoziationskonstanten ermittelt. Verdünnungs-, Lösungsmittel-und Temperatureffekte wurden berücksichtigt. Die unterschiedlichen Dissoziationskonstanten werden mit der Nichtplanarität des Phenylrings in den Liganden erklärt. Außerdem wurden die Komplexbildungskonstanten bestimmt; sie sind in die Diskussion miteinbezogen.

     

Bioavailability, bioaccumulation and tolerance of chromium: consequences in the food chain of freshwater ecosystems

Many abiotic and biotic factors can influence the partitioning equilibrium of heavy metals, thus influencing metal impact on aquatic environments. Unicellular algal species release soluble organic substances able to complex metals. In our laboratory a Cr-tolerant strain was selected and isolated from a wild type strain of Scenedesmus acutus. The exudates released by the two strains counteracted the growth inhibition caused by Cr(VI) and the exudates of the Cr-tolerant strain were more effective. On the contrary, the exudates did not reduce chromium toxicity to the cladoceran Daphnia magna. The reduction of chromium effect on algae seems the consequence of an algae-specific interaction among Cr(VI), exudates and algal cells. Chromium uptake resulted to be energy-dependent since bioaccumulation rate in subdued light condition was lower than at high light intensity. The effect of Cr(VI) on algae changed depending on metabolism of the cells and in particular it seemed to be related to the bioaccumulation rate. Tolerance in the selected strain could not be ascribed to a lower uptake of chromium. The difference in sensitivity to chromium between the two strains was exploited to evaluate if tolerance acquired by algae could have consequences for Daphnia. After treatment with Cr(VI), the two strains of S. acutus were used as food source for D. magna. The results indicate that chromium is accumulated by algae in a form not available for daphnids and that Cr tolerance acquired by the algae can be of some advantage to the consumer organism.     

Fibrous Networks with Incorporated Macrocycles: A Chiral Stimuli‐Responsive Supramolecular Supergelator and Its Application to Biocatalysis in Organic Media

A new and versatile, crown ether appended, chiral supergelator has been designed and synthesized based on the bis‐urea motif. The introduction of a stereogenic center improved its gelation ability significantly relative to its achiral analogue. This low‐molecular‐weight gelator forms supramolecular gels in a variety of organic solvents. It is sensitive to multiple chemical stimuli and the sol–gel phase transitions can be reversibly triggered by host–guest interactions. The gel can be used to trap enzymes and release them on demand by chemical stimuli. It stabilizes the microparticles in Pickering emulsions so that enzyme‐catalyzed organic reactions can take place in the polar phase inside the microparticles, the organic reactants diffusing through the biphasic interface from the surrounding organic phase. Because of the higher interface area between the organic and polar phases, enzyme activity is enhanced in comparison with simple biphasic systems.     

Catalysts for convenient aerobic alcohol oxidations in air: systematic ligand studies in Pd/pyridine systems

We report highly convenient Pd catalysts for the aerobic oxidation of alcohols, which are generated in situ by combining commercially available catalyst precursors. Systematic optimizations of the L- and X-type ligand environment and the employed additive allow the use of air as the sole oxidant without formation of Pd black. The resulting novel protocol provides quantitative yields of a broad variety of ketones and aldehydes.     

Calcium-based hydrated minerals: Promising halogen-free flame retardant and fire resistant additives for polyethylene and ethylene vinyl acetate copolymers

In this study, we evaluated the potential flame retardant effect of calcium-based hydrated minerals, such as hydrated lime, partially and completely hydrated dolomitic limes in polyethylene (MDPE) and ethylene vinyl acetate copolymers (EVA) and compared to that obtained with magnesium di-hydroxide (MDH). The most significant flame retardant effects, observed using the mass loss calorimeter test, indicated that Ca-based MDPE composites showed similar peak Heat Release Rate (pHRR) level to that obtained with MDH composite while the pHRR was lower for Ca-based fillers in EVA compositions. X-ray Diffraction (XRD) data, combined with thermal analysis results, indicated that the calcium di-hydroxide plays a role in the formation of an intumescent cohesive residue during the combustion. Indeed, Ca(OH)₂ reacts with CO₂ formed during the thermal degradation of the polymer to generate CaCO₃ (calcium carbonate) that contributes to the enhancement of the mechanical resistance of the residue.     

Developments of Asymmetric Synthesis Mediated by Chiral Sulfur Reagents

Abstract

Our work on the thio-Claisen rearrangement mediated by an adjacent sulfinyl group is reviewed. The substrates could easily be prepared on a large scale from diacetone-D-glucose. The rearrangement was effected with a diastereoselectivity of 95:5, in favor of the (S,S) or the (R,R) isomer. An approach to natural bis(lactones) was investigated, using a halolactonization reaction and a second [3,3] sigmatropic shift, again mediated by the sulfinyl group. The second part deals with the catalytic enantioselective benzylidenation of aldehydes, mediated by chiral sulfur ylides. We have introduced simple C ₂ symmetric thiolanes for that purpose. The procedure is very practical and enantiomeric excesses up to 96% have been reported for the model of stilbene oxide. A series of ferrocenyl sulfides with planar chirality has also been investigated, leading to unexpected diastereoselectivities and enantiomeric excesses up to 94%.