Milnor numbers and Euler obstruction*

Using a geometric approach, we determine the relations between the local Euler obstruction Eu_f of a holomorphic function f and several generalizations of the Milnor number for functions on singular spaces. *This work was partially supported by CNRS-CONACYT (12409) Cooperation Program. The first and third named authors partially supported by CONACYT grant G36357-E and DGPA (UNAM) grant IN 101 401.     

Spectroscopic investigation of local molecular dynamics in liquid crystals II. Polymers

In the analysis of spectroscopic data from liquid crystals consisting of either small molecules or polymer chains, it is essential that account be taken of some particular features due to the oriented nature of the phases investigated. For liquid crystal polymers some specific additional problems arise, such as the difficulties in orienting main-chain liquid crystal polymers, the occurrence of the glass-liquid transition and secondary transitions. These questions are first discussed, then the studies performed using ²H and ¹³C N.M.R., E.S.R. and dielectric relaxation on both side-chain and main-chain liquid crystal polymers are presented.     

Kollineationen auf Drei- und Vierecken in der Desarguesschen projektiven Ebene und Äquivalenz der Dreiecksnomogramme und der Dreigewebe von Loops mit der Isotopie-Isomorphie-Eigenschaft

Ohne ZusammenfassungHerrn Professor Dr. A. M. Ostrowski zu seinem 75-sten Geburtstag in Freundschaft und Verehrung gewidmet     

The ring closure and rearrangement of N-2-aminobenzoyl -N-methylhydrazones of β-dicarbonyl compounds

A novel rearrangement was observed during the cyclization of N-(2-aminobenzoyl)-N-methylhydrazones of β-dicarbonyl compounds, leading to pyrazole derivatives 2,4, and 5 depending on substituents and the reaction media.     

An investigation of short-lived isomers in the nuclei90,92Nb,99Mo,98,100,101Tc and101Ru

Short-lived isomers in the nuclei^90,92Nb,⁹⁹Mo,^98,100,101Tc and¹⁰¹Ru populated in photonuclear reactions were studied by pulsed beam techniques. Energy and half-life of theγ-rays deexciting the isomeric levels were measured by recording energy-time spectra. The delayedγ-rays andK X-rays were detected by means of an intrinsic Ge-detector of high resolution. From the measured intensity ratios internal conversion coefficients were determined. The multipolarities of the isomeric transitions could be deduced in most cases. A classification of the observed isomers has been tried on the basis of the obtained experimental results and most recent literature data.     

On Accurate Linear Approximations for Chance-Constrained Programming

This paper introduces the CHAPS (chance-constrained programming system) algorithm, which uses linearization techniques but gives more accurate solutions than earlier, similar methods.