A remark on the moduli field of a curve

We give a purely algebro-geometric proof of the fact that every nonsingular projective curve can be defined over a finite extension of its moduli field. This extends a result byWolfart [7] to curves over fields of arbitrary characteristic. Received: 30 November 2001     

Preperfect graphs

We say that a vertexx of a graph is predominant if there exists another vertexy ofG such that either every maximum clique ofG containingy containsx or every maximum stable set containingx containsy. A graph is then called preperfect if every induced subgraph has a predominant vertex. We show that preperfect graphs are perfect, and that several well-known classes of perfect graphs are preperfect. We also derive a new characterization of perfect graphs.     

Sub-Ramsey numbers for arithmetic progressions

Letm 3 andk 1 be two given integers. Asub-k-coloring of [n] = {1, 2,...,n} is an assignment of colors to the numbers of [n] in which each color is used at mostk times. Call an arainbow set if no two of its elements have the same color. Thesub-k-Ramsey number sr(m, k) is defined as the minimumn such that every sub-k-coloring of [n] contains a rainbow arithmetic progression ofm terms. We prove that((k – 1)m ²/logmk) sr(m, k) O((k – 1)m ² logmk) asm , and apply the same method to improve a previously known upper bound for a problem concerning mappings from [n] to [n] without fixed points.Research supported in part by Allon Fellowship and by a Bat Sheva de-Rothschild grant.Research supported in part by the AKA Research Fund of the Hungarian Academy of Sciences, grant No. 1-3-86-264.     

Spectroscopic investigation of the ionization kinetics in XeCl laser discharges by Xe* density measurements

Time and spatially resolved absorption measurements of Xe^* particle number densities performed at an X-ray preionized self-sustained XeCl^*-laser discharge were used to investigate the reaction kinetics of such discharges and to test the validity of the commonly-made assumption that they are fit well by spatially homogeneous numerical models. It turned out that the Xe^* density distribution over the discharge cross section remains homogeneous for less than 100 ns only. Comparing the experimental results of the homogeneous discharge phase with zero-dimensional model calculations, we conclude that induced emission modeled using two excited xenon levels must be taken into account for the quantitative interpretation of the absorption measurements. For the interpretation of the Xe 6s-6p absorption measurements even a multilevel model will be necessary. Further we conclude from the relative courses and the absolute values of the Xe^* particle number densities that realistic HCl kinetics should contain three vibrationally excited levels and stepwise excitation processes as proposed by Dem'yanov et al. [8].     

1,4-Phenylen-bis-diphenylderivate der Elemente der 5. Hauptgruppe des Periodensystems

Zusammenfassung Die Darstellung sämtlicher am mittleren Benzolkern p-substitutierten Verbindungen (C₆H₅)₂ MC₆H₄ M(C₆H₅)₂ mitM=N, P, As, Sb und Bi wird beschrieben. Für die bereits bekannte Stickstoff-bzw. Arsen-Verbindung konnte ein neuer Darstellungs-weg mit guten Ausbeuten gefunden werden, während die Antimon-und Wismutverbindung erstmals beschrieben werden. Durch Dipolmomentmessungen, UV- und IR-Aufnahmen ist ein Vergleich mit den einfachen Triphenylderivaten der genannten Elemente möglich.

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The compounds p-(C₆H₅)₂ MC₆H₄ M(C₆H₅)₂,M=N, P, As, Sb, and Bi, were prepared. New methods for the preparation of the N and As compound with good yields were found. The Sb and Bi compound were synthesized for the first time. Dipole moments, IR- and UV-spectra of these compounds were compared with those of the triphenyl derivates.

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Herrn Prof. Dr.F. Wessely zum 70. Geburtstag gewidmet.     

Synthesis,purification and spectroscopic characterization of potential impurities of hexamethylmelamine

The syntheses and spectroscopic properties (ir, ¹H nmr, ¹³C nmr, uv and ms) of pure samples of 2-chloro-4,6-bis(dimethylamino)-s-triazine 1 , 4,6-dichloro-2-dimethylamino-s-triazine 2 , 4,6-bis(dimethylamino)-s-triazin-2(lH)-one 3 , 4-chloro-6-dimethylamino-s-triazin-2(1H)-one 4 , 6-dimethylamino-s-triazine-2,4(1H,3H)-dione 5 , and 2,4,6-tris(dimethylamino)-s-triazine (altretamine, HMM) are reported. Evidence for enol-keto equilibria are also presented for 3 , in which the enol form exhibits as an H-bonded dimer structure similar to the dimer of organic carboxylic acids.