Minimal Contact Circuits for a Sequence of Boolean Functions

Mathematical Notes -     

Low-temperature specific heat of crystalline and amorphous Eu2(MoO4)3

The specific heat C _total of crystalline and amorphous Eu₂(MoO₄)₃ is measured in the temperature interval 4.5–30 K. The amorphous state is obtained by applying pressure ∼7 GPa at room temperature. It is found that the specific heat of the crystal at T⩽7.5 K is described by a cubic function of temperature, while the specific heat of the amorphous sample has a strongly non-Debye character in the entire experimental temperature interval. The curve of C _total for amorphous europium molybdate is analyzed in a model of soft atomic potentials, and it is shown that it agrees well with universal low-temperature anomalies of the specific heat of classical glasses obtained by quenching from the liquid. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 8, 623–627 (25 October 1998)     

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.     

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.

---

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.

---

---

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