A model-theoretic characterization of constant-depth arithmetic circuits

We study the class ${\mathrm{\#}\text{AC}}^0$ of functions computed by constant-depth polynomial-size arithmetic circuits of unbounded fan-in addition and multiplication gates. No model-theoretic characterization for arithmetic circuit classes is known so far. Inspired by Immerman's characterization of the Boolean circuit class ${\text{AC}}^0$, we remedy this situation and develop such a characterization of ${\mathrm{\#}\text{AC}}^0$. Our characterization can be interpreted as follows: Functions in ${\mathrm{\#}\text{AC}}^0$ are exactly those functions counting winning strategies in first-order model checking games. A consequence of our results is a new model-theoretic characterization of ${\text{TC}}^0$, the class of languages accepted by constant-depth polynomial-size majority circuits.     

Electron properties in GaAs for the design of MM-wave IMPATTs

A very staightforward method has been developed to apply space-charge resistance measurements for determining the high-field drift velocity of electrons in GaAs. The breakdown voltages of the single-drift flat-profile IMPATT diodes used in these measurements justify the validity of well known ionization rates for still higher electric fields.     

ATR-FTIR experiments with chlorosilanes

OH groups on the surface of semiconductors (SC) such as Si, Ge, TiO₂, SnO₂ react with Cl-Si groups to give stable SC-O-Si bonds. ATR-FTIR is applied to study the infrared spectra of adsorbed H₈Si₈O₁₂ on ZnSe and Cl₈Si₈O₁₂ which has reacted with the surface-OH group of Ge. A comparison is made with the spectra of the free molecules.     

Zur Trennung des Molybdäns von Wolfram mittels Ausschüttelungs-Methoden

Zusammenfassung Die Trennung des Molybdations vom Wolframation ist durch dreimaliges Ausschütteln des ersteren mit Acetylaceton—Chloroform (11) aus 2n salzsaurer Lösung möglich, wobei das Wolframation durch Zugabe von Citronensäure komplexiert werden muß. Das Molybdat wird zu 99,8% extrahiert.Mit 2 AbbildungenHerrn Prof. Dr.A. Zinke zum 70. Geburtstag.     

Über die Halogenide des Europiums

Monatshefte für Chemie - Chemical Monthly -     

Cobalt(III) complexes with aminothiolates

Summary This article describes some complexes of cobalt(III) with -mercaptopropylamine,N, N-dimethyl--mercaptopropylamme andN,N-dimethyl--mercaptoethylamine. The compounds are of stoichiometry [Co(ligand)₃], [Co₃(ligand)₆]_X (X=Cl or Br) and [Co(ligand)₃]X₃ (X=Cl or ClO₄). -Mercaptopropylamine yields both chelated and non-chelated compounds while theN,N-dimethyl derivatives yield only non-chelated complexes. This behaviour contrasts with the results obtained with nickel(II).     

Zur Bestimmung der spezifischen Wärme von Flüssigkeiten bei höheren Temperaturen

Ohne ZusammenfassungMit 2 Abbildungen.