Eine ErweiterungT(V′) des Ordinalzahlensystems 58-0158-0158-01(Λ0) von G. Jäger

Summary This paper gives a recursive generalization of a strong notation system of ordinals, which was devellopped by Jäger [3]. The generalized systemT(V) is based on a hierarchy of Veblen-functions for inaccessible ordinals. The definition ofT(V) assumes the existence of a weak Mahlo-ordinal. The wellordering ofT(V) is provable in a formal system of second order arithmetic with the axiom schema of ₂ ¹ -comprehension in a similar way, as it is proved in [6] for the weaker notation systemT(V).     

Periodic solutions of some infinite-dimensional Hamiltonian systems associated with non-linear partial difference equations. II

This is our second paper devoted to the study of some non-linear Schrödinger equations with random potential. We study the non-linear eigenvalue problems corresponding to these equations. We exhibit a countable family of eigenfunctions corresponding to simple eigenvalues densely embedded in the band tails. Contrary to our results in the first paper, the results established in the present paper hold for an arbitrary strength of the non-linear (cubic) term in the non-linear Schrödinger equation.     

Semi-insulating electrical properties of undoped inp after heat treatment in a phosphorus atmosphere

Nominally undoped InP wafers have been annealed in a phosphorus atmosphere under a pressure of about 5 bar at temperatures of 900 °C for about 80 h. It was found that the electrical properties of the samples changed considerably after this treatment. A room temperature resistivity of up to 2×10⁷cm (semi-insulating behaviour) was obtained in the bulk of the samples. The resistivity finally obtained depends on the starting carrier concentration of the untreated samples. The Hall coefficient and Hall mobility have been measured up to 600 °C. The results can be interpreted in terms of a deep electronic level (E _A=0.63 ... 0.65 eV below the conduction band). The Hall coefficient was always found to be negative resulting in a Hall mobility of 1.4 to 4.9×10³ cm²/Vs. The highest resistivity in nominally undoped bulk InP so far reported in the literature [1] was =3.6 × 10⁵cm. Therefore, this paper demonstrates for the first time that a really semi-insulating behaviour of >10⁷ cm can be achieved for bulk InP with the purity of nominally undoped material (10¹⁵ to 10¹⁶cm^–3).     

MO-LCAO Calculations of Polymethines

Idealized polymethines are defined as conjugated chain molecules with complete bond equilization and charge alternation. A constant π-bond order along the chain with N atoms has been derived for three types of polymethines which differ by the nature of the heteroatomic end groups. Corresponding to the number of π-electrons they are termined (N + 1)π-, Nπ- or (N ? 1)π-polymethines. This classification embraces closed shell as well as open shell systems. The relations for the energy eigenvalues, coefficients and derived quantities have been obtained in closed form. The results for the different classes of polymethines are strongly related. Their molecular properties should be similar.     

Preliminary analyses of natural radionuclides in selected Turkish power plant lignites

This preliminary study presents the experimental results concerning the concentrations of selected radionuclides (²³⁸U, ²³²K, ²²⁶Ra, ²³²Th) in Af?in-Elbistan, Çan, Çay?rhan, Erzurum, Göynük, Kangal, Orhaneli, Saray, Seyitömer, Soma, Tunçbilek, Yata?an and Yeniköy lignites, which are primarily utilized as fuel for thermal power plants in Turkey. Gamma-spectrometry of 39 representative lignite samples gave results with the following concentration ranges: 8 to 296 Bq/kg for ²³⁸U, 3 to 79 Bq/kg for ²³²Th, 17 to 360 Bq/kg for 40K, and 5 to 130 Bq/kg for ²²⁶Ra. The ²³⁸U results reported here are higher than other literature values for various world coals, earth's crust and world average.     

Buchbesprechungen

Ohne Zusammenfassung     

Das Solvosystem Phosphoroxychlorid, 23. Mitt.: Photometrische Titrationen von Chloriden mit Eisen(III)-chlorid

Zusammenfassung Zahlreiche kovalente Chloride bilden mit FeCl₃ in POCl₃ Chloroniumtetrachloroferrate. HgCl₂, BCl₃, TiCl₄, SnCl₄ und PCl₅ geben ein Chloridion, ZnCl₂ und AlCl₃ zwei Chloridionen, letzteres zum Teil auch das dritte Chloridion an FeCl₃ ab. Die Donorstärke nimmt in der Reihe Et₄NClKCl1/2 ZnCl₂ 1/2 AlCl₃>TiCl₄>PCl₅1/3 AlCl₃[SbCl₆]^–HgCl₂ >BCl₃SnCl₄ ab. SbCl₅ ist in POCl₃ ein stärkerer Akzeptor als FeCl₃. Die Unterschiede gegenüber dem Lösungsmittel Phenylphosphoroxychlorid werden diskutiert.Mit 1 Abbildung22. Mitt.:M. Baaz, V. Gutmann undL. Hübner, Mh. Chem.91, 694 (1960).     

Ionization in antiproton-hydrogen collisions

Employing the semiclassical approximation we calculate within the coupled-state formalism the ionization probability in antiproton-hydrogen (p+H) collisions. In particular we investigate the adiabatic ionization at the distance of closest approach in almost central collisions. Striking differences in the electron excitation probability compared with proton-hydrogen (p+H) collisions are predicted.