Felix Hausdorff: Gesammelte Werke. Band VI. Geometrie,Raum und Zahl,hg. von M. Epple (Berlin: Springer, 2021). ISBN 978-3-540-77838-7. XX 540 Seiten. 89,99 €

Mathematische Semesterberichte -     

Spin-orbit interaction in molecular photoelectron spectra An intermediate coupling approach

A new and general semiempirical method for calculating ionization energies of molecules containing heavy atoms is presented. The extended Hückel hamiltonian is amended with a phenomenological one-electron spin-orbit interaction operator, and ionization energies are equated to orbital energies according to Koopmans' theorem. Calculations are presented for molecules with Br and I as heavy atoms. The systems considered are the hydrogen halides, diatomic halogens and interhalogens, haloacetylenes, halomethanes, and boron trihalides. Good agreement with the observed spin-orbit splitting is obtained. New assignments are proposed for the trihalides considered.     

Double fluorescence lifetimes of metal-free phthalocyanine in a mixed-solvent Shpol'skii matrix at 4·2 K

We report identical double fluorescence lifetimes of τ = 3·7 and 6·3 ns for the 0-0 fluorescences of each of the two tautomeric species of metal-free phthalocyanine (H₂Pc) in a mixed solvent matrix of α-chloronaphthalene and n-octane at 4·2K. Such double lifetime feature has not been reported previously for this molecule nor, to our knowledge, for any of the related phthalocyanines and porphyrins.     

Formation and properties of rocksalt-type AlN and implications for high pressure phase relations in the system Si–Al–O–N

Pressure-dependent thermodynamic properties of the ambient and high pressure phases of aluminum nitride (w-AlN and rs-AlN) were calculated from first principles in order to determine their phase boundary in the p? T phase diagram. These predictions were checked by static HP/HT experiments, using a multianvil press and an Al/N/H precursor with low decomposition temperature as educt. The experimental data show that at temperatures between 1000 and 2000 K, the boundary line between the two phases is situated between 11 and 12 GPa, which is ～1.3 GPa lower than the theoretical result and generally lower than previously assumed. The hardness of rs-AlN – measured for the first time – is ～30 GPa (Knoop indenter at loads of 25–50 g), twice as hard as w-AlN. Shock wave recovery experiments on nano w-AlN allowed testing of the chemical and thermal stability of rs-AlN, and determination of its infrared absorption and ²⁷Al NMR data. The shock wave technique will eventually enable the synthesis of larger amounts of rs-AlN, making it available for technological use. Finally, implications on the high pressure stability of phases in the Si–Al–O–N system are discussed in the light of thermoelastic properties of AlN.     

A flexible framework for Group Decision Support: WINGDSS version 3.0

A flexible framework for Group Decision Support on PCs in Microsoft Windows environment is presented. WINGDSS does not replace human judgment but highly supports the entire process of decision making, from problem structuring to post-decision analysis. The latest version of WINGDSS is a modular, open system with a dynamical connection to relational databases, an interpreter for defining problem specific evaluation procedures, a lot of interactive features from setting up the tree of criteria until the sensitivity analysis on individual/group ranking. By providing tools for recursively redefining the decision problem, WINGDSS helps the decision makers in achieving a result satisfactory to the whole group.Research supported in part by the Hungarian Foundation for Scientific Research, Grant No. 2568 and by the Hungarian National Committee for Technical Research and Development, Grant No. 93-97-67-0553.