Collective states fed by weak α-transitions in the 230U chain

The ²³⁰U decay chain has been investigated using Ge(Li) spectrometers in singles and coincidence measurements. The internal-conversion spectra have been studied in a β-spectrometer with a Si(Li) detector placed in a homogeneous magnetic field. A total of 31 γ-ray transitions, 14 of which have not been reported before, have been observed in the decay of ²³⁰U and its descendants. All transitions could be unambiguously placed in the individual level schemes. The new band-heads at 805 and 914 keV in ²²⁶Th and ²²²Ra, respectively, are proposed as 0⁺ quadrupole-pairing vibrations. No evidence has been found for the existence of 0⁺ two-phonon harmonic octupole states in these nuclei. A possible anharmonicity of the octupole vibrations is discussed.     

A fuzzy approach to the transportation problem

The transportation problem with fuzzy supply values of the deliverers and with fuzzy demand values of the receivers is analysed. For the solution of the problem the technique of parametric programming is used. This makes it possible to obtain not only the maximizing solution (according to the Bellman-Zadeh criterion) but also other alternatives close to the optimal solution.     

Black hole uniqueness from a hidden symmetry of Einstein's gravity

A theorem is proven that the only possible exterior solution for a pseudostationary, rotating, electrovacuum black hole with nondegenerate event horizon is the Kerr-Newman solution withM ²-J²/M²-Q²>0. A special role played in the proof of this theorem by the hidden symmetry groupSU(1, 2) of Einstein's equations is established.This essay received the third award from the Gravity Research Foundation for the year 1983 [Ed.].     

A probabilistic analysis of the Next-Fit bin packing algorithm

An infinite supply of pieces, with i.i.d. sizes, is packed under the Next-Fit packing procedure. The process A_n, the number of bins required to pack n pieces, is investigated, and the first two moments are computed when the piece sizes are uniformly distributed. For this special case expressions for the distribution of A_n are also presented.     

Quantum phases and connections

Quantum phases and possible reductions of adiabatic connections are discussed. It is argued that only holonomy groups have physical meaning in that context.