ON THE INCOMPLETENESS OF A DESCENDING CHAIN OF EXTENSIONS OF IMPLICATIONAL S5

C5.ω is obtained by adding, schematically, to the strict-implicational fragment C5 of S5 the axiom ((p → q) → (q → p)) → (q → p). This paper presents a fully general proof that neither C5.ω nor any of a descending chain of its extensions is complete with respect to any class of frames, correcting the garbled details of a version skeched in an earlier paper (same Zeitschrift 31 (1985), 201-208).     

Band structures in73Se

Excited states of⁷³Se have been investigated up to spin, 21/2 using techniques of in-beamγ-ray spectroscopy in connection with the⁷⁰Ge(α, n) reaction. Mean lifetimes of 12 levels have been determined applying Doppler-shift andγ-RF-methods. Five different bands have been identified that reflect a variety of different excitation modes. The decoupled 9/2⁺ band is likely to correspond to an oblate deformation while the 5/2⁺ band is interpreted as a strongly coupled prolate band built on the Nilsson configuration [422] 5/2⁺. The 3/2^? band is a strongly coupled band built on the [301] 3/2^} configuration.Nuclear reactions:⁷⁰Ge(α,n),E=14, 16, 18, 19, 20MeV; measuredE _γ,I _γ,σ(E _γ,θ),γγ-coin, linear polarization, DSA,γ(t).⁷⁵Se deduced levels,I, π, τ, δ(E2/M1), B(σλ). Enriched targets, Ge detectors.     

The experimental structure of199Au and the interacting boson-fermion model

Gamma rays of¹⁹⁹Au obtained after double neutron capture in¹⁹⁷Au were measured at the ILL high flux reactor. A level scheme up to 1770 keV excitation energy is established. The result is compared with IBFM and Boson-Fermion-Symmetry calculations.     

Nodal surfaces of Fourier series: Fundamental invariants of structured matter

Periodic Nodal Surfaces (PNS) of Fourier series are derived and classified as fundamental invariants of structured matter. Relationships to periodic minimal surfaces PMS and to periodic zero potential surfaces (POPS) are given. A basic set of cubic PNS is represented in arithmetic form. The special importance of the invariance of the zeros to the type of the potential is stressed.