A remark on polynomial function over finite commutative rings with identity

In the present paper, the degree of polynomial functions on a finite commutative ringR with identity is investigated. An upper bound for the degree is given (Theorem 3) with the help of a reduction formula for powers (Theorem 1).     

A Mössbauer effect study of Dy impurities in the h.c.p. metal Zr

The 86.8 keV, 2⁺ → 0⁺ Mössbauer resonance of ¹⁶⁰Dy has been employed to study the paramagnetic hyperfine (hf) structure of Dy impurities in the hexagonal transition metal Zr. From the observed hf splitting it is concluded that the crystalline electric field ground state is an almost pure $\text{J}{}_{\mathrm{<mtext>z</mtext>}}\text{= ±}\text{1}\text{2}\text{Γ}{}_7$ Kramers' doublet with g_⊥ ? g_|. The quadrupole hf interaction and the effects of paramagnetic relaxation on the ME spectrum are also discussed.     

Lifting-Probleme für ℋ∞-Funktionen

Ohne Zusammenfassung     

Quadratische Formen und Galois-Cohomologie

Ohne ZusammenfassungDiese Arbeit ist im wesentlichen die gleichnamige Dissertation des Verfassers, Bonn 1967.     

Threshold 3He and 3H Transverse Electron Scattering Response Functions

The threshold transverse response functions R _T (q, ω) for ³He and ³H are calculated using the AV18 nucleon–nucleon potential, the UrbanaIX three-body force, and the Coulomb potential. Final states are completely taken into account via the Lorentz integral transform technique. Consistent two-body π- and ρ-meson exchange currents as deduced using the Arenhövel-Schwamb technique are included. The convergence of the method is shown and a comparison of the corresponding MEC contribution is made to that of a consistent MEC for the meson theoretical r-space BonnA potential. The response R _T is calculated in the threshold region at q = 174, 324, and 487 MeV/c and compared with available data. The strong MEC contributions in the threshold region are nicely confirmed by the data at q = 324 and 487 MeV/c although some differences between theoretical and experimental results remain. A comparison is also made with other calculations, where the same theoretical input is used. The agreement is generally rather good, but leaves also some space for further improvement.     

Non-vanishing of products of Fourier coefficients of modular forms of half-integral weight

We prove a non-vanishing result in weight aspect for the product of two Fourier coefficients of a Hecke eigenform of half-integral weight.