Asymptotic behavior of eigenvalues of two-parameter nonlinear Sturm-Liouville problems

The nonlinear two-parameter Sturm-Liouville problemu ^"+μg(u)=λf(u) is studied for μ, λ>0. By using Ljusternik-Schnirelman theory on the general level set developed by Zeidler, we shall show the existence of ann-th variational eigenvalue λ=λ_n(μ). Furthermore, for specialf andg, the asymptotic formula of λ₁(μ)) as μ→∞ is established.     

Identification of beta-decay of150La

The -decay of¹⁵⁰La, the heaviest isotope of lanthanum, has been identified by observing -rays from mass separated activities obtained at KUR-ISOL. From the decay curves of 97.0 and 208.7 keV -rays in¹⁵⁰Ce and of Ce-K X-ray, the half-life of¹⁵⁰La has been determined as 0.51(3) s. This value is in agreement with theoretical predictions from microscopic theory.     

Dynamical property of YFeMnO4

In order to interpret abrupt changes of distributions of orientations andmagnitudes of hyperfine fields in Mössbauer measurements of⁵⁷Fe in YFeMnO₄, a model is proposed. The origin is assumed to be not static but dynamic. Fluctuating fields are caused by spins in a fully frustrated spin system, namely, a Heisenberg spin system on a triangular lattice in a two-dimensional antiferromagnet. Extending the stochastic theory for the fluctuation between two states to that among many states with a Gaussian distribution, we fit the spectra with three parameters, hyperfine fieldH _hf, correlation time _c, andwidth of fluctuating field , within a limited condition of =_c=1. Obtained results represent the characteristic features of Mössbauer spectra well, in spite of a simplified model.