The double layer potential operator over polyhedral domains i: solvability in weighted sobolev spaces

We consider the integral equation, (λ-K)u=f, where K is the double layer (harmonic) potential operator on the boundary of a bounded polyhedron in R³ and λ∣λ∣≥1 is a complex constant. We study the mapping properties of λ - K in weighted Sobolev spaces, applying Mellin transformation techniques directly to the integral equation.     

On the Exponential Convergence of Spline Approximation Methods for Wiener-Hopf Equations

This paper deals with the study of some new multidimensional operators of fractional calculus. These operators are considered in certain spaces of test and generalized functions. Some mapping properties and product rules are obtained.     

Domain configuration and dynamic processes in orthorhombic NaCN studied by 23Na NMR satellite lines and relaxation times

The orientational dependences of the ²³Na NMR spectra which were measured in a NaCN single crystal below T_c1 are related to the EFG tensor at the Na sites in different domains. The results are consistent with the assumption that 12 different domains may arise in the orthorhombic phase. Below T_c1 also the temperature dependences of the spin relaxation times T₁ and T_1ρ of the ²³Na nucleus were measured and related to dynamic processes. Particularly the activation energy and the frequency of the flip motions of the CN^--dipoles are determined.     

Crystal field effects in superconducting tunneling

A comparison of the tunnel curves of superconducting $\text{La}$Pr, $\text{La}$Y and $\text{La}$Gd reveals that the character of the tunneling density of states of $\text{La}$Pr is between that of the BCS- and that of the Abrikosov-Gorkov theory. This is expected on theoretical grounds for pair-breaking caused by ions in a singlet ground state. The predicted crystal field induced structures in the tunnel curves could not be detected.     

Paramagnetic resonance of gadolinium in intermetallic compounds YAl2 and Y1−w Th w Al2

The paramagnetic resonance of Gd in YAl₂ was measured in the temperature range from 5 °K to 70 °K. The experimental results are discussed with Hasegawa's theory. The dependence of linewidth on temperature and Gd-concentration indicates the existence of a “bottleneck” in the relaxation between the conduction electrons and the lattice. If nonmagnetic thorium impurities are added an additional relaxation becomes effective, caused by spin-flip scattering of the conduction electrons at these impurities. In this case the bottleneck is removed.     

Crystal field splitting of gadolinium in single crystals of metallic LaBi

Resolved fine structure has been observed in the ESR of Gd³⁺ in metallic LaBi single crystals. The parameter b₄=+63.7 Oe characterizes a very large cubic crystal field splitting. The g factor of g=2.002 is interpreted as evidence of s-f exchange interaction.