Ons-sets and mutual absolute continuity of measures on homogeneous spaces

We extend a recent result of A. Jonsson about mutual absolute continuity of twoD _s -measures on ans-setF ⊂R ⁿ to the homogeneous spaces (X, d, μ) of Coifman, Weiss. Here we define Hausdorff measure, Hausdorff dimension,D _s -set andd-set relative to the measureμ. Our main result holds for so called (s, d)-sets,d ≥s, and is stronger than Jonssons result even inR ⁿ . As applications we interpret this Hausdorff dimension as a relative dimension for very regular sets and show that it in general depends strongly onμ. For this purpose we construct a strictly increasing functionf :R →R, whose measure is doubling and concentrated on a set of arbitrary small Hausdorff dimension. The extension off to a quasiconformal map of the half plane onto itself sharpens a classical example of Ahlfors-Beurling.     

The superconducting energy gap measured by tunneling into quench-condensed germanium-gold

Ge_0.5Au_0.5 films, quenched on a substrate below 2K are superconducting with T_c = 3.10 ± 0.12K, and 2Δ(0)k_BT_c= 3.75 ± 0.1. No phonon structure is visible in the second derivative of the tunnel current.     

Magnetoresistance of La<Subscript>0.67</Subscript>Sr<Subscript>0.33</Subscript>MnO<Subscript>3</Subscript> epitaxial films grown on a substrate with low lattice mismatch

The structure, electrical resistivity, and magnetoresistance of La_0.67Sr_0.33MnO₃ heteroepitaxial films (120-nm thick) practically unstrained by lattice mismatch with the substrate were studied. A strong maximum of negative magnetoresistance of ≈27% (for μ₀H = 4 T) was observed at T ≈360 K. While the magnetoresistance decreased monotonically in magnitude with decreasing temperature, it was still in excess of 2% at 150 K. For T < 250 K, the temperature dependence of the electrical resistivity ρ of La_0.67Sr_0.33MnO₃ films is fitted well by the relation ρ = ρ₀ + ρ ₁(H)T^2.3, where ρ₀ = 1.1×10^?4 Ω cm, ρ₁(H = 0) = 1.8×10^?9 Ω cm/K^2.3, and ρ₁(μ₀H = 4 T)/ρ₁(H = 0) ≈0.96. The temperature dependence of a parameter γ characterizing the extent to which the electrical resistivity of the ferromagnetic phase of La_0.67Sr_0.33MnO₃ films is suppressed by a magnetic field (μ ₀H = 5 T) was determined.     

YBa2Cu3O7−δ /CeO2 heterostructures on sapphire R-plane

(001)YBa₂Cu₃O_7−δ epitaxial films were prepared by laser ablation on surface. A thin (001)CeO₂ or (111)CeO₂ buffer layer was deposited between the substrate and the superconductor film to reduce their chemical interaction. In the initial stages of CeO₂ buffer formation, its orientation depended strongly on the intensity of cerium ion interaction with oxygen. Epitaxial growth of (001)YBa₂Cu₃O_7−δ films was achieved both on and . The T _c temperature of epitaxial (001)YBa₂Cu₃O_7−δ films was within 88–90 K, and the current J _c at 77 K was in excess of 10⁶ A/cm⁻². Fiz. Tverd. Tela (St. Petersburg) 40, 205–208 (February 1998)     

Estimates of the s-d interaction in CdCr from superconducting transition temperature and magnetic susceptibility

Cr has a well developed magnetic moment in a Cd host and the superconducting transition temperature, T_c, is strongly depressed. We estimate a spin, S = 1.5 leading to a depression rate - $\text{dT}{}_{\mathrm{c}}\text{dc}\text{= 140 K/at.\%}$. The s-d interaction strength is estimated to 0.5–0.7 eV leading to a Kondo temperature in the milliKelvin range.