Percolation and electrical resistivity in the YBa2Cu3O7−Ag composite system

We have measured the resistivity of the YBa₂Cu₃O₇–Ag composite system with Ag volume fraction,p _Ag ranging from 0–100%. The percolation behavior and the normal-state resistivity are studied. We find a three-dimensional threshold for the Ag matrix occurring atp _Ag 20% and a threshold for the superconducting matrix occurring at 1–p _Ag30%. The electrical resistivity is interpreted in terms of a resistivity model for granular YBa₂Cu₃O₇ proposed by Halbritter et al. [Z. Phys. B —Condensed Matter71, 411 (1988)]. Based on this model, we show that the resistivities between the YBa₂Cu₃O₇ grains and flaws in the grains are greatly diminished in the samples, indicating significantly improved grain growth behavior of the YBa₂Cu₃O₇ phase resulting from the addition of Ag. With the diminishing of the grain boundary resistivities, an intrinsic value for the temperature coefficient of resistivity, (1/gr)(d/dT), can be inferred, which is 3.3×10^–3/K at 300 K. This value is very close to that observed in the Cu–O₂ planes in single crystals and epitaxial films of YBa₂Cu₃O₇.     

The increments of partial sums of a dependent sequence when the moment generating functions do not exist

In the paper, we give the almost sure limiting behaviour of the increments of partial sums of a-mixing sequence when the moment generating functions do not exist. The results obtained are close to those for an independent sequence provided that the mixing coefficients tend to zero rapidly enough.The Project Supported by National Natural Science Foundation of China.     

Polyamide Layer Chromatography. VIII. Preparation of Polyamide Layer on Poly(ethylene terephthalate) Film and its Application to Aromatic Nitro Compounds

Poly(ethylene terephthalate) film was used as supporter for preparation of polyamide layer. The most convenient method of preparation was described. This layer can be cut into any size and its sensitivity is higher than the glass plate supported layer. Twenty aromatic nitro compounds were used to show the behavior of polyester film based polyamide layer.     

On the second eigenfunctions of the Laplacian in R2

A conjecture about the nodal line of a second eigenfunction states that the nodal line of a second eigenfunction divides the domain by intersecting with the boundary of transversely, where is a bounded convex domain ofR ². We prove this conjecture provided has a symmetry. Also, we prove the multiplicity of the second eigenvalue is two at most provided is a bounded convex domain ofR ².Supported in part by NSF DMS 84-09447Home Institution: Department of Mathematics, University of California, San Diego, La Jolla, CA 92093, USA