Evidence of order-parameter symmetry and of a normal metallic state in electron-irradiated YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7−δ</Subscript> (YBCO)

A key difference between a d-wave superconductor and an anisotropic s-wave one is the expected effect of nonmagnetic point defects on T_c. For the former, T_c becomes zero, whereas for the latter, T_c reaches a nonzero constant value beyond a critical concentration of impurities. We report that T_c of single-crystal YBCO becomes less than 12K, our lowest temperature, when 4.1% of the planar oxygens O(2,3) are displaced by 400keV electrons, incident along the c-axis. Our data therefore suggest that YBCO is a d-wave superconductor. We also report a disorder-induced transition from superconductor-to-normal metal.     

Some recent results in metric fixed point theory

This is a survey of recent results on best approximation and fixed point theory in certain geodesic spaces. Some of these results are related to fundamental fixed point theorems in topology that have been known for many years. However the metric approach is emphasized here. Dedicated to Edward Fadell and Albrecht Dold on the occasion of their 80th birthdays     

O.R. in the Company Car Fleet: When Simple is Efficient

The management of a large fleet of company vehicles represents a significant administrative activity, particularly when the company is a motor vehicle manufacturer and the fleet consists of its own products. The approach taken by the Operational Research Group was to cross departmental boundaries to smooth vehicle ordering, reduce inventories of vehicles awaiting delivery and optimize resale values. The method steers between two potential pitfalls: that of ‘optimizing’ one affected department to the detriment of others, and that of developing sophisticated scheduling and forecasting algorithms which the users would not understand and therefore not trust.     

A novel algorithm for chromatogram matching in qualitative analysis

The matching of the pattern of peaks produced during gas chromatography is of importance to many applications. At present, this task is generally performed manually, but this generates the usual problems associated with human inspection, such as a lack of objectivity and reproducibility, proneness to errors, and practical restriction of the volume of data which can reasonably be processed. This paper explores the use of a novel algorithm for automation of this task. The performance of the method on well controlled simulated data sets and real chromatograms is used to show not only how problems of manual inspection can be circumvented, but also how the existence of such a powerful method should open up the possibility of many new analyses for quality control, discrimination of varieties of sample, and the identification of specific components within a sample.     

Chern-Simons invariants of 3-manifolds decomposed along tori and the circle bundle over the representation space ofT 2

We describe a cut-and-paste method for computing Chern-Simons invariant of flatG-connections on 3-manifolds decomposed along tori, especially forG=SU(2) andSL(2,C). We use this method to make computations ofSU(2) Chern-Simons invariants of graph manifolds which generalize Fintushel and Stern's computations for Seifert-fibered spaces. We also use this technique to give a simple derivation of a formula of Yoshida relating the flatSL(2,C) Chern-Simons invariant of the holonomy representation to the volume and the metric Chern-Simons invariant for cusped hyperbolic 3-manifolds.