The Definition and Computation of a Metric on Plane Curves. The Meaning of a Face on a Geometric Model

Two topics in topology, the comparison of plane curves and faces on geometric models, are discussed. With regard to the first problem, a curve is defined to be a locus of points without any underlying parameterization. A metric on a class of plane curves is defined, a finite computation of this metric is given for the case of piecewise linear curves, and it is shown how to approximate curves that have bounded curvature by piecewise linear curves. In this way a bound on the distance between two curves can be computed. With regard to the second problem, the questions to be discussed are under what circumstances do geometrical faces make sense; how can they be explicity defined; and when are these geometrical faces homeomorphic to the realization of the abstract (topological) face

Exact Results for 1D Kondo Lattice from Bosonization

We find a solvable limit to the problem of the 1D electron gas interacting with a lattice of Kondo scattering centers. In this limit, we present exact results for the problems of incommensurate filling, commensurate filling, impurity vacancy states, and the commensurate-incommensurate transition.Comment: 4 pages, two columns, Latex fil

Stripe phases in high-temperature superconductors

Stripe phases are predicted and observed to occur in a class of strongly-correlated materials describable as doped antiferromagnets, of which the copper-oxide superconductors are the most prominent representative. The existence of stripe correlations necessitates the development of new principles for describing charge transport, and especially superconductivity, in these materials.Comment: 5 pp, 1 color eps fig., to appear as a Perspective in Proc. Natl. Acad. Sci. US

Local Electronic Structure and High Temperature Superconductivity

It is argued that a new mechanism and many-body theory of superconductivity are required for doped correlated insulators. Here we review the essential features of and the experimental support for such a theory, in which the physics is driven by the kinetic energy.Comment: 8 Pages Latex. For the Proceedings of HTS99, Miami, FL, Jan. 199

Enhancement of pairing in a boson-fermion model for coupled ladders

Motivated by the presence of various charge inhomogeneities in strongly correlated systems of coupled ladders, a model of spatially separated bosonic and fermionic degrees of freedom is numerically studied. In this model, bosonic chains are connected to fermionic chains by two types of generalized Andreev couplings. It is shown that for both types of couplings the long-distance pairing correlations are enhanced. Near quarter filling, this effect is much larger for the splitting of a pair in electrons which go to the two neighboring fermionic chains than for a pair hopping process. It is argued that the pairing enhancement is a result of the nearest neighbor Coulomb repulsion which tunes the competition between pairing and charge ordering.Comment: 7 pages, 7 eps figures, enlarged version accpeted in Phys. Rev.

Charge Gap in the One-Dimensional Extended Hubbard Model at Quarter Filling

We propose a new combined approach of the exact diagonalization, the renormalization group and the Bethe ansatz for precise estimates of the charge gap $\Delta$ in the one-dimensional extended Hubbard model with the onsite and the nearest-neighbor interactions $U$ and $V$ at quarter filling. This approach enables us to obtain the absolute value of $\Delta$ including the prefactor without ambiguity even in the critical regime of the metal-insulator transition (MIT) where $\Delta$ is exponentially small, beyond usual renormalization group methods and/or finite size scaling approaches. The detailed results of $\Delta$ down to of order of $10^{-10}$ near the MIT are shown as contour lines on the $U$-$V$ plane.Comment: 4 pages, 4 figure

The impact of rheumatoid arthritis on foot function in the early stages of disease: a clinical case series

BACKGROUND Foot involvement occurs early in rheumatoid arthritis but the extent to which this impacts on the structure and function leading to impairment and foot related disability is unknown. The purpose of this study was to compare clinical disease activity, impairment, disability, and foot function in normal and early rheumatoid arthritis (RA) feet using standardised clinical measures and 3D gait analysis. METHODS Twelve RA patients with disease duration ≤2 years and 12 able-bodied adults matched for age and sex underwent 3D gait analysis to measure foot function. Disease impact was measured using the Leeds Foot impact Scale (LFIS) along with standard clinical measures of disease activity, pain and foot deformity. For this small sample, the mean differences between the groups and associated confidence intervals were calculated using the t distribution RESULTS Moderate-to-high foot impairment and related disability were detected amongst the RA patients. In comparison with age- and sex-matched controls, the patients with early RA walked slower (1.05 m/s Vs 1.30 m/s) and had a longer double-support phase (19.3% Vs 15.8%). In terminal stance, the heel rise angle was reduced in the patients in comparison with normal (-78.9° Vs -85.7°). Medial arch height was lower and peak eversion in stance greater in the RA patients. The peak ankle plantarflexion power profile was lower in the patients in comparison with the controls (3.4 W/kg Vs 4.6 W/kg). Pressure analysis indicated that the RA patients had a reduced lesser toe contact area (7.6 cm2 Vs 8.1 cm2), elevated peak forefoot pressure (672 kPa Vs 553 kPa) and a larger mid-foot contact area (24.6 cm2 Vs 19.4 cm2). CONCLUSION Analysis detected small but clinically important changes in foot function in a small cohort of RA patients with disease duration <2 years. These were accompanied by active joint disease and impairment and disability