On Basis Constants and Duality in Banach Spaces

Every Banach space with a non-shrinking (unconditional) basis (Xi) can be renormed so that the biorthogonal sequence has a much smaller (unconditional) basis constant than (xi). On the other hand, if the unconditional constant of is C < 2 then the unconditional constant of (xi) is at most C/(2—C). This estimate is sharp.

A Parametric Study to Relate Railcar Speed to Permissible Combinations of Track Geometry Deviations

A passenger railcar was modeled using quasi-linear, frequency domain computer simulation models to compute lateral and vertical rms wheelset forces and relative displacements over a range of speeds, in response to power spectra representations of track geometry deviations in surface, alinement, and crosslevel. A simplified wheel-climb criterion (Lateral to Vertical Force Ratio, L/V) was used to estimate the margin of safety for wheel-climb and to impose limits on combined track geometry deviations which result in development of lateral and vertical forces which would cause a commonly used threshold value to be exceeded on a statistical basis. “Constant performance” contours of speed versus combined track geometry deviations are developed for selected L/V threshold values and exceedance probabilities.