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In this paper, we derive a physical argument for the existence of Period-luminosity and period-luminosity-colour relations at maximum light. We examine in detail a sample of Cepheids in the Large Magellanic Cloud, and compare the variance of some PL and PLC type distance indicators based on mean and maximum light. We show that a PLC relation based on maximum light leads to a distance estimator with a dispersion about $10 %$ smaller than its counterpart using mean light. We also show that a PLC type relation constructed using observations at both maximum and mean light has a significantly $( > 50 %)$ smaller dispersion than a PLC relation using either maximum or mean light alone. A comparable $( > 30 %)$ reduction in the dispersion of the corresponding distance estimator, however, in this case requires the relation be applied to a large $( n > 30)$ group of equidistant Cepheids in, e.g., a distant galaxy. Recent HST observations of IC4182, M81 and M100 already provide suitable candidate data sets for this relation.
We first discuss why there remains continuing, strong motivation to investigate Hubbles Constant. Then we review new evidence from an investigation of the Galactic Open Clusters containing Cepheids by Hoyle et al. that the metallicity dependence of t
Distances measured using Cepheid variable stars have been essential for establishing the cosmological distance scale and the value of the Hubble constant. These stars have remained the primary extragalactic distance indicator since 1929 because of th
The Hubble Space Telescope is being used to measure accurate Cepheid distances to nearby galaxies with the ultimate aim of determining the Hubble constant, H_0. For the first time, it has become feasible to use Cepheid variables to derive a distance
A collection of robust Mahalanobis distances for multivariate outlier detection is proposed, based on the notion of shrinkage. Robust intensity and scaling factors are optimally estimated to define the shrinkage. Some properties are investigated, suc
We present the results from a multi-epoch survey of two regions of M33 using the 3.5m WIYN telescope. The inner field is located close to the centre of the galaxy, with the outer region situated about 5.1 kpc away in the southern spiral arm, allowing