1. AS IS WELL KNOWN, the comparative method has been elaborated upon with reference to the lndo-European languages. For more than a century, it has been customary to view them from the angle of both the family-tree theory and the wave hypothesis. As far as the continuity of the territory of IndoEuropean languages can be posited, it is the wave hypothesis that best explains the relation of the l...

In this article, we propose a new method for selecting level dependent threshold in wavelet shrinkage using the empirical Bayes framework. We employ both Bayesian and frequentist testing hypothesis instead of point estimation method. The best test yields the best prior and hence the more appropriate wavelet thresholds. The standard model functions are used to illustrate the performance of the p...

It has long been known that, under the assumption of the Riemann Hypothesis, one can give upper and lower bounds for the error ∑ p≤x log p−x in the Prime Number Theorem, such bounds being within a factor of (log x)2 of each other and this fact being equivalent to the Riemann Hypothesis. In this paper we show that, provided “Riemann Hypothesis” is replaced by “Generalized Riemann Hypothesis”, re...