The Fréchet distance is a popular similarity measure between curves. For some applications, it desirable to match the curves under translation before computing them. This variant called Translation Invariant distance, and algorithms compute are well studied. query version, finding an optimal placement in plane for segment where becomes minimized, much less understood. We study queries restricte...

In this paper, we aim to overcome three major shortcomings of the FDH (Free Disposal Hull) directional distance function through developing two new, named Linear and Fractional CDFDH, complete FDH measures of efficiency. To accomplish this, we integrate the concepts of similarity and FDH directional distance function. We prove that the proposed measures are translation invariant and unit invari...

In many signal processing applications, an appropriate measure to compare two signals plays a fundamental role in both implementing the algorithm and evaluating its performance. Several techniques have been introduced in literature as similarity measures. However, the existing measures are often either impractical for some applications or they have unsatisfactory results in some other applicati...

In this paper we refined a criteria investigated in [BJKW] for a translation invariant factor state on one dimensional lattice to be pure. However the central aim here is to prove that such a condition is also necessary for a translation invariant factor state to be pure. As an easy fall out we also prove that a translation invariant pure state admits Haag duality property. Further a real latti...