All wavelets can be associated to a multiresolution like structure, i.e. an increasing sequence of subspaces of L(R). We consider the interaction of a wavelet and the translation operator in terms of which of the subspaces in this multiresolution like structure are invariant under the translation operator. This action defines the notion of the translation invariance property of order n. In this...

Representations that can compactly and effectively capture temporal evolution of semantic content are important to machine learning algorithms that operate on multi-variate time-series data. We investigate such representations motivated by the task of human action recognition. Here each data instance is encoded by a multivariate feature (such as via a deep CNN) where action dynamics are charact...

There are dierent ways to code the geodesic flows on surfaces with negative curvature. Such code spaces give a useful tool to verify the dynamical properties of geodesic flows. Here we consider special subspaces of geodesic flows on Hecke surface whose arithmetic codings varies on a set with innite alphabet. Then we will compare the topological complexity of them by computing their topological ...

In this paper, in addition to some elementary facts about the ultra-groups, which their structure based on the properties of the transversal of a subgroup of a group, we focus on the relation between a group and an ultra-group. It is verified that every group is an ultra-group, but the converse is not true generally. We present the conditions under which, for every normal subultra-group of an u...

The theory of localized frames is a recently introduced concept with broad implications to frame theory in general, as well as to the special cases of Gabor and wavelet frames. Using the new notion of a R-dual sequence associated with a Bessel sequence, we derive several duality principles concerning localization in abstract frame theory. As applications of our results we prove a duality princi...

Abstract We identify a norm-dense subspace of the dual sequence space $$l^{(p,\infty )}$$ l ( p , ∞ ) , thus closing existing gap in literature. based our approach on notion James...

Alireza Shabani* and Daniel A. Lidar Physics Department and Center for Quantum Information and Quantum Control, University of Toronto, 60 St. George Street, Toronto, Ontario, Canada M5S 1A7 Chemical Physics Theory Group, Chemistry Department, and Center for Quantum Information and Quantum Control, University of Toronto, 80 St. George Street, Toronto, Ontario, Canada M5S 3H6 Received 8 May 2005;...

We give two distinct approaches to finding bounds, as functions of the order ν, for the smallest real or purely imaginary zero of Bessel and some related functions. One approach is based on an old method due to Euler, Rayleigh, and others for evaluating the real zeros of the Bessel function Jν(x) when ν > −1. Here, among other things, we extend this method to get bounds for the two purely imagi...