In this paper I shall present the construction of Weyl-Heisenberg superframes and density results related to the noncoherent case. A superframe is a collection of r-frames F = ff i ; i 2 Ig H1, : : : , F r = ff i ; i 2 Ig Hr all having the same countable index set I such that F = ff i f r i ; i 2 Ig is a frame for the Hilbert spaceH = H1 Hr. For the Weyl-Heisenberg superframes we set H1 = = Hr ...

A new approach to probability theory based on quantum mechanical and Lie algebraic ideas is proposed and developed. The underlying fact is the observation that the coherent states of the Heisenberg-Weyl, su(2), su(r+1), su(1, 1) and su(r, 1) algebras in certain symmetric (bosonic) representations give the “probability amplitudes” (or the “square roots”) of the well-known Poisson, binomial, mult...

A new approach to probability theory based on quantum mechanical and Lie algebraic ideas is proposed and developed. The underlying fact is the observation that the coherent states of the Heisenberg-Weyl, su(2), su(r+1), su(1, 1) and su(r, 1) algebras in certain symmetric (bosonic) representations give the “probability amplitudes” (or the “square roots”) of the well-known Poisson, binomial, mult...

In this paper we apply a time frequency approach to the study of pseudodi er ential operators Both the Weyl and the Kohn Nirenberg correspondences are considered In order to quantify the time frequency content of a function or distribution we use certain function spaces called modulation spaces We deduce a time frequency characterization of the twisted product of two symbols and and we show tha...

Many practical machine learning tasks employ very deep convolutional neural networks. Such large depths pose formidable computational challenges in training and operating the network. It is therefore important to understand how many layers are actually needed to have most of the input signal’s features be contained in the feature vector generated by the network. This question can be formalized ...

in this paper, lagrangian and equations describing one-dimensional anisotropic non-heisenberg model are studied. in this study we used the generalized coherent states in real parametrizations and the feynman path integral for these states in su(3) group. these equations describe nonlinear dynamics of non-heisenberg ferromagnetic chain completely. solutions of these equations are magnetic solito...

We study entanglement and genuine of tripartite four-partite quantum states by using Heisenberg-Weyl (HW) representation density matrices. Based on the correlation tensors in HW representation, we present criteria to detect entanglement. Detailed examples show that our method can more entangled than previous criteria.

This work revolves around Gabor filters. It involves theoretical aspects such as the uncertainty principle as well as practical issues such as filter bank design and application of Gabor filters to texture segmentation. This thesis is composed of three main parts. In the first part, we explore the role of the metric of the Gabor feature space, and its usefulness in capturing what we refer to as...

Some classes of Deformed Special Relativity (DSR) theories are reconsidered within the Hopf algebraic formulation. For this purpose we shall explore a minimal framework of deformed Weyl–Heisenberg algebras provided by a smash product construction of DSR algebra. It is proved that this DSR algebra, which uniquely unifies κ-Minkowski spacetime coordinates with Poincaré generators, can be obtained...

We describe an algebra G of diagrams that faithfully gives a diagrammatic representation of the structures of both the Heisenberg–Weyl algebra H – the associative algebra of the creation and annihilation operators of quantum mechanics – and U(LH), the enveloping algebra of the Heisenberg Lie algebra LH. We show explicitly how G may be endowed with the structure of a Hopf algebra, which is also ...