Let L and K be two full rank lattices in R. We prove that if v(L) = v(K), i.e. they have the same volume, then there exists a measurable set Ω such that it tiles R by both L and K. A counterexample shows that the above tiling result is false for three or more lattices. Furthermore, we prove that if v(L) ≤ v(K) then there exists a measurable set Ω such that it tiles by L and packs by K. Using th...

In this paper, by using the sequence of adjointable operators from pro-C*-algebra $ mathcal{A} $ into a Hilbert $ mathcal{A} $-module $ E $. We introduce frames with bounds in pro-C*-algebra $ mathcal{A} $. New frames in Hilbert modules over pro-C*-algebras are called standard $ ast $-frames of multipliers. Meanwhile, we study several useful properties of standard $ ast $-frames in Hilbert modu...

The high prevalence of urban flooding in the world is increasing rapidly with rise extreme weather events. Consequently, this research uses an Automatic Flood Monitoring System (ARMS) through a video surveillance camera. Initially, videos are collected from camera and converted into frames. After converting frames, water level can be identified by using Histogram oriented Gradient (HoG), which ...

in this note‎, ‎we aim to show that several known generalizations of frames are equivalent to the continuous frame‎ ‎defined by ali et al‎. ‎in 1993‎. ‎indeed‎, ‎it is shown that these generalizations can be considered as an operator between two hilbert spaces‎.

This paper generalizes the mixed extension principle in L2(R) of [50] to a pair of dual Sobolev spaces H(R) and H−s(Rd). In terms of masks for φ, ψ, . . . , ψ ∈ H(R) and φ̃, ψ̃, . . . , ψ̃ ∈ H−s(Rd), simple sufficient conditions are given to ensure that (X(φ;ψ, . . . , ψ), X−s(φ̃; ψ̃, . . . , ψ̃)) forms a pair of dual wavelet frames in (Hs(Rd),H−s(Rd)), where X(φ;ψ, . . . , ψ) := {φ(· − k) : k ∈ Zd} ...

This study analyses (k,m)-type slant helices in compliance with the modified orthogonal frame 3-dimensional Euclidean space ($\mathbb{E}^{3}$). Furthermore, we perform some characterisations of curves frames $\mathbb{E}^{3}$.

In this paper we firstly propose simple and computationally efficient wireless channel modeling algorithm that explicitly takes into account firstand second-order statistics of frame error observations. For this purpose we use discrete-time Markov modulated processes with at most single event (error) at any time slot. We then adopt the special solution of the inverse eigenvalue problem initiall...

We introduce a new g-frame (singleton g-frame), g-orthonormal basis and g-Riesz basis and study corresponding notions in some other generalizations of frames.Also, we investigate duality  for some kinds of g-frames. Finally, we illustrate an example which provides a  suitable translation from discrete frames to Sun's g-frames.