partial frames provide a rich context in which to do pointfree structured and unstructured topology. a small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. these axioms are sufficiently general to include as examples bounded distributive lattices, $sigma$-frames, $ka...

This work presents a quantitative framework for describing the overcompleteness of a large class of frames. It introduces notions of localization and approximation between two frames F = {fi}i∈I and E = {ej}j∈G (G a discrete abelian group), relating the decay of the expansion of the elements of F in terms of the elements of E via a map a : I → G. A fundamental set of equalities are shown betwee...

Let g be a continuous, compactly supported function on R such that the integer translates of g constitute a partition of unity. We show that the Gabor system (g, a, b), with window g and time-shift and frequency-shift parameters a, b > 0 has no lower frame bound larger than 0 if b = 2, 3, . . . and a > 0. In particular, (g, a, b) is not a Gabor frame if g is a continuous, compactly supported wa...

pullback test has no scrupulous theoretical establishment. it is based on the hypothesis that the response ofthe structure can be related to the response of an equivalent single degree-of-freedom (sdof) system. this implies thatthe response is controlled by a single mode. in fact, the steel frame of each safe room, which is introduced within theunreinforced masonry buildings for protecting the ...

In this work we study families of pairs of window functions and lattices which lead to Gabor frames which all possess the same frame bounds. To be more precise, for every generalized Gaussian g, we will construct an uncountable family of lattices [Formula: see text] such that each pairing of g with some [Formula: see text] yields a Gabor frame, and all pairings yield the same frame bounds. On t...

We consider the frame property of the Gabor system G(g, α, β) = {eg(t − αm) : m,n ∈ Z} for the case of rational oversampling, i.e. α, β ∈ Q. A ’rational’ analogue of the Ron-Shen Gramian is constructed, and prove that for any odd window function g the system G(g, α, β) does not generate a frame if αβ = n−1 n . Special attention is paid to the first Hermite function h1(t) = te −πt .

Despite the growth in network capacity of wireless in-home networks, these networks often have insufficient capacity to support multiple simultaneous Audio/Video streams. Unpredictable behavior of these networks results in a drop of video quality for the end-user. A method for reducing the claim of an individual A/V stream on the network capacity is controlled frame dropping. However, controlle...

A (K1,3, λ)-frame of type g u is a K1,3-decomposition of a complete upartite graph with u parts of size g into partial parallel classes each of which is a partition of the vertex set except for those vertices in one of the u parts. In this paper, we completely solve the existence of a (K1,3, λ)-frame of type g .

The purpose of the paper is to analyze g-frames form \(\{\varphi T^{i} \in B(\mathcal {H},\mathcal {K})\}_{i=0}^\infty \), where \(T\in {H})\) and \(\varphi {K})\), discuss properties operator T. We consider stability g-Riesz sequences \). Finally, a weighted representation g frame introduced some its are presented. provide sufficient condition for given g-frame \(\Lambda =\{\Lambda _{i}\in {B(...

for all f ∈ H . The constant A (respectively, B) is a lower (resp. upper) frame bound for the frame. One of the most important frames for applications, especially signal processing, are the Weyl-Heisenberg frames. For g ∈ L(R) we define the translation parameter a > 0 and the modulation parameter b > 0 by: Embg(t) = e , Tnag(t) = g(t− na). For g ∈ L(R) and a, b > 0, we say for short that (g, a,...