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1
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A necessary and sufficient condition for the existence of a father wavelet

100%
Gripenberg G.
Studia Mathematica
|
1995
|
tom 114
|
nr 3
207-226
EN
It is proved that if ${2^{-m/2} ψ(2^{-m} • - k)}_{m,k ∈ ℤ}$ is an orthonormal basis in $L^2(ℝ;ℂ)$, then the mother wavelet ψ is obtained from a multiresolution generated by a father wavelet if and only if $∑_{p=1}^{∞| ∑_{k ∈ ℤ} |ψ̂(2^{p}(• + k))|^2 > 0$ a.e.
2
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Commutators based on the Calderón reproducing formula

100%
Nowak K.
Studia Mathematica
|
1993
|
tom 104
|
nr 3
285-306
EN
We prove the Schatten-Lorentz ideal criteria for commutators of multiplications and projections based on the Calderón reproducing formula and the decomposition theorem for the space of symbols corresponding to commutators in the Schatten ideal.
3
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Wavelet bases in $L^{p}(ℝ)$

88%
Gripenberg G.
Studia Mathematica
|
1993
|
tom 106
|
nr 2
175-187
EN
It is shown that an orthonormal wavelet basis for $L^2(ℝ)$ associated with a multiresolution is an unconditional basis for $L^p(ℝ)$, 1 < p < ∞, provided the father wavelet is bounded and decays sufficiently rapidly at infinity.
4
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A mathematical model for file fragment diffusion and a neural predictor to manage priority queues over BitTorrent

88%
Napoli C., Pappalardo G., Tramontana E.
International Journal of Applied Mathematics and Computer Science
|
2016
|
tom 26
|
nr 1
147-160
EN
BitTorrent splits the files that are shared on a P2P network into fragments and then spreads these by giving the highest priority to the rarest fragment. We propose a mathematical model that takes into account several factors such as the peer distance, communication delays, and file fragment availability in a future period also by using a neural network module designed to model the behaviour of the peers. The ensemble comprising the proposed mathematical model and a neural network provides a solution for choosing the file fragments that have to be spread first, in order to ensure their continuous availability, taking into account that some peers will disconnect.
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