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The basic principle of lifting scheme is to factorize the polyphase matrix of a wavelet filter into a sequence of alternating upper and lower triangular matrices and a diagonal matrix and convert the filter implementation into banded matrices multiplications[1] as shown by (1) and (2).

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For erasure recovery, we showed how to find the inverse of a matrix using a simple algorithm by exploiting the logarithmic operator of the elements of the Vandermonde matrix and converting the operations to simple modulo- additions.

The organic acids produced were converted to storage polymers, while the alcohols (produced and from influent) were absorbed onto the granular sludge matrix and converted aerobically.

The main feature of the lifting-based DWT scheme is to break up high-pass and low-pass filters into a sequence of upper and lower triangular matrices and convert the filter implementation into banded matrix multiplications.

Homologues of the PhoP box identified from the PhoP sites were then collected and displayed by the WebLogo program [ 23] to generate a sequence logo; additionally, the position count matrixes were built from them by using the consensus-matrix and convert-matrix tools [ 21].

Supercritical carbon dioxide anti-solvent precipitation and extraction, respectively, have been used as core techniques for depositing the secondary polymer within the BC matrix and to convert the formed composite organogels into aerogels.

Supercritical carbon dioxide anti-solvent precipitation and simultaneous extraction of the anti-solvent using scCO2 have been used as core techniques for incorporating the secondary polymer into the BC matrix and to convert the formed composite organogels into aerogels.

Firstly, the enzymatic pretreatment helps to break down the rigid solid matrix and to convert the large-molecule organic matter, such as cellulose, hemicellulose, and protein, into small monomers, and the non-hydrolyzed residue, such as lignin, is separated from the hydrolysates by solid liquid separation.

In [20], ICI is removed from the time domain signal (resulting in a diagonal frequency domain system matrix) and is converted to frequency domain.

The O2 − generated by complex I is released into the mitochondrial matrix and is converted to H2O2 by the mitochondrial manganese superoxide dismutase (MnSOD).

One of these consists of manganese-dependent superoxide dismutase (MnSOD or SOD2), an enzyme that is localized in the mitochondrial matrix and rapidly converts superoxide to hydrogen peroxide.

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