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Before proving Theorem 2, we need the following Lemma: [27] Consider a matrix decomposition X= A B T, where A ∈ ℂ I × F is a Vandermonde matrix with distinct nonzero generator and B ∈ ℂ J × F is a 'tall' or 'square' matrix with full column rank.
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Recall that the array response A θ and delay matrix F ϕ are both Vandermonde matrices with distinct generator (distinct angle and delay assumption).
To achieve the minimal total parallel execution time, the use of a blocking factor ℓ∈{2,p,2p} can be recommended for matrices with distinct singular values.
Artificial contamination of three different food matrices with distinct bacterial counts revealed a detection limit of 101 CFU/g B. cereus cells after overnight enrichment.
Assume that A θ = [ a θ 1, …, a θ r 1, …, a θ r ] ∈ C K × r, F ϕ = [ f ϕ 1, …, f ϕ r 1, …, f ϕ r ] ∈ C P × r are Vandermonde matrices with distinct nonzero generators, and S = [ s 1, …, s M ] ∈ C N × M. ( F ϕ, A θ, S ) represents a decomposition of X ¯ in the following formulation: X ¯ = ( F ϕ ⊙ A θ ) ( S J ) T. where J is the dependence matrix given in (7).
Three silk matrix groups with distinct structural and mechanical properties were investigated following 10 weeks of implantation including our original prototype previously shown to support bladder regeneration, Group 1 (2 mm/s, methanol) as well as Group 2 (40 mm/s, methanol) and Group 3 (40 mm/s, lyophilization) configurations.
Therefore, if a 3-state matrix M with distinct columns (up to relabeling) has a perfect phylogeny, m = O (n 2 ) = O (n 2 ).
As an example Figure 5 shows this region for c 0 = 0.2 and a covariance matrix with two distinct eigenvalues 2 and 1 with the multiplicity ratios α 1 = 1 3 and α 2 = 2 3.
"Superfibronectin" (sFn) is a form of Fn aggregates that resembles Fn matrices, but with distinct biological activities [9].
Framework is a systematic matrix based approach with distinct stages that allow transparent data management and interpretation.
Transition matrices in the K2P model have the same symmetric structure as the underlying rate matrices, with two distinct transition parameters: p α – the probability of a transition-type substitution; p β – the probability of a transversion-type substitution.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com