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The design methodology relies upon an assumption of left invertibility of a matrix.
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This assumption of left-to-right correction is commonly considered in works involving data of sequential nature such as in interactive machine translation (IMT) or interactive speech transcription (IST) [30, 31].
Note also that Theorems 4.1 and 4.2 need not the assumption of being a left-invariant -stable subspace of containing " " and to be a left-invariant mean on, although it is assumed to be strongly left regular so that it fulfils ; for all (Assumption 1, see Definition 3.6.
The assumption, of course, is that left to its own devices, the body will only crave vast amounts of chocolate.
Under this assumption, the left hand side of (29) becomes (30) E α r (x ) = E κ r ∏ s = 1 N s v - r s !
Under the assumption of equal noise PSD at the left and right ear and substituting (Phi _{n_{l}n_{r}}~= ~Phi _{n_{r}n_{l}}~=~Gamma _{n_{l}n_{r}} Phi _{n} ) into (38), we have begin{array}{*{20}l} mathbf{Phi}_{e} kappa,lambda) &= mathbf{B} kappa,lambda){Phi}_{n} kappa,lambda) &quad- 2textup{Re}left{widehat{H}^{ast}_{l}widehat{H}_{r}right}{Phi}_{n}Gamma_{n_{l}n_{r}}widehat{mathbf{H}}'.
The α value in the left figure satisfies the assumption of Theorem 3.1.
This led to a theory on lateralization based on the assumption of longer average conduction times in the left hemisphere than in the right (Miller 1996, 2008).
The initial characterizations of left atrial volume applied Simpson's method of discs to biplanar images, despite the known inaccurate geometric assumptions.
Our assumption of all of the GBCA pooling in the left ventricle together with the radiotracer is likely to be an overestimation of the true scenario.
Then there's the issue of entitlement, the suspicion, deeply held by some on the left, that the Clintons have an assumption of ownership over the Democratic party and over high office.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com