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Exact(15)
and is a dimensional unity vector with one in position.
where, with is a dimensional unity vector with one at position.
Let { e k } denote the column vector with one in position k and zeros elsewhere.
where, with is an dimensional unity vector with one at the th position and zeros elsewhere.
A generalized force vector, with one voltage and two forces as elements, is expressed as the product of an impedance matrix and a generalized velocity vector, with one current and two velocities, as elements.
returns transformed into a column vector with one column stacked onto the next., and stand for the Euclidian norm, the transpose and the inverse of matrix, respectively.
Similar(45)
where v m denotes a M × 1 vector with ones as the entities of the m th row.
is the vector with ones, where might be omitted if there is no ambiguity regarding the dimension.
Let Z be the scaled and centered g× m∈ p matrix with the similarity statistics for the metabolites in p. Further, let be a column vector with ones for the transcripts that are annotated to p and zeroes for those that are not (as defined by a pathway database such as KEGG).
Moreover, we have (20) lim N → ∞ ϕ B (O t N (c ) ) = c T (f P t FM − f P t M ) c, so the optimum contributions c t B for the breeding individuals with respect to objective function ϕ B minimize c T (1 1 T − (f P t FM − f P t M ) ) c under the side conditions described above, where 1 is a vector with ones.
In [27] the authors consider center stable manifolds for planar fractional damped equations involving two Caputo fractional derivatives with zero and first derivative initial conditions which act on two-dimensional vectors with one order belonging to ((1,2)), the other belonging to ((0,1)).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com