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Example 2 A is (5,2,3) -extendable to B. It is obvious that there exists a (k,a,b) -PPM matrix B m×n if and only if there exists an (m,a,b) -extendable matrix A k×n. Definition 3. A matrix B is called good if it can be decomposed as follows: The entries of its leftmost column are all 1's.
Since, it can be decomposed as (A3).
A function is called Stepanov-like pseudo-almost periodic if it can be decomposed as with and.
A function with, for each, is called Stepanov-like pseud-almost periodic in uniformly for if it can be decomposed as with and.
A continuous function (resp., ) is called pseudo-almost automorphic if it can be decomposed as where (resp., ) and is a bounded continuous function with vanishing mean value, that is, (2.1).
Definition 2.7 A function f ∈ PC ( R, X ) is said to be piecewise pseudo almost periodic if it can be decomposed as f = g + h, where g ∈ AP T ( R, X ) and h ∈ PAP T 0 ( R, X ).
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The main goal is to study under which conditions such a function can be decomposed as, where the components are extendable to two-sided -monogenic functions in the interior and the exterior of, respectively.
The main goal is to study under which conditions such a function can be decomposed as, where the components are extendable to -monogenic functions in the interior and the exterior of, respectively.
The probability of isotope i and adduct a is: (7) P (v n k a i = 1 | z n k = 1, d n, … ) ∝ p (d n | v n k a i = 1, … ) which can be decomposed as above.
That is, the probability of a time series gene expression O k given a HMM λ(1) and the hidden states x k can be decomposed as, What we need is to decompose the marginalized likelihood p(O k |λ(1)) into terms involving each gene only, : Unfortunately, expressions levels for individual genes are not independent once the hidden state are not known, so the above decomposition does not exist.
It follows from the spectral theory that E can be decomposed as the orthogonal sum of Ker(I - L), E+ and E- with I - L positive definite (resp. negative definite) on E+ (resp. E-).
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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