Sentence examples for a a k from inspiring English sources
The last inequality shows that there would exist an entry b such that M a a ( k ) - M b b 2 > 3 α.
It is also shown that the optimal value of each entry of A (A k ) does not depend on the other entries of the same column.
A A, k and A B, k are the IBD kinship matrices at the kth genetic position, calculated in groups A and B, respectively.
To do that, vectors of IBD coefficients constituting the IBD kinship matrices associated to QTL effects, A A, k and A B, k in the scan model (see statistical modeling section), were randomly shuffled before each replicate of genome scan, whereas all other components were unchanged comparing to the null model.
Here, we assume that A(a k ) is independent of h n.
For the purpose of clarification, A k is represented by A(a k ) explicitly in the following.
x a k ∈ 0, 1 ∀ a ∈ A, k ∈ K Open image in new window (7).
The elements of M can be regarded as ordered pairs ( a, k ), where a ∈ A, k ∈ K with multiplication given by ( a, k ) ( a ′, k ′ ) = ( a a ′, ( k θ a ′ ) k ′ ).
(We note that the reader can find some examples of monoid endomorphisms in [17].) The elements of ℳ can be regarded as ordered pairs ( a, k ) where a ∈ A, k ∈ K with multiplication given by ( a, k ) ( a ′, k ′ ) = ( a a ′, ( k θ a ′ ) k ′ ).
Supposing A, B quasi-stationary we have to find the positive solutions of the equations k A = A ˜ + k ˜ c A ˜ B ˜, k B = B ˜ + k ˜ c A ˜ B ˜, where A ˜ = k d e g, A A, B ˜ = k d e g, B B, k ˜ c = k c / (k d e g, A k d e g, B ).
A-A, K♥-Q♥, and A♣-J are examples of hole cards that you can always challenge a maniac with.
