Substituting expression (1.7) for into this equality, we get (3.1).
Substituting expression (5) into equation (4), after some operations, we obtain the following system of differential equations for determining (S (t )), (N (t )) and (omega (t )): begin{aligned} &dot{S} (t )=-F' (t )S (t )-S (t )F (t )+S (t )M (t )S (t )-Q (t ), &dot{N} (t )= bigl[S (t )M (t )-F' (t ) bigr]N (t ), &dot{omega} (t )= bigl[S (t )M (t )-F' (t ) bigr]omega (t )-S (t )v (t ).
Note that substituting expression (4) into (1) resolves into the equation z threshold (μΦ + fσΦ, μ c - fσ c ) = -2 f.
Thus, substituting Expression 4 and Λ in the score 2 for each node ν we have (5) S c o r e = { Λ × Γ (s for f (w [ 1.. k ] ) ≥ 1 0 otherwise where s is the proper longest suffix of w = ⟨ ν⟩, that is, the word from the root to the node referenced by the suffix link that goes out from ν.
Using the same method of power series and polynomial expansion which has been used to derive the substituted expression of f Y (y|L c e n t e r ) in subsection 3.2, we could get that E [ Y L edge ] = α M 1 − α M 0 1 − γ 2 R β (39).
However, a definition of substitution for FOL (and in general, for an abstract syntax, that is, for a language with a variable binding operator) has to guarantee that no free occurrence of a variable in the substituted expression becomes bound in the resulting expression.
end{aligned}Thus, after substituting these expressions in the expression of (x zeta,0)) and identifying with x we obtain the following relations between the coefficients: 1. (D_{1}+F_{1}=0,) 2.
Taking the mean of (18) and substituting the expressions (19), (20), and (21), we obtain the expression for the mean overall delay of the tagged -packet as (22).
Our assay could easily be applied to miRNA target identification by substituting shRNA expression with miRNA expression.
The explicit expression for the ballistic light transmitted through a cell of length D can be obtained by substituting the expressions (2) and (6) in Equation 1: (8).
