To compute the same-chromosome covariance terms, we split into two cases according to whether or not recombination has occurred between x and y since admixture.
The computation of the outer partition function of a base pair is split into two cases: The trivial case where no base pair is enclosing the base pair (i, j), and the case where there exists at least one base pair (k, l) with k < i < j < l. (4) The interior loop contribution is again kept cubic by the size restriction of the interior loops.
The proof of the lemma now splits into two cases.
The remainder of this part splits into two cases.
We split the problem in question into three cases: (a) products of nonnegative random variables, (b) products of random variables taking values in ({mathbb {R}},) and (c) the mixed case.
We split the situation into four cases.
In the following we will split the proof into two cases.
To verify that the above ingredients imply (C^{1,1}) regularity, we split the analysis into two cases.
where x is an arbitrary parameter in D. We split our approaches into two cases: diagonal parameters and off-diagonal parameters in matrix D. To find the required derivatives, we will use the following property.
where v + = max { 0, v ( t − τ ( t ), x ) }, ( x, t ) ∈ Q T, obviously, v + = max { 0, v ( t − τ ( t ), x ) } ≥ 0. On the one hand, we prove the existence of the periodic solution of problem (3.4 - 3.6 3.4 - 3.6e conditions of Theorem 3.1, we split the proof into two cases: (i) v + = 0 ; (ii) v + > 0. Case (i).
