Exact(2)
Any indecomposable preprojective Λ -module has defect -1, the indecomposable preinjective modules have defect 1, all the regular modules have defect 0. There are countably many indecomposable preprojective modules, they are labeled P i, and also countably many indecomposable preinjective modules, they are labeled Q i ; both P i and Q i have length 2 i + 1.
In a second phase, we map the length of each right-maximal occurrence i into l s 1 (i ), and, using Proposition 1, we check which occurrences i have length greater than or equal to the length stored in the location i−1 (for locations i ≥ 2).
Similar(6)
Each region s i = (b i, l i, t i) starts at position b i, has length l i and labels t i.
where Z j, w I ′ [ d 2 ] is the partition function starting and ending with a single-stranded base as defined in Equation (2), and Z i, j B, v [ d ℓ, d r ] is the partition function consisting of all structures of x[ i, j] containing the base pair { i, j} with the property that the shortest path from v to i has length d ℓ and the shortest path from v to j has length d r.
For each condition j in window i, the column vector x j i consists of K factors with R replicates (K≥1, R≥1), and therefore x j i has length P = K*R and is represented as x j i = x j, 1, 1, i x j, 1, 2 i, …, x j, K, R - 1 i, x j, K, R i = x j, 1 i x j, 2, i …, x j, P i.
As previously mentioned, f i (n) has length L, and t i (n) has length N+L−1.
They have length and size inside.
As the reader can verify it, analog of Theorem 4.6 for I p has length expression and makes appear hard computations.
Related(1)
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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