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The empirical copula puts a weight of 1/n ik on some points of an evenly spaced grid over [0,1] p with exactly one such point in every (p−1 -dimensional slice of the grid (rows and columns in 2 dimensions).
Each entity would like to be part of exactly one such group.
We form a subset (mathcal{C }^{prime }) of (mathcal{C }) by choosing exactly one such element for each (mathbf{k}).
If there is exactly one such component, it is the set ; if there is more than one, (mathcal {C} = varnothing ).
But there is exactly one such distribution (Lemma 3).This completes the proof of the theorem.
There is exactly one such point in ST, so this mapping is unique for each cluster in a gene tree.
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If, then we have the following: (A For each, there is exactly one in such that (2.15).
We show that in the case of sequential amplification (where each event is the addition of only one copy of the region) the sequence of events for which this will be true is limited: for a total number of copies equal to S, there is always exactly one history such that A is invertible and it is a history where all of the gains are on a single line of descent.
The deterministic edge-partition problem considers an undirected graph with weighted edges, and simultaneously assigns nodes and edges to subgraphs such that each edge appears in exactly one subgraph, and such that no edge is assigned to a subgraph unless both of its incident nodes are also assigned to that subgraph.
Then there exists exactly one sequence z such that z = o ( 1 ) and Δ m z = ( − 1 ) m x.
We prove that there existsε0so that for all 0<ε<ε0, Eq. possesses a solution having exactly one maximum pointxε∈Δ, such thatV(xε)→cand ∇V(xε)→0 asε→0.
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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