Inversely, if every peak has at least one assignment possibility at the end of the matching process, it is highly improbable to have an error in this result.
inductive if every chain in P has an upper bound in P; inversely inductive if every chain in P has a lower bound in P; bi-inductive whenever it is both inductive and inversely inductive.
A subset C of a poset P = ( P, ⪰ ) is called a chain if x ⪯ y or y ⪯ x for all x, y ∈ C. Definition 2.1 A poset P = ( P, ⪰ ) is said to be (i) inductive if every chain in P has an upper bound in P; (ii) inversely inductive if every chain in P has a lower bound in P; (iii) bi-inductive whenever it is both inductive and inversely inductive. .
(Csubset mathcal{P}); (ii) inversely inductive if every (c.c). in (mathcal{P}) has a lower bound in (mathcal{P}) and strongly inversely inductive whenever every (c.c).
(Csubset mathcal{P}); inversely inductive if every (c.c). in (mathcal{P}) has a lower bound in (mathcal{P}) and strongly inversely inductive whenever every (c.c).
every player's strategy set ((S_{i},preceq_{i})) ((iin N)) is a strongly inductive and inversely inductive poset, every player's payoff function (P_{i}:Srightarrow U) ((iin N)) satisfies P_{i}(x preceq^{U} P_{i} y quad textit{if and only if} quad xpreceq^{S} yquad textit{for any }x,yin Stextit{ and }iin N, Lemma 3.4 guarantees that S has at least a maximal (c.c).
However, it will be necessary to adjust the index according to the relationship between the number of citations and the date of publication, since they are not precisely inversely proportional in every time window.
Inversely, we check after every time step whether a polymer evaporates liberating a molecule.
strongly inductive whenever for every chain C in P, the supremum of C, supC, exists in P; strongly inversely inductive whenever for every chain C in P, the infimum of C, infC, exists in P; strongly bi-inductive whenever it is both strongly inductive and strongly inversely inductive.
Definition 2.2 A poset P = ( P, ⪰ ) is said to be (i) strongly inductive whenever for every chain C in P, the supremum of C, supC, exists in P; (ii) strongly inversely inductive whenever for every chain C in P, the infimum of C, infC, exists in P; (iii) strongly bi-inductive whenever it is both strongly inductive and strongly inversely inductive. .
