Since g i ≠ 0 and M i is indecomposable, the map g i is left minimal.
If J is empty, then we deal with the zero map X → 0 which of course is left minimal.
We want to show that for any finite subset J ⊆ I, the map g J X X → ⨁ i ∈ J M i is left minimal.
We call a family of maps ( g i : X → M i ) i ∈ I a fork provided for any finite subset J ⊆ I, the map g J = ( g i ) i ∈ J X X → ⨁ i ∈ J M i is left minimal.
In order to see that ( u i : S → M i ) i ∈ I ( S ) is a fork, we have to show the following: For any finite subset J of I, say J = { 1, 2, ⋯, t }, the map u J : ( u i ) i : S → ⨁ i = 1 t M i is left minimal.
However, only a small subsample (n = 19) was left with minimal treatments (standard self-management instructions), which did not allow for any multivariate linear regression analysis.
The best location of VOI setting was left ventricle because of minimal reduction of blood FBPA counts.
Except for a few frugal souls who now try to cross into Manhattan free by snaking their way to the toll-less Harlem River bridges, the fees exacted on Westchesterites by Mayor Michael R. Bloomberg's fruitless stab at easing traffic would have been zero to minimal — whatever was left after Triborough or Henry Hudson Bridge tolls were deducted, or $2.50 a day at most.
Only a minimal activity was left in the supernatant of the covalently functionalized particles, indicating that almost all tPA, added to the activated reaction mixes, were bound to the particles.
In August, Hurricane Dora, the strongest storm of the 1999 Pacific hurricane season, produced gusty winds and large waves on Johnston Atoll and the island of Hawaii, though minimal damage was left in its wake.
A recent test screening of "Jay and Silent Bob Strike Back" had gone so well, he said, that only minimal re-editing was left to be done, followed by the usual last-minute dubbing and color-correcting.
