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The fixed-effects approach models the equivalent of a unique intercept for each unit.
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The latter problem tends to determine a list of conjugacy inequivalent subalgebras with the property that any other subalgebra is equivalent to a unique member of the list under some element of the adjoint representation for some element of a considered Lie group.
Once such inconsistent constituents are omitted, every sentence in a monadic language (without identity or constants) is equivalent to a disjunction of a unique set of these constituents.
One is Cirrus, which makes simple little aeroplanes, aiming for the airborne equivalent of a modern car with the unique safety feature of a parachute for the entire aircraft.
Hence, proving the existence and uniqueness of solution (8) is equivalent to proving the existence of a unique zero point of map (mathcal{H}:mathbb{C}^{n}tomathbb{C}^{n}), where mathcal{H} z)=-Cz+Af z)+Bf(z)+J.
Lindesay Irvine When I discovered her short stories, Jackie Kay quickly became my literary equivalent of that unique relative or friend who provides reassuring non-judgemental comfort in bleak situations.
Under the contractive condition (2.1) assumed in the above proposition, the assumption of PD-operators and the existence of a unique common fixed point are equivalent conditions.
Obviously, the existence of a unique almost periodic solution of system (2.1) is equivalent to that of system (3.2).
This could represent a case of a unique adaptive peak or a case of various peaks of equivalent fitness, spread over a rugged landscape, and potentially connected between them.
For less tech-centric folks, he pitches it as the digital equivalent of a picture frame, though he thinks there will be more unique uses possible.
This is sort of a unique suburb.
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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