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Although Turing's proof was published shortly after Alonzo Church's equivalent proof using his lambda calculus, Turing had been unaware of Church's work.
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The system can be shown to be equivalent to Tarski's (1929) axiomatization of Leśniewski mereology (see Ridder 2002 for the equivalence proof).
Moreover, through a computational fluid dynamic (CFD) analysis, we set fluid dynamic conditions for a non-planar skin equivalent growth, as proof of potential application in creating skin grafts tailored on-demand for in vivo wound shape.
Applying the Schur complement shows that (14) is equivalent to (12b .The proof is completed.
If none is returned this should be equivalent to the proof that such a solution does not exist.
All of them are equivalent, but the proofs of this are also quite heavy.
In the forwarder's dilemma game, the strong Nash equilibrium profile (F,F) is not equivalent to coalition-proof Nash equilibrium.
This appears to be a very conservative position, as one of the in vitro conditions (40% alcohol) suggests a real-life situation where one would consume the formulated product with a glass of alcohol equivalent to 80-proof whiskey.
(These pandas also can swim). The zoo performed the equivalent of baby-proofing the yard, however, trimming tree branches and "collaring" trees.
When Deadspin's genius supercut of Sinclair's latest promo went viral last weekend, my heart broke for the anchors who were used to make the equivalent of a proof-of-life hostage video.
All but one of the trials were powered to test superiority, not equivalence or non-inferiority41, so it would be premature to construe our findings as proof of equivalent effects.
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