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This is equivalent to a weak signal in surge acceleration (Fig. 5C), indicating that the bird was motionless.
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We prove that the notion of rigidity (or relative property (T)) for inclusions of finite von Neumann algebras recently defined by the second author is equivalent to a weaker property, in which no "continuity constants" are required.
NFP is equivalent to a weaker fragment of arithmetic, but does (unlike NFU) prove Infinity: this is the only application of the Specker proof of ¬AC to a provably consistent theory.
It is equivalent to a neighborhood association.
That's equivalent to a DIY Hindenburg.
But if the 'only if' is taken to be a material conditional, it is equivalent instead to a weaker modal entailment account: if numbers are in the domain of every world, then when '∃x Unicorn(x)' is evaluated with respect to any world, numbers "are counted amongst the values of the variables".
which is equivalent to the weak formulation of the nonlinear boundary value problem (1.7).
(iii) The upper doubling condition is equivalent to the weak growth condition introduced by Tan-Li in [33]. .
If X is compact, for any (pge 1) the function (W_p) is a distance over (mathcal {P}(X)) and the convergence with respect to this distance is equivalent to the weak convergence of probability measures.
(This is roughly equivalent to Weak Reasons Sufficiency, formulated in §2 of the main text).
To prove that the convergence according to (W_p) is equivalent to weak convergence one first establish this result for (p=1), through the use of the duality formula in the form (4.7).
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