If S _ 0 satisfies the above asymptotic conditions, then the above assumption is consistent.
2.
All defined and understood descriptions of string / M-theory deal with fixed asymptotic conditions on the background spacetime.
3.
Function ` tanh'in Eq . 8 is the simplest function satisfying two asymptotic conditions ensuing from the diffusion theory : 1 ) for short times \ bar \ epsilon _ { sh } \ propto \ sqrt { t-t _ 0 }, and 2 ) the final shrinkage must be approached exponentially.
4.
The purpose of the approximation made is : ( a ) to prevent \ sigma _ N from becoming negative for very small D, for which the foregoing argument does not apply; and ( b ) to satisfy the asymptotic condition that the deterministic size effect must vanish for D / l _ 0 \ to \ infty.
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