place

1

[see also: location, position, replace, instead]

......where 1 appears in $\langle$at$\rangle$ the $n$th place

Any vector with three or fewer 1s in the last twelve places has at least eight 1s in all.

Values computed for the right side of (2) were rounded up in the fourth decimal place.

We tabulate the outcome for $n\ge 10$; in particular, the column headed $R$ lists $R(n)$ truncated to three decimal places.

Apply this to $f$ in place of $g$ to obtain ......

Then the conclusion holds with `P-cell' in place of `cell'.

All of the action in creating $S_{i+1}$ takes place in the individual cells of type 2 or 3.

Moreover, one has estimates on the rate at which this convergence is taking place.

2

[see also: put, insert, impose]

Some restrictions must be placed on the behaviour of $f$.

To place Theorem 1 in context, consider two real vector fields ......

In this section we gather some miscellaneous results that are more or less standard. These will be used to calculate the constants $c_{\alpha}$, and we place them here to avoid interrupting the forthcoming arguments.



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