It says that if first-order arithmetic is ω-consistent (which it is believed to be), then there must be arithmetical sentences that can neither be proved nor disproved by the formal procedures of first-order arithmetic.
Thus, many of the usual set-theoretic procedures of twentieth-century mathematics go back to his work.
We have designed new methods with memory from Steffensen' or Traub's schemes, as well as from a parametric family of iterative procedures of third- and fourth-order of convergence.
MR imaging of the brain was obtained in all participants, as a standard procedure of first visit to the headache center.
To investigate hydrogen's effect on RAFM steels' elastic properties and the mechanism of that effect, a procedure of first principles simulation combined with experiment was designed.
Instead of embedding the watermark in the DCT domain of the normalized image, we follow the equivalent procedure of first performing the inverse DCT of the original watermark, inversely normalizing it and finally embedding it in the original image.
While this can be a very effective way of consolidating the signal information, one could argue that this procedure of "first sample, then compress" is somewhat wasteful because we must measure N pieces of information only to retain K < N coefficients.
The traditional procedure of first isolating the rhizobial cultures and then screening them for IAA production was time consuming as, Sahasrabudhe [1] have isolated 60 cultures from rhizosphere of groundnut among them 40 cultures showed IAA production.
For these reasons, FNAC should not be considered the diagnostic procedure of first choice for solid breast lesions.
A more subtle reason may be the authors' procedure of first removing the deaths from breast cancer estimated to be prevented by innovations in therapy, then applying the relative reduction from screening to the remaining deaths.
The governing non-linear ODEs and auxiliary boundary conditions those obtained by applying assisting similarity transformations have been handled numerically with shooting scheme through Runge-Kutta-integration procedure of fourth-fifth order.
