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To create a hole type transformation, we select a λ that is zero everywhere excepting in some sufficiently small region of space and time where it comes smoothly to differ from zero.
That is, a hole transformation is a diffeomorphism on M that is the identity outside some arbitrarily selected neighborhood but comes smoothly to differ from the identity within that neighborhood.
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But cultural change does not come smoothly.
Not all this change has come smoothly, of course.
Their deaths left him so drugged up that the transition to Degeneration came smoothly.
In the end, however, the No. 7 train rumbled down the track and came smoothly to a stop.
No matter how much the kids tried to challenge him, the picture still came smoothly, inevitably forth from Smalley's imagination.
Many of today's young American Muslims are the children of educated, successful immigrants whose passage to the United States came smoothly, in contrast to Europe's largely working-class Muslims.
Such new connections opened up the terrain to young professionals, helping gentrification already well-advanced in places such as Shoreditch by 2007 to spread farther east and south.But the continuing success of the Overground will not come smoothly.
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Reprints Related items Austria's collapsing government: Back to square oneSep 12th 2002But this time he had fallen out with too many of his colleagues to let him come smoothly back as party boss.
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