Application To Higher Dimensions
For every radius r > 0,
with Euclidean norm ||x|| defines a smooth function on n-dimensional Euclidean space with support in the ball of radius r.
Read more about this topic: Non-analytic Smooth Function
Famous quotes containing the words application to, application, higher and/or dimensions:
“It would be disingenuous, however, not to point out that some things are considered as morally certain, that is, as having sufficient certainty for application to ordinary life, even though they may be uncertain in relation to the absolute power of God.”
—René Descartes (1596–1650)
“The best political economy is the care and culture of men; for, in these crises, all are ruined except such as are proper individuals, capable of thought, and of new choice and the application of their talent to new labor.”
—Ralph Waldo Emerson (1803–1882)
“A man should have a farm or a mechanical craft for his culture. We must have a basis for our higher accomplishments, our delicate entertainments of poetry and philosophy, in the work of our hands.”
—Ralph Waldo Emerson (1803–1882)
“I was surprised by Joe’s asking me how far it was to the Moosehorn. He was pretty well acquainted with this stream, but he had noticed that I was curious about distances, and had several maps. He and Indians generally, with whom I have talked, are not able to describe dimensions or distances in our measures with any accuracy. He could tell, perhaps, at what time we should arrive, but not how far it was.”
—Henry David Thoreau (1817–1862)