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:
“Preaching is the expression of the moral sentiment in application to the duties of life.”
—Ralph Waldo Emerson (1803–1882)
“I think that a young state, like a young virgin, should modestly stay at home, and wait the application of suitors for an alliance with her; and not run about offering her amity to all the world; and hazarding their refusal.... Our virgin is a jolly one; and tho at present not very rich, will in time be a great fortune, and where she has a favorable predisposition, it seems to me well worth cultivating.”
—Benjamin Franklin (1706–1790)
“They say the seeds of what we will do are in all of us, but it always seemed to me that in those who make jokes in life the seeds are covered with better soil and with a higher grade of manure.”
—Ernest Hemingway (1899–1961)
“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)