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 (15961650)
“Science is intimately integrated with the whole social structure and cultural tradition. They mutually support one otheronly in certain types of society can science flourish, and conversely without a continuous and healthy development and application of science such a society cannot function properly.”
—Talcott Parsons (19021979)
“Whoever can discern truth has received his commission from a higher source than the chiefest justice in the world who can discern only law. He finds himself constituted judge of the judge. Strange that it should be necessary to state such simple truths!”
—Henry David Thoreau (18171862)
“It seems to me that we do not know nearly enough about ourselves; that we do not often enough wonder if our lives, or some events and times in our lives, may not be analogues or metaphors or echoes of evolvements and happenings going on in other people?or animals?even forests or oceans or rocks?in this world of ours or, even, in worlds or dimensions elsewhere.”
—Doris Lessing (b. 1919)