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:
“If you would be a favourite of your king, address yourself to his weaknesses. An application to his reason will seldom prove very successful.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (1694–1773)
“Great abilites are not requisite for an Historian; for in historical composition, all the greatest powers of the human mind are quiescent. He has facts ready to his hand; so there is no exercise of invention. Imagination is not required in any degree; only about as much as is used in the lowest kinds of poetry. Some penetration, accuracy, and colouring, will fit a man for the task, if he can give the application which is necessary.”
—Samuel Johnson (1709–1784)
“Three factors—the belief that child care is female work, the failure of ex-husbands to support their children, and higher male wages at work—have taken the economic rug from under that half of married women who divorce.”
—Arlie Hochschild (20th century)
“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)