Examples
The function given by
is an example of a bump function in one dimension. It is clear from the construction that this function has compact support. The proof of smoothness follows along the same lines as for the related function discussed in the Non-analytic smooth function article. This function can be interpreted as the Gaussian function scaled to fit into the unit disc: the substitution corresponds to sending to
A simple example of a bump function in variables is obtained by taking the product of copies of the above bump function in one variable, so
Read more about this topic: Bump Function
Famous quotes containing the word examples:
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)
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—G.C. (Georg Christoph)