Examples
- Eikonal equation
The simplest fully nonlinear equation is the eikonal equation. This has the form
so that the function F is given by
The dual cone consists of 1-forms adx+bdy+cdz satisfying
Taken projectively, this defines a circle. The dual curve is also a circle, and so the Monge cone at each point is a proper cone.
Read more about this topic: Monge Cone
Famous quotes containing the word examples:
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“No rules exist, and examples are simply life-savers answering the appeals of rules making vain attempts to exist.”
—André Breton (1896–1966)