Download e-book for kindle: Nonlinear functional analysis vol.3: Variational methods and by E. Zeidler, L.F. Boron

By E. Zeidler, L.F. Boron

ISBN-10: 038790915X

ISBN-13: 9780387909158

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Additional resources for Nonlinear functional analysis vol.3: Variational methods and optimization

Example text

In the example above, Descartes’ law of optics enables us to understand the behavior of light when, traveling in a given medium, it strikes another medium. It is easy to realize that something occurs at the interface, leading to the refraction of light, so that the phenomenon is perfectly understandable. However, with the principle of least time, the understanding becomes problematic. Here is what Feynmann (1969) had to say about the principle of least time: The principle of least time is a completely different philosophical principle about the way light works.

However, the coherence of the results obtained in biology is such that it could hardly be due to mere chance. qxd 24/08/04 11:05 AM Page 57 Physical and Biological Interactions him that the human mind was surely more than just a “collection of microscopic wires and circuits”, and added: Because of the fact that mathematical truths are necessary truths, no real information, in the technical sense of the term, is conveyed to the discoverer. All the information was there all the time. One had simply to put things together to see the answer!

We obtain the same type of solution for the heat equation. The irreversibility of the phenomenon of diffusion is thus included in the solution of these models, since the solutions are found to be identical. Although the problem of the propagation of heat and the problem of the random walk involve apparently very different phenomena, the profound analogy between them is expressed by the identity of the solutions obtained. Here we may admire the power of mathematics that has led to the discovery of a fundamental unity that would otherwise have remained hidden.

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Nonlinear functional analysis vol.3: Variational methods and optimization by E. Zeidler, L.F. Boron


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