Sentence examples for maximum principle the from inspiring English sources

He also stated, but did not prove, that the maximum principle, the axiom of choice, and German mathematician Ernst Zermelo's well-ordering principle were equivalent; that is, accepting any one of them enables the other two to be proved.

Although it is now known that Zorn was not the first to suggest the maximum principle (the Polish mathematician Kazimierz Kuratowski discovered it in 1922), he demonstrated how useful this particular formulation could be in applications, particularly in algebra and analysis.

To enforce the discrete maximum principle, the standard Galerkin discretization is constrained using a local extremum diminishing flux limiter.

Although the difference scheme does not satisfy the discrete maximum principle, the maximum norm stability of the scheme is established.

By employing Pontryagin's maximum principle, the optimal solution is acquired when the emergency response incurs nonlinear costs.

By constructing an appropriate Hamiltonian function and using Pontryagin's maximum principle, the optimal harvesting policy has been discussed.

In this section, we investigate the higher regularity and prove the maximum principle for the regularized system (1.3).

In 1935 the German-born American mathematician Max Zorn proposed adding the maximum principle to the standard axioms of set theory.

Finally, the maximum principle completes the proof of our theorem.

A method for deriving the maximum principle is the variational principle.

Furthermore, Luchko established the maximum principle for the generalized fractional differential equations [11].