Sentence examples for the maximal principle from inspiring English sources

end{cases} (2.16) It follows from the maximal principle that (u^_{k}< r).

The grid spacings of difference scheme are obtained by analyzing numerical stability and convergence based on the maximal principle.

We obtain the following criteria according to the maximal principle and they are a sufficient condition for convergence to an accurate solution.

A necessary and sufficient condition for the existence of smooth positive solutions is given by constructing lower and upper solutions and with the maximal principle.

By analyzing the numerical stability and convergence of the difference scheme, the grid spacings, including temperature step and time step, are properly determined according to the maximal principle.

Then Balakrishnan proved a maximal principle for the optimal control and which can imply the bang bang property (see [4]), Friedman discussed the time optimal control problem on Banach spaces (see [5]), Fattorini proved that the maximal principle in 1974 for some special Banach spaces.

To prove the main result, we need the following maximal principle.

In the maximal entropy principle, assuming stationarity, one looks for the probability distribution which maximizes the statistical entropy given those constraints.

By calculating using general ordinary differential equation theory and maximal principle, we obtain that the radial function ϕ 0 ( x ) = q ( h 1 − h 2 ) ρ N − 2 ( ρ + 1 ) N − 2 ( ρ + 1 ) N − 2 − ρ N − 2 | x | N − 2 + [ q h 1 − ω − q ( h 1 − h 2 ) ( ρ + 1 ) N − 2 ( ρ + 1 ) N − 2 − ρ N − 2 ]. is the unique solution of equation (27).

In statistical physics, they are usually derived from the maximal entropy principle [14].

It utilizes the Nevanlinna factorization and the maximal selection principle in each decomposition step, and achieves a faster convergence rate with higher fidelity.