Sentence examples for using the maximal principle from inspiring English sources

Using the maximal principle to the transport equation about ρ, rho_{t}+urho_{x}=-u_{x}rho, we have bigl| rho(t bigr| _{L^{infty}(mathbb{S})}leq | rho_{0}|_{L^{infty}(mathbb{S})}+C int^{t}_{0}bigl| partial_{x}u tau) bigr| _{L^{infty}}bigl| rho tau bigr| _{L^{infty}},dtau.

Thus, using the maximal entropy principle to characterize spike statistics in the gIF model by expressing constraints in terms of spike events (monomials), one can at best find an approximation which can be rather bad, especially if those constraints focus on instantaneous spike patterns ( D = 0 ) or short memory patterns.

Those conclusions where obtained using the maximal entropy principle[14].

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.

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.

subject to the state Eq. (1.2) by using Pontryagin's maximal principle.

All analyses were performed according to the intention-to-treat principle (using the carry forward principle).

A maximal tuning range about 9% and 24% was achieved using the dielectric tuning principle and the inductive tuning principle, respectively.

We used the principle of maximal variation of the use of (Facebook®) for personal and teaching purposes.

Moreover, in [15] the maximal L p - L q regularity in a domain is derived automatically with the help of the Weis' operator valued Fourier multiplier theorem, so that a local in time unique existence theorem is proved by using the usual contraction mapping principle based on the maximal L p - L q regularity.