Sentence examples for minimizing sequence on from inspiring English sources

For equation (1.1), Liu-Wang [4] first posed the SQ condition to get the bounds of a minimizing sequence on the Nehari manifold.

Theorem 8 Let I be a weakly lower semi-continuous operator that has a bounded minimizing sequence on a reflexive real Banach space E. Then I has a minimum c = min u ∈ E I ( u ) = I ( u 0 ).

The proof again consists of testing the functional on minimizing sequences of the form (eta U_epsilon ), where (U_epsilon ) is an extremal for (mu _{gamma, s}(mathbb {R}^n)) and (eta in C^infty _c(Omega )) is a cut-off function equal to 1 in a neigbourhood of 0, and showing that (mu _{gamma,s, lambda }(Omega )

Firstly, we provide the existence of minimizing sequences for J λ on M λ and M λ − as λ is sufficiently small.

(ii) Any minimizing sequence ofτisρ-convergent.

The following lemma establishes some relationship between LP approximating solution sequence and LP minimizing sequence.

The proof consists of testing the functional on minimizing sequences arising from suitably truncated extremals of (mu _{gamma, s}(mathbb {R}^n_+)), whenever they are attained, and showing that (mu _{gamma,s, lambda }(Omega )

In case there is no minimizer, we determine the asymptotic behavior of minimizing sequences.

Then the new approach of setting up minimizing sequences twice is used to derive the optimal pairs without Lipschitz assumptions on nonlinear functions and nonlocal items.

To minimize sequence based effects on probe intensity, we took adjacent probe intensities into account and applied a pseudomedian filter [ 26].

To minimize sequence errors, all assembled sequences were manually checked.