Sentence examples for restricted variation from inspiring English sources

Considering L q [ f ( t, u n ) ] as a restricted variation so that after taking the classical variational derivative to both sides of (56), we can obtain δ L q [ u n + 1 ] = δ L q [ u n ] + a ¯ ( s ) s α ( 1 − q ) α − 1 δ L q [ u n ], (57).

where is the Lagrange multiplier and denotes restricted variation that is.

The subscript denotes the th approximation, and is considered as a restricted variation [1 4], that is,.

Employing the restricted variation in (2.2) makes it easy to compute the Lagrange multiplier; see [22, 23].

where the function u ˜ n ( x, t ) is considered as a restricted variation function, i.e., δ u ˜ n ( x, t ) = 0.

where λ is a Lagrangian multiplier and u ˜ ( x, t ) is considered as a restricted variation function, i.e., δ u ˜ ( x, t ) = 0. Extremizing the variation of the correction functional (2) leads to the Lagrangian multiplier λ.

where λ ̲ and λ ¯ are general Lagrange multipliers, which can be identified optimally via the variational, and u ˜ ̲ n and u ˜ ¯ n are restricted variations that are δ u ˜ ̲ n = 0 and δ u ¯ ˜ n = 0. Therefore, we first determine the Lagrange multipliers λ ̲ and λ ¯ that will be identified via integration by parts.

where u ¯ n ( s ) = L [ u n ( t ) ]. Assuming the terms R [ u n ] and N [ u n ] are restricted variations, respectively, we only need to consider the term I t α 0 λ 0 C D t α u n = 1 Γ ∫ 0 t ( t − τ ) α − 1 λ ( t, τ ) 0 C D τ α u n d τ. (30).

We only use the leading term d q 2 x d q t 2, while other terms are restricted variations x n + 1 = x n + ∫ 0 t λ ( t, q 2 τ ) ( d q 2 x n d q τ 2 + f ( τ, x n ) ) d q τ. (13).

Finally, we show that restricting variation discovery to coding regions does not adequately describe all common haplotypes or the true haplotype block structure observed when all common variation is used to infer haplotypes.

Do epigenetic structures restrict variation?