Sentence examples for supplementary condition from inspiring English sources

So, condition (18) does not imply any supplementary condition on system parameters.

where f ( x ) is the unknown source and u ( x, 1 ) = g ( x ) is the supplementary condition.

where f ( x ) is the unknown source depending only on one spatial variable and u ( x, 1 ) = g ( x ) is the supplementary condition.

Suppose this supplementary condition is the existence of another entity, U. Then "T+U would appear to be the true and necessitating truth-maker for p" (2004: 7).

For dim(X) ⩾ 2 (with a supplementary condition in the case dim(X) = 2, we show that this representation is irreducible and that the representations associated to different Riemannian flags are inequivalent.

Suppose that the set-valued maps T and S defined before satisfy the supplementary condition: For all (iin I) and ((x,y )in G_{S}), there exist (zin Txcapmathbb{K}) and (tin S (z )) such that max bigl{ a_{i}lVert x-z rVert_{mathbb{X}},b_{i}lVert y-trVert _{mathbb{X}} bigr} leqslant varphi_{i} (y )-varphi_{i} (t ).

For the all examples, we consider the supplementary conditions from the exact solution.

With supplementary conditions, u ( x, 0 ) = 0, ∂u ∂t ( x, 0 ) = x.

Results about the existence of a fixed point and then its uniqueness under supplementary conditions are proved in those articles.

Previously, most works treated digital IIR filter design as a single objective optimization problem of minimizing the magnitude response error with supplementary conditions.

Proceeding as before, the existence and uniqueness of a common fixed points can be shown under some supplementary conditions, as stated in the following theorem.